A catapult launches a boulder with an upward velocity of 112 ft/s. The height of the Boulder, h, in feet after t seconds is given by te function h=-16t^2+112t+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 . Please , help . I am really stuck here
Answers
Answer:
Boulder's maximum height is 226 ft.
It take 3.5 seconds the Boulder to reach its maximum height.
Step-by-step explanation:
Given :
A catapult launches a boulder with an upward velocity of 112 ft/s.
The height of the Boulder, h, in feet
After t seconds is given by the function :
--(a)
A quadratic function can be graphed using a table of values. The graph creates a parabola.
If the coefficient of the squared term is positive then the parabola opens up and The vertex of this parabola is known as the minimum point.
If the coefficient of the squared term is negative then the parabola opens down and The vertex of this parabola is known as the maximum point.
Now we will use vertex formula to calculate t
When
then vertex will be
Now consider the given function:
where a = -16
b=112
so using vertex formula :
Thus, it take 3.5 seconds the Boulder to reach its maximum height.
Now to calculate the Boulder's maximum height . Put value of t = 3.5 in given function (a)
Thus, Boulder's maximum height is 226 ft.
-b/2a = -112/2(16) = 3.5 s t= 3.5s h = -16t^2 + 112t + 30 h = -16(3.5)^2 +122(3.5) +30 h = 226
adjust the windows to y=300
3.5 s; 226 ft
Related Questions
What is the area of 9 cm 3 cm of the rectangle
The sum of thesquare root of a number and six *
What is 3/5 minus 1/4?
There are 5280 feet in a mile how many feet are there in a marathon which is 26.2 miles
Answers
Final answer:
The system of linear equations 3x + 7y = 22 and 12x + 28y = 88 actually represents the same line, indicating that there are infinite solutions. Any pair of (x, y) that satisfies one equation will satisfy the other.
Explanation:
To solve the system of linear equations 3x + 7y = 22 and 12x + 28y = 88, let's use substitution or elimination method. Here, the elimination method works best since the equations are multiples of each other. Divide the second equation by 4, you get 3x + 7y = 22, which is exactly the same equation as the first equation.
This means both equations represent the same line, so there are infinite solutions. Any x, y that satisfy one equation will satisfy the other. Therefore, the system is dependent.
Example of such solutions (x, y) can be obtained by isolating y in the first equation:
7y = 22 - 3x
y = (22 - 3x) / 7 or y = 9 + 3x
Learn more about System of linear equations here:
#SPJ12
Final answer:
The given system of equations has infinitely many solutions.
Explanation:
To solve for x and y in the given system of equations:
3x + 7y = 22
12x + 28y = 88
Multiply the first equation by 4 to eliminate the y variable:
12x + 28y = 88
12x + 28y = 88
Subtract the second equation from the first equation:
12x + 28y - 12x - 28y = 88 - 88
0 = 0
Since both variables have been eliminated, the equations are dependent and have infinitely many solutions. The solution is any pair of (x, y) values that satisfies the original equations.
Learn more about Solving systems of equations here:
#SPJ12
Answers
The next term is : an=an-1+2= a1 8; 18
Based on the information given 2 is added ton each sequence
Sequence:
8+2=10
10+2=12
12+2=14
14+2=16
The next term will be:
16+2=8
Inconclusion The next term is an=an-1+2= a1 8; 18
Learn more here:
Answer:
answer is b
Step-by-step explanation:
Answers
Probability of a coin coming up tails = 1/2
now we multiply the two probabilities together to find what the probability of BOTH occurring at the same time is.
1/6 × 1/2 = 1/12
Answer is D. 1 over 12
Answer:
D. 1/12 is the answer
Step-by-step explanation:
the probability of rolling a 4 is 1/6, and the probability of flipping tails is 1/2. If you multiply 1/2 and 1/6 you get 1/12.
Answers
Distance of racoon = V * (t-2) =5*(t-2)
Distance of armadillo + distance of racoon = 38
3t + 5(t-2)=38
3t + t5 - 10 =38
8t=48
t=6
The anwser is: they will be 38 km apart after 6 hours, so it is 6p.m (12a.m+6 hours)
Answers
Answers
The meters of fencing that is needed is = 3.36m
Calculation of needed meters
The garden is designed in a trapezoid form with sides= a; 3.3m and b; 5.28m.
The area of the trapezoid garden = 13.92 m²
Therefore the meters of fencing needed which is height = ?
The formula for the area of trapezoid = A = (a+b/2)h
From the formula make h the subject of formula;
h = A *2/a+b
h = 13.92*2/3.3+5.28
h =27.84/8.28
h= 3.36m
Therefore, the meters of fencing that is needed is = 3.36m.
Learn more about trapezoid here:
#SPJ1
Final answer:
The amount of fencing needed is 15.96 m.
Explanation:
To find the amount of fencing needed, we need to calculate the perimeter of the garden. Since the area is given as 13.92 square meters.
The perimeter is the total length of all the sides of the garden added together.
The area of the garden is 13.92 square meters, which means that the garden is a rectangle with a length of 4 meters and a width of 3.48 meters.
Perimeter = 2 * (length + width)
Perimeter = 2 * (4 + 3.48)
Perimeter = 15.96 meters
Therefore, 15.96 meters of fencing are needed.
Learn more about Perimeter of a garden here:
#SPJ11