Can someone explain to me why the answer is 3cos3x (it has something to do with chain rule i think)

Answers

Answer 1

Answer:

Use the fundamental theorem of calculus. It says that

$\displaystyle(\mathrm d)/(\mathrm dx)\int_{\text{constant}}^(g(x))f(t)\,\mathrm dt=f(g(x))\cdot(\mathrm dg)/(\mathrm dx)$

In this case, $g(x)=3x$ and $f(t)=\cos t$ . Then

$\displaystyle(\mathrm d)/(\mathrm dx)\int_0^(3x)\cos t\,\mathrm dt=\cos(3x)\cdot(\mathrm d)/(\mathrm dx)3x=3\cos3x$

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chad has two pieces of wood.one piece is7\12 foot long the second piece is 5\12 foot longer then the first piece. how long is the second one

Answers

These fractions both have the same denominators so we can add them without having the equate them first.

The only thing you have to do is add the numerators (7 and 5), and keep the denominators the same.

7 5 12
-- + --- = ------
12 12 12

When you simplify 12/12 it becomes 1.

The second piece of wood is 1 foot long

If 2.5 is a root of the equation 2x2+5x−q=0, what are the possible values of q?

Answers

Answer:

The possible value of q is $25$

Step-by-step explanation:

step 1

we have

$2x^(2) +5x-q=0$

If 2.5 is a root of the equation

then

substitute the value of x=2.5 in the equation and solve for q

$2(2.5)^(2) +5(2.5)-q=0$

$12.5 +12.5-q=0$

$25-q=0$

$q=25$

Gabriella wants to tile a room with an area of 320 square feet. The width of the room is 4/5 its length. What are tge length and width of the room?

Answers

Area = length x width
But width = 4/5 x length
so 320 = length x 4/5length
Rearranged, 320 = 4/5(length)(length)
length x length = length^2
Divide both sides by 4/5
400 = (length)^2
Square root both sides
20 = length

So now you know the length, you can calculate the width.
Width = 4/5 x length
= 4/5 x 20
= 16

Length = 20ft, Width = 16ft

X^2=14x-49. i just dont know how to do the steps to solve this equation

Answers

$x^2=14x-49 \n \n x^2 - 14x + 49 = 0 \ / \ move \ terms \n \n x^2 - 2(x)(7) + 7^2 = 0 \ / \ rewrite \n \n (x - 7)^2 = 0 \ / \ square \ of \ difference \ method \n \n x - 7 = 0 \ / \ square \ root \ each \ side \n \n x = 7 \ / \ add \ 7 \n \n$

The answer is: x = 7.

A triangular pyramid has a base that is 31 feet and a height that is three times its base. What is the volume of the triangular pyramid?

Answers

Answer:

2,883

Step-by-step explanation:

Well the base of the triangle is

The manager of a company recorded the number of hourse his employees worked during each two weeks. The following statistics were calculated.Week 1: the mean was 35 hourse with a standard deviation of 1.5 hours.

Week 2: The mean was 40 hourse with a standrad deviation of 2.0 hours.

The manager concluded that there was more variation in the number of hours worked for week 2 that for week 1. The manager's conclusion was-?

Answers

It may have been busy so more staff were needed for a longer period of time.

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Rounding to the nearest Tenth? 0.496

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