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3 years ago

6

I have a kit for constructing a chicken coop. The kit comes with 10-foot long beams. The instructions say to cut each beam into

two pieces such that one piece is 3 times the length of the other. How many feet long should the long piece be?

1 answer:

vagabundo [1.1K]3 years ago

5 0

The pieces are 2.5 and 7.5 the 7.5 is the piece that is 3 times the length of the first one

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What is the f of x over the g of x when f(x)=6x^3-19x^2+16x-4 and g(x)=x-2?

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Answer:

no four is not better than 7679_727=2873

Step-by-step explanation: 89 is 48-23

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3 years ago

The sum of three numbers is 35. The first number is three less than the second and the third is two more than 4 times the second

saul85 [17]

Step-by-step explanation:

$x + y + z = 35 \\ x = y - 3 \\ z = 4y + 2 \\ \\ (y - 3) + y + (4y + 2) = 35 \\ 6y - 1 = 35 \\ 6y = 36 \\ y = \frac{36}{6} \\ y = 6 \\ \\ x = y - 3 \\ x = 6 - 3 \\ x = 3 \\ \\ z= 4y + 2 \\ z= (4 \times 6) + 2 \\ z = 26$

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2 years ago

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Johnny spent $28.50 at a parking garage in downtown Asheville. The garage

just olya [345]

Answer:3 hour

Step-by-step explanation:

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3 years ago

The circumference of the inner circle is 44 ft. The distance between the inner circle and the outer circle is 3 ft. By how many

Citrus2011 [14]

Answer: 18.86 feet

Step-by-step explanation:

The formula for determining the circumference of a circle is expressed as

Circumference = πD

Where D represents the diameter of the circle.

The circumference of the inner circle is 44 ft. It means that

22/7 × D = 44

22D = 7 × 44 = 308

D = 308/22

D = 14 ft

The distance between the inner circle and the outer circle is 3 ft. This means that the diameter of the outer circle would be

14 + 3 + 3 = 20 ft

Circumference of the outer circle is

22/7 × 20 = 62.86 ft

The number of feet by which the circumference of outer circle is greater than the circumference of the inner circle is

62.86 - 44 = 18.86 feet

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3 years ago

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>

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3 years ago