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3 years ago

PLEASE HELP WITH STEPS 25 POINTS!!!! Simplify

Mathematics

1 answer:

valentinak56 [21]3 years ago

5 0

Answer:

- 1 - sin α

Step-by-step explanation:

<u>Use identity:</u>

sin² α + cos² α = 1 ⇒ cos² α = 1 - sin² α = (1 + sin α)(1 - sin α)

<u>Substitute this into given expression and simplify:</u>

cos² α / (sin α - 1) =
(1 + sin α)(1 - sin α) / (sin α - 1) =
- (1 + sin α) =
- 1 - sin α

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85% of all cars sold in chicago are some color other than black. if three hundred black cars were sold in chicago, how many cars

hram777 [196]

Of 85% of cars sold where not black then 100-85% where black = 15%
let the number of cars sold be y
then 15%*y=300
y= 300 divided by 15%
= (300*100)/15
=2000
therefore 2000 cars were sold

7 0

3 years ago

You are to manufacture a rectangular box with 3 dimensions x, y and z, and volume v=8000. Find the dimensions which minimize the

Inga [223]

Answer:

20 by 20 by 20

Step-by-step explanation:

Let the total surface of the rectangular box be expressed as S = 2xy + 2yz + 2xz

x is the length of the box

y is the width and

z is the height of the box.

S = 2xy + 2yz + 2xz ... 1

Given the volume V = xyz = 8000 ... 2

From equation 2;

z = 8000/xy

Substituting into equation 1;

S = 2xy + 2y(8000/xy)+ 2x(8000/xy)

S = 2xy+16000/x+16000/y

Differentiating the resulting equation with respect to x and y will give;

dS/dx = 2y + (-16000x⁻²)

dS/dx = 2y - 16000/x²

Similarly,

dS/dy = 2x + (-160000y⁻²)

dS/dy = 2x - 16000/y²

Note that at the turning point, ds/dx = 0 and ds/dy = 0, hence;

2y - 16000/x² = 0 and 2x - 16000/y² = 0

2y = 16000/x² and 2x = 16000/y²

2y = 16000/(8000/y²)²

2y = 16000×y⁴/64,000,000

2y = y⁴/4000

y³ = 8000

y =³√8000

y = 20

Given 2x = 16000/y²

2x = 16000/20²

2x = 16000/400

2x = 40

x = 20

Since Volume of the box is V = xyz

8000 = 20(20)z

8000 = 400z

z = 8000/400

z = 20

Hence, the dimensions which minimize the surface area of this box is 20 by 20 by 20.

3 0

3 years ago

Solve by substitution x-y=12 x+y=18

slamgirl [31]

X = y + 12. You then substitute or plug in that from the first equation into the second equation. You get (y+12)+y=18, then you simplify to get your y value. In this case y = 3. The you can plug your y value into either equation. (x+3=18) or (x-3=12) or (x=3+12) either way you get x=15 and y=3.

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3 years ago

What is the rule in the input/output table? A) add 4 B) subtract 4 C) divide by 2 D) multiply by 2 | inputs | 4 6 and 8 | output

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The rule in the input/out is D multiply by 2

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3 years ago

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Katie collects stamps. She has stamps from Canada, the U.S.A, and the rest of the world in a ratio of 1: 1.2: 1.5. She has 135 s

adoni [48]

Answer:

Step-by-step explanation: