Hi, Phil! The derivative of arctan functions is a formula that should show up in the table of derivatives on the inside cover of your textbook. You can also Google it, but for your reference, the formula is: d/dx (arctan x) = 1 /(1 + x2) So,...

Hi, Phil! The derivative of arctan functions is a formula that should show up in the table of derivatives on the inside cover of your textbook. You can also Google it, but for your reference, the formula is: d/dx (arctan x) = 1 /(1 + x2) So,...

Word problems (answer)

v = d/t --> t = d/v (this is the velocity equation rearranged to solve for t) Total time = time upstream + time downstream 1.5 hours = d/v (upstream) + d/v (downstream) 1.5 hours = 16 miles/ vupstream + 16 miles/ vdownstream *vupstream...

Hi, Kathryn! I'm not sure what level class this is for, but we can prove that the bicyclists traveled at the same velocity sometime during the race by simple logic. To begin the proof, we need to address all three possible ways for the race to start: The bicyclists start...

What is its value? (answer)

Hi, Anna! I take this question to read: "The cube [of a number] less the square of the [same] number is twice the number." From here, we need to convert this english sentence into a math sentence. Here are the key elements in the sentence: "a...

Exact value of a right triangle? (answer)

Hi, Taka! To answer this question, you need to know which basic trig function goes with the reciprocal trig function of secant. You will also need to have your double angle formulas handy. Quick recap on basic vs. reciprocal trig functions: Basic...

calculus question (answer)

Hi, Ashley! To find the derivative of this function, there are a couple of derivative rules you need to know: 1. Product Rule: Part1 * (derivative of Part2) + (derivative of Part1) * Part2 2. Quotient Rule: ho d hi - hi d ho ...

translate sentences into equations (answer)

Hi, Jenna! First of all, since this forum is designed as a place for tutors to provide academic support to students, I am not going to answer all of the questions that you posted. However, I will do a couple to help you get an idea of how to translate english sentences into...

Step 1: Identify variables. Let x = # lbs of $0.71/lb candy Let y = # lbs of $1.25/lb candy Step 2: Set up equations. Since there are 2 variables, we need at least 2 equations. Final mixture is a total of 8 lbs, so EQ 1: x + y = 8 Selling price is $0.91/lb, so...

Find the lengths of three sides. (answer)

Hi, Kitesha! For this question (and the other question that you posted), you want to identify what all of the measurements refer to. What is the common element in each measurement? For instance, in this question, each side length of the triangle is given by referring to...

Hi, Claire! To answer this question, I always like to start with a picture. Or at least create one in my mind! A square is a shape with equal side lengths and right angles. Since the question is asking you to find the length of the side, I'm going to use x to represent...

using the order of operations, how do I get 5 as an answer using the number 8 only 4 times? (answer)

Hi, Suzy! I love these kinds of problems! They always remind me of the math game 24 where you are given 4 numbers and the objective is to use those 4 numbers (only once) and addition, subtraction, multiplication, and division to equal 24. Great game (at least for a math...

Word problem (answer)

Hi, Grace! These kinds of word problems can be tricky because it talks about more than one variable: the days that Walter gets paid $3.33 and the days that Walter gets paid 1/3 more (3.33 + (1/3)*3.33 = $4.44). To solve any situation where you have more than one variable, you need to set...

relative min and max (answer)

Hi, Jasmyn! The number of local maximums and minimums of a function are calculated by determining how many places have a slope of zero. In other words, you need to answer the question "how many zeroes does the function f'(x) have?" In this case, you...

Hi, Ke! So the idea with literal equations is to get one variable in terms of all the rest. In this equation, we are trying to solve for x in terms of y (meaning that we are trying to get x all by itself with y on the other side of the equal sign). Whenever you have a...

If the raw score is 62, the mean is 58 with a standard deviation of 8, what is the Z score? (answer)

Hi, Paula! I know that you asked this a few days ago and have two excellent answers above, but I just wanted to add in my two cents! :) The z-score of any raw data point tells you exactly how many standard deviations away from the mean an individual data point is. In high...

Hi, Bron! With any question like this that describes a situation, I always like to start out by drawing a picture. That makes everything much easier to visualize. Now, it's not easy to draw a picture on a computer, but here's my best attempt! :) 101 ↓ (left...

math questions (answer)

Hi, Duane! To find out how much tax is paid, you need to find 7% of $96. If you translate the phrase "7% of 96" into a math equation, the word "of" means to multiply. This gives you: 7% of 96 7% * 96 Now write 7% as...

How to write 9 squared as a power? (answer)

Hi, Brooke! The word "squared" means to raise a number to the power of two - so 2 becomes the exponent. In the case of writing "9 squared", that would look like 92. As a side note, the word "cubed" means to raise a number...

Hi, Issamar! Step 1: Set up your equations based on the descriptions in the question. (Note: "varies directly" means that the first part is equal to the second part multiplied by some constant, k.) 16y = k1 * x z = k2 * y2 Step 2: Use the...

Hi, Brittany! The best way to find two integers when you've given a problem like this is to assign a variable to each integer, write two equations expressing what is written in the question, and then solve the system of equations. Step 1: Assign the variables using...