Solve for x in the equation x^2-14 x + 31 = 63.

Can anyone help me figure out the 2 square 3 is? and show step by step. Thank you

taurus [48]

like 3 squared? or 2 cubed?

8 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

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

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

3 0

3 years ago

What is the amount, base, and percent in the expression.

Illusion [34]

Answer:

The correct answer is :

Amount: 2

Base: 100

Percent: 2%

Step-by-step explanation:

So, we get the answer by using whatever we know. The first step is that 2 is the percent because it is having the percent sign . In addition we know that 100 is the base. And the one which is left is 2 so it's the amount.

<h3>Hope it works out, brainliest appreciated! </h3>

~Adrianna

8 0

3 years ago

What is 0.55 in a decimal as a fraction in simplest form ?

anzhelika [568]

0.55 is equal to 55/100, and by dividing the numerator and denominator by 5, we get 11/20. Hope this helps!

8 0

3 years ago

what are a) the ratio of the perimeters and b) the ratio of the areas of the larger figure to the smaller figure? the figures ar

Alla [95]

We know that

a) find the ratio of the perimeters

the ratio of the perimeters is equal to the scale factor
scale factor=26/6-----> 13/3
the answer Part a) is
the ratio of the perimeters is 13/3

b) find the ratio of the areas of the larger figure to the smaller figure
we know that
area larger figure=[scale factor]²*area smaller figure
scale factor²=area larger figure/area smaller figure

the ratio of the areas of the larger figure to the smaller figure is equal to scale factor squared
scale factor²=(13/3)²----> 169/9

the answer Part b) is
169/9

the complete answer is
13/3 and 169/9

6 0

3 years ago