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3 years ago

15

Two points are located at (2,3) and (8,-5) complete the equations below to show how you can use the pythagorean theorem to find

the distance between these two points

1 answer:

daser333 [38]3 years ago

8 0

Answer:

3

Step-by-step explanation:

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8 friends go to Subway and each get 1/2 of a sandwich. How many sandwiches did they get altogether?

Vadim26 [7]

8 sandwiches just half the size

3 0

3 years ago

The tangent to the circle x^2+y^2=18 is parallel to the tangent x+y=6

liubo4ka [24]

Answer:

y = -x - 6

Step-by-step explanation:

If we are looking for the equation of the line tangent to the circle, we have to find the first derivative of the circle function. If that tangent line is to be parallel to the given tangent line, we need to find the slope of the the given tangent line and make sure the slope of the line we are looking for is the same. First let's find the slope of the given tangent. If the given tangent is x+y=6, then to find the slope, solve for y:

y = -x + 6. So the slope of that line, and also the slope of the tangent we are solving for, is -1. Hold that thought while we find the derivative of the function. Using implicit differentiation, we find the derivative to be:

$2x+2y\frac{dy}{dx}=0$

Solving for the slope (dy/dx) gives us:

$2y\frac{dy}{dx}=-2x$ and

$\frac{dy}{dx}=\frac{-2x}{2y}$ so

$\frac{dy}{dx}=-\frac{x}{y}$

Subbing in the value of the slope we found:

$-1=-\frac{x}{y}$ so

-y = -x or, equivalently,

y = x. Now that we know that y and x are the same value, we can go back to the original circle to find out what they both are by substitution. If y = x, we make the substution:

If $x^2+y^2=18$ , then

$y^2+y^2=18$ and

$2y^2=18$ and

$y^2=9$ so

y = ±3

We will choose the negative root (you'll see why in a second) and sub that in for both y and x since y and x are th same number. Going back to the fact that the slope is -1:

y - (-3) = -1(x - (-3)) simplifies a bit to:

y + 3 = -x - 3 which gives us, in slope-intercept form:

y = -x - 6

That is the equation of the tangent to the circle that is parallel to the given tangent.

If we would have chosen the principle (or positive) root of 3, our equation would have looked like this:

y - 3 = -1(x - 3) and

y = -x + 3 + 3 so

y = -x + 6. Notice that that is the EXACT SAME EQUATION as the given tangent. That's why we have to pick the negative 3 as our root.

Good luck in your calculus class! Make sure you post your questions in here! Many of us LOVE the challenge of calculus!

3 0

4 years ago

Mia buys 3 gallons of gas that cost d dollars per gallon.Bob buys g gallons of gas that cost 3 per gallon. Write an expression f

xxTIMURxx [149]

3(d) and 3 (g)
d represents the price. so you multiply 3 by however much the has cost.
g represents the gallons and 3 represents the cost and again you multiply

3 0

3 years ago

Read 2 more answers

Find x and y in the parallelogram

REY [17]

X=7
Y=14

4x=28
X=7
2y=28
Y=14

7 0

4 years ago

The amount of force one exerts on a wrench handle to loosen a bolt is inversely

Inessa [10]

Answer:

a)

$F = \frac{1152}{l}$

b) l=19.2 units

Step-by-step explanation:

a)Let F represent the force and l represents the length of the wrench handle.

Then inverse variation relation is:

$F\propto \: \frac{1}{l}$

When we introduce the variation constant, we get:

$F = \: \frac{k}{l}$

From the question when F=96, l=12

$96= \: \frac{k}{12}$

$k = 1152$

The equation is

$F = \: \frac{1152}{l}$

b) If a person can only exert 60 pounds of force on a wrench,then

$60 = \frac{1152}{l}$

$\implies \: l = \frac{1152}{60}$

$l = 19.2$

Hence the length of the wrench must be 19.2 units

4 0

3 years ago