MATHEMATICS HIGH SCHOOL

The center of a circle is at the origin. An endpoint of a diameter of the circle is at (-3, -4). How long is the diameter of the circle?

Answers

Answer 1

Answer:

Answer:

The length of the diameter of the circle is 10 unit.

Step-by-step explanation:

Given : The center of a circle is at the origin. An endpoint of a diameter of the circle is at (-3, -4).

To find : How long is the diameter of the circle?

Solution :

The center of a circle is at the origin i.e. $C=(x_1,y_1)=(0,0)$

An endpoint of a diameter of the circle is at $D=(x_2,y_2)=(-3,-4)$

The distance between the center and the end point of the diameter is the radius of the circle.

So, we find the radius with the help of distance formula,

$d=√((x_2-x_1)^2+(y_2-y_1)^2)$

Substitute the value in the formula,

$r=√((-3-0)^2+(-4-0)^2)$

$r=√(9+16)$

$r=√(25)$

$r=5$

Diameter is twice of radius $d=5* 2=10$

Therefore, The length of the diameter of the circle is 10 unit.

Answer 2

Answer: Use the distance formula
$√((-4-4)^2+(-3-3)^2) = √(100)=10$

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A rollercoaster ride reaches a height of 80 feet before it sharply drops. The height above the ground of the rollercoaster car during the drop is modeled by the function, h(t)=10t2−40t+80 , where t is measured in seconds since the car started its decline. The model is accurate for 0≤t≤4 . On this portion of the ride, how long does the car take to reach a minimum height from the ground before rising again?

Answers

Answer:

Therefore the car takes 2 s to reach a minimum height from the ground before rising again.

Step-by-step explanation:

Given that a roller coaster ride reach a height of 80 feet.

The height above the ground of the roller coaster is modeled by the function

h(t)=10t²-40t+80

where t is measured in second.

h(t)=10t²-40t+80

Differentiating with respect to t

h'(t)= 10(2t)-40

⇒h'(t)=20t-40

To find the minimum height we set h'(t)=0

∴20t-40=0

⇒20t =40

⇒t=2

The height of the roller coaster minimum when t=2 s.

The minimum height of of the roller coaster is

h(2)= 10(2)²-40.2+80

=40-80+80

=40 feet.

Therefore the car takes 2 s to reach a minimum height from the ground before rising again.

Answer:

Step-by-step explanation:

Which statements are true about the linear inequality y > 3/4 x – 2? Check all that apply.The slope of the line is –2.

The graph of y > 3/4 x – 2 is a dashed line.

The area below the line is shaded.

One solution to the inequality is (0, 0).

The graph intercepts the y-axis at (0, –2).

Answers

The correct statements regarding the inequality given above are as follows:

The area below the line is shaded since it is an inequality with a number of possible solution. The graph intercepts the y-axis at (0, –2) as seen from the equation above.

Hope this answers the question.

Answer:

The area below the line is shaded

since it is an inequality with a number of possible solution.

The graph intercepts the y-axis at (0, –2) as seen from the equation above.

Step-by-step explanation:

What's does 2 alternate interior angle equals?

Answers

they are equal if u already have one answer

A) dilations always increase the length of line segmentsB) dilations take right angles to right angles

C) dilations of an angle are congruent to the original angle

D) dilations increase the measure of angles

E) dilations of a triangle are congruent to the original triangle

F) dilations dilations of a triangle are similar to the original triangle

Answers

Answer:

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Step-by-step explanation:

the line passing through the points A (-1,3k) and B (k , 3) is parallel to the line whose equation is 2y+3x=9. write down the co-ordinates of A and B

Answers

Answer:

k = 3

Step-by-step explanation:

If the line passing through the points A (-1,3k) and B (k , 3) is parallel to the line whose equation is 2y+3x=9, then their slopes are equal

For coordinate AB;

slope m1 = 3 - 3k/k-(-1)

m1 = 3-3k/k+1

For the line 2y+3x = 9

2y = -3x + 9

y = -3/2 x + 9/2

Slope m2 = -3/2

Since m1 = m2

3-3k/k+1 = -3/2

Cross multiply

2(3-3k) = -3(k+1)

Expand

6 - 6k = -3k - 3

-6k+3k = -3 - 6

-3k = -9

k = -9/-3

k = 3

Hence the value of k is 3

Which of the following is NOT a characteristic of an inner planet? A. rocky B. solid surface C. near the sun D. made mostly of gas

Answers

it is D, made mostly of gas. that's an outer planet characteristc.

The correct answer is D. Made mostly of gas. Hope this helps! :)

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