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3 years ago

Use the distance formula to find the distance between the two points

Mathematics

1 answer:

Snezhnost [94]3 years ago

5 0

Answer:

9.) -2/2 = -1

10.) -6/-11 or 6/11

11.) -3/-11 or 3/11

Step-by-step explanation:

this is easy XD

So, first step the midpoint formula: (x1 + x2 / 2, y1 + y2 /2 )

9.) c(-9,-1) and D(7,3) ----> you should know the x and y and plug in :D

10.) E(5,-5) and F(1,-6) ----> you should know the x and y and plug in :D

11.) G(-5,3) and H(2,-8)----> you should know the x and y and plug in :D

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Find the equation of a line tangent to the circle x2+(y−3)2=34 at the point (5, 0).

salantis [7]

Answer:

Step-by-step explanation:

In order to find the equation of the line tangent to that circle, we have to find the derivative by implicit differentiation which will give us the slope formula of that tangent line. Let's begin by expanding through the parenthesis to get the standard form of the circle:

$x^2+y^2-6y+9=34$

Moving the 9 to the other side since the derivative of a constant is 0 gives us

$x^2+y^2-6y=25$

By implicit differentation, the derivative of that function is

$2x+2y\frac{dy}{dx}-6\frac{dy}{dx}=0$

To find the derivative, we have to solve for dy/dx:

$2y\frac{dy}{dx}-6\frac{dy}{dx}=-2x$

Factor out the dy/dx to get:

$\frac{dy}{dx}(2y-6)=-2x$

Now divide to get your slope formula (first derivative):

$\frac{dy}{dx}=\frac{-2x}{2y-6}$

Now we can sub in the x and y values from the coodinate to get the slope of that tangent line:

$\frac{dy}{dx}=\frac{-2(5)}{2(0)-6}=\frac{-10}{-6}=\frac{5}{3}$

So now that have the slope, we can use the point-slope form of a line to write the equation of the tangent line. The point-slop form of a line is:

y-y₁ = m(x-x₁)

Filling in we get:

y - 0 = 5/3(x - 5) so the equation of the tangent line is:

$y=\frac{5}{3}x-\frac{25}{3}$

Good luck in your calculus class!

3 0

3 years ago

A company sell men basketball with a circumference of 29.5 in they also sell youth basketball with a circumference 27.75 in the

Vedmedyk [2.9K]

Answer:

9 INCHES

Step-by-step explanation:

8 0

4 years ago

What is an equation of the line that passes through the points (-2, -5) and (-1, 1)?

Dennis_Churaev [7]

Answer: y=6x+7

Step-by-step explanation:

To find the equation of the line, we want to find the slope with the formula $m=\frac{y_2-y_1}{x_2-x_1}$ .

$m=\frac{1-(-5)}{-1-(-2)} =\frac{6}{1}=6$

Now that we know th eslope, we can start to fill out the equation. To find the y-intercept, we can plug in a given point and solve.

y=6x+b

1=6(-1)+b [multiply]

1=-6+b [add both sides by 6]

b=7

Now, we know the equation is y=6x+7.

8 0

3 years ago

Read 2 more answers

Height for each toddler at Mrs.orlando daycare

Tatiana [17]

1=81 centimetres
1=82 centimetres
2=83 centimetres
3=84 centimetres
1=85 centimetres

8 0

3 years ago

Help me pls i don't understand the problem so can u give me the answers and also explain

WARRIOR [948]

Step-by-step explanation:

$\frac{2}{3} +\frac{4}{5} =\frac{10+12}{15}=\frac{22}{15} .$

2) the same value of the denominator of the fractions.

3) 4²*2²=16*4=64 or 4²*2²=(4*2)²=8²=64.

Megan's answer is correct.

4) if the given length is 2,25=9/4 (feet), then the length of each piece is 9/4 :3=3/4=0.75 (feet) or 3/4*12=9 (inches).

5) a. 4-6= -2; b. -4+6=2; c. -4-6= -10, so the required order is c<a<b.

6) A. -8+3= -5; B. -8*3= -24, so the greater value is (-5) - answer A.

7) if to calculate every option, then A. 2.3*6.5=14.95; B. 21.45-6.5=14.95; C. 8.32+6.63=14.95, - all of them are equal.

6 0

3 years ago