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Pavlova-9 [17]
1 year ago
9

Find the equation of the line through point (8,−9) and perpendicular to 3+8=4.

Mathematics
1 answer:
raketka [301]1 year ago
4 0

The equation of the line through the point (8,−9) and perpendicular to 3x+8y=4 is given by 8x - 3y = 91.

We are aware that any straight line's equation can be expressed as

y = mx + c,

where m denotes the slope and c denotes a constant.

Also, two perpendicular lines' slopes are the negative reciprocals of one another.

Here, the equation of the given straight line is

3x+8y=4

i.e. 8y = 4 -3x

i.e. y = (4/8) - (3/8)x

Now the negative reciprocal of - 3/8 is 8/3.

Then we can write the equation of the perpendicular line is

y = (8/3)x + c ...(1)

Since (1) passes through the point (8, -9), so we can put x = 8 and y = -9 in (1) to get the value of c.

So, -9 = (8/3)*8 + c

i.e. -9 = 64/3 + c

i.e. c = -9 -64/3 = - (27 + 64)/3 = - 91/3

(1) can be written as

y = (8/3)x - (91/3)

i.e. 3y = 8x - 91

i.e. 8x - 3y = 91

Therefore the equation of the line through the point (8,−9) and perpendicular to 3x+8y=4 is given by 8x - 3y = 91.

Learn more about perpendicular lines here -

brainly.com/question/12209021

#SPJ10

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Step-by-step explanation:

<u>Given equation:</u>

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<u>Now, let's solve the equation:</u>

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Their rate was 85 toys per day.

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X^4 -(3m+2)x^2 +3m+1 +0 <br> tìm m để phương trình có 4 nghiệm phân biệt nhỏ hơn 2
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Newton's law of cooling is:
Mnenie [13.5K]

Answer:

t = \frac{ln(\frac{21}{59})}{-0.15}=6.887 hr

So it would takes approximately 6.9 hours to reach 32 F.

Step-by-step explanation:

For this case we have the following differential equationÑ

\frac{du}{dt}= -k (u-T)

We can reorder the expression like this:

\frac{du}{u-T} = -k dt

We can use the substitution w = u-T and dw =du so then we have:

\frac{dw}{w} =-k dt

IF we integrate both sides we got:

ln |w| = -kt +C

If we apply exponential in both sides we got:

w = e^{-kt} *e^c

And if we replace w = u-T we got:

u(t)= T + C_1 e^{-kt}

We can also express the solution in the following terms:

u(t) = (T_i -T_{amb}) e^{kt} +T_{amb}

For this case we know that k =-0.15 hr since w ehave a cooloing, T_{i}= 70 F, T_{amb}=11F, we have this model:

u(t) = (70-11) e^{-0.15t} +11

And if we want that the temperature would be 32F we can solve for t like this:

32 = 59 e^{-0.15 t} +11

21=59 e^{-0.15 t}

\frac{21}{59} = e^{-0.15 t}

If we apply natural logs on both sides we got:

ln (\frac{21}{59}) =-0.15 t

t = \frac{ln(\frac{21}{59})}{-0.15}=6.887 hr

So it would takes approximately 6.9 hours to reach 32 F.

7 0
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