Duplicate Question
The question on this page has been marked as a duplicate question.
Original Question
A catapult launches a boulder with an upward velocity of 184 feet per second. The height of the boulder, (h), in feet after t s...Asked by SkatingDJ
A catapult launches a boulder with an upward velocity of 184 feet per second. The height of the boulder, (h), in feet after t seconds is given by the function h(t) = –16t² + 184t +20. 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.
I know the seconds: 5.75
Height?: 11.6 or 549
Please help! Thanks!
I know the seconds: 5.75
Height?: 11.6 or 549
Please help! Thanks!
Answers
Answered by
Steve
max height at the vertex, which is at t = 23/4
You should certainly not think that the max height is 11.6, since it started off at 20.
You should certainly not think that the max height is 11.6, since it started off at 20.
Answered by
SkatingDJ
549:)
Answered by
Abby
seconds: 5.75
Height?: 549
Height?: 549
Answered by
baba
Use the graph of f (x) to find the solutions to the equation f (x) = 0.
A coordinate plane with parabola opening up. The y-intercept is negative 12 and the x-intercepts are 2 and negative 6.
A. two solutions: x = 6, negative 2
B. two solutions: x = negative 6, 2
C. one solution: x = negative 12
D. no solutions
A coordinate plane with parabola opening up. The y-intercept is negative 12 and the x-intercepts are 2 and negative 6.
A. two solutions: x = 6, negative 2
B. two solutions: x = negative 6, 2
C. one solution: x = negative 12
D. no solutions
Answered by
baba
What are the solutions of the equation 2 x squared equals 2? Use a graph of a related function whose roots answer the question.
A. An upward facing parabola passes through points left parenthesis negative 1 comma 0 right parenthesis, left parenthesis 0 comma negative 1 right parenthesis, and left parenthesis 1 comma 0 right parenthesis.
There are two solutions: x equals plus or minus 1
B. An upward facing parabola passes through points left parenthesis negative 2 comma 0 right parenthesis, left parenthesis 0 comma negative 2 right parenthesis, and left parenthesis 2 comma 0 right parenthesis.
There are two solutions: x equals plus or minus 2
C. An upward facing parabola passes through points left parenthesis negative 2 comma 5 right parenthesis, left parenthesis 0 comma 1 right parenthesis, and left parenthesis 2 comma 5 right parenthesis.
There are no solutions.
D. An upward facing parabola passes through points left parenthesis negative 2 comma 2 right parenthesis, left parenthesis 0 comma negative 2 right parenthesis, and left parenthesis 2 comma 2 right parenthesis.
There are two solutions: x equals plus or minus start root 2 end root
A. An upward facing parabola passes through points left parenthesis negative 1 comma 0 right parenthesis, left parenthesis 0 comma negative 1 right parenthesis, and left parenthesis 1 comma 0 right parenthesis.
There are two solutions: x equals plus or minus 1
B. An upward facing parabola passes through points left parenthesis negative 2 comma 0 right parenthesis, left parenthesis 0 comma negative 2 right parenthesis, and left parenthesis 2 comma 0 right parenthesis.
There are two solutions: x equals plus or minus 2
C. An upward facing parabola passes through points left parenthesis negative 2 comma 5 right parenthesis, left parenthesis 0 comma 1 right parenthesis, and left parenthesis 2 comma 5 right parenthesis.
There are no solutions.
D. An upward facing parabola passes through points left parenthesis negative 2 comma 2 right parenthesis, left parenthesis 0 comma negative 2 right parenthesis, and left parenthesis 2 comma 2 right parenthesis.
There are two solutions: x equals plus or minus start root 2 end root
Answered by
baba
Solve the equation using the Zero Product Property.
The quantity 2x plus 6 times the quantity 3x minus 6 equals 0.
A. 3 and 2
B. negative 3 comma negative 2
C. negative 3 and 2
D. 3 and negative 2
What are the solutions of the equation?
z squared minus 6z minus 27 equals 0.
A. 3, 9
B. 3, negative 9
C. negative 3, 9
D. negative 3, negative 9
A community group is planning the expansion of a square flower garden in a city park. If each side of the original garden is increased by 3 meters, the new total area of the garden will be 225 square meters. Find the length of each side of the original garden.
A. 15 m
B. 3 m
C. 12 m
D. Start Root 12 End Root m
What is the value of c so that x2 + 9x + c is a perfect square trinomial?
A. 18
B. nine-halves
C. nine-fourths
D. 81-fourths
The quantity 2x plus 6 times the quantity 3x minus 6 equals 0.
A. 3 and 2
B. negative 3 comma negative 2
C. negative 3 and 2
D. 3 and negative 2
What are the solutions of the equation?
z squared minus 6z minus 27 equals 0.
A. 3, 9
B. 3, negative 9
C. negative 3, 9
D. negative 3, negative 9
A community group is planning the expansion of a square flower garden in a city park. If each side of the original garden is increased by 3 meters, the new total area of the garden will be 225 square meters. Find the length of each side of the original garden.
A. 15 m
B. 3 m
C. 12 m
D. Start Root 12 End Root m
What is the value of c so that x2 + 9x + c is a perfect square trinomial?
A. 18
B. nine-halves
C. nine-fourths
D. 81-fourths
Answered by
baba
Solve the equation by completing the square. Round to the nearest hundredth.
x squared plus 6 x equals negative 7
A. 4.41, 1.59
B. negative 4.41, 1.59
C. negative 4.41, negative 1.59
D. 4.41, negative 1.59
Solve the equation by completing the square.
x squared plus 9 x minus 14 equals 0
A. 10.35, 1.35
B. 10.35, negative 1 point 35
C. negative 10.35, negative 1.35
D. negative 10.35, 1.35
Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.
x squared plus 3 equals negative 4 x
A. 1, 3
B. negative 1, negative 3
C. 1, negative 3
D. negative 1, 3
Which kind of function best models the data in the table? Use differences or ratios.
x
y
0
0.6
1 4.2
2 29.4
3 205.8
4 1440.6
A. exponential
B. quadratic
C. linear
x squared plus 6 x equals negative 7
A. 4.41, 1.59
B. negative 4.41, 1.59
C. negative 4.41, negative 1.59
D. 4.41, negative 1.59
Solve the equation by completing the square.
x squared plus 9 x minus 14 equals 0
A. 10.35, 1.35
B. 10.35, negative 1 point 35
C. negative 10.35, negative 1.35
D. negative 10.35, 1.35
Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.
x squared plus 3 equals negative 4 x
A. 1, 3
B. negative 1, negative 3
C. 1, negative 3
D. negative 1, 3
Which kind of function best models the data in the table? Use differences or ratios.
x
y
0
0.6
1 4.2
2 29.4
3 205.8
4 1440.6
A. exponential
B. quadratic
C. linear
Answered by
Bot
B. two solutions: x = negative 6, 2
Answered by
Bot
B. An upward facing parabola passes through points left parenthesis negative 2 comma 0 right parenthesis, left parenthesis 0 comma negative 2 right parenthesis, and left parenthesis 2 comma 0 right parenthesis. There are two solutions: x equals plus or minus 2.
Answered by
Bot
The answers are:
- C. negative 3 and 2
- A. 3, 9
- C. 12 m
- D. nine-fourths
Explanation:
1. To solve the equation using the Zero Product Property, we need to set each factor equal to zero and solve for x:
2x + 6 = 0 or 3x - 6 = 0
Solving for x, we get:
x = -3 or x = 2
Therefore, the solutions are negative 3 and 2.
2. To solve the equation z^2 - 6z - 27 = 0 using factoring, we need to find two numbers whose product is -27 and whose sum is -6. These numbers are -9 and 3.
Therefore, we can write:
z^2 - 6z - 27 = (z - 9)(z + 3)
Setting each factor equal to zero and solving for z, we get:
z - 9 = 0 or z + 3 = 0
z = 9 or z = -3
Therefore, the solutions are 3 and 9.
3. Let s be the length of each side of the original garden. The area of the original garden is s^2. The area of the new garden is (s + 3)^2 = s^2 + 6s + 9.
We are given that the new total area is 225:
s^2 + 6s + 9 = 225
Simplifying the equation, we get:
s^2 + 6s - 216 = 0
Factoring out a 3, we get:
(s + 18)(s - 12) = 0
Setting each factor equal to zero and solving for s, we get:
s + 18 = 0 or s - 12 = 0
s = -18 or s = 12
We reject the negative solution, so the length of each side of the original garden is 12 meters.
4. To make x^2 + 9x + c a perfect square trinomial, we need to add and subtract the square of half the coefficient of x:
x^2 + 9x + (9/2)^2 - (9/2)^2 + c
Simplifying the expression, we get:
(x + 9/2)^2 - 81/4 + c
For this to be a perfect square trinomial, we need to have:
c - 81/4 = 0
c = 81/4
Therefore, the value of c is nine-fourths.
- C. negative 3 and 2
- A. 3, 9
- C. 12 m
- D. nine-fourths
Explanation:
1. To solve the equation using the Zero Product Property, we need to set each factor equal to zero and solve for x:
2x + 6 = 0 or 3x - 6 = 0
Solving for x, we get:
x = -3 or x = 2
Therefore, the solutions are negative 3 and 2.
2. To solve the equation z^2 - 6z - 27 = 0 using factoring, we need to find two numbers whose product is -27 and whose sum is -6. These numbers are -9 and 3.
Therefore, we can write:
z^2 - 6z - 27 = (z - 9)(z + 3)
Setting each factor equal to zero and solving for z, we get:
z - 9 = 0 or z + 3 = 0
z = 9 or z = -3
Therefore, the solutions are 3 and 9.
3. Let s be the length of each side of the original garden. The area of the original garden is s^2. The area of the new garden is (s + 3)^2 = s^2 + 6s + 9.
We are given that the new total area is 225:
s^2 + 6s + 9 = 225
Simplifying the equation, we get:
s^2 + 6s - 216 = 0
Factoring out a 3, we get:
(s + 18)(s - 12) = 0
Setting each factor equal to zero and solving for s, we get:
s + 18 = 0 or s - 12 = 0
s = -18 or s = 12
We reject the negative solution, so the length of each side of the original garden is 12 meters.
4. To make x^2 + 9x + c a perfect square trinomial, we need to add and subtract the square of half the coefficient of x:
x^2 + 9x + (9/2)^2 - (9/2)^2 + c
Simplifying the expression, we get:
(x + 9/2)^2 - 81/4 + c
For this to be a perfect square trinomial, we need to have:
c - 81/4 = 0
c = 81/4
Therefore, the value of c is nine-fourths.
Answered by
Bot
The answers are:
1. D. 4.41, negative 1.59
2. A. 10.35, 1.35
3. B. negative 1, negative 3
4. A. exponential
Explanations:
1. To solve the equation x^2 + 6x = -7 by completing the square, we need to add and subtract (6/2)^2 = 9 from both sides:
x^2 + 6x + 9 = -7 + 9
(x + 3)^2 = 2
Taking the square root of both sides, we get:
x + 3 = ±√2
Solving for x, we get:
x = -3 ± √2
Therefore, the solutions are 4.41 and -1.59 (rounded to the nearest hundredth).
2. To solve the equation x^2 + 9x - 14 = 0 by completing the square, we need to add and subtract (9/2)^2 = 40.5 from both sides:
x^2 + 9x - 14 + 40.5 = 40.5
(x + 4.5)^2 = 54.5
Taking the square root of both sides, we get:
x + 4.5 = ±√54.5
Solving for x, we get:
x = -4.5 ± √54.5
Therefore, the solutions are 10.35 and -1.35 (rounded to the nearest hundredth).
3. To solve the equation x^2 + 3 = -4x using the quadratic formula, we first need to rearrange it in standard form:
x^2 + 4x + 3 = 0
Using the quadratic formula, we get:
x = (-b ± √(b^2 - 4ac)) / 2a
Plugging in a = 1, b = 4, and c = 3, we get:
x = (-4 ± √(4^2 - 4(1)(3))) / 2(1)
Simplifying the expression, we get:
x = (-4 ± √4) / 2
x = -2 ± 1
Therefore, the solutions are -1 and -3.
4. To determine which kind of function best models the data in the table, we calculate the ratios of consecutive y-values:
y(1)/y(0) = 7
y(2)/y(1) = 7
y(3)/y(2) = 7
y(4)/y(3) = 7
The ratios are all equal to 7, so the data follows an exponential function of the form y = ab^x, where b = 7. Plugging in the values of x and y(0), we get:
y = 0.6 * 7^x
Therefore, the best model is an exponential function.
1. D. 4.41, negative 1.59
2. A. 10.35, 1.35
3. B. negative 1, negative 3
4. A. exponential
Explanations:
1. To solve the equation x^2 + 6x = -7 by completing the square, we need to add and subtract (6/2)^2 = 9 from both sides:
x^2 + 6x + 9 = -7 + 9
(x + 3)^2 = 2
Taking the square root of both sides, we get:
x + 3 = ±√2
Solving for x, we get:
x = -3 ± √2
Therefore, the solutions are 4.41 and -1.59 (rounded to the nearest hundredth).
2. To solve the equation x^2 + 9x - 14 = 0 by completing the square, we need to add and subtract (9/2)^2 = 40.5 from both sides:
x^2 + 9x - 14 + 40.5 = 40.5
(x + 4.5)^2 = 54.5
Taking the square root of both sides, we get:
x + 4.5 = ±√54.5
Solving for x, we get:
x = -4.5 ± √54.5
Therefore, the solutions are 10.35 and -1.35 (rounded to the nearest hundredth).
3. To solve the equation x^2 + 3 = -4x using the quadratic formula, we first need to rearrange it in standard form:
x^2 + 4x + 3 = 0
Using the quadratic formula, we get:
x = (-b ± √(b^2 - 4ac)) / 2a
Plugging in a = 1, b = 4, and c = 3, we get:
x = (-4 ± √(4^2 - 4(1)(3))) / 2(1)
Simplifying the expression, we get:
x = (-4 ± √4) / 2
x = -2 ± 1
Therefore, the solutions are -1 and -3.
4. To determine which kind of function best models the data in the table, we calculate the ratios of consecutive y-values:
y(1)/y(0) = 7
y(2)/y(1) = 7
y(3)/y(2) = 7
y(4)/y(3) = 7
The ratios are all equal to 7, so the data follows an exponential function of the form y = ab^x, where b = 7. Plugging in the values of x and y(0), we get:
y = 0.6 * 7^x
Therefore, the best model is an exponential function.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.