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3 years ago

ITS URGENT PLEASE HELP Which equation represents the line that is parallel to y=3/7x+11 and passes through (-21,42)?

Mathematics

1 answer:

Pepsi [2]3 years ago

3 0

Answer:

y = 3/7x + 51

Step-by-step explanation:

y = 3/7x + 11 is parallel to the line so it means that both of their gradient are same so:

y = mx + c

m= gradient point = (-21 , 42)

= 3/7

now we sub the m and the point into the formula which is y= mx+c because we should find the c first then we can find the equation of the line:

42 = 3/7 (-21) + c

42 = -9 + c

42 + 9 = c

51 = c

c = 51

now you hv to rewrite again the equation become y= 3/7x + 51

So now your final answer is : y = 3/7x +51

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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

Which equation describes a line parallel<br> to y= 4x+ 5 through point (-2, 1)?

Tema [17]

Hi there!

For a line to be PARALLEL, it must contain the same slope.

The given line has a slope of 4, so we can use the point-slope formula to solve:

$\large\boxed{y - y_1 = m(x - x_1)}$

y1 = y-coordinate of given point

x1 = x-coordinate of given point

m = slope

Plug in the values:

$y - 1 = 4(x - (-2))\\\\y - 1 = 4(x + 2)$

Simplify:

$y - 1 = 4x + 8\\\\\boxed{y = 4x + 9}$

8 0

2 years ago

Your current test average in Biology is a 73. If the standard deviation is 25.1, you are a consistent Biology student.

Ugo [173]

Your answer is true! I hope that helps ;)

5 0

3 years ago

Someone please help, is due tonight, will give brainly if helped. Thank you...

Alina [70]

Answer:

1. f & c, d & e,

2. h & a, g & b

3. h & d, f & b, g & c, a & e

here ya go, i hope this is correct if i remember right

Step-by-step explanation:

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3 years ago

The linear equation 99(xminus−77)equals=99(xplus 88) is

Natalija [7]

99(x-77)=99(x+88)
99x-7623=99x+8712
99x-99x=8712+7623
0=670824.no solution as x becomes 0

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3 years ago