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3 years ago

Simplify the expression by using a double-angle formula. 2 cos^2 4 theta -1

1 answer:

3 0

You are given 2cos² (4θ - 1). You are asked to s<span>implify the expression by using a double-angle formula.

Apply the double angle of the cosine function
</span>cos2θ = 2cos² θ - 1

Rearranging the expression and then substituting them
2cos² θ = cos2θ + 1
2cos² (4θ - 1) = cos 2(4θ - 1) + 1
cos2(4θ - 1) + 1

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A survey of 285 adults found that during the last year, 75 traveled by plane but not by train, 55 traveled by train but not by p

meriva

Answer:

Step-by-step explanation:

Given that

Total number of adults, U = 285

Number of plane travellers, P = 75

Number of train travellers, T = 55

To find the number of people that didn't travel by any means of transportation listed in the question, then we say

Total number of adults minus number people who traveled by plane or train minus number of people who traveled by bus but not by plane or train.

This means that number of people who didn't travel by any of the three means of transportation, N =

N = U - pt - b

N = 285 - 215 - 30

N = 40

Therefore, the total number needed is 40

7 0

2 years ago

Which function has an inverse function?

daser333 [38]

Answer: Option B

Step-by-step explanation:

By definition, only those functions that are one to one have an inverse function.

A function is one by one if there are not two different input values, $x_1$ and $x_2$ , that have the same output value y

Note that the function $f(x)= \frac{|x+3|}{5}$ is not a one-to-one function

When x=2 $f(x)= \frac{|2+3|}{5}=1\ ,\ \ y=1$

When x=8 $f(x)= \frac{|-8+3|}{5}=1\ \ ,\ y=1$

Note that the function $f(x)= \frac{x^4}{7}+ 27$ is not a one-to-one function

When x=1 $f(x)= \frac{(1)^4}{7}+27\ ,\ \ y=\frac{190}{7}$

When x=-1 $f(x)= \frac{(-1)^4}{7}+27\ ,\ \ y=\frac{190}{7}$

Note that the function $f(x)= \frac{1}{x^2}$ is not a one-to-one function

When x=1 $f(x)= \frac{1}{(1)^2}\ ,\ \ y=1$

When x=-1 $f(x)= \frac{1}{(-1)^2}\ ,\ \ y=1$

Then the answer is the option B.

You can verify that The function $f (x) = x ^ 5-3$ is a one-to-one function and therefore its inverse is a function

5 0

2 years ago

The volume of a sphere can be described by the following formula, where V = volume and r = radius of the sphere.

Anika [276]

Option C: $r = \sqrt[3]{\frac{3V}{4\pi} }$ is the right answer

Step-by-step explanation:

Given formula for volume of a sphere is:

$V = \frac{4}{3}\pi r^3$

We have to make r the subject of the formula

Multiplying equation by 3/4

$\frac{3}{4}V = \frac{4}{3} * \frac{3}{4} \pi r^3\\\frac{3}{4}V = \pi r^3$

Dividing both sides by pi

$\frac{3}{4\pi}V =\frac{ \pi r^3}{\pi}\\\frac{3V}{4\pi} = r^3$

Taking cube root on both sides

$\sqrt[3]{\frac{3V}{4\pi} } = \sqrt[3]{r^3} \\ r = \sqrt[3]{\frac{3V}{4\pi} }$

Hence,

Option C: $r = \sqrt[3]{\frac{3V}{4\pi} }$ is the right answer

Keywords: Volume, Sphere

Learn more about volume at:

#LearnwithBrainly

5 0

3 years ago

Evaluate the expression: (–2)2 + (–42) + (18 – 23).

marta [7]

Answer:

-51 (no options are matching)

Step-by-step explanation:

Given: (–2)2 + (–42) + (18 – 23).

we know, 2*2 = 4, and in integer multiplication if any negative integer is multiplied with positive integer, then the result will have a negative sign.

= -4 + (-42) + (18 – 23)

Here, we have open the brackets, and written the respective signs with the integers,

= - 4 - 42 - 5

now, we will perform the integer addition. Adding all the positives together & he negative numbers together

= -51

PS: It happens to be that none of the given options match with the correct answer. But, i have solved taking the expression, i hope it helps

6 0

2 years ago

Read 2 more answers

Answer number 31 and 32. For what value of x is the figure the given parallelogram?

sp2606 [1]

Answer:

cant see 32

Step-by-step explanation:

5 0

2 years ago