# 2 AP Test questions I can't solve

• nivek114
In summary, the conversation discusses two questions related to Calculus and the volume of a spherical hot air balloon. The first question asks to find the area and volume of the region enclosed by the graphs of two functions, and the second question involves using a table of values to approximate the integral of a function. The conversation also includes a request for guidance and advice on solving the problems.
nivek114
Hi, the AP test is approaching and I'm struggling with these two Calculus questions and need some guidance. If you can provide a general (or detailed if possible =)) explanation on how you solved the problem, or the strategy you used for the problem, I would be extremely grateful. Solving even just one part will help me immensely! So here goes...

1. Let f and g be the functions given by f(x)=e^x and g(x) = ln(x)
a. Find the area of the region enclosed by the graphs of f and g between x = 1/2 and x=1.
b. Find the volume of the solid generated when the region enclosed by the graphs of f and g between x= 1/2 and x=1 is revolved around the line y=4.
c. Let h be the function given by h(x) = f(x) - g(x). Find the absolute minimum value of h(x) on the closed interval [1/2,1] and find the absolute maximum value of h(x) on the closed interval [1/2,1].

2.
t(minutes) 0 2 5 7 11 12
r ' (t) (feet/min) 5.7 4.0 2.0 1.2 0.6 0.5 (Note: this is a table)

The volume of a spherical hot air balloon expands as the air inside the balloon is heated. The radius of the balloon, in feet, is modeled by a twice-differentiable function r of time t, where t is measured in minutes. For 0<t<12, the graph of r is concave down. The table above gives seleceted values of the rate of change, r ' (t), of the radius of the balloon over the time interval [0,12]. The radius of the balloon is 30 feet when t = 5. (Note: The volume of a sphere of radius r is given by V = 4/3(pi)(r^3).

a. Find the rate of change of the volume of the balloon with respect to time when t=5. Indicate units of measure.
b. Use a right reimann sum with the five subintervals indicated by the data in the table to approximate the integral(antidifferentiation) from 0 to 12 of r ' (t) dt.
c. Using the correct units, explain the meaning of your solution from part b in terms of the radius of the balloon.

So there it is...any help is appreciated, good luck, and thanks in advance :X

do you have no idea where to start? if you know what concepts this deals with but are having trouble filling in the gaps do this:

draw a picture for both problems. for the first plot the functions, their intersections y=4 etc. for the second plot the points and then draw the riemann rectangles.

## What are the 2 AP Test questions you can't solve?

The first question is about projectile motion and the second question is about calculating the rate of reaction in a chemical reaction.

## Can you provide any hints or tips for solving these questions?

For the projectile motion question, make sure to break down the problem into smaller parts and use the equations for displacement, velocity, and acceleration. For the rate of reaction question, remember to use the formula for rate of reaction and pay attention to the units of measurement.

## What if I still can't solve the questions after trying these tips?

If you are still having trouble, try reviewing the relevant concepts and equations or seeking help from a tutor or teacher. It's also important to not get discouraged and keep practicing similar types of questions to improve your understanding.

## Are these types of questions common on the AP test?

Yes, questions involving projectile motion and chemical reactions are commonly tested on the AP Physics and Chemistry exams. It's important to have a solid understanding of these concepts to do well on the test.

## How can I prepare for these types of questions before taking the AP test?

Practice is key when it comes to solving these types of questions. Utilize practice tests and review materials to familiarize yourself with the types of questions that may appear on the AP test. You can also attend review sessions or join study groups to get additional help and clarification on these topics.

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