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AfilCa [17]
3 years ago
15

A golf ball is hit off a tee toward the green. The height of the ball is modeled by the function h(t) = −16t2 + 96t, where t equ

als the time in seconds and h(t) represents the height of the ball at time t seconds. What is the axis of symmetry, and what does it represent? t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground. t = 3; It takes the ball 3 seconds to reach the maximum height and 3 seconds to fall back to the ground. t = 6; It takes the ball 6 seconds to reach the maximum height and 3 seconds to fall back to the ground. t = 6; It takes the ball 6 seconds to reach the maximum height and 6 seconds to fall back to the ground.
Mathematics
1 answer:
Ierofanga [76]3 years ago
6 0

Answer:

t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.

Step-by-step explanation:

To find the axis of symmetry, we need to find the vertex by turning this equation into vertex form (this is y = a(x - c)² + d where (c, d) is the vertex). To do this, we can use the "completing the square" strategy.

h(t) = -16t² + 96t

= -16(t² - 6t)

= -16(t² - 6t + 9) - (-16) * 9

= -16(t - 3)² + 144

Therefore, we know that the vertex is (3, 144) so the axis of symmetry is t = 3. Since the coefficient of the squared term, -16, is negative, it means that the vertex is the maximum. We know that it takes the golf ball 3 seconds to reach the maximum height (since the t value of the vertex is 3) and because the vertex is on the axis of symmetry, it would take 3 more seconds for the ball to fall to the ground, therefore it takes 3 + 3 = 6 seconds to fall to the ground. The final answer is "t = 3; It takes the ball 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.".

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Free_Kalibri [48]
Checking for each option

Option A: A(w) = -w^2+200w

Substitute w = 10 and check if we'd get 900 as the answer
A(10) = -(10)^2+200(10) = -100+2000 = 1900

Option B: A(w) = -w^2+100w
Substitute w = 10 and check if we'd get 900 as the answer
A(10)=-(10)^2+100(10)=-100+1000=900

Option C: A(w)=w^2+40w
Substitute  w = 10 and check if we'd get 900 as the answer
A(10) = 10^2+40(10)=100+400=500

Option D: A(w) = w^2+90w
Substitue w = 10 and check if we'd get 900 as the answer
A(10)=10^2+90(10) = 100+900=1000

Answer: Option B



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3 years ago
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What's 7 hours - 30mins ?
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Answer:

390 mins (or) 6 hours 30 mins

Step-by-step explanation:

7 hours = 420 mins

420 mins - 30 mins = 390 mins

390 mins = 6 hours 30 mins

Have a nice day!

8 0
3 years ago
Help me jim! geometry homework
Maksim231197 [3]

Question 1

The angles 52 degrees match up. So if the sides are in proportion, then the triangles are similar.

Notice how 8/12 = 18/27 is a true equation. So the sides are in proportion to one another.

Therefore, the triangles <u>are similar</u>. I used the <u>SAS similarity theorem</u>.

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Question 2

Let's find the missing angle of the triangle on the right. For now, make that missing angle to be x.

Rule: For any triangle, the three angles always add up to 180

x+70+32 = 180

x+102 = 180

x = 180-102

x = 78

The missing angle of the triangle on the left is 78 degrees

Repeat for the other triangle as well

y+78+32 = 180

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y = 180-110

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Both triangles have the angles 32, 70, 78 in whatever order you wish.

Since the angles match up like this, <u>the triangles are similar</u> because of the <u>AA Similarity theorem</u>

Technically, we only need 2 pairs of congruent angles at minimum. But having 3 congruent pairs doesn't hurt either.

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We have a pair of congruent 54 degree angles shown. There's another pair of angles at the very top that overlap (aka shared angles).

Since we have two pairs of congruent angles, <u>the two triangles are similar</u>.

This time we use the <u>AA Similarity theorem</u>

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Let's divide the longest side of the bottom triangle by the longest side of the triangle on top

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Now let's divide the shortest sides of each triangle in the same order

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Answer:

The length of apothem of given hexagon is 8.66 cm

Step-by-step explanation:

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apothem = \frac{s}{2\ tan\ (\frac{180}{n})}

Here

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and n denotes number of sides

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