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3 years ago

Give the final simplified result.

Mathematics

1 answer:

grin007 [14]3 years ago

3 0

Answer:

-8 a

Step-by-step explanation:

i simplified -3 a (70+3a) wich came out to negative eight A

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A. Show

nydimaria [60]

a. Recall the double angle identities:

$\sin^2x=\dfrac{1-\cos2x}2$

$\cos^2x=\dfrac{1+\cos2x}2$

Then

$\sin^2x\cos^2x=\dfrac{(1-\cos2x)(1+\cos2x)}4=\dfrac{1-\cos^22x}4$

Applying the identity again, we have

$\sin^2x\cos^2x=\dfrac{1-\frac{1+\cos4x}2}4=\dfrac{2-(1+\cos4x)}8=\dfrac{1-\cos4x}8$

as required.

b. Using the result from part (a),

$\sin^2x\cos^2x=\dfrac{1-\cos4x}8=\dfrac{2-\sqrt2}{16}$

$\implies\cos4x=\dfrac1{\sqrt2}$

$\implies4x=\dfrac\pi4+2n\pi\text{ or }4x=-\dfrac\pi4+2n\pi$

(where $n$ is any integer)

$\implies\boxed{x=\pm\dfrac\pi{16}+\dfrac{n\pi}2}$

8 0

4 years ago

A sleeping bag weighs 6 pounds. Your backpack and sleeping bag together weigh 29 pounds. Use x as your variable to write an equa

Sedaia [141]

Answer:

29 - 6 = x

x = 23

The backpack without the sleeping bag weighs 23 pounds

Step-by-step explanation:

Sleeping bag = 6 lbs

Backpack and sleeping bag = 29

4 0

3 years ago

Read 2 more answers

Solve the equation. What is the value of x? x minus 6.8 = 356.3 x =

Crank

X= 363.1 do you need me to show you the work?

5 0

3 years ago

Read 2 more answers

Solve system of equations<br><img src="https://tex.z-dn.net/?f=x%20%2B%202y%20-%20z%20%3D%204%20%5C%5C%202x%20-%20y%20%2B%203z%2

Natasha2012 [34]

First, using elimination method for eq. 1 and 2 to eliminate one of the variables.

2x - y + 3z = 8

-2x + 3y - 2z = 10

------------------------------

2y + z = 18

z = 18 - 2y

Now eq. 1 and 3, but multiple eq.1 with 2.

2x + 4y - 2z = 8

-2x + 3y - 2z = 10

----------------------------

7y - 4z = 18

Now you have two new equations 7y -4z = 18 and z = 18 - 2y. Solve for y and z, using substitute method.

7y - 4z = 18

7y - 4(18 - 2y) = 18

7y - 72 + 8y = 18

15y = 18+72

y = 90/15

y = 6

Find z using one of the two new equations.

z = 18 - 2y

z = 18 - 2(6)

z = 18 - 12

z = 6

Now you got y and z, find x using any one of the main three equations.

x + 2y - z = 4

X + 2(6) - 6 = 4

x + 12 - 6 = 4

x = 4 - 6

x = -2

Solutions:

x = -2

y = 6

z = 6

3 0

4 years ago

The amount that results when $6,000 is compounded at 7% annually over eight years. the interest earned in this case.

SVEN [57.7K]

Answer:

The Final Investment Value is $\$10,309.12$

The interest earned is $\$4,309.12$

Step-by-step explanation:

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$t=8\ years\\ P=\$6,000\\ r=0.07\\n=1$

substitute in the formula above

$A=6,000(1+\frac{0.07}{1})^{1*8}$

$A=\$10,309.12$

Find the interest earned

$I=A-P$

$I=\$10,309.12-\$6,000=\$4,309.12$

4 0

3 years ago

Read 2 more answers