10/18/23

The rate of change of the area is ______ square meters per minute.
The radius of a circle is decreasing at a rate of 2 meters per minute.When the radius is 14 meters, then how fast is the area changing?The rate of change of the area is ______ square meters per... more
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10/18/23

The rate of change of area is ______  square meters per hour.
The length of a rectangle is decreasing at a rate of 2 meters per hour and the width is increasing at a rate of 3 meters per hour.When the length is 11 meters and the width is 16 meters, then how... more
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10/17/23

Exponential Probability Distribution: The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 13 seconds.
What is the probability that the arrival time between vehicles is 12 seconds or less (to 4 decimals)? What is the probability that the arrival time between vehicles is 6 seconds or less (to 4... more
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10/16/23

quadratic functions

NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t) = − 4.9t^2 + 343t + 430. Assuming that the rocket will splash down into the... more
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10/15/23

A spherical balloon is inflated with gas at the rate of 20 ft^3/min. How fast is the radius of the balloon changing at the instant that r=2ft. FIND dr/dt
pls help
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10/15/23

Using the chain rule
Differentiate the function below with respect to t, where r=r(t) is a function of t e^r^2+ar+b
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10/15/23

Find two nontrivial functions f ( x ) and g ( x ) so f ( g ( x ) ) = 1/ ( x + 7 ) ^5
Solve for f(x) and g(x)
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10/15/23

Using the Chain rule

F(x)= sin^2(x) -sin (x^2)
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10/15/23

Showing all of your working, calculate
Showing all of your working, calculate ∫ t /1 − t^2 dt, using the substitution t = sin θ (and limiting the domain to t ∈ (−1, 1)). Ensure that you write your final answer in terms of t. [Note: this... more
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10/15/23

Flip a fair coin repeatedly until you get a head. If you repeat this scenario five times, what are the chances that you’ll need the exact same number of flips each time to get that first head?
Imagine a scenario where you flip a fair coin repeatedly until you get a head. If you repeat this scenario five times, what are the chances that you’ll need the exact same number of flips each time... more
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10/12/23

What is the smallest positive integer which is divisible by 225 and uses only the digits 0, 1 and 2?

Show work please
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10/11/23

AP Calculus BC - Linearization

Find the linearization of the given function centered at x = a, use it to estimate f(b).f(x) = sqrt(17 sin(x)), a = π/6, b = 0.5
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10/11/23

Probability Analysis of Opposition to Government-Controlled Health Plans
In a May, 2009 Rasmussen Reports survey, 58% of U.S. adults surveyed opposed "any kind of government-controlled health plan if it meant they had to change their own insurance company". We will... more
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10/08/23

How did this sin(𝜃) /1 − cos(𝜃) end up with csc(𝜃) + cot(𝜃)
My professor is a bit bad at explaining so I am holding hope for the explanation for this. sin(𝜃) /1 − cos(𝜃)= csc(𝜃) + cot(𝜃)
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10/06/23

A point (x, y) is to be selected from the square S containing all points (x, y) such that 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. Suppose that the probability that the selected point will belong to each specified..
A point (x, y) is to be selected from the square S containing all points (x, y) such that 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. Suppose that the probability that the selected point will belong to each specified... more
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10/06/23

Evaluate the indefinite integral
(a) Evaluate the indefinite integral ∫1/u(1+u) du Hint: 1/u(1 + u) = 1 + u − u /u(1 + u) .(b) Using a substitution, and your answer in part (a), evaluate the indefinite integral ∫ 1/(1+ e^x) dx
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10/05/23

Growth, I’ve been trying to solve this for hours and I just can’t get it.

Suppose a new breed of rabbit appears on Leroy Jenkins' farm. Initially there are 24 rabbits on the farm, but they population will double each month. Write a model to calculate the number of... more
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09/28/23

Understanding a Piecewise Probability Density Function and Deriving Its CDF
I have a piecewise Probability Density Function (PDF) defined as follows:h(x) = { 0 if x < 1 1.5 * (x - 1)^2 if 1 <= x < 2 1.5 * (3 - x)^2 if 2 <= x < 3 0 if... more
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09/26/23

Consider the constraints 2x + y ≤ 6 , y − x ≤ 2 , y + 1 ≥ x , x, y ≥ 0 .
Consider the constraints 2x + y ≤ 6, y − x ≤ 2, y + 1 ≥ x, x, y ≥ 0 . (a) Plot the constraints and shade the feasible region. In your plot, label each line which forms the boundary of the feasible... more
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09/25/23

At noon, ship A is 180 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 4:00 PM?
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09/25/23

Trigonometric substitution
My daughter is having problems with this question. Any help is appreciated.a. Calculate the integral ((SR9x^2-4)/x^3)dx by using trigonometric substitution.b. Determine the Integrand obtained... more
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09/23/23

Unit Circle: Quadrant
The point P is on the unit circle. If the y-coordinate of P is 1/2, and P is in quadrant II, then:x=Can I have an explanation? It's a bit confusing to me.
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09/22/23

Suppose that 𝑎 is a fixed number, and consider the function  𝑔(𝑥)=sin(𝑥−𝑎)+cos(𝑥+𝑎) 
Suppose that 𝑎 is a fixed number, and consider the function  𝑔(𝑥)=sin(𝑥−𝑎)+cos(𝑥+𝑎) Answer the following questions. Show and explain your work.(a) If 𝑎≠𝜋/4 what is the period of the function 𝑔(𝑥)?... more
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09/22/23

Calculus 2 question, Find the volume of the solid obtained by rotating the region under the graph of the function f(x) = x^9/5 about the x-axis over the interval [1,5].
Find the volume of the solid obtained by rotating the region under the graph of the function f(x) = x^9/5 about the x-axis over the interval [1,5].
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09/20/23

Use the additive law of probability if possible to solve the following problem
A monkey is to demonstrate that she recognizes colors by tossing one red, one black, one white ball, one orange ball, and one purple ball into boxes of the same respective colors, one ball to a... more
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