How do i convert this to standard form?<br><br> y+4=-3(x-1)

Find the volume of a pyramid with a square base, where the side length of the base is

ValentinkaMS [17]

Answer:

Step-by-step explanation:

Volume of a pyramid can be found by using the formula

$v = \frac{1}{3} \times a \times h \\$

a is the area of the base

h is the height

Since the base is a square we have

$v = \frac{1}{3} \times {15.3}^{2} \times 19.6 \\ = 78.03 \times 19.6 \\ = 1529.388$

We have the final answer as

Hope this helps you

3 0

3 years ago

Find the least common multiple of 6 , 2 and 9

Goryan [66]

Answer:

18

Step-by-step explanation:

The multiples of 6 are : 6, 12, 18, 24, 30, ......

The multiples of 2 are : 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ......

The multiples of 9 are : 9, 18, 27, 36, ......

The common multiple is 18

The least common multiple is 18

8 0

4 years ago

The sum of two numbers is -14 one number is 20 less than the other find the numbers

Lisa [10]

Answer:

x=-17,y=3

Step-by-step explanation:

x+y=-14

x=x

y=x+20

x+(x+20)=-14

2x+20=-14

2x=-14-20

2x=-34

x=-34/2

x=-17

y=-17+20

y=3

3 0

3 years ago

Please help me guys with this problem.

Anna71 [15]

I think the answer is 152 but I’m not 100% sure

7 0

3 years ago

Read 2 more answers

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

How do i convert this to standard form? y+4=-3(x-1)