To find when the ball will hit the ground, we need to find when the height (h) is equal to 0.
So, we set H = -16t² + 46t + 6 equal to 0:
-16t² + 46t + 6 = 0
Now, we can solve this quadratic equation using the quadratic formula:
t = (-b ± √(b² - 4ac)) / 2a
where a = -16, b = 46, and c = 6.
Plugging the values into the formula:
t = (-46 ± √(46² - 4*(-16)*6)) / 2*(-16)
t = (-46 ± √(2116 + 384)) / -32
t = (-46 ± √2500) / -32
t = (-46 ± 50) / -32
This gives us two possible solutions:
t = (-46 + 50) / -32 = 4 / -32 = -1/8
t = (-46 - 50) / -32 = -96 / -32 = 3
Since time cannot be negative in this context, we discard the negative solution. Therefore, the ball will hit the ground after approximately 3 seconds.
A ball is thrown into the air with an initial upward velocity of 46 ft/s. Its height (h) in feet after t seconds is given by the function
H=-16t² +46t+6. After how many seconds will the ball hit the ground?
(1 point)
3
4
5
6
7 answers
A ball is thrown into the air with an initial upward velocity of 60 ft/s. Its height (h) in feet after t seconds is given by the function h = –16t2 + 60t + 6. What will the height be at t = 3 seconds?
(1 point)
35 feet 40 feet 42 feet 45 feet
(1 point)
35 feet 40 feet 42 feet 45 feet
To find the height of the ball at t = 3 seconds, we need to substitute t = 3 into the given equation h = -16t^2 + 60t + 6.
h(3) = -16(3)^2 + 60(3) + 6
h(3) = -16(9) + 180 + 6
h(3) = -144 + 180 + 6
h(3) = 42 feet
So, the height of the ball at t = 3 seconds will be 42 feet.
Therefore, the correct answer is:
42 feet
h(3) = -16(3)^2 + 60(3) + 6
h(3) = -16(9) + 180 + 6
h(3) = -144 + 180 + 6
h(3) = 42 feet
So, the height of the ball at t = 3 seconds will be 42 feet.
Therefore, the correct answer is:
42 feet
Solve. x2 – 121 = 0 (1 point)
0
–11
11
11, –11
0
–11
11
11, –11
To solve the equation x^2 - 121 = 0, we can add 121 to both sides:
x^2 - 121 + 121 = 0 + 121
x^2 = 121
Then, we can take the square root of both sides to solve for x:
x = ±√121
x = ±11
Therefore, the solution to the equation x^2 - 121 = 0 is:
x = 11, -11
So the correct answer is:
11, -11
x^2 - 121 + 121 = 0 + 121
x^2 = 121
Then, we can take the square root of both sides to solve for x:
x = ±√121
x = ±11
Therefore, the solution to the equation x^2 - 121 = 0 is:
x = 11, -11
So the correct answer is:
11, -11
Solve by factoring. m2 + 8m + 7 = 0 (1 point)
8, 7 –7, 1 –7, –1 7, 1
8, 7 –7, 1 –7, –1 7, 1
To solve the quadratic equation m^2 + 8m + 7 = 0 by factoring, we need to find two numbers that multiply to 7 (the constant term) and add up to 8 (the coefficient of m).
The two numbers are 7 and 1, because 7 * 1 = 7 and 7 + 1 = 8.
Now, we rewrite the middle term (8m) using the numbers 7 and 1:
m^2 + 7m + 1m + 7 = 0
Now, we factor by grouping:
m(m + 7) + 1(m + 7) = 0
(m + 7)(m + 1) = 0
Setting each factor to 0 gives us the roots:
m + 7 = 0 -> m = -7
m + 1 = 0 -> m = -1
Therefore, the solutions to the equation m^2 + 8m + 7 = 0 are:
m = -7, -1
So the complete answer is: -7, -1
The two numbers are 7 and 1, because 7 * 1 = 7 and 7 + 1 = 8.
Now, we rewrite the middle term (8m) using the numbers 7 and 1:
m^2 + 7m + 1m + 7 = 0
Now, we factor by grouping:
m(m + 7) + 1(m + 7) = 0
(m + 7)(m + 1) = 0
Setting each factor to 0 gives us the roots:
m + 7 = 0 -> m = -7
m + 1 = 0 -> m = -1
Therefore, the solutions to the equation m^2 + 8m + 7 = 0 are:
m = -7, -1
So the complete answer is: -7, -1