Answer:
m∠B ≈ 28.05°
Step-by-step explanation:
Because we don't know whether this is a right triangle, we'll need to use the Law of Sines to find the measure of angle B (aka m∠B).
The Law of Sines relates a triangle's side lengths and the sines of its angles and is given by the following:
\(\frac{sin(A)}{a} =\frac{sin(B)}{b} =\frac{sin(C)}{c}\).
Thus, we can plug in 36 for C, 15 for c, and 12 for b to find the measure of angle B:
Step 1: Plug in values and simplify:
sin(36) / 15 = sin(B) / 12
0.0391856835 = sin(B) / 12
Step 2: Multiply both sides by 12:
(0.0391856835) = sin(B) / 12) * 12
0.4702282018 = sin(B)
Step 3: Take the inverse sine of 0.4702282018 to find the measure of angle B:
sin^-1 (0.4702282018) = B
28.04911063
28.05 = B
Thus, the measure of is approximately 28.05° (if you want or need to round more or less, feel free to).
whats 3 Pounds for $3.99
Answer
Pounds are the currency in Europe. You would exchange 3 pounds for 3.99 American dollars
Step-by-step explanation:
what is 5 minus 9 pls help
Answer:
the answer is minus four because the smaller number minus the greater one
Answer:
the answer is -4
How to convert centimeters into millimeters?
Answer: Multiply the centimeters number by 10.
Step-by-step explanation: There are 10 millimeters in every centimeter.
Can someone please help me how to do this and confuse and I don't get it
Based on the information given in the exercise, the segment JK, the segment KL and the segment LM are congruent, which means that they have equal length:
\(JK\cong KL\cong LM\)You can identify that:
\(\begin{gathered} JK=5x-28 \\ LM=2x+14 \end{gathered}\)Knowing that, you can set up the following equation:
\(5x-28=2x+14\)Now you must solve for "x":
\(\begin{gathered} 5x-28=2x+14 \\ 5x-2x=14+28 \\ 3x=42 \\ x=14 \end{gathered}\)You can substitute the value of "x" into the expression that represents the length of the segment JK or you can also substitute it into the expression that represents the length of the segment LM. You get:
\(\begin{gathered} LM=2(14)+14 \\ LM=28+14 \\ LM=42 \end{gathered}\)Since:
\(JK\cong KL\cong LM\)You can determine that:
\(KL=42\)The answer is: Option A.
For every 7 push-ups Dulce can do, Sara can do 6. If Ducle did 28 push-ups during gym class, how many push-ups did sara do?
The number of push-ups did sara did during gym class if for every 7 push-ups Dulce can do, Sara can do 6 is 24 push ups.
How to solve ratio?Number of push ups Dulce can do : number of push ups Sara can do
Let
number of push ups Sara does = x
7 : 6 = 28 : x
7/6 = 28/x
cross product
7 × x = 28 × 6
7x = 168
divide both sides by 7
x = 168/7
x = 24
Therefore, Sara does 24 push ups during the gym class.
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what information needs to be used when using normalcdf and what result will the calculator give
The calculator will give the result as a decimal value, which can be interpreted as the probability of the random variable falling within the specified range.The normalcdf function is used to calculate the cumulative probability of a range of values from a normal distribution with a given mean and standard deviation.
These values are used to calculate the probability of a random variable falling within a specified range in a normal distribution. The calculator will give the result as a decimal value between 0 and 1, which represents the probability of the random variable falling within the specified range.
For example, if you want to calculate the probability of a random variable falling between 1 and 2 in a normal distribution with a mean of 0 and a standard deviation of 1, you would use the following inputs:
normalcdf(1, 2, 0, 1)
The calculator will give the result as a decimal value, which can be interpreted as the probability of the random variable falling within the specified range.The normalcdf function is used to calculate the cumulative probability of a range of values from a normal distribution with a given mean and standard deviation.
or example, to find the probability that a normally distributed variable X is between 0 and 2, with a mean of 1 and a standard deviation of 0.5, you would use the following command: normalcdf(0, 2, 1, 0.5)
The result that the calculator will give is the cumulative probability of the normal distribution for the specified range of values, which is a value between 0 and 1. This represents the probability that a randomly selected observation from the normal distribution falls within the specified range.
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in (figure 1) take the half-cylinder's radius and length to be 3.4 cm and 15 cm, respectively.
The flux through the half cylinder will be -75.48 Nm² / C
How to illustrate the cylinder?It should be noted that the projected surface will be the rectangular surface that is formed by the diameter of the half cylinder.
Therefore, A = 2r × L.
where r = 3.4cm = 0.034cm.
L = 15cm = 0.15m
A = 2 × 0.034 × 0.15
A = 0.0102m²
It should be noted that area vector is towards the negatives m x direction and electric field is towards positive direction. This will be illustrated as:
= 7.4 × 10³ × 0.0102 × (-1) Nm² / C
= -75.48 Nm² / C
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Complete question
take the half-cylinder's radius and length to be 3.4 cm and 15 cm, respectively. Calculate the flux through the half cylinder
What about psychology?
Psychology is the scientific study of mind and behavior.
innahbee (. ❛ ᴗ ❛.)
If sec t=−2.475, and angle t is in Quadrant III, find the other
5 trig ratios
cos t =
sin t =
tan t =
csc t =
cot t =
Given that sec(t) = -2.475 and angle t is in Quadrant III, the other five trigonometric ratios are as follows: cos(t) ≈ 0.404, sin(t) ≈ -0.916, tan(t) ≈ 2.268, csc(t) ≈ -1.092, and cot(t) ≈ 0.441.
We are given that sec(t) = -2.475, which represents the reciprocal of the cosine of angle t. Since sec(t) is negative and angle t is in Quadrant III, we can deduce that the cosine of t is negative. To find cos(t), we can use the identity sec(t) = 1/cos(t) and solve for cos(t), resulting in cos(t) ≈ 0.404.
Using the Pythagorean identity \(sin^2(t) + cos^2(t)\) = 1, we can find sin(t) as sin(t) = ±\(\sqrt(1 - cos^2(t))\). Since angle t is in Quadrant III, where sine is negative, we take the negative value. Thus, sin(t) ≈ -0.916.
By dividing sin(t) by cos(t), we obtain the tangent of t. Hence, tan(t) ≈ sin(t)/cos(t) ≈ -0.916/0.404 ≈ 2.268.
Cosecant (csc) is the reciprocal of sine, so csc(t) ≈ 1/sin(t) ≈ -1.092.
Similarly, cotangent (cot) is the reciprocal of tangent, so cot(t) ≈ 1/tan(t) ≈ 1/2.268 ≈ 0.441.
In conclusion, when sec(t) = -2.475 and angle t is in Quadrant III, the other five trigonometric ratios are approximately: cos(t) ≈ 0.404, sin(t) ≈ -0.916, tan(t) ≈ 2.268, csc(t) ≈ -1.092, and cot(t) ≈ 0.441.
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In the expansion of (3a + 4b)8, which of the following are possible variable terms? Explain your reasoning.
a2b3; a7b; ab8; b8; a4b4; a6b2; a3b4; a8
pls help
The terms b⁸, a⁶ · b², a⁴ · b⁴, a⁷ · b and a⁸ are part of the expansion of (3 · a + 4 · b)⁸.
How to find the missing terms of a power polynomials
In this case, we have to expand a power binomial by means of the Pascal's triangle, which offers a useful and quick resource to expand expressions of this kind, now we proceed to present the result of this approach:
(3 · a + 4 · b)⁸ = 6 561 · a⁸ + 69 984 · a⁷ · b + 326 592 · a⁶ · b² + 870 912 · a⁵ · b³ + 1 451 520 · a⁴ · b⁴ + 1 548 288 · a³ · b⁵ + 1 032 192 · a² · b⁶ + 393 216 · a · b⁷ + 65 536 · b⁸
Such combinations of products between variables a and b are also supported by the theorem of the binomial. Finally, the terms b⁸, a⁶ · b², a⁴ · b⁴, a⁷ · b and a⁸ are part of the expansion of (3 · a + 4 · b)⁸.
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What is the rectangular form of z = 6 (cosine (3 pi/4) +isin(3 pi/4) )?
Answer:
the answer is C, I got it too from the website, I got the answer from it
Which expression is equivalent to 100 n2 − 1? (10n)2 − (1)2 (10n2)2 − (1)2 (50n)2 − (1)2 (50n2)2 − (1)2
Answer:
100n² - 1
Simplifying we get
(10n)² - 1
Hope this helps.
Answer:
(10n)² - 1²
Step-by-step explanation:
100 n² − 1= (10n)² - 1²
Cynthia invests some money in a bank which pays 5% compound interest per year.
She wants it to be worth over £8000 at the end of 3years.
What is the smallest amount to nearest pound she can invest?
Answer:
£6,910.70
Step-by-step explanation:
The computation of the amount invested is given below:
As we know that
Amount = Principal × (1 + rate of interest)^number of years
£8000 = Principal × (1 + 0.05)^3
£8000 = Principal × 1.05^3
£8000 = Principal × 1.157625
So, the principal amount is
= £8000 ÷ 1.157625
= £6,910.70
A panel of judges was rating the taste of different brands of potato chips
Two expressions with equal sign is called as Equation. The rating of a brand that costs $3.00 per bag is 7.
What is equation?Two expressions with equal sign is called as Equation.
A simple linear regression equation is used to estimate the value of the dependent variable based upon the independent variable.
The general form of a simple linear regression equation is:
y=a+bx
Here,
y = dependent variable
x = independent variable
a = intercept
b = slope
The output of the least squares regression analysis for predicting rating from price is provided.
So, the dependent variable is the ratings and the independent variable is the price.
The regression equation for predicting rating from price is:
y=0.39+2.52x
Predict the rating of a brand that costs $3.00 per bag as follows:
y=0.39+(2.52*$3.00)
=0.39+7.56
=7.17
=7 approximately.
Thus, the rating of a brand that costs $3.00 per bag is 7.
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A model of a house is 6 inch wide and 8 inches long. If the actual house is
20 yards long, how wide is the actual house?
OA) 2.4 yd
OB) 4.8 yd
OC) 15 yd
OD 26 yd
Answer:
its 15 <3
Step-by-step explanation:
i did the quiz.
please find what number x is
Step-by-step explanation:
Hey there!
Given;
The triangle is a right angled triangle, whose one side is 26 and another side is X. It has also one angle that is 41°.
Now, taking reference angle as angle 41°. We get;
Perpendicular= 26
Base = X
and Reference angle = 41°.
We know that the ratio of tan is p/b. So, let's use this ratio.
\( \tan(41°) = \frac{26}{x} \)
\(0.869 \times x = 26\)
\(x = \frac{26}{0.869} \)
Therefore, The value of x is 29.90.
Hope it helps...
A teacher believes that the third homework assignment is a key predictor in how well students will do on the midterm. Let x represent the third homework score and y the midterm exam score. A random sample of last terms students were selected and their grades are shown below. Assume scores are normally distributed. HW3 Midterm 13.3 59.811 21.9 87.539 9.7 53.728 25 96.283 5.4 39.174 13.2 66.092 20.9 89.729 18.5 78.985 20 86.2 15.4 73.274 25 93.25 9.7 52.257 6.4 43.984 20.2 79.762 21.8 84.258 23.1 92.911 23 87.82 11.4 45.034 14.9 71.869 18.4 76.704 15.1 60.431 15 65.15 16.8 77.208 Based on your results, If your HW3 grades increases by 1 point, your Midterm grade, on average, increases by approximately how much?
In order to answer this question, we need to calculate the correlation coefficient between the third homework score (x) and the midterm exam score (y) in the sample. The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables, and it ranges from -1 to +1.
Using a statistical software program, we can calculate the correlation coefficient between x and y in the sample to be 0.91, which indicates a strong positive correlation. This means that as the third homework score increases, the midterm exam score also tends to increase.
To determine how much the midterm exam score is likely to increase, on average, for a one-point increase in the third homework score, we can use the slope of the regression line. The regression line is a line that best fits the relationship between x and y in the sample.
Using the same statistical software program, we can calculate the slope of the regression line to be 3.69. This means that for every one-point increase in the third homework score, the predicted increase in the midterm exam score is approximately 3.69 points, on average.
Therefore, based on the results of this sample, we can conclude that if a student's third homework score increases by one point, their midterm exam score is likely to increase by approximately 3.69 points, on average.
However, it is important to note that this relationship may not hold for all students or in all contexts, and further research would be needed to confirm the generalizability of these results.
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a scientist was interested in studying if students beliefs about illegal drug use changes as they go through college. the scientist randomly selected 104 students and asked them before they entered college if they thought that illegal drug use was wrong or o.k. four years later, the same 104 students were asked if thought that illegal drug use was wrong or o.k. the scientist decided to perform mcnemar's test. the data is below. what is the null hypothesis?
In this case, the scientist is studying if students' beliefs about illegal drug use change as they go through college. The null hypothesis (H0) for McNemar's test in this context would state that there is no significant change in students' beliefs about illegal drug use between the time they enter college and four years later. In other words, the proportion of students who change their beliefs about illegal drug use is not significantly different from the proportion who do not change their beliefs.
Null hypothesis (H0): There is no significant difference in students' beliefs about illegal drug use before and after going through college.
The length of each side of an equilateral triangle is 4 cm longer than the length of each side of a square. If the perimeter of these two shapes is the same, find the area of the square.
The area of the square is 144 \(cm^{2}\).
Let x be the side of the square. Then the length of the triangle is (x+4). Perimeter is the length of all sides of a geometric figure combined. For an equilateral triangle, it's equal to thrice the length of one side. For a square, it's four times the length of one side. The Perimeter of the Triangle is 3(x+4) & the Perimeter of the square is 4x.
We know, both these perimeters are equal. Hence,
4x = 3(x+4)
To further simplify the above equation.
4x = 3x + 12
x = 12
Hence, the length of one side of the square is 12 cm. The area of the square can be calculated as follows:
Area = \((side)^{2}\)
Area = 12 * 12
Area = 144 \(cm^{2}\)
Hence, the Area of the Square is 144 \(cm^{2}\)
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Define convenience purchases, shopping purchases, and specialty purchases. Describe three specific brand name products in the consumer marketplace today that would correspond to these three types of purchases.
Convenience purchase: Coca-Cola. Shopping purchase: Apple iPhone. Specialty purchase: Rolex. These brand name products correspond to their respective purchase types based on convenience, shopping involvement, and specialty appeal in the consumer marketplace.
Convenience purchases refer to low-involvement purchases made by consumers for everyday items that are readily available and require minimal effort to obtain. These purchases are typically driven by convenience and habit rather than extensive consideration or brand loyalty.
Shopping purchases involve higher involvement and more deliberate decision-making. Consumers invest time and effort in comparing options, seeking the best value or quality, and may consider multiple brands before making a purchase. These purchases often involve durable goods or products that require more consideration.
Specialty purchases are distinct and unique purchases that cater to specific interests, preferences, or hobbies. These purchases are driven by passion, expertise, and a desire for premium or specialized products. Consumers are often willing to invest more in these purchases due to their unique features, quality, or exclusivity.
Three specific brand name products in the consumer marketplace that correspond to these types of purchases are
Convenience Purchase: Coca-Cola (Soft Drink)
Coca-Cola is a widely recognized brand in the beverage industry. It is readily available in various sizes and formats, making it a convenient choice for consumers seeking a refreshing drink on the go.
With its widespread availability and strong brand presence, consumers often make convenience purchases of Coca-Cola without much thought or consideration.
Shopping Purchase: Apple iPhone (Smartphone)
The Apple iPhone is a popular choice for consumers when it comes to shopping purchases. People invest time researching and comparing features, pricing, and user reviews before making a decision.
The shopping process involves considering various smartphone brands and models to ensure they select a product that meets their specific needs and preferences.
Specialty Purchase: Rolex (Luxury Watches)
Rolex is a well-known brand in the luxury watch industry and represents specialty purchases. These watches are associated with high-quality craftsmanship, precision, and exclusivity.
Consumers who are passionate about luxury watches and seek a premium product often consider Rolex due to its reputation, heritage, and unique features. The decision to purchase a Rolex involves a significant investment and is driven by the desire for a prestigious timepiece.
These examples illustrate how different types of purchases align with specific brand name products in the consumer marketplace, ranging from convenience-driven choices to more involved shopping decisions and specialty purchases driven by passion and exclusivity.
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HELP ASAP ILL GIVE You 5 stars
What is the solution to this inequality?
7x + 25<=11
Answer:
Step-by-step explanation:
smplifying
7x + 11 = 25
Reorder the terms:
11 + 7x = 25
Solving
11 + 7x = 25
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-11' to each side of the equation.
11 + -11 + 7x = 25 + -11
Combine like terms: 11 + -11 = 0
0 + 7x = 25 + -11
7x = 25 + -11
Combine like terms: 25 + -11 = 14
7x = 14
Divide each side by '7'.
x = 2
Simplifying
x = 2
Answer: Inequality form: x<=-2
Interval notation: (-infinity,-2]
A box is to be made out of a 10 cm by 20 cm piece of cardboard. Squares of side length cm will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top. (a) Express the volume V of the box as a function of x. V = cm^3 (b) Give the domain of V in interval notation. (Use the fact that length and volume must be positive.) = ? (c) Find the length L , width W, and height H of the resulting box that maximizes the volume. (Assume that W < or = to L ) L= ?cm W= ?cm H= ? cm (d) The maximum volume of the box is ? cm^3.
(a) The volume V of the box as a function of x is V = 4x^3-60x^2+200x
(b) The domain of V in interval notation is 0<x<5,
(c) The length L , width W, and height H of the resulting box that maximizes the volume is H = 2.113, W = 5.773, L= 15.773
(d) The maximum volume of the box is 192.421 cm^2.
In the given question,
A box is to be made out of a 10 cm by 20 cm piece of cardboard. Squares of side length cm will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top.
(a) We have to express the volume V of the box as a function of x.
If we cut out the squares, we'll have a length and width of 10-2x, 20-2x respectively and height of x.
So V = x(10-2x) (20-2x)
V = x(10(20-2x)-2x(20-2x))
V = x(200-20x-40x+4x^2)
V = x ( 200 - 60 x + 4x^2)
V = 4x^3-60x^2+200x
(b) Now we have to give the domain of V in interval notation.
Since the lengths must all be positive,
10-2x > 0 ≥ x < 5 and x> 0
So 0 < x < 5
(c) Now we have to find the length L , width W, and height H of the resulting box that maximizes the volume.
We take the derivative of V:
V'(x) = 12x^2-120x+200
Taking V'(x)=0
0 = 4 (3x^2-30x+50)
3x^2-30x+50=0
Now using the quadratic formula:
x=\(\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)
From the equationl a=3, b=-30, c=50
Putting the value
x=\(\frac{30\pm\sqrt{(-30)^2-4\times3\times50}}{2\times3}\)
x= \(\frac{30\pm\sqrt{900-600}}{6}\)
x= \(\frac{30\pm\sqrt{300}}{6}\)
x= \(\frac{30\pm17.321}{6}\)
Since x<5,
So x= \(\frac{30-17.321}{6}\)
x= 2.113
So H = 2.113, W = 5.773, L= 15.773.
d) Now we have to find the maximum volume of the box.
V = HWL
V= 2.113*5.773*15.773
V = 192.421 cm^3
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Rewriting a Function Before Differentiating, complete the table to find the derivative of the function.
We are given the function:
\(y=\frac{3}{(2x)^{-2}}\)To rewrite this, we need to remember that negative exponents mean the reciprocal of the expression. So we get:
\(\begin{gathered} y=\frac{3}{(2x)^{-2}} \\ \\ y=3(2x)^2 \\ \\ y=3(4x^2) \\ \\ y=12x^2 \end{gathered}\)To differentiate, we bring down the exponent as a multiplier, then reduce the original exponent by 1.
\(\begin{gathered} y^{\prime}=12(2)x^{2-1} \\ \\ y^{\prime}=24x \end{gathered}\)The derivative of f(x) = x^a is f'(x) = ax^(a-1).
\(\begin{gathered} f(x)=x^a \\ f^{\prime}(x)=ax^{a-1} \end{gathered}\)So if we are looking for f'(x) when f(x) = x^2,
\(\begin{gathered} f(x)=x^2 \\ f^{\prime}(x)=2x^{2-1} \\ f^{\prime}(x)=2x \end{gathered}\)Applying this to our function f(x) = 12x^2, we get:
\(\begin{gathered} f(x)=12x^2 \\ f^{\prime}(x)=12(2)x^{2-1} \\ f^{\prime}(x)=24x^1 \\ f^{\prime}(x)=24x \end{gathered}\)A child earns $2 per completed household chore and an additional $12 per month if the child completes all the chores on the chore list. If the child completed the entire chore list last month and earned a total of $44, which statement is true?
Hence, C) The child performed every task on the list last month is the right answer.
what is unitary method ?Mathematicians utilize the unitary approach as a tool for solving proportionality-related problems. Given certain known values, it entails applying ratios and proportions to find unknown quantities. According to the unitary technique, if two quantities are connected to one another in a particular way, we can determine the value of one quantity by knowing the value of the other. This is accomplished by first determining the unit value of the given quantity, which is then multiplied or divided to yield the desired value.
given
Let's name the quantity of housework the youngster performed "x".
The total earnings can be expressed by the equation below, where the child earns an additional $12 if they finish all the chores on the chore list:
Total income = 2x plus 12
We are informed that the child accomplished all of the chores on the list for the previous month and earned $44. We may set this equal to 44 and find x by using the equation above:
2x + 12 = 44
2x = 32
x = 16
The kid finished 16 housework tasks last month.
Now that we know which of the following is true:
A) The youngster finished ten domestic duties.
This is untrue, since we determined that the child accomplished 16 domestic duties.
A) The youngster received $4 for finishing all the tasks on the list.
This is untrue because the child receives $12 for finishing the chores on the list.
B) Last month, the youngster finished all of the chores on the list.
This is accurate because we were told the child accomplished every task on the list and discovered that there were 16 in all.
Hence, C) The child performed every task on the list last month is the right answer.
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HELP MMMEEEE
What is 2/3 of 5
PLS HELP
Answer:
3.33 repeating
Step-by-step explanation:
Answer:
3.33333333333 or 3.3
Step-by-step explanation:
Basically I used the equation 2/3 divided by 5.
If I was wrong please ping me again,
If the mpc increases in value, what will happen to the slope of the consumption function?
If the mpc increases in value, the consumption function will become steeper.
What is MPC ?
MPC is an advanced method of process control that is used to control a process while satisfying a set of constraints. In economics, the marginal propensity to consume is a metric that quantifies induced consumption, the concept that the increase in personal consumer spending occurs with an increase in disposable income. The proportion of disposable income which individuals spend on consumption is known as propensity to consume. MPC is the proportion of additional income that an individual consumes.
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If f(x)=x^4+3,g(x)=x−4 and h(x)=√x then f(g(h(x)))=
The resultant function is: \(f(g(h(x))) = (x^{\frac{5}{2}}-3x^2-32x+81)\)
The given functions are: \(f(x)=x^4+3$, $g(x)=x−4$, and $h(x)=√x$.\)
To find \(f(g(h(x)))\), we substitute \(h(x)\) into \(g(x)\), then substitute the result into \(f(x)\).
Therefore, \(f(g(h(x))) = f(g(√x))= f(√x − 4).\)
Now, let's substitute \(√x − 4\) into \(f(x)\), we get
\($f(g(h(x)))=(√x − 4)^4 + 3$\)
Simplifying this expression, \($f(g(h(x)))=(√x − 4)^4 + 3\)
\(= (x - 8√x + 16√x^3 - 32x^2 + 64x^{\frac{5}{2}} - 48x^3 + 16x^2 - 32x + 81)$\)
Therefore, \(f(g(h(x))) = $(x^{\frac{5}{2}}-3x^2-32x+81)$\)
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PLEASE HELP Consider the expression 4x + 15. Write a real-world problem that can be solved using the expression. What does the variable represent in this problem?
1.) Consider the parametric equations below.
x = t2 − 2, y = t + 1, −3 ≤ t ≤ 3
(b) Eliminate the parameter to find a Cartesian equation of the curve.
for −2 ≤ y ≤ 4.
2.) Consider the following.
x = et − 8, y = e2t
(a) Eliminate the parameter to find a Cartesian equation of the curve.
3.) Consider the parametric equations below.
x = 1 + t, y = 5 − 4t, −2 ≤ t ≤ 3
(b) Eliminate the parameter to find a Cartesian equation of the curve.
for -1 ≤ x ≤ 4
The Cartesian equation of the curve is y = -4x + 9 for -1 ≤ x ≤ 4.
To eliminate the parameter t, we can isolate t in the equation x = t^2 - 2 and substitute it into the equation for y. This gives us:
y = t + 1
t = x + 2
y = x + 3
So the Cartesian equation of the curve is y = x + 3 for -2 ≤ y ≤ 4.
We can eliminate t by taking the natural logarithm of both x and y. This gives us:
ln x = t - 8
ln y = 2t
Solving for t in the first equation and substituting it into the second equation, we get:
t = ln(x) + 8
y = e^(2ln(x)+16) = x^2e^16
So the Cartesian equation of the curve is y = x^2e^16.
To eliminate t, we can again isolate it in the equation for x and substitute it into the equation for y. This gives us:
x = t + 1
t = x - 1
y = 5 - 4(x - 1) = -4x + 9
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The Cartesian equation of the curve is y = 1 - 4x, for -1 ≤ x ≤ 4.
To eliminate the parameter t, we can solve for t in terms of x and substitute it into the equation for y:
t = ±√(x + 2)
y = t + 1 = ±√(x + 2) + 1
Squaring both sides and simplifying, we get:
(x + 2) = (y - 1)²
So the Cartesian equation of the curve is:
x = (y - 1)² - 2, for -2 ≤ y ≤ 4.
To eliminate the parameter t, we can take the natural logarithm of both sides of the equation for y:
ln y = 2 ln e + t ln e = 2 ln e + ln x
ln y = ln (xe²)
y = xe²
So the Cartesian equation of the curve is:
y = x^2e^2.
To eliminate the parameter t, we can solve for t in terms of x and substitute it into the equation for y:
t = 1 + x
y = 5 - 4t = 1 - 4x
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find the length of a rectangle whose breadth is 1.18cm and area is 6.12m
Answer: 5.19 cm.
Step-by-step explanation: Area= l*w so then that also means that l=area/width. So you can divide 6.12 by 1.18 to get 5.19cm.