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Strike441 [17]
3 years ago
7

Felicity set the thermostat in her living room to 68°F. The room temperature t, in degrees Fahrenheit, m minutes after the therm

ostat is activated, satisfies t = 2cos(0.21m) + 68. Determine the period of the function and explain what it represents. Include the maximum and minimum temperatures in your answer.
Mathematics
1 answer:
Ahat [919]3 years ago
6 0

Answer with explanation:

Temperature in the living room =68°F

The equation which satisfies ,the  room temperature t, in degrees Fahrenheit, m minutes after the thermostat is activated, satisfies

 t=2 Cos (0.21 m) +68----------(1)

⇒To determine the period of the function

Z= A cos (sx+q)+r

As period of cos x is 2 π.

So,the given function has period

        =\frac{2\pi}{s}            

So, the period of function 1, is given by

        =\frac{2\pi}{0.21}  

⇒The meaning of period of the function is that after every period of   =\frac{2\pi}{0.21} the temperature of the room increases or decreases by an integer equal to 2.

⇒Cosine function has maximum value of 1 , and Minimum value of -1.

-1 ≤ Cos x ≤ 1

So, the Maximum value of function = 2 ×1+68°=70°----Maximum Temperature

And, the minimum value of function = 2 ×(- 1)+68°=66°----Minimum Temperature

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<em> </em>

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3 years ago
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ollegr [7]
Data:
r (radius) = 3.5 in
h (height) = 8 in
Adopt: \pi \approx3.14
V (volume) = ?
Ink cost per cubic inch = $0.05/in³
Total cost: ?

<span>Calculate the volume of the paint bucket (its formed being cylindrical), we have:
</span>V =  \pi *r^2*h 
V = 3.14 *3.5^2*8 
V = 3.14*12.25*8
\boxed{V = 307.72\:in^3}

<span>What was the total cost of the paint?

</span>price($)___measure(in³)
0.05 ---------- 1
y -------------- 307.72

It is made the rule of three: (<span>directly proportional)
</span>
\frac{0.05}{y} = \frac{1}{307.72}
multiply cross
1*y = 0.05*307.72
y = 15.386\:\to\:\boxed{\boxed{y\approx\$15}}\end{array}}\qquad\quad\checkmark

Answer:
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3 years ago
Help, I need help with this math question as soon as possible!!
mina [271]

Answer:

Step-by-step explanation:

4x what = 98

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Explain why the function of f(x)=4x^2+8x is neither even or odd
myrzilka [38]

Answer:

By putting x = -x in f(x) i.e. f(-x) we didn't get f(x) or -f(x) so, the function is neither even nor odd.

Step-by-step explanation:

We need to explain why the function of f(x)=4x^2+8x is neither even or odd

First we will understand, when the function is even and odd

Even function:

<em>A function is even if f(-x) = f(x) </em>

Odd function:

<em>A function is odd if f(-x) = -f(x) </em>

So, if we get the above result by putting x = -x, then we can say that the function is even or odd.

If we don't get any of the above results then the function is neither even nor odd.

So, for the given function: f(x)=4x^2+8x

Put x = -x

f(x)=4x^2+8x\\Put x=-x\\f(-x)=4(-x)^2+8(-x)\\f(-x)=4x^2-8x

So, by putting x=-x in f(x) i.e. f(-x) we didn't get f(x) or -f(x) so, the function is neither even nor odd.

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Bob has $178.74 in his checking account. He wrote checks for $36.52, $18.92, and $25.93. He also deposited $300.00, $100.00, and
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The correct answer should be $702.53
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4 years ago
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