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yan [13]
3 years ago
6

for a short time after a wave is created by wind, the height of the wave can be modeled using y = a sin 2π/T, where a is the amp

litude and T is the period of the wave in seconds. How many times over the first 5 seconds does the graph predict the wave to be 2 feet height?
Mathematics
2 answers:
nadezda [96]3 years ago
8 0
I think the wave is 2x)t
pentagon [3]3 years ago
5 0

Answer:

2 times

Step-by-step explanation:

We are given that the height of the wave can be modeled using

y=asin \frac{2\pi}{T}

We have to find the value of amplitude

T=5 seconds

Height =y=2 feet

Where a = Amplitude

Substitute the values then we get

2 =a sin \frac{2\times 180}{5}

Because pi=180 ^{\circ}

2=a sin 72^{\circ}

2= a\times 0.952[/txe][tex]a=\frac{2}{0.952}

a=2.1

Amplitude =2 feet

Hence, the graph is 2 times over the first 5 seconds when the wave to be 2 feet height.

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When the area in square units of an expanding circle is increasing twice as fast as its radius in linear units, the radius is...
enot [183]

Answer:

c. \frac{1}{\pi}

Step-by-step explanation:

We have been given that the area in square units of an expanding circle is increasing twice as fast as its radius in linear units

We will use derivatives to solve our given problem.

We know that area (A) of a circle is equal to A=\pi r^2.

Let us find derivative of area function with respect to time.

\frac{dA}{dt}=\frac{d}{dt}(\pi r^2)

Bring out constant:

\frac{dA}{dt}=\pi \frac{d}{dt}(r^2)

Using power rule and chain rule, we will get:

\frac{dA}{dt}=\pi(2r)* \frac{dr}{dt}

\frac{dA}{dt}=2\pi r*\frac{dr}{dt} Here \frac{dr}{dt} represents change is radius with respect to time.

We have been given that area of an expanding circle is increasing twice as fast as its radius in linear units. We can represent this information in an equation as:

\frac{dA}{dt}=2\frac{dr}{dt}

2\pi r* \frac{dr}{dt}=2\frac{dr}{dt}

2\pi r=2

\frac{2\pi r}{2\pi}=\frac{2}{2\pi}

r=\frac{1}{\pi}

Therefore, the radius is \frac{1}{\pi} and option 'c' is the correct choice.

6 0
3 years ago
Calcular el volumen en m3 de la esfera en el que el área de uno de sus círculos maximos es 36pim2
Strike441 [17]

Answer:

The volume of the sphere is V=288\pi\ m^3

Step-by-step explanation:

<u><em>The question in English is</em></u>

Calculate the volume in m^3 of the sphere in which the area of one of its maximum circles is 36pi m^2

we know that

The radius of the maximum circle in the sphere is equal to the radius of the sphere

Step 1

Find the radius of the maximum circle

The area of the circle is

A=\pi r^{2}

we have

A=36\pi\ m^2

substitute and solve for r

36\pi=\pi r^{2}

Simplify

36=r^{2}

take the square root both sides

r=6\ m

Step 2

Find the volume of the sphere

The volume of the sphere is

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

substitute the value of r

V=\frac{4}{3}\pi (6)^{3}

V=288\pi\ m^3

6 0
4 years ago
Need help on this please
stellarik [79]
The answer to that question is 15.51
4 0
3 years ago
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Sasha buys a rowboat priced at $486.40. Shipping and handling are an additional 16% of
Maru [420]
486.40*16%= around 77.82 dollars
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2 years ago
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What is the slope of (-1,4) and(1,-2)
nordsb [41]

Answer:

Step-by-step explanation:

use the distance formula.

x1=-1

x2=1

y1=4

y2=-2

d=√((x2-x1)^2+(y2-y1)^2)

d=√(30) or 5.4772

5 0
3 years ago
Read 2 more answers
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