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3 years ago

Consider these functions

Mathematics

1 answer:

Evgen [1.6K]3 years ago

7 0

<h3>Answer: D) 31</h3>

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Explanation:

The expression g(f(2)) has f(2) as the inner function.

Let's compute f(2)

This means we plug x = 2 into the f(x) function

f(x) = 4x^3 - 10

f(x) = 4(x)^3 - 10

f(2) = 4(2)^3-10

f(2) = 4*8-10

f(2) = 32-10

f(2) = 22

Now we'll plug this into the g(x) function

This is because g(f(2)) = g(22). I've replaced f(2) with 22

So,

g(x) = (3x-4)/2

g(22) = (3*22-4)/2

g(22) = (66-4)/2

g(22) = 62/2

g(22) = 31

Therefore, g(f(2)) = 31

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Find the value of a square + b square when a+b = 8 and ab = 10

Ne4ueva [31]

As we know,

$\boxed{ \boxed{(a + b) {}^{2} = {a}^{2} + {b}^{2} + 2ab}}$

now, let's plug the given values to find a² + b²

$(8) {}^{2} = {a}^{2} + {b}^{2} + (2 \times 10)$

$64 = {a}^{2} + {b}^{2} + 20$

${a}^{2} + {b}^{2} = 64 - 20$

$a {}^{2} + b {}^{2} = 44$

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3 years ago

What is the volume of the composite figure? Express the answer in terms of pie.

zhenek [66]

Answer:

3127 mm3

Step-by-step explanation:

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3 years ago

Can someone please help me with this?

dedylja [7]

Answer:

e = 29.0 will be the answer.

Step-by-step explanation:

Use the sine rule in the given triangle,

$\frac{EF}{\text{sin}(\angle D)}=\frac{DE}{\text{sin}(\angle F)}=\frac{DF}{\text{sin}(\angle E)}$

$\frac{d}{\text{sin}(35)}=\frac{16}{\text{sin}(30)}=\frac{e}{\text{sin}(115)}$

$d=\frac{16\times \text{sin}(35)}{\text{sin}(30)}$

d = 18.35

$\frac{16}{\text{sin}(30)}=\frac{e}{\text{sin}(115)}$

$e=\frac{16\times \text{sin}(115)}{\text{sin}(30)}$

e = 29.002

e ≈ 29.0

Therefore, e = 29.0 will be the answer.

3 0

3 years ago

Lou has an account with $10,000 which pays 6% interest compounded annually. If to that account, Lou deposits $5,000 at the begin

katovenus [111]

Answer:

Option d. $22154 is the right answer.

Step-by-step explanation:

To solve this question we will use the formula $A=P(1+\frac{r}{n})^{nt}$

In this formula A = amount after time t

P = principal amount

r = rate of interest

n = number of times interest gets compounded in a year

t = time

Now Lou has principal amount on the starting of first year = 10000+5000 = $15000

So for one year $A=15000(1+\frac{\frac{6}{100}}{1})^{1\times1}$

$= 15000(1+.06)^{1}$

$= 15000(1.06)$ = $15900

After one year Lou added $5000 in this amount and we have to calculate the final amount he got

Now principal amount becomes $15900 + $ 5000 = $20900

Then putting the values again in the formula

$A=20900(1+\frac{\frac{6}{100}}{1})^{1\times1}$

$= 20900(1+.06)^{1}$

$= 20900(1.06)=22154$

So the final amount will be $22154.

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3 years ago

Given that the value of x is between 0 and 360 degrees (0 and 360

Brums [2.3K]

Answer:

150° and 210°
0

Step-by-step explanation:

It is convenient to memorize the trig functions of the "special angles" of 30°, 45°, 60°, as well as the way the signs of trig functions change in the different quadrants. Realizing that the (x, y) coordinates on the unit circle correspond to (cos(θ), sin(θ)) can make it somewhat easier.

You have memorized that cos(x) = (√3)/2 is true for x = 30°. That is the reference angle for the 2nd-quadrant angle 180° -30° = 150°, and for the 3rd-quadrant angle 180° +30° = 210°.

Cos(x) is negative in the 2nd and 3rd quadrants, so the angles you're looking for are

150° and 210°

<h3>Bonus</h3>

You have memorized that sin(π/4) = √2/2, and that cos(3π/4) = -√2/2. The sum of these values is ...

√2/2 + (-√2/2) = 0

_____

<em>Additional comments</em>

Your calculator can help you with both of these problems.

The coordinates given on the attached unit circle chart are (cos(θ), sin(θ)).

6 0

2 years ago