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3 years ago

Pythagorean Theorem Word

Mathematics

1 answer:

diamong [38]3 years ago

7 0

Answer:

40 miles

Step-by-step explanation:

In the attached diagram, Point A is the starting point and C is the end point. We want to determine the distance from A to C.

The path driven forms a right triangle in which AC is the hypotenuse.

We therefore use the<u> Pythagorean Theorem</u> to solve for the AC.

Pythagorean Theorem: $Hypotenuse^2=Opposite^2+Adjacent^2$

$|AC|^2=32^2+24^2\\|AC|^2=1600\\|AC|=\sqrt{1600}\\ |AC|=40$ miles$

The straight line distance from the starting point is 40 miles.

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A ball is thrown into the air from a height of 4 feet at time t = 0. The function that models this situation is h(t) = -16t2 + 6

katrin2010 [14]

Answer:

Part a) The height of the ball after 3 seconds is $49\ ft$

Part b) The maximum height is 66 ft

Part c) The ball hit the ground for t=4 sec

Part d) The domain of the function that makes sense is the interval

[0,4]

Step-by-step explanation:

we have

$h(t)=-16t^{2} +63t+4$

Part a) What is the height of the ball after 3 seconds?

For t=3 sec

Substitute in the function and solve for h

$h(3)=-16(3)^{2} +63(3)+4=49\ ft$

Part b) What is the maximum height of the ball? Round to the nearest foot.

we know that

The maximum height of the ball is the vertex of the quadratic equation

Convert the function into a vertex form

$h(t)=-16t^{2} +63t+4$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$h(t)-4=-16t^{2} +63t$

Factor the leading coefficient

$h(t)-4=-16(t^{2} -(63/16)t)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$h(t)-4-16(63/32)^{2}=-16(t^{2} -(63/16)t+(63/32)^{2})$

$h(t)-(67,600/1,024)=-16(t^{2} -(63/16)t+(63/32)^{2})$

Rewrite as perfect squares

$h(t)-(67,600/1,024)=-16(t-(63/32))^{2}$

$h(t)=-16(t-(63/32))^{2}+(67,600/1,024)$

the vertex is the point (1.97,66.02)

therefore

The maximum height is 66 ft

Part c) When will the ball hit the ground?

we know that

The ball hit the ground when h(t)=0 (the x-intercepts of the function)

$h(t)=-16t^{2} +63t+4$

For h(t)=0

$0=-16t^{2} +63t+4$

using a graphing tool

The solution is t=4 sec

see the attached figure

Part d) What domain makes sense for the function?

The domain of the function that makes sense is the interval

[0,4]

All real numbers greater than or equal to 0 seconds and less than or equal to 4 seconds

Remember that the time can not be a negative number

6 0

3 years ago

Factor completely <br>5x^2-9x-2

wariber [46]

Answer:

(5x+1)(x - 2)

Step-by-step explanation:

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3 years ago

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Mariana tried to drink a slushy as fast as she could. She drank the slushy at a rate of 4.5 milliliters per second. After 17 sec

Fynjy0 [20]

This is what i did to get the answer.

225/ 4.5 = 50 seconds to finish the slushy.

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3 years ago

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Can someone please help me and fast I'm stuck

vovikov84 [41]

Answer:

3 5/8

Step-by-step explanation:

6 4/8 - 2 7/8 = 4 -3/8 = 3 5/8

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a sporting goods store receives a shipment of 124 golf bags. The shipment includes two types of bags, full-sized and collapsible

Dominik [7]

The sporting goods store receives the shipment of 124 golf bags in total.
Let us assume that the number of full-sized bags = X
Then the number of collapsible golf bags = 124 - X
Cost of each full sized bags = $38.50
Cost of each collapsible bags = $22.50
Total cost of the 124 bags received by the sporting goods store = $3430
Then
(38.50)X + (124 - X)22.50 = 3430
(38.50X - 22.50X) + 2790 = 3430
16X = 3430 - 2790
16X = 640
X = 640/16
= 40
So the number of full-sized golf bags received = 40
Then the number of collapsible golf bags received = 124 - 40
= 84

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3 years ago