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3 years ago

Complete the expression 2×³-2×²-12×

Mathematics

1 answer:

torisob [31]3 years ago

7 0

2x³-2x²-12x = 2x (x²-x-6) =2x (x²-3x+2x-6) = 2x (x+2) (x-3)

Hope this helps!

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An electric current, I, in amps, is given by I=cos(wt)+√8sin(wt), where w≠0 is a constant. What are the maximum and minimum valu

exis [7]

Take the derivative with respect to t
$- w \sin(wt) + \sqrt{8} w cos(wt)$
the maximum and minimum values occur when the tangent line is zero so we set the derivative to zero
$0 = -w \sin(wt) + \sqrt{8} w cos(wt)$
divide by w
$0 =- \sin(wt) + \sqrt{8} cos(wt)$
we add sin(wt) to both sides

$\sin(wt)= \sqrt{8} cos(wt)$
divide both sides by cos(wt)
$\frac{sin(wt)}{cos(wt)}= \sqrt{8} \\ \\ arctan(tan(wt))=arctan( \sqrt{8} ) \\ \\ wt=arctan(2 \sqrt{2)}$ OR $\\$ $wt=arctan( { \frac{1}{ \sqrt{2} } )$
(wt)=2(n*pi-arctan(2^0.5))
(wt)=2(n*pi+arctan(2^-0.5))
where n is an integer
the absolute max and min will be

$I=cos(2n \pi -2arctan( \sqrt{2} ))$
since 2npi is just the period of cos
$cos(2arctan( \sqrt{2} ))= \frac{-1}{3} 
$
substituting our second soultion we get
$I=cos(2n \pi +2arctan( \frac{1}{ \sqrt{2} } ))$
since 2npi is the period
$I=cos(2arctan( \frac{1}{ \sqrt{2}} ))= \frac{1}{3}$
so the maximum value = $\frac{1}{3}$
minimum value = $- \frac{1}{3}$

4 0

3 years ago

How many stickers can Kendall put in each bag

chubhunter [2.5K]

B. 1 and 5 are factors of all three numbers :)

5 0

4 years ago

Given the exact value for sides a and c.

Over [174]

Answer:

See below

Step-by-step explanation:

a = 15 sqrt 2 sin 45

= 15 sqrt 2 * sqrt( 2 ) /2 = 15 * 2 /2 = 15

sin 60 = a/c

sqrt(3)/2 = 15/c

c = 15 / ( sqrt(3)/2) = 30 / sqrt 3 = 30 sqrt 3 /3 = 10 sqrt 3

5 0

2 years ago

Find the area of the shaded region. Express your answer in terms of π.

Bogdan [553]

Answer:

335.115

Step-by-step explanation:

First you find the area of the circles to do that you do pi times radius squared

For the top square do 3.14(pi)time 3²=28.26

For the middle square do 3.14 times 4.5²=63.585

For the bottom square do 3.14 times 6²=113.04

Now find the area of the entire thing do 18×12+9+6+3=18×30=540

Finally do 540-the area of the squares 28.26-63.585-113.04= 335.115

So the shaded region is 335.115

Hope this helps and have a great day!

6 0

3 years ago

List the steps to solve the following equation: 5x - 6 = 44 then solve x

Dafna1 [17]

Answer:

1. Add 6 to both sides, cause that is the inverse of subtraction, so you get 5x = 50 as 6 cancels 6 out.

2. Divide 5 from both sides and get x = 10

7 0

3 years ago

Read 2 more answers