the ends of a water trough 14 ft. long are equilateral triangles whose sides are 5 ft. long. if the water is being pumped into the trough at a rate of 10 cu. ft. per min., find the rate at which the water level is rising when the depth is 6 in.
Answers
According to the triangle, the water level in the trough is rising at a rate of approximately 44.1 inches per minute when the depth is 6 inches and water is being pumped into the trough at a rate of 10 cubic feet per minute.
The hypotenuse of each right triangle is a side of the equilateral triangle, which we know is 5 feet. Using the Pythagorean theorem, we can find the height of the right triangle:
h = √((5²) - ((5/2)²)) = (√(75))/2 = (5√(3))/2 feet
Therefore, when the water level is at a depth of 6 inches, the height of the water in the trough is (5√(3))/2 feet, and the volume of water in the trough is:
V = (25√(3))/4 * (5√(3))/2 = (125√(3))/8 cubic feet
To find the rate at which the water level is rising, we need to take the derivative of the volume with respect to time. Since the volume is changing with time, we can use the chain rule:
dV/dt = dV/dh * dh/dt
We already know dV/dh from the formula for the volume of a prism:
dV/dh = B
where B is the area of the base. We found B earlier to be (25√(3))/4 square feet. To find dh/dt, we need to use the fact that the trough is being filled at a rate of 10 cubic feet per minute. This means that the volume of water in the trough is increasing at a rate of 10 cubic feet per minute. We can set this rate equal to dV/dt:
dV/dt = 10
Substituting in dV/dh and solving for dh/dt, we get:
B * dh/dt = 10
(25√(3))/4 * dh/dt = 10
dh/dt = (40/(25(3))) feet per minute
Therefore, the rate at which the water level is rising when the depth is 6 inches is (40/(25√(3))) feet per minute. To convert this to inches per minute, we can multiply by 12:
dh/dt = (40/(25√(3))) * 12 = (480/25√(3)) inches per minute
Using a calculator, we can approximate this to be about 44.1 inches per minute.
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Related Questions
HELPPP ME WITH THIS I DONT GET IT PLEASE
Answers
The value of x for the given triangle will be 4√3.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
As per the given triangle,
The unknown third angle will be 180° - 60° - 30° = 90°.
Thus, it is a right-angle triangle so a trigonometric ratio will apply.
By sin60° = x/8
x = 8(√3/2) = 4√3
Hence "The value of x for the given triangle will be 4√3".
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\(square root x+25 = 2\)
Answers
Answer:
unsolvable
Step-by-step explanation:
sqrt(x) = 2 - 25
sqrt(x) = -23
This is unsolvable because no squareroot of x results in a negative number
What is the common ratio in the sequence? 2,3,4.5,6.75, A. 1 B. 1.5 C. 2.25 D. 0.6666
Answers
I hope It's right
Select the correct answer from each drop-down menu.Consider this polynomial equation.6(x – 3)(x^2 + 4)(x + 1) = 0Use the equation to complete this statement.The equation hassolutions. Its real solutions are I
Answers
ANSWER:
The equation has 4 solutions.
Its real solutions are x =3 and x = 1
EXPLANATION:
Given:
\(6(x-3)(x^2+4)(x+1)=0\)To find how many solutions the equation has, we have:
The solution will be the values of x.
There are factors already, which are:
(x - 3) = 0
x² + 4 = 0
x + 1 = 0
Therefore, the solutions are:
x = 3
Problem 2:
The lifespan of a particular brand of light bulb follows a normal distribution with a mean of 1000 hours and a standard deviation of 50 hours.
Find:
a) the z-score of light bulb with a mean of 500 hours.
b) If a customer buys 20 of these light bulbs, what is the probability that the average lifespan of these bulbs will be less than 980 hours?
c) the probability of light bulbs with the mean of 400 hours.
d) the number of light bulbs with the mean less than 1000 hours
Answers
The answers are:
a) The z-score for a light bulb that lasts 500 hours is -10.
b) For a sample of 20 light bulbs, the probability that the average lifespan will be less than 980 hours is approximately 0.0367, or 3.67%.
c) The z-score for a light bulb that lasts 400 hours is -12. This is even more unusual than a lifespan of 500 hours.
d) Given the lifespan follows a normal distribution with a mean of 1000 hours, 50% of the light bulbs will have a lifespan less than 1000 hours.
How to solve the problema) The z-score is calculated as:
z = (X - μ) / σ
Where X is the data point, μ is the mean, and σ is the standard deviation. Here, X = 500 hours, μ = 1000 hours, and σ = 50 hours. So,
z = (500 - 1000) / 50 = -10.
The z-score for a bulb that lasts 500 hours is -10. This is far from the mean, indicating that a bulb lasting only 500 hours is very unusual for this brand of bulbs.
b) If a customer buys 20 of these light bulbs, we're now interested in the average lifespan of these bulbs. . In this case, n = 20, so the standard error is
50/√20
≈ 11.18 hours.
z = (980 - 1000) / 11.18 ≈ -1.79.
The probability that z is less than -1.79 is approximately 0.0367, or 3.67%.
c) The z-score for a bulb with a lifespan of 400 hours can be calculated as:
z = (400 - 1000) / 50 = -12.
The probability associated with z = -12 is virtually zero. So the probability of getting a bulb with a mean lifespan of 400 hours is virtually zero.
d) The mean lifespan is 1000 hours, so half of the light bulbs will have a lifespan less than 1000 hours. Since the lifespan follows a normal distribution, the mean, median, and mode are the same. So, 50% of light bulbs will have a lifespan less than 1000 hours.
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Kiri has red and white roses in groups of 8. She has x groups of red roses and y groups of white roses. Which expression shows the total number of roses that Kiri has?
x over 8 + y over 8
8x + 8y
8x + y
x + 8y
Answers
x + 8y heres the answer
Sara started adding and subtracting the rational expressions . LCD = 2(3)(7)(g)(g)(g) Finish Sara's work. What is the resulting rational expression?
Answers
Answer: A
Step-by-step explanation: on Edge
Answer:
D
Step-by-step explanation:
A salesperson works 40 hours per week at a job where he has two options for being paid. Option A is an hourly wage of $28. Option B is a commission rate of 4% on weekly sales. How much does he need to sell this week to earn the same amount with the two options?
Answers
Based on the information, it can be inferred that this salesperson must make sales equivalent to $28,000 to obtain an equal profit with both options.
How to find the amount of money that he would have to sell to make the same profit with both options?To find the amount of money that we must sell to have the same profit with both options we must carry out the following mathematical procedure.
1. We must calculate how much you would earn with option A in a week.
$28 * 40 = $1,120
2. We must make a rule of three to find a value of which 4% is equal to 1,120
4% - $1,120100% - x100% * $1,120 / 4 = $28,000Based on the above, the salesperson must sell $28,000 to make the same profit on both options in one week.
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A bag contains red and blue marbles, such that the probability of drawing a blue marble is 3/8. An experiment consists of drawing a marble, replacing it, and drawing another marble. The two draws are independent. A random variable assigns the number of blue marbles to each outcome. Complete the probability distribution table on your own paper. Answer the question in the text box below. / What is the probability of drawing exactly one blue marble? Write a simplified fraction.
Answers
Answer:
The probability of drawing exactly one blue marble is 15 over 32
Step-by-step explanation:
did test
Given the function y = 3x + 5, find the range if the domain is {-4, -1, 2, 5}
Answers
Answer:
range is {‒7, 2, 11, 20}
Step-by-step explanation:
a y=3(‒4)+5 c y=3(2)+5
=‒12+5 =6+5
= ‒7 =11
b y=3(‒1)+5 d y= 3(5)+5
=‒3+5 =15+5
=2 =20
so the range is {‒7, 2, 11, 20}
i think it is clear answer i hope it helps you
What is 8c-4-2c + 5 simplified?
Answers
Answer:6c+1
Step-by-step explanation:
i think it’s that
What is the function of the “whiskers” in a box and whisker plot?
A
They represent the interquartile range.
B
They link the interquartile range to the minimum and maximum.
C
They compare the lower quartile to the upper quartile.
D
They compare the median to the interquartile range.
Answers
Answer:
the answer should be c
Step-by-step explanation:
A Box and Whisker Plot (or Box Plot) is a convenient way of visually displaying the data distribution through their quartiles. The lines extending parallel from the boxes are known as the “whiskers”, which are used to indicate variability outside the upper and lower quartiles
Whiskers function in a box and whisker plot represent the interquartile range. Therefore, option A is the correct answer.
What is a box-and-whisker plot?A special kind of graph called a box and whisker plot is used to display the distribution of groupings of numerical data. It displays the median—the average value of the numbers in your data—as well as the lowest and greatest values as well as the quartiles, which divide the data into four equally-sized groups.
The whiskers are the two lines that extend outside the box and run from the minimum to the lower quartile (the box's beginning) and from the higher quartile (the box's end) to the maximum value.
Therefore, option A is the correct answer.
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Evaluate the Expression 64 / (2 x 4)
Answers
Here, we want to evaluate the given expression. Multiply the numbers in the denominator to get a single number. Then proceed to divide the numerator by the single number
We proceed as follows;
\(\frac{64}{2\text{ }\times\text{ 4}}=_{}\frac{64}{8}\text{ = 8}\)Which type of rigid transformation is the equivalent of two reflections across intersecting lines?
Answers
according to the question,
given data in the question,
the type of rigid transformation is the equivalent of two across intersecting lines
Rotation is the process of changing the orientation of a shape by mirroring two intersecting line segments.
The intersection of the two reflection lines is the center of rotation.
An isometric drawing is a composite of two isometric drawings. The combination of two reflections on two parallel lines corresponds to translation.
The configuration of the two reflections is either translational or rotational. A translation occurs when a reflection is followed by a parallel reflection. Reflections following reflections from intersecting lines cause rotation
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The type of transformation that is equivalent to 2 reflections across intersecting lines is rotation
Which transformation is equivalent to a double reflection over parallel lines?A slide or a shift is a translation. By executing two composite reflections along parallel lines, translations may be produced. Translations maintain orientation and are isometric.
Which type of isometry is the equivalent of two reflections in parallel lines?An isometry is made up of two other isometries. The translation is equal to the combination of two reflections over two parallel lines.
according to the question,
the type of rigid transformation is the equivalent of two across intersecting lines
Rotation is the process of changing the orientation of a shape by mirroring two intersecting line segments.
The intersection of the two reflection lines is the center of rotation.
An isometric drawing is a composite of two isometric drawings. The combination of two reflections on two parallel lines corresponds to translation.
The configuration of the two reflections is either translational or rotational. A translation occurs when a reflection is followed by a parallel reflection. Reflections following reflections from intersecting lines cause rotation
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Find the measure of the complement for the angle 1 degree
Answers
89 degrees
Explanations:
The sum of an angle and its complement is equal to 90 degrees.
Let the measure of the complement be "x"
Given the information below:
Angle = 1 degrees
Taking the sum of the angle and its complement will give:
\(x+1^0=90^0\)Subtract 1 from both sides
\(\begin{gathered} x+1-1=90-1 \\ x+0=90-1 \\ x=89^0 \end{gathered}\)Therefore the measure of the complement for the angle given is 89 degrees
If a rock is thrown vertically upward from the surface of Mars with velocity of 20 m/s, its height (in meters) after t seconds is h= 20t - 1.86t^2.
(a) What is the velocity (in m/s) of the rock after 2 s? _______ m/s
(b) What is the velocity (in m/s) of the rock when its height is 30 m on its way up? On its way down? (Round your answers to two decimal places.)
up ________ m/s
Down ________ m/s
Answers
Given,Initial velocity of the rock, u = 20 m/sHeight of the rock at t seconds, h = 20t - 1.86t²
(a) To find the velocity of the rock after 2 seconds:We can find the velocity using the formula of velocity: v = u + atSubstitute the values:u = 20 m/st = 2 sWe know that acceleration on mars is equal to -3.72 m/s² (negative because of gravity)Let's put all the values and find the velocity:v = 20 - 3.72 × 2v = 12.56 m/sTherefore, the velocity of the rock after 2 seconds is 12.56 m/s
(b) To find the velocity of the rock when its height is 30 m on its way up:On its way up, the velocity of the rock will be decreasing and becomes zero at the maximum height.Let's consider, when the height is 30 m. We have to find the velocity, v.Substitute the value of h in the equation, h = 20t - 1.86t²30 = 20t - 1.86t²1.86t² - 20t + 30 = 0We have to solve this quadratic equation to find t.Let's use the quadratic formula:t = (20 ± √(20² - 4 × 1.86 × 30)) / 2 × 1.86t = (20 ± √(400 - 223.2)) / 3.72t = (20 ± √(176.8)) / 3.72Let's find the positive value of t, since we need to find the velocity of the rock when its height is 30 m on its way up.t = (20 + √(176.8)) / 3.72t = 4.99 sNow, we can find the velocity of the rock using the formula:v = u + atv = 20 - 3.72 × 4.99v = 1.6 m/sTherefore, the velocity of the rock when its height is 30 m on its way up is 1.6 m/sOn its way down, the velocity of the rock will be increasing. Let's find the velocity of the rock when its height is 30 m on its way down.
Since the time of ascent = time of descent (symmetric), the time taken to reach a height of 30m is the time taken to fall from a height of max height. Therefore, the time taken by the rock to fall from the max height to 30m is given as:t = 4.99 seconds - 4.99 secondst = 0sLet's find the velocity of the rock using the formula:v = u + atv = 20 - 3.72 × 0v = 20 m/sTherefore, the velocity of the rock when its height is 30 m on its way down is 20 m/s.
To summarize, the velocity of the rock after 2 seconds is 12.56 m/s.The velocity of the rock when its height is 30 m on its way up is 1.6 m/s.The velocity of the rock when its height is 30 m on its way down is 20 m/s.
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Whats the unit rate for 49 points in 28 minutes?
Answers
Answer:
1.75 points per minute
Answer:
1.75 points per min
The ans is in the picture with the steps how i got it
(hope this helps can i plz have brainlist :D hehe)
Step-by-step explanation:
f(x) = x+2
g(x) = 3x
workout the value of gf(5)
Answers
Answer:
g(5) = 15 and f(5) = 7
Step-by-step explanation:
f(5) = x + 2
f(5) = 5 + 2
f(5) = 7
g(5) = 3x
g(5) = 3(5)
g(5) = 15
plz mark as brainliest if correct!!!
Answer:
21
Step-by-step explanation:
because firstly u substitute 5 into x in the f equation
so it will be f(x)=5+2=7
the substitute 7 into the g equation
so g(x)= 3 x 7= 21
HELP IS OVERDUED AND I NEED THE CORRECT ANSWER AND WORK BY TODAY BEFORE SHE COUNTS IT LATE!!!!! ALMOST 3:20am!!!!! The answer written is NOT my answer.
Answers
Answer:
978 in^2
Step-by-step explanation:
the area of the rectangle:
24in X 30in = 720 in^2
the area of the two similar triangles:
12 X 9 / 2 + 12 X 9 / 2 = 108 in^2
the area of the last triangle:
20 in X 15 in /2 = 150in^2
.
the total area is the sum of the areas:
720in^2 + 108in^2 + 150in^2 = 978in^2.
hurry please answer!!!
Answers
The gas used and miles are proportional for each scooter.
What is proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent.
A proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if:
y = k x
for some constant k , called the constant of proportionality .
Therefore, let's check whether the scooter A and scooter B shows proportional relationships.
Hence,
For scooter A:
y = kx
where
x = miles coveredy = gas usedTherefore,
2 = 150 k
k = 2 /150
k = 1 / 75
Hence,
y = 1 / 75 x
From the table of scooter A, the ratio is constant, therefore, the relationships of gas used and distance covered is proportional for scooter A.
For the Scooter B the graph is also proportional because the ratios of the variables are constant.
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Help me pls! I need help! Ill give you FIVE star, plsssss!
Answers
Answer:
Yes they are perpendicular
Step-by-step explanation:
This is simply because these line intersect creating 90* angles
journal articles and research reports are by far the most common secondary sources used in education.
Answers
Journal articles and research reports are widely recognized as the most common types of secondary sources used in education. In the field of education, secondary sources play a crucial role in providing researchers and educators with valuable information and scholarly insights.
Among the various types of secondary sources, journal articles and research reports hold a prominent position. These sources are often peer-reviewed and published in reputable academic journals or research institutions. They provide detailed accounts of research studies, experiments, analyses, and findings conducted by experts in the field. Journal articles and research reports serve as reliable references for educators and researchers, offering up-to-date information and contributing to the advancement of knowledge in the education domain. Their prevalence and credibility make them highly valued and frequently consulted secondary sources in educational settings.
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Which expression is equivalent to m + 3m + 3(m - 1)
Answers
Answer:
7m-3
Step-by-step explanation:
first, distribute
m+3m+3m-3
then, combine all like terms
m+6m-3
7m-3
i hope this helps! have a nice day!
A student receives the following grades with and A worth 4 points, a B worth 3 point, a C worth 2 points, and a D worth 1 point. What is the students weighted mean grade point score?
B in 2 three-credit classes
D in 1 three-credit class
A in 1 four-credit class
C in 1 four-credit class
Mean grade point is ___
Answers
2.33 is the student's GPA using the average weighted mean.
What is Mean?The mathematical average of a group of two or more numbers is called the mean. There are two different types of means that can be calculated: the arithmetic means and the geometric mean. The arithmetic mean is calculated by adding all of the numbers in a set and dividing by the total number of numbers in the set.So, the weighted average is calculated by multiplying each grade by its weight and dividing the result by the total weights.
In three three-credit classes, the student earned three Bs.A D in three-credit course results in a grade of 1, weighted at 3.Consequently, a C earns a grade of 2, which has a weight of 4.Consequently, a C earns a student two credits and a weight of 2.It is as follows:
\(M=\frac{3 \times 3 \times 3+1(3)+2(4)+2(2)}{9+3+4+2}=\frac{12}{18}=2.33\)
Therefore, 2.33 is the student's GPA using the average weighted mean.
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Favorite days of the week Monday 55% Tuesday 45% 4) If 220 people were surveyed, how many more people voted for Monday than for Tuesday?
Answers
Answer: 22
Step-by-step explanation:
Ok, so the way I do it I multiply then divide.
For Monday I did: ?/220=55/100. what you would do is multiply across then divide by the other number, so 220x55 which is 12100 then you will divide it by 100. So 121 people voted on Monday
For Tuesday: Using the same method. ?/220=45/100 you will multiply 45x220 giving you 9900 then you will divide by 100 giving you 99. 99 people voted on Tuesday.
So to find the DIFFERENCE you need to subtract, so 121-99 leaving you with 22. Also, if you are confused how on where I got 100 from you put the percentage over 100, because percentages go from 0%-100% so you put the partial percentage over the maximum (100)
Marsha deposited $5000 into a savings account 3years ago. The simple interest rate is 5%. How much money did Marsha earn in interest?
Answers
\(~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (5000)(0.05)(3) \implies I = 750\)
4. Consider the ODE blow: Use a step size of 0.25, where y(0) = 1. dy dx :(1+2x) √y (b) Euler's method of y (0.25). Evaluate the error. (5pt.)
Answers
Using Euler's approach, the error in the estimated value of y(0.25) is approximately 0.09375 or 0.094.
Given the ODE and initial condition as:
dy/dx = (1+2x)√y, y(0) = 1
Using Euler's method, we have to evaluate the value of y(0.25) with a step size of h = 0.25.
Step 1: Calculation of f(x,y)f(x, y) = dy/dx = (1+2x)√y
Step 2: Calculation of y(0.25)
Using Euler's method, we can approximate the value of y at x=0.25 as follows:y1 = y0 + hf(x0, y0)where y0 = 1, x0 = 0 and h = 0.25f(x0, y0) = f(0, 1) = (1+2(0))√1 = 1y1 = 1 + 0.25(1) = 1.25
Therefore, y(0.25) = 1.25.
Step 3: Calculation of the exact value of y(0.25)We can find the exact value of y(0.25) by solving the ODE:
dy/dx = (1+2x)√ydy/√y = (1+2x) dxIntegrating both sides:
∫dy/√y = ∫(1+2x)dx2√y = x^2 + 2x + C, where C is athe constant of integration Since y(0) = 1,
we can solve for C as follows: 2√1 = 0^2 + 2(0) + C => C = 2
Therefore, the exact solution of the ODE is given by:2√y = x^2 + 2x + 2Solving for y, we get:y = [(x^2 + 2x + 2)/2]^2
The exact value of y(0.25) is given by:y(0.25) = [(0.25^2 + 2(0.25) + 2)/2]^2= (2.3125/2)^2= 1.15625
Step 4: Calculation of the errorError = |Exact value - Approximate value|Error = |1.15625 - 1.25| = 0.09375
Therefore, the error in the approximate value of y(0.25) using Euler's method is 0.09375 or 0.094 (approx).
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Ecological approach to algal bloom control. Algal blooms can have negative effects on an ecosystem by dominating its phytoplankton communities. Gonyostomum semen is a nuisance alga infesting many parts of northern Europe. Could the overall biomass of G. semen be controlled by grazing zooplankton species? A research team examined the relationship between the net growth rate of G. semen and the number of Daphnia magna grazers introduced in test tubes. A net growth rate was computed by comparing the initial and final abundances of G. semen in the experiment, with a negative value indicating a decrease in abundance. Here are the findings: 13 1 2 3 4 5 6 Number of grazers Net growth rate -1.9 -2.5 -2.2 -3.9 -4.1 -4.3 a. Make a scatterplot of number of grazers and net growth rate. Do you think that D. magna is an effective grazer of the G. semen alga? b. Find the correlation 1. How does it support your interpretation?
Answers
a. D. magna is an effective grazer of the G. semen alga. b. a very strong negative correlation between the number of grazers and the net growth rate of G. semen.
a. The scatterplot of the data shows a clear negative correlation between the number of D. magna grazers and the net growth rate of G. semen. As the number of grazers increases, the net growth rate of G. semen decreases. This suggests that D. magna is an effective grazer of the G. semen alga.
b. The correlation coefficient between the number of grazers and the net growth rate is -0.996. This indicates a strong negative correlation between the two variables, which supports the interpretation that D. magna is an effective grazer of G. semen. The closer the correlation coefficient is to -1, the stronger the negative correlation between the two variables. In this case, the correlation coefficient is very close to -1, which indicates a very strong negative correlation between the number of grazers and the net growth rate of G. semen.
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causes of the expulsion of acadians
Answers
Answer: Once the Acadians refused to sign an oath of allegiance to Britain, which would make them loyal to the crown, the British Lieutenant Governor, Charles Lawrence, as well as the Nova Scotia Council on July 28, 1755 made the decision to deport the Acadians. The Expulsion (1755–1764) occurred during the French and Indian War (the North American theatre of the Seven Years' War) and was part of the British military campaign against New France. The British first deported Acadians to the Thirteen Colonies, and after 1758 transported additional Acadians to France. When the French and Indian War began in 1754, the British government, doubting the neutrality of the Acadians, demanded that they take an oath of allegiance to the Crown. ... British Governor Charles Lawrence decided to deport the Acadians from Nova Scotia without giving his colleagues any notice. They migrated to Louisiana because they had better fishing grounds, its territory controlled the gulf of St. Lawrence, and shipping routes and British colonies along the Atlantic coast.
Step-by-step explanation:
John read the first 114 Pages of a novel, which was 3 pages less than 1/3 of the novel
Answers
Answer:
pretty sure its (114+3)x3
Step-by-step explanation:
114+3= one-third of the novel
then you multiply that by 3 to get the total