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2 years ago

Y varies directly as the square of x when x=2 then y =16 find y when x=8

Mathematics

1 answer:

Leviafan [203]2 years ago

8 0

Answer: y= 64

Step-by-step explanation:

If y is 16 when x is 2 This means if x is 8 y will be 64.

Set up the proportional equation

$\frac{2}{16} = \frac{8}{y}$ Cross multiply

2y = 128

y= 64

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A bacteria colony increases in size at a rate of 4.0581e1.6t bacteria per hour. If the initial population is 36 bacteria, find t

Harrizon [31]

Answer:

1560

Step-by-step explanation:

The rate of Increase of the population (P) of the bacteria is given as:

$\frac{dP}{dt} =4.058e^{1.6t}$

$dP =4.058e^{1.6t}}dt\\Taking\: Integrals\\\int dP =4.058 \int e^{1.6t}dt\\P(t)=\frac{4.058}{1.6} (e^{1.6t} +K)\\P(t)=2.53625 (e^{1.6t} +K)$

Where k is a constant of Integration.

At t=0, P(t)=36

$36=2.53625 (e^{1.6*0} +K)\\36=2.53625 (e^{0} +K)\\36=2.53625 (1 +K)\\36=2.53625 +2.53625K\\K=13.19$

Therefore:

$P(t)=2.53625 (e^{1.6t} +13.19)\\At \: t=4\\P(4)=2.53625 (e^{1.6*4} +13.19)\\=1559.88\\P(4)=1560$

3 0

3 years ago

A baseball player hit 57 home runs in a season. Of the 57 home runs, 15 went to right field, 20 went to right center field, 1

Sidana [21]

Place the part (amount going to the left field), over the total amount of homerun:

(a) 2/57 is your probability

(b) Divide 2/57

2/57 = 0.035, or 3.5%

YES, it is unusual for this player to hit a home run to left field, for he only has a 3.5% chance.

hope this helps

8 0

2 years ago

Simplify the expression -2+6.45z-6+(-3.25z)

erik [133]

Answer:

-8 + 3.2z

Step-by-step explanation:

when there is a "+" in front of an expression in parentheses, the expression remains the same
-2 + 6.45z - 6 - 3.25z
calculate the difference

-8 + 6.45z - 3.25z

collect like terms

-8 + 3.2z

8 0

2 years ago

a bottle of ketchup contains 40 oz of ketchup. How many 1/2 oz servings can you get out of one bottle?

In-s [12.5K]

Answer:

you can get 80 1/2 oz servings.

Step-by-step explanation:

8 0

2 years ago

Jake can mulch a garden in 30 minutes. together, jake and ross can mulch the same garden in 16 minutes. how much time t, in minu

Gelneren [198K]

"Jake can mulch a garden in 30 minutes." So, for 1 min Jake can mulch 1/30 part of a garden.

Ross can mulch the park for x minutes. So, for 1 min Jake can mulch 1/x part of a garden.

If they work together, for 1 min they will mulch (1/30 + 1/x) part of the garden.

At the same time, we know, that of they work together they can mulch the garden in 16 min, so for 1 min they will mulch 1/16 part of the garden.

Now, we can write an equation

$\frac{1}{30} + \frac{1}{x} = \frac{1}{16} \\ \\ \frac{1}{x} = \frac{1}{16} - \frac{1}{30} \\ \\ \frac{1}{x} =\frac{30-16}{16*30} \\ \\ \frac{1}{x} =\frac{14}{16*30} \\ \\x=\frac{16*30}{14}$

x≈34.3 (min)

8 0

3 years ago