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4 years ago

For each of the terms below, give a brief definition.

Mathematics

1 answer:

irinina [24]4 years ago

5 0

Answer:

term

a word or phrase used to describe a thing

Coefficient

a number for constant quantity

constant

occurring continuously over a period of time

Algebraic expression

In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations.

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What products result in a difference of squares?

lesya [120]

Answer:

cubes?

Step-by-step explanation:

4 0

3 years ago

a. If cosθ=−45 where θ is in quadrant 3, find sin2θ. b. If cosθ=2√2 where θ is in quadrant 1, find cos2θ. c. If sinθ=817 where θ

sesenic [268]

Answer:

Part A) $sin(2\theta)=\frac{24}{25}$

Part B) $cos(2\theta)=0$

Part C) $tan(2\theta)=-\frac{240}{161}$

Step-by-step explanation:

Part A) we have $cos(\theta)=-\frac{4}{5}$

θ is in quadrant 3 ----> the sine is negative

Find $sin(2\theta)$

we know that

$sin(2\theta)=2sin(\theta)cos(\theta)$

Remember that

$cos^{2} (\theta)+sin^{2} (\theta)=1$

substitute

$(-\frac{4}{5})^{2}+sin^{2} (\theta)=1$

$(\frac{16}{25})+sin^{2} (\theta)=1$

$sin^{2} (\theta)=1-\frac{16}{25}$

$sin^{2} (\theta)=\frac{9}{25}$

$sin(\theta)=-\frac{3}{5}$ ---> remember that the sine is negative (3 quadrant)

Find $sin(2\theta)$

we have

$cos(\theta)=-\frac{4}{5}$

$sin(\theta)=-\frac{3}{5}$

$sin(2\theta)=2sin(\theta)cos(\theta)$

substitute

$sin(2\theta)=2(-\frac{3}{5})(-\frac{4}{5})$

$sin(2\theta)=\frac{24}{25}$

Part B) we have $cos(\theta)=\frac{\sqrt{2}}{2}$

θ is in quadrant 1

Find $cos(2\theta)$

we know that

$cos(2\theta)=2cos^{2} (\theta)-1$

substitute

$cos(2\theta)=2(\frac{\sqrt{2}}{2} )^{2}-1$

$cos(2\theta)=0$

Part C) we have $sin(\theta)=\frac{8}{17}$

θ is in quadrant 2 ----> the cosine is negative

Find $tan(2\theta)$

we know that

$tan(2\theta)=\frac{2tan(\theta)}{1-tan^{2} (\theta)}$

Remember that

$cos^{2} (\theta)+sin^{2} (\theta)=1$

substitute

$cos^{2} (\theta)+(\frac{8}{17})^{2}=1$

$cos^{2} (\theta)=1-\frac{64}{289}$

$cos^{2} (\theta)=\frac{225}{289}$

$cos(\theta)=-\frac{15}{17}$

Find $tan(\theta)$

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}$

substitute

$tan(\theta)=\frac{(8/17)}{(-15/17)}$

$tan(\theta)=-\frac{8}{15}$

Find $tan(2\theta)$

$tan(2\theta)=\frac{2tan(\theta)}{1-tan^{2} (\theta)}$

substitute

$tan(2\theta)=\frac{2(-\frac{8}{15})}{1-(-\frac{8}{15})^{2}}$

$tan(2\theta)=\frac{(-\frac{16}{15})}{1-(\frac{64}{225})}$

$tan(2\theta)=\frac{(-\frac{16}{15})}{1-\frac{64}{225}}$

$tan(2\theta)=\frac{(-\frac{16}{15})}{\frac{161}{225}}$

$tan(2\theta)=-\frac{240}{161}$

3 0

3 years ago

A 31-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third

Nostrana [21]

Answer:

The length of the first piece is 4 inches, that of the second is 8 inches and the third 19 inches.

Step-by-step explanation:

Total length of the steel = 31 inches

Let the length of the first piece = x

let the length of the second piece = y

Let the length of the third piece = z

So,

y = 2x

z = 4x + 3

x + 2x + 4x +3 = total length of the steel = 31

7x + 3 + 31

7x = 31 - 3

7x = 28

x= 4 inches

Thus; y = 2x = 2 × 4 = 8 inches

z = 4x +3 = 4×4 +3 =19 inches

∴The length of the first piece is 4 inches, that of the second is 8 inches and the third 19 inches.

6 0

3 years ago

Read 2 more answers

marie and jessie fly from detroit to new york their flight leaves at 1:00 pm and they arrive at 5:00pm if they flew avout 600 mi

enot [183]

150 miles per hour (pretty slow for a plane so I hope that's correct)

3 0

3 years ago

Complete the slope-intercept form equation of the line with slope 9 that passes through the point (0,2)

sergij07 [2.7K]

Answer:

2=2

Step-by-step

Y=mx+b

2=9(0)+2

9 x 0=0

2=2

I hope I got it correct and helped you.

3 0

3 years ago