-4/7 + 2/7 x –14x + 4/7
Answers
Can you pls mark brainleist
Related Questions
help me solve this!!
Answers
The surface area of the prism is 485 in².
We have,
The prism has two types of surfaces:
- 2 triangles
- 3 rectangles
Now,
Area of the triangles.
This is given by:
= 1/2 x base x height
= 1/2 x 13 x 5
= 65/2
= 32.5 in²
So,
32.5 + 32.5
= 65 in²
Area of the rectangles.
This is given by:
= 1/2 x base x height
= 5 x 14 = 70 in²
And
= 13 x 14 = 182 in²
And,
= 12 x 14 = 168 in²
Now,
The surface area means the surface area for all the sides in the figure.
We add all the surface area above.
So,
The surface area of the prism.
= 65 + 70 + 182 + 168
= 485 in²
Thus,
The surface area of the prism is 485 in².
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Using distributive property what is the value of the expression for 2(-5 + 3)
Answers
Answer:
-4
Step-by-step explanation:
According to the rules of the distributive property, you have to multiply the term outside of the parentheses with the terms inside the parentheses first.
1. 2(-5)=-10
2. 2(3)=6
The terms that we have are now -10 and 6. Add them together to get the final answer.
-10+6=-4
As people exited a movie theater, they were informally surveyed about whether they enjoyed the movie or not.
What are the values of a and b in the relative frequency table for the survey results? Round answers to the nearest percent.
Answers
si a= 2 m y b= 3m,¿Cual es el valor numerico del area en metros cuadrados?
Answers
Please help me marking brainless
Answers
Answer:
9/12 & 5/12
Step-by-step explanation:
You can easily multiply 4 (the denominator of the 1st fraction) by 3, which is 12
Use differentiation to find the gradient of the curve y = (a + bx)² at x = 1
Answers
We can see that equation (1) is quadratic in nature To find the gradient of the given curve, we need to differentiate the equation (1) with respect to x Gradient is given by
Function is \(y = (a + bx)²At x = 1, y = (a + b(1))²⇒ y = (a + b)²\)
Expanding the above equation, we get y = a² + b² + 2abx …(1)
\(dy/dx⇒ d/dx (a² + b² + 2abx)\) …(2)
Taking the derivative of the above equation, we get⇒
\(d/dx (a² + b² + 2abx) = d/dx(a²) + d/dx(b²) + d/dx(2abx)⇒ 0 + 0 + 2ab⇒ 2ab\)
Now, substituting the value of x in equation (2), we getx = 1, gradient = 2ab
We have to differentiate the given function y = (a + bx)² using the differentiation rule.
To find the gradient of the curve, we need to differentiate the above function, which is given as follows;
\(y = (a + bx)²y = (a + bx) (a + bx)\)
By using the product rule of differentiation, we have
\(dy/dx = (a + bx)d(a + bx)/dx + (a + bx)d(a + bx)/dx= (a + bx) * b + (a + bx) * b= 2b(a + bx)\)
Substituting the value of x = 1, we get the gradient of the curve;
\(y' = 2b(a + b)\)
Therefore, the gradient of the curve \(y = (a + bx)² at x = 1 is 2b(a + b)\).
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Kathy has 68 coins in total. She has 5 more dimes than quarters and 5 times as many nickels than quarters. How many of each coin does she have?
Answers
Kathy has 28 dimes, 33 quarters, and 7 nickels, for a total of 68 coins which was found by solving three simultaneous equations.
What exactly are simultaneous equations?Two or more algebraic equations that share variables, such as x and y, are referred to as simultaneous equations. Because the equations are solved simultaneously, they are referred to as simultaneous equations. Each of these equations could have an infinite number of solutions.Given: Kathy possesses a total of 68 coins. She has 5 more dimes than quarters and 5 times as many nickels as quarters.
Let,
number of of coins of dimes = d
number of coins of quarters = q
number of coins of nickels = n
From the given information, we can form equations as follows:
q = 5 + d
q = 5n
d + q + n = 68
Arranging these equations,
q = 5n
d = 5n - 5
n = q/5
On solving these three equations simultaneously,
we get
d = 28
q = 33
n = 7
Therefore, Kathy has 28 dimes, 33 quarters and 7 nickels which together form 68 coins in total.
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Please give the proof process: 2n3 + 3n +10 = Q( n³).
Answers
2n^3 + 3n + 10 can be written as a polynomial of the form Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3).
To prove that the expression 2n^3 + 3n + 10 is in the set Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3), we need to show that the expression can be written in the form a(n^3) for some constant "a".
Let's start by factoring out the common factor of n^3 from each term:
2n^3 + 3n + 10 = n^3(2 + 3/n^2 + 10/n^3)
Now, let's rewrite the expression as a single term multiplied by n^3:
2n^3 + 3n + 10 = (2 + 3/n^2 + 10/n^3)n^3
Simplifying the expression inside the parentheses:
= (2n^3 + 3n^2 + 10n^3)/n^3
= (12n^3 + 3n^2)/n^3
= 12 + 3/n
ow, we can see that the expression can be written in the form a(n^3), where a = 12 and n^3 = 3/n.
Therefore, we have shown that 2n^3 + 3n + 10 can be written as a polynomial of the form Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3).
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a) Show that for any real numbers x < y, the interval [x, y] has the same cardinality as the interval [O, 1]
b) Given that [O, 1] is uncountable, what is cardinality of the set of irrational numbers between x and y if x
c) why does the above result from b guarantee the existence of an irrational number strictly between x and y, and hence the density of the irrationals?
Answers
a) The interval [x, y] has the same cardinality as [0, 1].
b) The set of irrational numbers between x and y, denoted as I(x, y), has the same cardinality as [0, 1]. This is due to the uncountability of [0, 1].
a) It can be shown that the interval [x, y] has the same cardinality as the interval [0, 1] for any real numbers x < y. This means that there is a one-to-one correspondence between the two intervals, implying that they have the same number of elements.
To show that [x, y] and [0, 1] have the same cardinality, we need to establish a function that maps elements of one interval to the other in a one-to-one manner. One such function is f(t) = (t - x) / (y - x), which maps elements from [x, y] to [0, 1]. This function is continuous and monotonic, ensuring a unique mapping for each element. Thus, the cardinality of [x, y] is the same as [0, 1].
b) The interval [0, 1] is known to be uncountable, which means its cardinality is greater than that of the set of natural numbers. The cardinality of the set of irrational numbers between x and y, denoted as I(x, y), can be shown to be the same as that of [0, 1] since we can establish a one-to-one correspondence between I(x, y) and [0, 1].
Since [0, 1] is uncountable, which means it has a higher cardinality than the set of natural numbers, we can conclude that the cardinality of I(x, y) is also uncountable. This implies that the set of irrational numbers between x and y is infinitely large and dense within the interval. In other words, between any two real numbers x and y, there exists an infinite number of irrational numbers, demonstrating the density of irrational numbers.
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Lisa smiled at her reflection, then made a funny face. She wore a cap, and her long hair blew in the wind. Her cheeks were pinkish from the cold and the wind, and her nose was moist. Lisa stepped away from nature’s mirror and was debating what after-school snack she would fix when she spied a lake of rainwater that extended from their squat trailer to the rusting tractors parked in the back.
“Oh, wow,” she remarked. The afternoon glare off the lake made her squint. How strange, she mused. It had rained just after lunch at school, but the downpour hadn’t seemed that heavy. Had a cloud stalled above their trailer and poured out its little heart?
She strolled around the new lake, occasionally gazing back at her footprints in the soggy earth. The chickens in the yard were soggy, too, their feathers parted and showing the yellow skin underneath. Still, they scratched and pecked at the ground and left their own shallow prints in the wet earth.
I’ll draw the lake, Lisa decided. She liked drawing birds, but had grown tired of sparrows, blue jays, and blackbirds wrapped in glossiness. These days she liked doing portraits, though she could draw objects, too. The previous week she had drawn the pile of tires behind the tractors; the drawing now adorned the front of the refrigerator.
Lisa produced a pencil and her sketch pad from her backpack. She had to capture this lake before it disappeared into the earth, taking with it the fluffy clouds mirrored on its surface. Birds the color of asphalt flittered about the edges of the puddle, and she recognized them as common finches. She knelt on the wet ground, putting down on paper what her eye beheld, what her fingers were able to portray.
Her gift was a mystery, as neither of her parents could draw. Their talent was to bring their faces together, like lovebirds, and warble Mexican songs, although most of the time they were working. Her father was employed by a dairy and her mother, from windy March to scorching July, worked in the fields—she thinned beets and cotton and was sometimes on a women’s crew that harvested cantaloupes. There were also two seasons when she packed peaches.
Lisa’s dog, Pecas, roamed in the background. He paused, head raised and fur parting from the wind. Lisa had to smile. He seemed to be posing as the subject of her artwork. His breath hung in the air when he barked at movement in the grass—a rabbit, she wondered, or a quail in search of a mate? The gopher that had tunneled under their garden patch last summer and nibbled at everything her father had planted: cucumbers, tomatoes, chilies, and eggplant?
I’ll surprise my parents with this new drawing, Lisa thought. “Cállate!” 1 she ordered Pecas, who turned, head lifted and tail wagging, and happily trotted toward her. But when two large white birds dropped from the sky, Pecas lurched in fear, kicking up water. “Oh my gosh,” Lisa uttered, dropping her pencil. She searched the sky for other birds. But the sky was vacant, except for blackbirds wheeling over the fields across the street.
As she took a cautious step toward the birds, she remembered that the night before she had been looking in her Audubon book at a picture of a bird that she would like to draw: the egret. Now before her stood a pair of egrets, which, against the backdrop of the grayish lake, were white as snow.
Lisa’s heart thumped with excitement and Pecas’s tail wagged briskly. Lisa again turned her attention skyward: Where had they come from? What wind had brought them here at this moment? She reached for the pencil on the ground and rolled it between her palms to spark the fires of creation. She had to draw these rare and silent birds, who, if she remembered right, seldom whistled or twittered with song.
Lisa turned and gasped. Over the lake arched a rainbow that began somewhere behind the tractors. The centerpiece was the pair of egrets, still as statues. Even Pecas stopped his whining. Lisa wondered, Can he really see the rainbow? She had read that dogs were mostly color-blind, but that birds, even common ones like the sparrow and finch, could slice the color red into a dozen shades. Their world was richer in color than some of the greatest paintings.
Lisa tried to sketch the scene quickly before it disappeared: First the egrets would fly away, then the rainbow fade, and finally the deposit of rain sink into the earth.
“It’s so beautiful,” she remarked.
A black-and-white calf ambled out from between the rusty tractors. Splattered with mud, it moved with a heavy sway toward the water. The calf stopped, then raised its heavy head to Lisa, as if saying, “Go ahead—draw me.” It lowered its gaze to turn and present a mournful profile, spittle hanging from its mouth.
“Oh,” Lisa let out, and added the cow to the scene. She made a face when she heard the telephone ring.
Answers
Answer:
1. A
2. Part A: B
3. Part B: C
4. Part C: B
5. B
6. Part A: B
7. Part B: C
8. A
Hope this helps!! :)
Answer:tyer5aghfdtr
Step-by-step explanation:
Answer:tyer5aghfdtr
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Step-by-step explanation:
Answer:tyer5aghfdtr
gdgdhjkygkyuity7uindr6n6usre6rsnu6nrsu
Step-by-step explanation:
6nrus6nru5unrys6sr5n6urn56ur5n6usr6un
Suppose that the mean retail price per gallon of regular grade gasoline in the United States is $3.45 with a standard deviation of $0.20 and that the retail price per gallon has a bell-shaped distribution. (a) What percentage of regular grade gasoline sold between $3.25 and $3.65 per gallon? % (b) What percentage of regular grade gasoline sold between $3.25 and $3.85 per gallon? % (c) What percentage of regular grade gasoline sold for more than $3.85 per gallon? %
Answers
The required percentage of regular grade gasoline are;
a) 34%
b) 95.5%
c)4.5%
How we determine the percentage of regular grade gasoline?(a) To determine the percentage of regular grade gasoline sold between $3.25 and $3.65 per gallon, we need to find the proportion of the data that falls within this range. Assuming a bell-shaped distribution, we can use the standard deviation and mean to find the z-scores for these two prices, and then look up the cumulative probability in a standard normal table.
$3.25$ is $1$ standard deviation below the mean and $3.65$ is $0.5$ standard deviation above the mean.
Using a standard normal table, we find that approximately 68% of the data falls within one standard deviation of the mean, and approximately 34% falls between $-0.5$ and $0.5$ standard deviations.
Therefore, approximately 34% of regular grade gasoline is sold between $3.25 and 3.65 per gallon.
(b) To find the percentage of regular grade gasoline sold between $3.25 and $3.85 per gallon, we need to find the cumulative probability for the range $3.25$ to $3.85$.
$3.85$ is $1.5$ standard deviations above the mean.
Using a standard normal table, we find that approximately 95.5% of the data falls within $1.5$ standard deviations of the mean.
Therefore, approximately 95.5% of regular grade gasoline is sold between $3.25 and $3.85 per gallon.
(c) To find the percentage of regular grade gasoline sold for more than $3.85 per gallon, we need to find the cumulative probability for values greater than $3.85$.
Using a standard normal table, we find that approximately 100% - 95.5% = 4.5% of the data falls above $1.5$ standard deviations from the mean.
Therefore, approximately 4.5% of regular grade gasoline is sold for more than $3.85 per gallon.
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2.
Write an expression to represent the sum of x
and 2y. Evaluate your expression for x = 4 and
y=7
Answers
Plug in the variables
4+2(7)
4+14
x+2y=18
Name:
1.
O
a) Is the graph linear?
b) What is the domain?
c) What is the range?
d) What are the x and y intercepts?
e) Does the graph have symmetry? Type?
f) What are the extrema and end behavior? 20 points
Answers
The Graph is not linear.
To graph f, we graph the equation y = f(x). To this end, we use the techniques outlined in Section 1.2.1. Specifically, we check for intercepts, test for symmetry, and plot additional points as needed. To find the x-intercepts, we set y = 0. Since y = f(x), this means f(x) = 0. f(x) = x2−x−6 0 = x2−x−6 0 = (x−3)(x+2) factor x−3=0 or x+2=0 x = −2,3 So we get (−2,0) and (3,0) as x-intercepts. To find the y-intercept, we set x = 0. Using function notation, this is the same as finding f(0) and f(0) = 02 − 0 − 6 = −6. Thus the y-intercept is (0, −6). As far as symmetry is concerned, we can tell from the intercepts that the graph possesses none of the three symmetries discussed thus far. (You should verify this.) We can make a table analogous to the ones we made in Section 1.2.1, plot the points and connect the dots in a somewhat pleasing fashion to get the graph below on the right. y x f(x) (x, f(x)) −3 6 (−3,6) −2 0 (−2,0) −1 −4 (−1,−4) 0 −6 (0, −6) 1 2 3 4 5 6 7 −3−2−11 2 3 4 1 −6 (1, −6) 2 −4 (2, −4) 3 0 (3, 0) 4 6 (4, 6)
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please solve this for me ASAP
Answers
The correct answer is thermoelectric generator because it transfers heat to electricity directly or converts electrical energy to thermal power for heating or cooling.
What is a thermoelectric generator?Thermoelectric generators are semiconductor solid-state devices that convert a temperature difference and heat flow into a usable DC power source.
The Seebeck effect is used to create voltage in thermoelectric generator semiconductor devices. This voltage is used to drive electrical current and generate usable power at a load.
From the statement given, it is a thermoelectric generator because a thermoelectric power generator transfers heat to electricity directly or converts electrical energy to thermal power for heating or cooling.
Thus, the correct answer is thermoelectric generator because it transfers heat to electricity directly or converts electrical energy to thermal power for heating or cooling.
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The first two steps in determining the solution set of the system of equations, y = x2 – 6x + 12 and y = 2x – 4, algebraically are shown in the table.
Which represents the solution(s) of this system of equations?
(4, 4)
(–4, –12)
(4, 4) and (–4, 12)
(–4, 4) and (4, 12)
Answers
Answer:
(4,4)
Step-by-step explanation:
The solution set of the system of equations can be found by setting the two equations equal to each other and solving for x.
x^2 - 6x + 12 = 2x - 4
x^2 - 8x + 16 = 0
(x - 4)^2 = 0
x = 4
Since both equations in the system are equal to y, we can substitute x = 4 into either equation to find the corresponding value of y.
y = 2x - 4 = 2(4) - 4 = 4
Therefore, the solution of this system of equations is (4, 4).
Therefore, the correct answer is (4, 4).
6- A two-dimensional strain field is given by: Ex =c(-4.5x2+10.5y?) &y=c(1.5x27.5y?) Yxy =1.5bxy where b and c are nonzero constants. a) What should the relationship between b and c be if this field is to satisfy the strain compatibility conditions? b) Determine the displacements u and v corresponding to this field of strain at point (3,7) if they are zero at point(0,0). Use as a value of 2.5 for c.
Answers
a) The relationship between b and c is that c cannot be zero.
b) b can be any nonzero constant and c is equal to 2.5 in this case.
In two dimensions, the compatibility equations for strain are,0
∂εx/∂y + ∂γxy/∂x = 0
∂εy/∂x + ∂γxy/∂y = 0
where εx and εy are the normal strains in the x and y directions, respectively, and γxy is the shear strain.
Using the given strain field, we can calculate the strains,
εx = -4.5cx² + 10.5cy
εy = 1.5cx² - 7.5cy²
γxy = 1.5bxy
Taking partial derivatives and plugging them into the compatibility equations, we get,
⇒ -9cx + 0 = 0
⇒ 0 + (-15cy) = 0
These equations must be satisfied for the strain field to be compatible. From the first equation,
We get cx = 0, which means c cannot be zero.
From the second equation, we get cy = 0,
Which means b can be any nonzero constant.
For part b:
We are asked to find the displacements u and v corresponding to the given strain field at points (3, 7), assuming they are zero at point (0, 0) and using c = 2.5.
To find the displacement components,
We need to integrate the strains with respect to x and y. We get,
u = ∫∫εx dx dy = ∫(10.5cy) dy = 5.25cy²
v = ∫∫εy dx dy = ∫(1.5cx² ) dx - ∫(7.5cy²) dy = 0.5cx³ - 2.5cy³
Plugging in the values of c and b, we get,
u = 5.25(2.5)(7)² = 767.62
v = 0.5(2.5)(3)³ - 2.5(7)³ = -8583.75
Therefore,
The displacements at points (3, 7) are u = 767.62 and v = -8583.75.
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a researcher wishes to see if there is a difference between the mean number of hours per week that a family with no children participates in recreational activities and a family with children participates in recreational activities. she selects two random samples and the data are shown. use for the mean number of families with no children. at , is there a difference between the means? use the critical value method and tables. no children children
Answers
To test if there is a difference between the means of the two populations, we can perform a two-sample t-test. The null hypothesis is that there is no difference between the mean number of hours per week that a family with no children participates in recreational activities and a family with children participates in recreational activities.
Let's assume that the researcher has collected the following data:
Sample of families with no children: n1 = 30, sample mean = 4.5 hours per week, sample standard deviation = 1.2 hours per week.
Sample of families with children: n2 = 40, sample mean = 3.8 hours per week, sample standard deviation = 1.5 hours per week.
Using the critical value method, we need to calculate the t-statistic and compare it to the critical value from the t-distribution table with n1+n2-2 degrees of freedom and a significance level of α = 0.05.
The formula for the t-statistic is:
t = (x1 - x2) / sqrt(s1^2/n1 + s2^2/n2)
where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.
Plugging in the numbers, we get:
t = (4.5 - 3.8) / sqrt((1.2^2/30) + (1.5^2/40)) = 2.08
The degrees of freedom for the t-distribution is df = n1 + n2 - 2 = 68.
Using a t-distribution table, we find the critical value for a two-tailed test with α = 0.05 and df = 68 is ±1.997.
Since our calculated t-statistic of 2.08 is greater than the critical value of 1.997, we can reject the null hypothesis and conclude that there is a statistically significant difference between the mean number of hours per week that a family with no children participates in recreational activities and a family with children participates in recreational activities.
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The level of significance in hypothesis testing is the probability of:A. Accepting a true null hypothesisB. Accepting a false null hypothesisC. Rejecting a true null hypothesisD. None of these alternatives is correct
Answers
The correct option C. Rejecting a true null hypothesis, is the probability in significance level in hypothesis testing.
Explain about the null hypothesis significance testing?By testing an experimental component against a no effect or even no relationship hypothesis based on a specific observation, NHST is a statistical inference technique.
The idea that there is no influence on the population is known as the null hypothesis. We may refuse the null hypothesis if the sample contains sufficient data to refute the assertion that there is no effect with in population (p ).In the biological, biomedical, and social sciences, null hypothesis significance testing (NHST) continues to be the statistical technique of choice for presenting evidence of an effect.Thus, the likelihood of rejecting a valid null hypothesis determines the significance level in hypothesis testing.
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In a team, the ratio of attackers : defenders is 11:7.
Given that there are 36 players in the squad, how many more attackers are there than defenders?
fast answers pls
Answers
Answer:
8 more attackers than defenders
Step-by-step explanation:
36÷18=2
2x11=22
2x7=14
Answer:
8
Step-by-step explanation:
sum the parts of the ratio, 11 + 7 = 18 parts
Divide the number of players by 18 to find the value of one part of the ratio
36 ÷ 18 = 2 players ← value of 1 part of the ratio, then
11 parts = 11 × 2 = 22 ← number of attackers
7 parts = 7 × 2 = 14 ← number of defenders
22 - 14 = 8
There are 8 more attackers than defenders
An isosceles triangle in which the two equal sides, labeled a, are longer than the base, labeled b.
This isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the triangle is 15.7 centimeters. The equation can be used to find the side lengths.
If one of the longer sides is 6.3 centimeters, what is the length of the base?
cm
Answers
If one of the longer sides of the Isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.
Let's solve the problem step by step:
1. Identify the given information:
- The triangle is isosceles, meaning it has two equal sides.
- The two equal sides, labeled "a," are longer than the base, labeled "b."
- The perimeter of the triangle is 15.7 centimeters.
- One of the longer sides is 6.3 centimeters.
2. Set up the equation based on the given information:
Since the triangle is isosceles, the sum of the lengths of the two equal sides is twice the length of the base. Therefore, we can write the equation:
2a + b = 15.7
3. Substitute the known value into the equation:
One of the longer sides is given as 6.3 centimeters, so we can substitute it into the equation:
2(6.3) + b = 15.7
4. Simplify and solve the equation:
12.6 + b = 15.7
Subtract 12.6 from both sides:
b = 15.7 - 12.6
b = 3.1
5. Interpret the result:
The length of the base, labeled "b," is found to be 3.1 centimeters.
Therefore, if one of the longer sides of the isosceles triangle is 6.3 centimeters, the length of the base is 3.1 centimeters.
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10. There are 5 gallons of lemonade in a
container. Sylvia fills glasses with 18 of a
gallon of lemonade from the container.
How many gallons of lemonade are left
in the container if Sylvia fills:
a. 7 glasses?
b. 20 glasses?
c. 32 glasses?
Answers
Answer:
b
Step-by-step explanation:
A rectangular tank that is 8788 f3 with a square base and open top is to be constructed of sheet steel of a given thickness. Find the dimensions of the tank with minimum weight. The dimensions of the tank with minimum weight are (Simplify your answer. Use a comma to separate answers.)
Answers
The dimensions of the tank with minimum weight are approximately x ≈ 14.55 ft and h ≈ 34.34 ft.
To find the dimensions of the tank with minimum weight, we need to consider the relationship between the volume of the tank and the weight of the sheet steel.
Let's assume the side length of the square base of the tank is x, and the height of the tank is h.
The volume of the tank is given as 8788 ft³, so we have the equation x²h = 8788.
To determine the weight, we need to consider the surface area of the tank. Since the tank has an open top and a square base, the surface area consists of the base and four sides.
The base area is x², and the area of each side is xh. Therefore, the total surface area is 5x² + 4xh.
The weight of the sheet steel is directly proportional to the surface area. Thus, to minimize the weight, we need to minimize the surface area.
Using the equation for volume, we can express h in terms of x: h = 8788/x².
Substituting this expression for h into the surface area equation, we have A(x) = 5x² + 4x(8788/x²).
Simplifying the equation, we get A(x) = 5x² + 35152/x.
To find the dimensions of the tank with minimum weight, we need to minimize the surface area. This can be achieved by finding the value of x that minimizes the function A(x).
We can differentiate A(x) with respect to x and set it equal to zero to find the critical points:
A'(x) = 10x - 35152/x² = 0.
Solving this equation, we get x³ = 3515.2, which yields x ≈ 14.55.
Since the dimensions of the tank need to be positive, we discard the negative solution.
Therefore, the dimensions of the tank with minimum weight are approximately x ≈ 14.55 ft and h ≈ 8788/(14.55)² ≈ 34.34 ft.
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Use Osborne's rule to write down the hyperbolic counterparts of the following trigonometrio identities. 1. sin
2
x=
2
1
(1−cos2x) 2. sin(x−y)=sinxcosy−cosxsiny 4. cos(x−y)=cosxcosy+sinxsiny 3. cos
2
x=
2
1
(1+cos2x) 5. tan2x=
1−tan
2
x
2tanx
6. sin3t=3sint−4sin
3
t Use the definitions of the hyperbolio functions to prove that: 7. 2sinhxcoshx=sinh2x 8. coshxcoshy+sinhxsinhy=cosh(x+y) 9. tanh(ln
3
)=
8
1
10. 4cosh
3
t=cosh3t+3cosht 11.
dx
d
(cothx)=−cosech
2
x 12.
dx
d
(sechx)=−sechxtanhx 13.
1−tanh
2
1
x
1+tanh
2
1
x
=e
x
14.
1+cosh2z
sinh2z
=tanhz Make use of the basic hyperbolic identities (the hyperbolic counterparts of the trigonometric identities listed in section 1.1) to prove the following identities. 15.
1+tanh
2
x
1−tanh
2
x
=sech2x 16.
sechx+tanhx
coshx+tanhx−sinhxtanhx
=1 17. cosh
4
t−sinh
4
t=cosh2t 18. coth2u−cosech2u=tanhu
Answers
1. sinh(2x) = 2sinh(x)cosh(x) Using Osborne's rule, replace sin^2(x) with (1-cos^2(x)). Apply the hyperbolic definitions of sin(2x), sin^2(x), and cos^2(x) to obtain the hyperbolic counterpart.
2. sinh(x-y) = sinh(x)cosh(y) - cosh(x)sinh(y) Apply Osborne's rule to the trigonometric identity sin(x-y) = sin(x)cos(y) - cos(x)sin(y), replacing sin(x), cos(x), sin(y), and cos(y) with their hyperbolic counterparts.
3. cosh(2x) = 2cosh^2(x) - 1Substitute cos^2(x) with (1+cos^2(x)) using Osborne's rule. cosh(2x) and cos^2(x) to derive the hyperbolic identity.
4. cosh(x-y) = cosh(x)cosh(y) - sinh(x)sinh(y) Replace cos(x), sin(x), cos(y), and sin(y) in the trigonometric identity cos(x-y) = cos(x)cos(y) + sin(x)sin(y) with their hyperbolic counterparts using Osborne's rule.
5. tanh(2x) = (2tanh(x))/(1 + tanh^2(x))
Use Osborne's rule to replace sin^2(x) and cos^2(x) in the trigonometric identity tan^2(x) = (1 - cos^2(x))/(cos^2(x)). tanh(2x) and tan^2(x) to obtain the hyperbolic counterpart.
6. sinh(3t) = 3sinh(t) - 4sinh^3(t) Apply Osborne's rule to the trigonometric identity sin(3t) = 3sin(t) - 4sin^3(t), replacing sin(t) with sinh(t) to derive the hyperbolic counterpart.
7. 2sinh(x)cosh(x) = sinh(2x)Use the hyperbolic definitions of sinh(2x), sinh(x), and cosh(x) to calculate both sides.
8. cosh(x)cosh(y) + sinh(x)sinh(y) = cosh(x+y)Substitute the hyperbolic definitions of cosh(x), cosh(y), sinh(x), and sinh(y) into the left side. Simplify the expression to cosh(x+y) to establish the equality.
9. tanh(ln(3)) = 1/8 Replace the natural logarithm with its corresponding hyperbolic function. Evaluate tanh(ln(3)) using the hyperbolic tangent of the logarithm of 3, resulting in 1/8.
10. 4cosh^3(t) = cosh(3t) + 3cosh(t)
11. d/dx(coth(x)) = -cosech^2(x)
Take the derivative of coth(x) using the derivative of its hyperbolic counterpart. Simplify the expression to -cosech^2(x) to establish the equality.
12. d/dx(sech(x)) = -sech(x)
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Write and simplify an expression for the ratio of the volume of the cylindrical tank to its surface area (including the bases).
Answers
The ratio of the volume of the cylindrical tank to its surface area will be r / 2.
What is a cylinder?A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.
Let r be the radius and h be the height of the cylinder.
Then the volume of the cylinder will be
V = π r²h cubic units
Then the surface area of the cylinder will be
SA = 2πrh square units
Then the ratio of the volume of the cylindrical tank to its surface area will be
V / SA = π r²h / 2πrh
V / SA = r / 2
The ratio of the volume of the cylindrical tank to its surface area will be r / 2.
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Find the GCF (Greatest Common Factor)
\(7 \div \frac{2}{5} \)
Answers
Answer:
17/1/2
Step-by-step explanation:
7 ÷ 2/5 = 7/1 × 5/2
= 35/2
= 17/1/2
Answer:
7 ÷ 2/5 = 7/1 × 5/2
= 35/2
= 17/1/2
Step-by-step explanation:
rite an expression that looks like sarah’s expression: 5(2j 3 j). replace the coefficients so that your expression is not equivalent. you may use any number that you choose to replace the coefficients. be sure to leave the variables the same. for example, 8(3j 7 3j) looks like sarah’s expression but is not equivalent.
Answers
The expressions are not equivalent, even though they look similar.
Sarah's expression is 5(2j + 3j), which simplifies to 5(5j) or 25j.
To write an expression that looks like Sarah's expression but is not equivalent, we can use any other set of coefficients that multiply the same sum of terms. For example:
3(2j + 3j)
This expression has the same form as Sarah's expression (a coefficient multiplied by the sum of two terms involving the variable j), but the coefficient 3 is different from the coefficient 5 in Sarah's expression. Therefore, the expressions are not equivalent, even though they look similar.
Note that when we say two expressions are equivalent, we mean that they have the same value for all possible values of the variable j. In this case, the expression 5(2j + 3j) is equivalent to 25j because they have the same value for all possible values of j. However, the expression 3(2j + 3j) is not equivalent to 25j because it has a different value for some values of j.
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2. After election results of 378 votes were tallied, the new student-body president won by a margin of 5 to 4. How many votes did she get?
Answers
Answer:
473 or 472, depends on how you round
Step-by-step explanation:
378/4 = 94.5
94.5 x 5 = 472.5
The number of votes she gets will be 473.
What is multiplication?It is also known as the product. If the object n is given to m times then we just simply multiply them.
2. After election results of 378 votes were tallied, the new student-body president won by a margin of 5 to 4.
Then the number of votes she gets that will be
→ 378 x 5 / 4
→ 378 x 1.25
→ 472.5 ≅ 473
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A tub contains red, green and blue counters. 20% of the counters are blue. The ratio of red to green counters is 2 : 3. If there are 24green counters, what is the probability of picking a red counter?
Answers
The probability of picking a red counter is therefore; 8/25.
What is the probability of picking a red counter?Since the ratio of red to green is 2 :3 and there are 24 green counters, it follows that the number of red counters is;
x = (2/3)× 24 = 16 red.
The total of red and green is; 16 +24 = 40 which constitutes 80% of the total counters.
The total number of counters is therefore; 40/0.8 = 50 counters.
The probability of picking a red counter is therefore; 16/50 = 8/25.
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The entire graph of the function h is shown in the figure below. Write the domain and range of h using interval notation.
Answers
Answer:
(A) Domain : (-4, 3]
(B) Range : [ -2, 4)
solve the equation 2y + 5x = 4 for y
pls help
Answers
Answer:
-3
I think hope this helps.
Answer:
y = 2- \(\frac{5x}{2}\)
Step-by-step explanation: