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2 years ago

6

Rewrite each of the following expressions without using absolute value bars.

1 answer:

Slav-nsk [51]2 years ago

8 0

Answer:

A |x−4| if x>4

Step-by-step explanation:

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Simply 1/2 × 1/8 ÷ 1<br><br><br><img src="https://tex.z-dn.net/?f=simplify%201%5C2%20%5Ctimes%201%5C8%20%5Cdiv%201%5C2" id="TexF

Ivan

The answer is = 1/16

7 0

3 years ago

Read 2 more answers

Convert the following sum into a product. cosx + cos3x + cos5x + cos7x

kvv77 [185]

Answer:

$4\cos x\cos (4x)\cos (2x)$

Step-by-step explanation:

Given: $cosx + cos3x + cos5x + cos7x$

To convert: the given sum into product

Solution:

Use formula: $\cos A+\cos B=2\cos \left ( \frac{A+B}{2} \right )\cos \left ( \frac{A-B}{2} \right )$

$cosx + cos3x + cos5x + cos7x=2\cos \left ( \frac{x+3x}{2} \right )\cos \left ( \frac{x-3x}{2} \right )+2\cos \left ( \frac{5x+7x}{2} \right )\cos \left ( \frac{5x-7x}{2} \right )\\=2\cos (2x)\cos (-x)+2\cos (6x)\cos (-x)\\=2\cos (2x)\cos (x)+2\cos (6x)\cos (x)\\=2\cos x\left [ \cos (2x)+\cos (6x) \right ]$

$cosx + cos3x + cos5x + cos7x=2\cos \left ( \frac{x+3x}{2} \right )\cos \left ( \frac{x-3x}{2} \right )+2\cos \left ( \frac{5x+7x}{2} \right )\cos \left ( \frac{5x-7x}{2} \right )\\=2\cos x\left [ \cos (2x)+\cos (6x) \right ]\\=2\cos x\left [2 \cos \left ( \frac{2x+6x}{2} \right )\cos \left ( \frac{2x-6x}{2} \right ) \right ]\\=2\cos x\left [ 2\cos (4x) \cos (-2x) \right ]\\=4\cos x\cos (4x)\cos (2x)$

4 0

3 years ago

Find X in both problems using the pythagorean theorem

malfutka [58]

Answer:

first X=8.94

second X=34

Step-by-step explanation:

5) x^2=4^2+8^2

x^2=16+64=80

x=8.94

6)x^2= 31^2+14^2

x^2=961+196

x^2=1157

x=34

5 0

3 years ago

If sine theta equals three over four, what are the values of cos θ and tan θ?

ankoles [38]

Answer:

Part 1) $cos(\theta)=(+/-)\frac{\sqrt{7}}{4}$

cosine theta equals plus or minus square root of seven over 4

Part 2) $tan(\theta)=(+/-)\frac{3}{\sqrt{7}}$

tangent theta equals plus or minus three over square root of seven

or

$tan(\theta)=(+/-)3\frac{\sqrt{7}}{7}$

tangent theta equals plus or minus three times square root of seven over seven

Step-by-step explanation:

we have that

The sine of angle theta is equal to

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

Is positive

therefore

The angle theta lie on the I Quadrant or in the II Quadrant

Part 1) Find the value of the cosine of angle theta

Remember that

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

we have

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

substitute and solve for cosine of angle theta

$(\frac{3}{4})^{2}+cos^{2} (\theta)=1$

$cos^{2} (\theta)=1-(\frac{3}{4})^{2}$

$cos^{2} (\theta)=1-\frac{9}{16}$

$cos^{2} (\theta)=\frac{7}{16}$

$cos(\theta)=(+/-)\frac{\sqrt{7}}{4}$

cosine theta equals plus or minus square root of seven over 4

Part 2) Find the value of tangent of angle theta

we know that

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

we have

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

$cos(\theta)=(+/-)\frac{\sqrt{7}}{4}$

substitute

$tan(\theta)=\frac{\frac{3}{4}}{(+/-)\frac{\sqrt{7}}{4}}$

$tan(\theta)=(+/-)\frac{3}{\sqrt{7}}$

tangent theta equals plus or minus three over square root of seven

Simplify

$tan(\theta)=(+/-)3\frac{\sqrt{7}}{7}$

tangent theta equals plus or minus three times square root of seven over seven

4 0

3 years ago

max read 1/8 of his book on Monday and 1/6 of his book on Tuesday. what fraction of his book did he read altogether on these day

miskamm [114]

1/8 + 1/6
= 1 x 3 + 1 x 4
——- ——
8 x 3 6 x 4

= 3/24 + 4/24
= 3 + 4
———-
24
= 7/24

8 0

3 years ago