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bogdanovich [222]
2 years ago
15

Marco leaves the bathroom faucet running for 22 minutes while he gets ready in the morning. running the faucet for 5 minutes was

tes the same amount of energy as leaving a 60-watt light bulb on for 14 hours. how much energy did marco waste, in terms of hours which a 60-watt light bulb would remain on? a. 7.9 hours b. 61.6 hours c. 56.0 hours d. 264.0 hours
Mathematics
1 answer:
lord [1]2 years ago
5 0

The amount of energy waste, in terms of hours which a 60-watt light bulb would remain on, is 61.6 hours then the correct option is B.

<h3>What are ratio and proportion?</h3>

A ratio is an ordered couple of numbers a and b, written as a/b where b can not equal 0. A proportion is an equation in which two ratios are set equal to each other.

Marco leaves the bathroom faucet running for 22 minutes while he gets ready in the morning.

Running the faucet for 5 minutes wastes the same amount of energy as leaving a 60-watt light bulb on for 14 hours.

Then we have

\begin{aligned} \dfrac{5\ minutes}{14 \ hours } &=\dfrac{1\ minute }{x \ hours}\\\\x &= 2.8  \ hours \end{aligned}

So, the rate is 2.8 hours per minute.

Since macro leaves the bathroom faucet running for 22 minutes. Then the waste of energy is leaving a 60-watt light bulb will be

→22 minutes × 2.8 hours/minute = 61.6 hours.

More about the ratio and the proportion link is given below.

brainly.com/question/14335762

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What is 3.56 * 10 with an exponent negative 5 in standard form
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Answer: .0000356

<u>Step-by-step explanation:</u>

3.56 x 10⁻⁵

the exponent of 5 tells you to move the decimal 5 places

the negative sign tells you to move the decimal to the left.

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Consider the following vector function. R(t) = 9 2 t, e9t, e−9t (a) find the unit tangent and unit normal vectors t(t) and n(t)
garik1379 [7]

The unit tangent vector is T(u) and the unit normal vector is N(t) if the  vector function. R(t) is equal to 9 2 t, e9t, e−9t.

<h3>What is vector?</h3>

It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.

We have vectored function:

\rm R(t) = (9\sqrt{2t}, e^{9t}, e^{-9t})

Find its derivative:

\rm R'(t) = (9\sqrt{2}, 9e^{9t}, -9e^{-9t})

Now its magnitude:

\rm |R'(t) |= \sqrt{(9\sqrt{2})^2+ (9e^{9t})^2+ (-9e^{-9t})^2}

After simplifying:

\rm R'(t) = 9 \dfrac{e^{18t}+1}{e^{9t}}

Now the unit tangent is:

\rm T(u) = \dfrac{R'(t)}{|R'(t)|}

After dividing and simplifying, we get:

\rm T(u) = \dfrac{1}{e^{18t}+1} (\sqrt{2}e^{9t}, e^{18t}, -1)

Now, finding the derivative of T(u), we get:

\rm T'(u) = \dfrac{1}{(e^{18t}+1)^2} (9\sqrt{2}e^{9t}(1-e^{18t}), 18e^{18t}, 18e^{18t})

Now finding its magnitude:

\rm |T'(u) |= \dfrac{1}{(e^{18t}+1)^2} (9\sqrt{2}e^{9t}(1-e^{18t})^2+ (18e^{18t})^2+( 18e^{18t})^2)

After simplifying, we get:

\rm |T'(u)|= \dfrac{9\sqrt{2}e^{9t}}{e^{18t}+1}

Now for the normal vector:

Divide T'(u) and |T'(u)|

We get:

\rm N(t) = \dfrac{1}{e^{18t}+1} ( 1-e^{18t},          \sqrt{2}e^{9t},  \sqrt{2}e^{9t})

Thus, the unit tangent vector is T(u) and the unit normal vector is N(t) if the  vector function. R(t) is equal to 9 2 t, e9t, e−9t.

Learn more about the vector here:

brainly.com/question/8607618

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Indicate which property is illustrated in step 1
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Answer:

Step-by-step explanation:

communicative because you moved the three to the other side

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The number of caps a new online store sells increases by a factor of 4 each month. The function f(x)=4^x represents the number o
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For this case we have the following variables:

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The function that models the problem is given by:

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From here, we clear the number of months:

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Answer:

the store sells 64 caps in 3 monts

A. month 3

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