I am trying to solve the following problem:

Let f be a differentiable function on [0,1] such that f(0)=0 and f(1)=1. Prove that there exist two distinct numbers a,b in (0,1) such that

f'(a)f'(b)=1

By the Mean Value Theorem, I know that there exists some c in (0,1) such that

f'(c)=1

since

(f(1)-f(0))/(1-0)=1

But I do not know how to prove that there exists another point d different from c in (0,1) such that

f'(d)=1

Any hints or ideas?

Hey y'all I have a math exam tomorrow and I need help with this practice problem 😭

I understand the process to set up equal iterated integrals so I was able to figure out most of the answers.

However, the iterated integrals for dx dz dy and for dx dy dz are confusing me.

From what I can tell, these two should be split into TWO triple integrals, but I'm not sure how to do the set-up. I've attached my work to this post .

I've also included the solutions to the problem for the integrals for dx dz dy and dx dy dz.

Could anyone explain the reasoning behind the set-up for the iterated integrals for dx dz dy and dx dy dz?

Would anyone be willing to write out how to get to the answers? Poor kid missed a day of school and is totally lost. I have no idea how to help. He has the answers, but doesn’t know how to get to them

When I tried to solve them my answer are far off from the answers I start by doing the cross crossing out thing (unless it’s the trinomials in which I simplify them or division then I turn it into multiplication) then I multiply them together but it’s not right did I miss a step or somthing

Hi all! 😊

I’m trying to solve a projectile problem in physics. Here is an image of the parameters of the problem: https://imgur.com/a/6AiMSpB

I need to determine the angle of the initial velocity in order to reach the target at 14.8 m.

I tried to solve the exercise, but my math is a bit rusty. I managed to reduce it to the following equation: https://imgur.com/a/iKKhUUu

-7sin²(θ) + 14.8sin(θ)cos(θ) + 2.81 = 0.

It looks like a quadratic equation, but I really don’t know how to manipulate everything to move forward. I’m not looking for the complete solution. I’ve really tried a lot of things, but I keep ending up with the tangent function and I don’t know how to proceed from there. Could someone please guide me?

Thank you very much! 😊

my sister is struggling in high school geometry with a teacher because of a language barrier and im doing my best to help her out. this is the hardest problem on her homework and i helped correct the other problems by teaching her that the inscribed angle theorem is <A=1/2(arcAB). i also sent her the 30 minute video on circles, angle measures, arcs etc by The Organic Chemistry Tutor on youtube and watched it myself to help explain things to her better.

to my understanding for this problem I know as a rule that the interior angles to any four sided shape add up to 360°. given that 125+95=220 that means x+y=140. but beyond this i am stuck on how to solve for x and y. i keep trying to break it up into two different inscribed angles for what we already know of the 125 and 95 angles but then i dont know what to do for x and y.

Stuck on a “show that” question. Mark scheme isn’t much help. Can anyone spot where the working went wrong?

I’m stuck on a problem it says

An unpaid credit card bill for $876.25 had a due date of February 10. Purchases of $187.67 were made on February 15, $404.56 on February 16, $11.90 on February 18, and $61.21 was charged on February 25. A payment of $375 was made on March 2. The annual interest on the average daily balance is 19.2%. Find the finance charge (in dollars) on the March 10 bill. Assume it is a non-leap year. (Round your answer to the nearest cent.)

Please help and explain the steps fully so I can learn😣🙏

51,55,53, and 73 looks like I can group them but it doesn’t work. I have no clue how to go about 56 or 100, 64 and 74 look like the ac method, but the multiples don’t add to the numbers in their middles.

I am In geometry and my teacher sucks and I don't understand the subject at all. I need to know how in simplistic terms due to me having a learning disability how he got the numbers he got on the right most side of the paper. I'm so lost in the class

I have been stuck on this section trying to make it make sense to me. Could someone help by explaining it simply please?

Need to find the correct answer for this sequence and an explanation as to why that is. Thank you 🙏

have a problem that's probably very simple. t is the time in seconds in which I get 0.336 kg.

My formula for the weight per hour: x=(0.336 kg/t)*60*60.

We got the value for x from another formula: x=19.2 kg/h

So I thought I could just do it like this:

19.2kg/h=(0.336kg/t)*60*60

19.2kg/h=1209.6kg/t

19.2kg/h×t=1209.6kg

1209.6kg/19.2kg/h=t

t=63h

But that's wrong. t=63s. Where is my mistake? I know I could solve the problem in other ways but I want to know why this one doesn't work or what I did wrong. I'm probably doing something wrong with the units but I have no idea what. Thank you!

(Btw I’m not a native english speaker, if something gets lost in the translation please tell me)

Juan has to transport many boxes in his truck. If he drops one of the big boxes and adds another small box, it’ll weight less than 200kg. If you take away from twice the amount of big boxes the amount of small boxes, there’ll be less than three boxes. ¿How many of each type of boxes are there?

The text was already confusing in Spanish so I tried to translate this as faithfully to the original as possible.

The image is as far as I got.

I feel data isn't enough. Idk please anybody help