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inysia [295]
2 years ago
6

Find the equation of the line through the points (-9,3) and (-6, -3).

Mathematics
1 answer:
IgorLugansk [536]2 years ago
4 0

Answer:

y = -2x -15

Step-by-step explanation:

Y2-Y1/ X2-X1

= - 9 -- 6  / 3 - - 3

- 15 / 6 = -2.5

-1/-2.5 = .4

0.4 x - 15  = 6

6/-3 = -2

therefore y = mx+c

= -2x -15

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Find an equation of the tangent plane to the given surface at the specified point. z = ln(x − 8y), (9, 1, 0)
Archy [21]

Answer:

x - 8y - z = 1

Step-by-step explanation:

Data provided according to the question is as follows

f(x,y) = z = ln(x - 8y)

Now the equation for the tangent plane to the surface

For z = f (x,y) at the point P (x_0,y_0,z_0) is

z - z_0 = f_x(x_0,y_0)(x-x_0) + f_y(x_0,y_0)(y-y_0)\\

Now the partial derivatives of f are

f_x(x,y) = \frac{1}{x-8y} \\\\f_y(x,y) = \frac{8}{x-8y} \\\\P(x_0,y_0,z_0) = (9,1,0)\\\\f_z(9,1,0) = (\frac{1}{x-8y})_^{(9,1,0)}

\\\\=\frac{1}{9-8}

= 1

Now

f_y(9,1,0)=(\frac{8}{x-8y})_{(9,1,0)}\\\\ = -\frac{8}{9 - 8}

= -8

So, the tangent equation is

z - 0 = 1\times (x - 9) -8\times (y - 1)

Now after solving this, the following equation arise

z = x - 9 - 8y + 8

z = x - 8y - 1

Therefore

x - 8y - z = 1

4 0
3 years ago
The length of a rectangle is seven times its width. The area of the rectangle is 175 square centimeters. Find the dimensions of
dimulka [17.4K]

Answer:

<h3>The length is 35cm</h3><h3>The width is 5cm</h3><h3 />

Step-by-step explanation:

Area of a rectangle = l × w

where

l is the length

w is the width

The length is seven times the width is written as

l = 7w

Area of the rectangle = 175 cm²

7w × w = 175

7w² = 175

Divide both sides by 7

w² = 25

Find the square root of both sides

w = √25

w = 5cm

But l = 7w

l = 7(5)

l = 35cm

The length is 35cm

The width is 5cm

Hope this helps you.

7 0
3 years ago
X+7+=-14<br><br> ASAP! PLease!
umka21 [38]

Hey there!

Answer = -21

Explanation:

Let's solve your equation step-by-step.

x + 7 = -14

Subtract seven from both sides:

x + 7 - 7 = -14 - 7

x = -21

So therefore, that is how you found your answer: x = -21

8 0
3 years ago
Read 2 more answers
All positive integers $t$ such that $1.2t \leq 9.6$?
serious [3.7K]
Haha me don’t know sorry okay
7 0
2 years ago
Can someone help pleas
Lena [83]

Step-by-step explanation:

According to picture 1, it is <u>A. </u><u>corresponding.</u>

Also according to picture 2, it is <u>E.</u><u> </u><u>same </u><u>side</u><u> </u><u>interior.</u>

And according to picture 3, it is <u>D.</u><u> </u><u>vertical</u>

6 0
2 years ago
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