7 inches, and one of the legs is inches. Find the length of the other leg.

Elevator 1 in a building moved from ground position to a final position of +17 feet. Elevator 2 in the same building moved from

Marianna [84]

I would go with the first one

3 0

3 years ago

How many minutes is it before 12 noon if 68 minutes ago it was three times as many minutes past 10 a.m.?

umka21 [38]

If 68 minutes ago it (then) was three times as many minutes past 10 am (now)

x + 68 = 3 ×
×
(120 - x) →
→
x = 73 min
… if 68 minutes ago it (now) was three times as many minutes past 10 am (then)

x = 3 ×
×
[120 - (x + 68)] →
→
x = 39 min
… if 68 minutes ago it (then) was three times as many minutes past 10 am (then)

x + 68 = 3 ×
×
[120 - (x + 68)] →
→
x = 22 min

7 0

3 years ago

The diameter of the moon is 2,160 miles. A model has a scale of 1 in : 150 mi. What is the diameter of the model?

Charra [1.4K]

Answer:

The diameter of the model is 14.4 inches.

Step-by-step explanation:

The Diameter of the moon = 2,160 miles

The scale on the model represents 1 in = 150 miles

Let the model represents k inches in 2,160 miles.

So, by the Ratio of Proportionality:

$\frac{1}{150} = \frac{k}{2160}$

⇒ $k = \frac{2160}{150} \\\implies k = 14.4$

or, k = 14.4 inches

⇒On the scale 2160 miles is represented as 14.4 inches

Hence the diameter of the model is 14.4 inches.

3 0

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>

3 0

3 years ago

What is the value of x in the equation 1/5x – 2/3y = 30, when y = 15?

lianna [129]

Answer:

x = 200

Step-by-step explanation:

1/5x – 2/3y = 30

substitute in y

1/5x - 2/3(15) = 30

multiply

1/5x - 10 = 30

isolate the variable

1/5x = 40

multiply each side by 5

x = 200

4 0

3 years ago

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