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3 years ago

A line has a slope of -2/3 and passes through the point (-3,8). What is the equation of the line?

Mathematics

2 answers:

USPshnik [31]3 years ago

8 0

Answer:y=-2/3x+6

Step-by-step explanation:

took unit test on edge2020

LiRa [457]3 years ago

7 0

Answer:

Step-by-step explanation:

We'll use the standard equation y=mx+b to solve this problem. m is the slope of the line and b is the y intercept.

We know the slope, but we have to solve for the y intercept. To do this (I mean solve for 'b'), we need to know the slope, x value, and y value. We know the slope (-2/3), x= -3, and y=8. Let's plug this into y=mx+b and solve for b.

$y=mx+b\\8=-\frac{2}{3}*-3 +b\\8=2+b\\b=8-2\\b=6$

Let's plug all of this back into the first equation y=mx+b.

$y=mx+b\\y=-\frac{2}{3}x+6$

That's the answer to this problem.

I hope this helps.

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If 3x^2 + y^2 = 7 then evaluate d^2y/dx^2 when x = 1 and y = 2. Round your answer to 2 decimal places. Use the hyphen symbol, -,

S_A_V [24]

Taking $y=y(x)$ and differentiating both sides with respect to $x$ yields

$\dfrac{\mathrm d}{\mathrm dx}\bigg[3x^2+y^2\bigg]=\dfrac{\mathrm d}{\mathrm dx}\bigg[7\bigg]\implies 6x+2y\dfrac{\mathrm dy}{\mathrm dx}=0$

Solving for the first derivative, we have

$\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{3x}y$

Differentiating again gives

$\dfrac{\mathrm d}{\mathrm dx}\bigg[6x+2y\dfrac{\mathrm dy}{\mathrm dx}\bigg]=\dfrac{\mathrm d}{\mathrm dx}\bigg[0\bigg]\implies 6+2\left(\dfrac{\mathrm dy}{\mathrm dx}\right)^2+2y\dfrac{\mathrm d^2y}{\mathrm dx^2}=0$

Solving for the second derivative, we have

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=-\dfrac{3+\left(\frac{\mathrm dy}{\mathrm dx}\right)^2}y=-\dfrac{3+\frac{9x^2}{y^2}}y=-\dfrac{3y^2+9x^2}{y^3}$

Now, when $x=1$ and $y=2$ , we have

$\dfrac{\mathrm d^2y}{\mathrm dx^2}\bigg|_{x=1,y=2}=-\dfrac{3\cdot2^2+9\cdot1^2}{2^3}=\dfrac{21}8\approx2.63$

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3 years ago

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abruzzese [7]

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Step-by-step explanation:

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3 years ago

What is an absolute value? What does it do? When would we need to use an absolute value

Nana76 [90]

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... only how far a number is from zero:

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More Examples:

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So in practice "absolute value" means to remove any negative sign in front of a number, and to think of all numbers as positive (or zero).

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To show that we want the absolute value of something, we put "|" marks either side (they are called "bars" and are found on the right side of a keyboard), like these examples:

|−5| = 5 |7| = 7 Sometimes absolute value is also written as "abs()", so abs(−1) = 1 is the same as |−1| = 1

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3 years ago

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You can draw a quadrilateral with two sets of parallel lines and no right angles. true false

yuradex [85]

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