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2 answers:
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We know that
case a)
the equation of the vertical parabola write in vertex form is
y=a(x-h)²+k,
where (h, k) is the vertex.
Using our vertex, we have:
y=a(x-2)²-1
We know that the parabola goes through (5, 0),
so
we can use these coordinates to find the value of a:
0=a(5-2)²-1
0=a(3)²-1
0=9a-1
Add 1 to both sides:
0+1=9a-1+1
1=9a
Divide both sides by 9:
1/9 = 9a/9
1/9 = a
y=(1/9)(x-2)²-1
the answer is
a=1/9
case b)
the equation of the horizontal parabola write in vertex form is
x=a(y-k)²+h,
where (h, k) is the vertex.
Using our vertex, we have:
x=a(y+1)²+2,
We know that the parabola goes through (5, 0),
so
we can use these coordinates to find the value of a:
5=a(0+1)²+2
5=a+2
a=5-2
a=3
x=3(y+1)²+2
the answer is
a=3
see the attached figure
case a)
the equation of the vertical parabola write in vertex form is
y=a(x-h)²+k,
where (h, k) is the vertex.
Using our vertex, we have:
y=a(x-2)²-1
We know that the parabola goes through (5, 0),
so
we can use these coordinates to find the value of a:
0=a(5-2)²-1
0=a(3)²-1
0=9a-1
Add 1 to both sides:
0+1=9a-1+1
1=9a
Divide both sides by 9:
1/9 = 9a/9
1/9 = a
y=(1/9)(x-2)²-1
the answer is
a=1/9
case b)
the equation of the horizontal parabola write in vertex form is
x=a(y-k)²+h,
where (h, k) is the vertex.
Using our vertex, we have:
x=a(y+1)²+2,
We know that the parabola goes through (5, 0),
so
we can use these coordinates to find the value of a:
5=a(0+1)²+2
5=a+2
a=5-2
a=3
x=3(y+1)²+2
the answer is
a=3
see the attached figure
Answer:
Step-by-step explanation:
we know that
The formula of slope is "rise over run", where the "rise" (means change in y, up or down) and the "run" (means change in x, left or right)
In this problem
The tangent of angle of 5 degrees is equal to the quotient of "rise over run"
Let
y ----> the rise of the ramp
x ----> the run of the ramp
we have
substitute and solve for x
Answer:
h(x) = -16x² + 192x + 208
784ft
6 sec
13 sec
Step-by-step explanation:
a)
h(x) = -16x² +vx + h
here v represent velocity
represent initial height of launch
h(x) = -16x² + 192x + 208
b)
h(x) = -16x² + 192x + 208
here a = -16
b = 192
c = 208
x = -b/2a
= -192/2(-16)
= 6
plug this value in the equation
h(x) = -16(6)² + 192(6) + 208
= 784ft
e)
Plug h(x)=0 in the equation
0 = -16x² + 192x + 208
divide equation by -16
x² - 12x - 13 = 0
Factors
1x * -13x = -13
1x - 13x = -12
Factorised form
x² - 12x - 13 = 0
x² + x - 13x - 13 = 0
x(x+1) -13(x+1) = 0
(x+1)(x-13) = 0
x = -1
x = 13
Since time can not be negative so we will reject x = -1