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3 years ago

State the amplitude, period, phase shift, and vertical shift of the function m(t)= 7 cos (t+3)

Mathematics

1 answer:

tiny-mole [99]3 years ago

3 0

Answer:

Step-by-step explanation:

Given a sinusoidal function in the form $f(x)=Acos(Bx+C)+D$ , we can say:

A is the amplitude
$\frac{2\pi}{B}$ is the period
$-\frac{C}{B}$ is the phase shift
D is the vertical shift

From the function given m(t) = 7 Cos (t+3), we see that

A = 7

B = 1

C = 3

D = 0

Thus, from the info, we can say

Amplitude = 7

Period = 2π

Phase Shift = -3

Vertical Shift = 0

Answer choice B is right.

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Can anyone help me!

zhenek [66]

Answer:

$\large \text{$ \sf 2^{-64}$}$

Step-by-step explanation:

Given:

$\large \text{$ \sf (256)^{-4^{\frac{3}{2}}}$}$

This reads as: 256 to the power of "-4 to the power of 3/2".

Therefore, we need to deal with the "-4 to the power of 3/2" first.

Rewrite the 4 as 2²:

$\large \text{$ \sf \implies -(2^2)^{\frac{3}{2}}$}$

$\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:$

$\large \text{$ \sf \implies -2^{\left(2 \times \frac{3}{2}\right)}$}$

$\large \text{$ \sf \implies -2^{3}$}$

Therefore:

$\large \text{$ \sf \implies -2^3=(-2)(-2)(-2) = -8$}$

Replace "-4 to the power of 3/2" with -8 :

$\large \text{$ \sf \implies 256^{-8}$}$

Rewrite 256 as 2⁸ :

$\large \text{$ \sf \implies (2^8)^{-8}$}$

$\textsf{Again, apply exponent rule} \quad (a^b)^c=a^{bc}:$

$\large \text{$ \sf \implies 2^{(8 \times -8)}$}$

$\large \text{$ \sf \implies 2^{-64}$}$

In one complete calculation:

$\large\begin{aligned} \sf (256)^{-4^{\frac{3}{2}}} & = \sf (256)^{-(2^2)^{\frac{3}{2}}}\\& = \sf (256)^{-2^{\left(2 \times \frac{3}{2}\right)}}\\& =\sf (256)^{-2^{3}}\\& = \sf (256)^{-8}\\& \sf = (2^8)^{-8}\\& = \sf 2^{(8 \times -8)}\\& =\sf 2^{-64}\end{aligned}$

Learn more about exponent rules here:

brainly.com/question/28211147

brainly.com/question/27959936

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1 year ago

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A rectangular jewelry box costs $125 to gold plate. Calculate the cost of gold plating a box which is similar in shape and that

Alja [10]

To determine the amount of gold plating necessary for the similar box, you will use the fact that it is 8 times larger in volume to determine how many times larger the area is. This would be what you will multiply $125 by.

Volume is a three dimensional measurement, so the fact that it is 8 times larger tells us each dimension was 2 times larger (2 x 2 x 2=8).

Area is a two dimensional measurement, so the area would have been 2 x 2 or 4 times larger. This means the price would be 4 times as much.
$125 x 4 = $500.

It will cost $500 to gold plate the similar jewelry box.

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3 years ago

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DiKsa [7]

Answer:

I think this is right

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Jason rolls the die 14 times. What is the experimental probability that he will roll a 2

Vaselesa [24]

There’s 14 rolls. The probability he lands on a 2 would be 2/14. Once you simplify it it would give you a probability of 1/7