Question
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
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
Answers
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
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
thanks Jim!!!!!
If anyone found that confusing what he means to say is that if your in connexus the answer is d.
If anyone found that confusing what he means to say is that if your in connexus the answer is d.
sadly u have to find the answers urself i searched everywhere
lmao @boo
Thank you Jim do much ;-D
Damon literately gives you the answer and Jim has the correct answer. By the way Damon your name is from Vampire Diaries loving it.
Thanks both Damon and Jim. Both had correct answer. Both should be appreciated.
@Approved I love Damon Salvatore #DelenaAllTheWay
we love both JIM and DAMON
41 question exam anyone?
36 for me but its just part 1 and i have 3 parts
Thanks 👍👍👍👍👍👍👍👍👍👍👍👍👍👍👍 jim
Appreciate it
Still D
Reaches a maximum height of 372.25 feet after 4.63 seconds.
Reaches a maximum height of 372.25 feet after 4.63 seconds.
DAMON IS HOOTTTT
I'm sorry, but let's keep the conversation relevant to academics and refrain from making inappropriate comments. Thank you.
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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.
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.
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).
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).
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
6x(3x + 1) = 0
A.
x = 0, one-third
B. x = 0, 1
C. x = 0, negative one-third
D. x = 0, –1
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).
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).
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
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.
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.
Solve the equation using the zero product property -2x(5x-2)=0
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.
-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.
Use the quadratic formula to solve the equation. If necessary round to the nearest hundredth
x^2-6=x
x^2-6=x
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.
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.
how many real number solutions does the equation have?
0=-5x^2+8x-7
0=-5x^2+8x-7
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.
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.
What are the solutions to the system?
y=x^2-6x+7
y=-x+13
y=x^2-6x+7
y=-x+13
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).
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).
what is a simpler form of the following expression?
(-10^3+30x-20) / (-5x+5)
(-10^3+30x-20) / (-5x+5)
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).
(-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).
solve the equation.
1/2x+14 - 9/x+7 =-6
1/2x+14 - 9/x+7 =-6
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.
(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.
solve -9n(5n-5)=0 using zero product property
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.
-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.
Use the quadratic formula to solve the equation. If necessary, round to the nearest hundreth x^2+10=-7x
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.
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.
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?
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.
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.
how many real-number solutions does the equation have 0 = -5x^2+8x-7
To determine the number of real-number solutions of the equation 0 = -5x^2 + 8x -
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