1 − 2 + 3 − 4 + ⋯ Puns

Use the graph of f(x) = |(x2 − 4)(x2 + 2)| to find how many numbers in the interval [0, 1] satisfy the conclusion of the Mean Value Theorem.

None

1

2

3

Let n be an integer. Prove that 2 | (n^4 − 3) if and only if 4 | (n^2 + 3).

This is review for my exam. I don't know how to get this going

Note: ϕ should be in the interval −π<ϕ<π

So I first solve for A

a^2 = (-2)^2 - (-4)^2

a^2 = 20

a = sqrt 20

simplify

2 sqrt 5

Honestly not entirely sure what to do after this point.

I can get one of the two points needed for the answer by just getting the answer of 2 sqrt 5 = 4.4721

but the second answer is -2.0344439357957 and I have no idea how to get that. I've tried subtracting from all the different pi, 2pi, and other answers from inverse sin, cos, of every number I've encountered.

Every video I come across doesn't even help me...

(why is it that whenever someone is teaching you how to do math, they only ever choose to show you the easiest example possible, and then leave you to figure out the hardest ones on your own?)

I have been able to solve the equation but I still don't fully understand why the 2nd bracket is 4 + 3x.

1st bracket = 8 - 12x + 4

2nd bracket:

= 6 - 2 = 4

= 6 - -3x = +3x

It's this 2nd part of the 2nd bracket that I don't fully understand (despite my tutors best efforts) so I'd really appreciate it someone could ELI5 it to me. My tutor explained it that it is 6 take away one lot of -3x. But as subtracting a negative number is equivalent to adding (two negatives make a positive) it so why is it not +9x?

Thank you.

I have stumbled upon this inequation in my homework, and I honestly have no idea how I can solve it. Tried to do it in a "per case" (Forgive my English, I usually do math in my native language) path by dividing the various solutions based on the absolute value, but apparently my solutions are in direct contrast with Wolfram Alpha.

EDIT: Thanks to everyone for the replies, they definitely helped me solving this problem.

Can someone please explain to me step by step how to factor by grouping x^4 + 21x^2 − 100? Thanks!

shniggity diggity

How do I prove this ? Its from "book of proofs" chapter 4, exercise 10. Couldn't find the solution anywhere and, not sure how to solve it.

http://www.math.utah.edu/~petersen/1210/LimitProofs Somehow it was evaluated that |x − 1| < 2, and then in the equation 2 was substituted for |x - 1|? I don't understand why. The question is 3rd one from the top.

The question is, Let x, y ∈ R. Prove that if xy + 2x − 3y − 6 < 0, then x < 3 or y < −2. I know this is a fairly simple proof problem, but I can't seem to grasp it.

I don't know whether to use direct proof or some other method. If I assume xy + 2x - 3y - 6 < 0 then I can possibly rearrange it to something more useful, though I'm not sure what.

A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. f(t) = t^3 − 9t^2 + 15t

(a) Find the velocity at time t. v(t) = 3t^2-18t+15

(b) What is the velocity after 3 s? v(3) = -12 ft/s

(c) When is the particle at rest? t = 1 s (smaller value) t = 5 s (larger value)

(d) When is the particle moving in the positive direction? (Enter your answer in interval notation.) t is [0,1) U (5,infinity)

(e) Find the total distance traveled during the first 8 s. ??? ft

I know I need to calculate the values between each distance separately then add them up which I did but its saying I'm wrong.

This is what I did: |f(1)-f(0)| = |7=0| = 7 |f(5)-f(1)| = |-25-7| = 18 |f(8)-f(5)| = |56-25|= 31 31 + 18 + 7 = 56

Seems pretty simple to me but it says its wrong. Help meh...

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2 + y2 = (3^2 + 2y^2 − x)^2 (0, 0.5) (cardioid)

y = ???

Ulfric and I spoke rapidly to each other about what had been found. We were in a bit of a difficult spot; with the Emperor en route and an invasion poised, we were going to need to work rapidly to get things done. It was determined that we'd be best served taking a boat to near the keep and then take a captains' punt that evening to take a good long look at what had been happening. The bad news was that we were going to need to work with the Empire we'd just finished rebelling against (and were currently negotiating with) in order to maintain Skyrims' independence as well as the Empires' current status of nominal independence.

The gods do love their jests.

We went back to Hjerim to change and bring some extras just in case someone needed a spare sword or armor - for this I was wrapping my dragon armor in black cloth and keeping the sword under wraps as we prepared. Rigmor was jittery and it showed. And when I questioned her about it, she and I had a bit of an angry discussion. I told her quite frankly that I'd been to war with people who were uncertain, and that she had the time it took our ship to get around Solitude; if I could see anything in her eyes I didn't like, she was getting left. She was a young nord and was ready to have a very nordlike discussion with me that would have been the end of Hjerim. However, we were stopped by the ships' second mate hammering on the door and telling us to move it to the docks, as the tide was turning favorable.

We elected to discuss it on the boat. Rigmor put her own battle history out front. I countered with the simple reality that this wasn't going to be a partisan assault, and that she knew it and it was getting the best of her. No doubt was cast upon her skill, but extreme doubt was cast upon her focus. I kept hammering it home that we needed to do the job. No more, no less. It was weird, because there was an odd familiarity to this. As we rounded to Broken Oar Grotto and just past in the lingering dusk, we readied ourselves to go spend most of the night in Lower Steepfall Burrow.

Once we'd cleared it, we decided a little look-around would not go amiss, and something very strange happened. Rigmor beelined up to a mostly deserted watchtower with a bear in a cage, and a corpse in front of said cage, presumably the bear handler who'd made a fatal error. Rigmor implored me to release it, saying it would be okay. I was rather against it on principle, being that the bear seemed a bit unhappy and would quite possi

minscore: 2

Can someone please explain to me step by step how to factor by grouping x^4 + 21x^2 − 100? Thanks!