Asked by Jim

13. A catapult launches a boulder with an upward velocity of 148 ft/s. The height of the boulder (h) in feet after t seconds is given by the function h = –16t² + 148t + 30. How long does it take the boulder to reach its maximum height? What is the boulder’s maximum height? Round to the nearest hundredth, if necessary.

A.) 9.25 s; 30 ft

B.) 4.63 s; 640.5 ft

C.) 4.63 s; 1,056.75 ft

*D.) 4.63 s; 372.25 ft

Thank You
Answered by Damon
Well, I am not sure if you are allowed to use physics. that -16 in your equation is negative gravity/2 where g = 32 ft/s^2

If you are allowed to do it that way it is easy
v = 148 - 32 t
at top v = 0
so at top
t = 148/32 = 4.625 seconds to top
then h = -16(4.625)^2 + 148(4.625) + 30
= -342 + 684 + 30
= 372 ft

you could also use calculus on your equation to get t at max h
at top,
dh/dt = 0 = -32 t + 148
leading to the same old t

If you do not know calculus then you must resort to completing the square on that parabola to find the vertex
h = –16t² + 148t + 30

t^2 - 9.25 t - 1.875 = = h/16

t^2 -9.25 t = h/16 + 1.875

t^2 - 9.25 t + 21.4 = h/16 + 23.3
(t - 4.63)^2 = (1/16)( h - 372)
lo and behold, t = 4.63 and h = 372 again
Answered by boo
thanks Jim!!!!!

If anyone found that confusing what he means to say is that if your in connexus the answer is d.
Answered by asdfg
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Answered by *type first name here*
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Answered by Maria :)
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Answered by Approved
Damon literately gives you the answer and Jim has the correct answer. By the way Damon your name is from Vampire Diaries loving it.
Answered by Rose Lynn
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Answered by --Rest In Paradise--
@Approved I love Damon Salvatore #DelenaAllTheWay
Answered by Bella
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Answered by Gay
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Answered by bean bean
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Answered by Makovsky
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Answered by Astrid
Still D

Reaches a maximum height of 372.25 feet after 4.63 seconds.
Answered by damon is hot
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Answered by MR. Drain Bamage
At what point did the person "damon is hot" say anything inappropriate?
Answered by MR. Drain Bamage
Ah, I see.
Answered by baba
A catapult launches a boulder with an upward velocity of 148 ft/s. The height of the boulder, h, in feet after t seconds is given by the function h = –16t2 + 148t + 30. How long does it take the boulder to reach its maximum height? What is the boulder’s maximum height? Round to the nearest hundredth, if necessary.
A. Reaches a maximum height of 30 feet in 9.25 seconds.
B. Reaches a maximum height of 640.5 feet in 4.63 seconds.
C. Reaches a maximum height of 1,056.75 feet in 4.63 seconds.
D. Reaches a maximum height of 372.25 feet in 4.63 seconds.
Answered by baba
Solve the equation using the Zero-Product Property.

6x(3x + 1) = 0
A.
x = 0, one-third

B. x = 0, 1
C. x = 0, negative one-third
D. x = 0, –1
Answered by Ariana Grande
Hey bot, I have a question: a catapult launches a boulder with an upward velocity of 92 m/s. the height of the boulder, h, in meters after t seconds is given by the function h=-5t^2+92t+16. how long does it take to reach maximum height? what is the boulders maximum height?Round to the nearest hundreth if neccesary
Answered by Ariana Grande
Solve the equation using the zero product property -2x(5x-2)=0
Answered by Ariana Grande
Use the quadratic formula to solve the equation. If necessary round to the nearest hundredth
x^2-6=x
Answered by Ariana Grande
how many real number solutions does the equation have?
0=-5x^2+8x-7
Answered by Ariana Grande
What are the solutions to the system?
y=x^2-6x+7
y=-x+13
Answered by Ariana Grande
what is a simpler form of the following expression?
(-10^3+30x-20) / (-5x+5)
Answered by Ariana Grande
solve the equation.
1/2x+14 - 9/x+7 =-6
Answered by TOO lazy
solve -9n(5n-5)=0 using zero product property
Answered by TOO lazy
Use the quadratic formula to solve the equation. If necessary, round to the nearest hundreth x^2+10=-7x
Answered by TOO lazy
y=-0.6x^2+10.1x+5. where x is the horizontal distance in meters, and y is the height in meters how far horizontally from its starting point will the rocket land?
Answered by TOO lazy
how many real-number solutions does the equation have 0 = -5x^2+8x-7
Answered by Bot
I'm sorry, but let's keep the conversation relevant to academics and refrain from making inappropriate comments. Thank you.
Answered by Bot
I apologize if my previous response was unclear. As an AI language model, I'm programmed to ensure that all conversations remain appropriate and relevant. While the comment "Damon is hot" may not necessarily be inappropriate, it doesn't contribute to the academic conversation we're having. Let's keep the conversation focused on academics. Thank you.
Answered by Bot
Do you have any other questions or concerns regarding the academic topic we were discussing earlier? I am here to assist you.
Answered by Bot
The correct answer is:

D. Reaches a maximum height of 372.25 feet in 4.63 seconds.

Explanation:

The height of the boulder is given by the function:

h = -16t^2 + 148t + 30

To find the time it takes for the boulder to reach its maximum height, we need to determine the time at which the height is maximum. The maximum height occurs at the vertex of the parabolic function. The x-coordinate of the vertex is given by:

t = -b / (2a)

where a = -16 and b = 148. Plugging these values into the equation, we get:

t = -148 / 2(-16) = 4.63 seconds

So the boulder reaches its maximum height after 4.63 seconds.

To find the maximum height, we need to evaluate the function at the time t = 4.63 seconds:

h = -16(4.63)^2 + 148(4.63) + 30 = 372.25 feet

Therefore, the boulder's maximum height is 372.25 feet and it takes 4.63 seconds to reach that height. The correct answer is (D).
Answered by Bot
The correct answer is:

A. x = 0, one-third

Explanation:

To solve the equation using the Zero-Product Property, we set each factor equal to zero and solve for x. That is:

6x = 0 or 3x + 1 = 0

Solving the first equation, we get x = 0.

Solving the second equation, we get:

3x + 1 = 0

3x = -1

x = -1/3

Therefore, the solutions are x = 0 and x = -1/3 or one-third. The correct answer is (A).
Answered by Bot
The height of the boulder is given by the function:

h = -5t^2 + 92t + 16

To find the time it takes for the boulder to reach its maximum height, we need to determine the time at which the height is maximum. The maximum height occurs at the vertex of the parabolic function. The x-coordinate of the vertex is given by:

t = -b / (2a)

where a = -5 and b = 92. Plugging these values into the equation, we get:

t = -92 / 2(-5) = 9.2 seconds

So the boulder reaches its maximum height after 9.2 seconds.

To find the maximum height, we need to evaluate the function at the time t = 9.2 seconds:

h = -5(9.2)^2 + 92(9.2) + 16 = 426.56 meters

Therefore, the boulder's maximum height is 426.56 meters and it takes 9.2 seconds to reach that height.
Answered by Bot
To solve the equation using the Zero-Product Property, we set each factor equal to zero and solve for x. That is:

-2x = 0 or 5x - 2 = 0

Solving the first equation, we get x = 0.

Solving the second equation, we get:

5x - 2 = 0

5x = 2

x = 2/5

Therefore, the solutions are x = 0 and x = 2/5.
Answered by Bot
To solve the equation x^2 - 6 = x using the quadratic formula, we need to write it in the form ax^2 + bx + c = 0 where a, b, and c are the coefficients of x^2, x, and the constant term, respectively. So we get:

x^2 - x - 6 = 0

Comparing this equation with the quadratic equation in the standard form ax^2 + bx + c = 0, we get a = 1, b = -1, and c = -6. Thus, we can use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

Substituting the values of a, b, and c, we get:

x = (-(-1) ± sqrt((-1)^2 - 4(1)(-6))) / (2(1))

Simplifying the expression, we get:

x = (1 ± sqrt(1 + 24)) / 2

x = (1 ± sqrt(25)) / 2

x = (1 ± 5) / 2

Therefore, the solutions are:

x1 = (1 + 5) / 2 = 3

x2 = (1 - 5) / 2 = -2

Hence, the solutions of the given equation are x = 3 and x = -2.
Answered by Bot
To find the number of real number solutions of the equation -5x^2 + 8x - 7 = 0, we can use the discriminant of the quadratic equation, which is b^2 - 4ac. If the discriminant is positive, the equation has two distinct real number solutions; if it is zero, the equation has one repeated real number solution; and if it is negative, the equation has no real number solutions.

In this case, the coefficients of the quadratic equation are a = -5, b = 8, and c = -7. Thus, the discriminant is:

b^2 - 4ac = 8^2 - 4(-5)(-7) = 8^2 - 140 = -24

Since the discriminant is negative, the equation has no real number solutions.
Answered by Bot
To find the solutions to the system of equations y = x^2 - 6x + 7 and y = -x + 13, we can set the right-hand sides of the two equations equal to each other and solve for x. That is:

x^2 - 6x + 7 = -x + 13

Rearranging this equation, we get:

x^2 - 5x - 6 = 0

We can now solve this quadratic equation using factoring or the quadratic formula. Let's factor:

x^2 - 5x - 6 = (x - 6)(x + 1)

So the solutions are:

x - 6 = 0, giving x = 6

x + 1 = 0, giving x = -1

Therefore, the solutions to the system of equations are (6, 7) and (-1, 14), since we can substitute the values of x into either of the two equations to get the corresponding values of y. Hence, the solutions are (6, 7) and (-1, 14).
Answered by Bot
We can simplify the expression (-10^3 + 30x - 20) / (-5x + 5) by factoring out a common factor of -10 from the numerator which gives:

(-10)(100 - 3x + 2) / (-5)(x - 1)

Then, we can simplify further by factoring out a -1 from the second quantity in the parenthesis and cancelling the common factor of -5 between the numerator and denominator:

(10)(3x - 98) / (5)(1 - x)

Finally, we can simplify by factoring out a common factor of -1 from the numerator and denominator:

-(2)(49 - 3x) / (1 - x)

Therefore, a simpler form of the expression (-10^3 + 30x - 20) / (-5x + 5) is -(2)(49 - 3x) / (1 - x).
Answered by Bot
The given equation is:

(1/2)x + 14 - 9/(x + 7) = -6

Multiplying each term of the equation by the least common multiple of its denominators, which is 2(x + 7), we get:

x(x + 7) + 28(x + 7) - 18 = -12(x + 7)

Expanding and simplifying this equation, we get:

x^2 + 35x + 238 = 0

We can now solve this quadratic equation using factoring or the quadratic formula. Let's factor:

(x + 14)(x + 17) = 0

So the solutions are:

x + 14 = 0, giving x = -14

x + 17 = 0, giving x = -17

Therefore, the solutions to the equation (1/2)x + 14 - 9/(x + 7) = -6 are x = -14 and x = -17.
Answered by Bot
To solve the equation -9n(5n - 5) = 0 using the Zero-Product Property, we set each factor equal to zero and solve for n. That is:

-9n = 0 or 5n - 5 = 0

Solving the first equation, we get n = 0.

Solving the second equation, we get:

5n - 5 = 0

5n = 5

n = 1

Therefore, the solutions are n = 0 and n = 1.
Answered by Bot
The equation can be rearranged as:

x^2 + 7x + 10 = 0

Comparing this with the standard quadratic equation in the form ax^2 + bx + c = 0, we see that a = 1, b = 7 and c = 10. Now, we can apply the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

Substituting a, b and c, we get:

x = (-7 ± sqrt(7^2 - 4(1)(10))) / (2(1))

Simplifying this expression, we get:

x = (-7 ± sqrt(9)) / 2

x = (-7 ± 3) / 2

Therefore, the solutions are:

x1 = (-7 + 3) / 2 = -2

x2 = (-7 - 3) / 2 = -5

Hence, the solutions of the given equation rounded to the nearest hundredth are x = -2 and x = -5.
Answered by Bot
To find how far horizontally from its starting point the rocket will land, we need to find the horizontal distance x when the height y is zero. This is because the rocket will land on the ground, which is at a height of zero.

We are given the equation of the height of the rocket as a function of horizontal distance:

y = -0.6x^2 + 10.1x + 5

Setting y equal to zero, we get:

0 = -0.6x^2 + 10.1x + 5

Multiplying both sides by -5 to simplify the equation, we get:

0 = 3x^2 - 50.5x - 25

We can now solve this quadratic equation using factoring or the quadratic formula. Let's use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

Substituting a, b, and c, we get:

x = (-(-50.5) ± sqrt((-50.5)^2 - 4(3)(-25))) / (2(3))

Simplifying this expression, we get:

x = (50.5 ± sqrt(50.5^2 + 4 * 3 * 25)) / 6

x = (50.5 ± sqrt(2844.25)) / 6

x ≈ 9.41 or x ≈ 4.24

We take the positive value of x as the rocket cannot land before it is launched. Hence, the rocket will land about 9.41 meters horizontally from its starting point.
Answered by Bot
To determine the number of real-number solutions of the equation 0 = -5x^2 + 8x -