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2 years ago

Find the inverse function of F(x) = 2arccosx. F-1(x) = ____

Mathematics

1 answer:

Dmitriy789 [7]2 years ago

5 0

ANSWER

${f}^{ - 1} (x) = \cos( \frac{x}{2} )$

EXPLANATION

The given function is

$f(x) = 2 \arccos(x)$

Let

$y= 2 \arccos(x)$

Interchange x and y.

$x= 2 \arccos(y)$

Divide both sides by 2.

$\frac{x}{2} = \arccos(y)$

We take cosines to get,

$\cos( \frac{x}{2} ) = y$

${f}^{ - 1} (x) = \cos( \frac{x}{2} )$

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marissa [1.9K]

If you would like to find the inequality to determine the number of full-time employees Tom must schedule, you can calculate this using the following steps:

n ... the number of full-time employees

260 <= 20 + n * 40
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n >= 240/40
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The correct result would be at least 6 full-time employees.

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2 years ago

Which solids have infinitely many planes of symmetry? Check all that apply. right square pyramid cube right cylinder right hexag

allsm [11]

The answer is: Sphere and Right cylinder.

The explanation for this answer is shown below:

By definition, the numbers of planes of symmetry depends of each solid (a figure of three dimensions). The plane of symmetry divides the solid into two congruent halves which have mirror images.

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2 years ago

What is 2 (m+3) Pls i need help bad

snow_tiger [21]

Answer:

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2 years ago

Ice cream usually comes in 1.5-quart boxes (48 fluid ounces), and ice cream scoops hold about 2 ounces. However, there is some v

Troyanec [42]

Answer:

(a) The expected value and standard deviation of the amount of ice cream served at the party are 54 ounces and 1.25 ounces respectively.

(b) The expected value and standard deviation of the amount of ice cream left in the box after scooping out one scoop are 46 ounces and 1.031 ounces respectively.

Step-by-step explanation:

The random variable X and Y are defined as follows:

X = amount of ice cream in the box

Y = amount of ice cream scooped out

The information provided is:

E (X) = 48

SD (X) = 1

V (X) = 1

E (Y) = 2

SD (Y) = 0.25

V (Y) = 0.0625

(a)

The total amount of ice-cream served at the party can be expressed as:

X + 3Y.

Compute the expected value of (X + 3Y) as follows:

$E(X+3Y)=E(X)+3E(Y)\\= 48+(3\times2)\\=48+6\\=54$

Compute the variance of (X + 3Y) as follows:

$V(X+3Y) = V (X)+3^{2}V(Y)+2\times 3Cov (X,Y)\\=1+(9\times0.0625)+0\\=1.5625$

Then the standard deviation of (X + 3Y) is:

$SD(X + 3Y) =\sqrt{V(X + 3Y)}\\\sqrt{1.5625}\\=1.25$

Thus, the expected value and standard deviation of the amount of ice cream served at the party are 54 ounces and 1.25 ounces respectively.

(b)

The amount of ice-cream left in the box after scooping out one scoop is represented as follows:

X - Y.

Compute the expected value of (X - Y) as follows:

$E(X-Y)=E(X)-E(Y)\\=48-2\\=46$

Compute the variance of (X - Y) as follows:

$V(X - Y) =V(X)+V(Y)-2Cov(X,Y)\\=1+0.0625-0\\=1.0625$

Then the standard deviation of (X - Y) is:

$SD(X-Y) =\sqrt{V(X -Y)}\\\sqrt{1.0625}\\=1.031$

Thus, the expected value and standard deviation of the amount of ice cream left in the box after scooping out one scoop are 46 ounces and 1.031 ounces respectively.

(c)

The variance of the sum or difference of two variables is computed by adding the individual variances. This is because the variance of each variable is dependent on the others.

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2 years ago

Trigonometry, just the first one, will mark as brainliest if helpful

jek_recluse [69]

Answer:

a = -0.5

b = −1.73

c = −0.70

d = $-\frac{\sqrt{2} }{2}$ ≈ -0.70710678

Step-by-step explanation:

EXPLAIN Q(a):

sin(−30)

Use the property sin(−x)=−sin(x).

−sin(30)

Get the value of sin(30) from trigonometric values table.

-0.5

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1 year ago