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omeli [17]
3 years ago
5

The volume of a rectangular prism is given by the formula V = lwh, where l is the length of the prism, w is the width, and h is

the height. Which expression represents the volume of the following rectangular prism?
Mathematics
2 answers:
Artemon [7]3 years ago
8 0
If the given are h =2x+9, l = x+2, w = 3x, then the answer is 6x^3+39x^2+54x

V = lwh
    = (2x+9)(x+2)(3x)
    = (2x^2 + 4x + 9x + 18)(3x)
    = 6x^3 + 12x^2 + 27x^2 + 54x
    = 6x^3 + 39x^2 + 54x
Alinara [238K]3 years ago
8 0

Answer:

C. 6x^3+39x^2+54x

Step-by-step explanation:

got it right on test

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In am election, Mrs.Jones received 70% of the 1,500 votes cast. How many votes did Mrs. Jones receive
WARRIOR [948]

Hello!

To calculate how many votes Mrs. Jones had received, you would begin by converting 70% into a decimal, and then multiplying that decimal by the total number of votes.

Remember, all percentages are out of 100. So, 70/100 can be simplified into 7/10. As a decimal, 7/10 would be 0.7.

Next, we multiply 0.7 by the total number of votes, which is 1,500.

0.7 · 1500 = 1050

Therefore, in this election, Mrs. Jones received 1,050 votes out of the total 1,500 votes casted.

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Kryptonite is a material found on the planet Krypton and has various effects, most importantly on Superman. The most common type
Rashid [163]

Answer:

The maximum amount of red kryptonite present is 33.27 g after 4.93 hours.

Step-by-step explanation:

dy/dt = y(1/t - k)

separating the variables, we have

dy/y = (1/t - k)dt

dy/y = dt/t - kdt

integrating both sides, we have

∫dy/y = ∫dt/t - ∫kdt

㏑y = ㏑t - kt + C

㏑y - ㏑t = -kt + C

㏑(y/t) = -kt + C

taking exponents of both sides, we have

\frac{y}{t} = e^{-kt + C}  \\\frac{y}{t} = e^{-kt}e^{C} \\\frac{y}{t} = Ae^{-kt}   (A = e^{C})\\y = Ate^{-kt}

when t = 1 hour, y = 15 grams. So,

y = Ate^{-kt}\\15 = A(1)e^{-kX1}\\15 = Ae^{-k}(1)

when t = 3 hours, y = 30 grams. So,

y = Ate^{-kt}\\30 = A(3)e^{-kX3}\\30 = 3Ae^{-3k} (2)

dividing (2) by (1), we have

\frac{30}{15}  = \frac{3Ae^{-3k}}{Ae^{-k}} \\2 = 3e^{-2k}\\\frac{2}{3} = e^{-2k}

taking natural logarithm of both sides, we have

-2k = ㏑(2/3)

-2k = -0.4055

k = -0.4055/-2

k = 0.203

From (1)

A = 15e^{k} \\A = 15e^{0.203} \\A = 15 X 1.225\\A = 18.36

Substituting A and k into y, we have

y = 18.36te^{-0.203t}

The maximum value of y is obtained when dy/dt = 0

dy/dt = y(1/t - k) = 0

y(1/t - k) = 0

Since y ≠ 0, (1/t - k) = 0.

So, 1/t = k

t = 1/k

So, the maximum value of y is obtained when t = 1/k = 1/0.203 = 4.93 hours

y = 18.36(1/0.203)e^{-0.203t}\\y = \frac{18.36}{0.203}e^{-0.203X1/0.203}\\y = 90.44e^{-1}\\y = 90.44 X 0.3679\\y = 33.27 g

<u>So the maximum amount of red kryptonite present is 33.27 g after 4.93 hours.</u>

3 0
3 years ago
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