Dear Math helper, I am writing to you to ask for your help with my question I drew a rough sketch but i still dont know what to do after it Thank you

2^2 x 2^3 = 2^2+3 = 2^5 = 32
3. ### Was asked to integrate: "x ln(x)" by parts, but my answer ≠ the textbook's?

I was asked to integrate: "x ln(x)" by parts and received the following answer: ln(x) (x^2 / 2) - (1 / x) (x^2 / 2) + c. However, the answer in the back of the book is: "ln(x) (x^2 / 2) - (x^2 / 4) + c. Why is the term to the right of the minus sign different in the book's answer?

The problem is:a,b,c are edges of triangle, prove that the equation: ax^2+2(b+c)x+a=0 . has two distinct real root ​and my answer is: a,b,c are edges therefore they are absolute values. so a>0 b>0 c>0 also Δ=4(b+c)^2-4a^2 and I need to prove that Δ>0 so 4(b+c)^2-4a^2>0 which led me for...
5. ### Smart people needed! Answer in full, no copy and paste.

Mr Greengold had received a consignment of gold in the form of one-centimetre cubes. To conceal them, he ordered that the cubes be glued together to form a solid cuboid and had all the outside faces of this cuboid painted camouflage green. Jimmy Bold carefully spied on these proceedings and...

7. ### I need help with a geometry question.

I would like the steps and solution, please. For triangles ABC and DEF, ∠A ≅ ∠D and ∠B ≅ ∠E. Based on this information, which statement is a reasonable conclusion? Thanks.
8. ### Enter the exact answer as a single fraction. Rationalize the denominator, if required

cos(cos-13/4+tan-13) Enter the exact answer as a single fraction. Rationalize the denominator, if required

I am working on trying to figure out why the worked out example of this difference quotient give a simplified answer with radicals in the denominator. I have been told by more than one person in the past that having radicals in the denominator is bad practice and should be avoided. Also, there...
10. ### Can anyone help me on this... im not confident with my answer :(

a*a=a, a=0 -> 0*0=0, 0=0 true a*a=a, a=1 -> 1*1=1, 1=1 true Thank you
11. ### Cannot solve this or find answer anywhere!

I'm starting a construction agency. When a contractor bills a customer, I will bill him 10% of his invoice as my commission for finding him the work. The contractor will want to add on my commission, so that after he's paid my bill, he will be left with what he would have originally charged...
12. ### Right Triangle Problem (Answer Checking)

A building contractor wants to put a fence around the perimeter of a flat lot that has the shape of a right triangle. one angle of the triangle is 41.4 degrees, and the length of hypotenuse is 58.5m. Find the length of the fencing required. Round the answer to one decimal place. I got h =58.5...
13. ### Simplified expression: man vs. algorithm. Which answer do you prefer?

Original problem - rationalize the denominator and simplify: \frac {x} {2-3\sqrt{x}} Mathway.com's answer: - \frac{x(2+x \sqrt{x})} {9x-4} How I answered: \frac {2x+3x\sqrt{x}} {4-9x} Two main differences I see: 1) In mine, the x in the numerator is distributed, whereas theirs is...
14. ### Need answer to shells method question checked

It is somewhat tedious to show the work I did in order to arrive at the answer, so instead I would like somebody to simply tell me if the answer I got to this question is correct: My answer: V = 268.6061719 cm^3
15. ### Trig problem w/ answer - help me understand this answer

Hi, PROBLEM: "Find all values of x such that sin2x = sinx and 0 ≤ x ≤ 2π" (that last symbol is "Pi" in case it's hard to read) ANSWERS: 0, π/3, π, 5π/3, 2π MY THOUGHT PROCESS BEFORE SEEING THE ANSWER WAS: (1) double-angle formula: sin2x = (2)(sinx)(cosx) (2) sin2x = sinx only when...
16. ### Can someone verify if my answer is correct?

For all real numbers x and y, square root of x+y is equal to the square root of X plus square root of Y. Find a counter example to show that this statement is false. basically its sqrt(x+y) = sqrt(x) + sqrt(y) which i gave a counterexample of ---------------------------------------...
17. ### Checking answer for improper integral

I evaluated the improper integral and got 1/2. I checked wolfram and typed in two versions of the problem and got 2 different answers. Which version is correct?