M= -2, b 7/2 Enter the equation of the line in slope-intercept form.
1 answer:
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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:
a.) depth of the lake = (volume of the lake) / area of lake
= 173,693,585,360,000 / 624,305,840,400 = 278.22 feet
b.) 11 inches = 0.9167 feet
Water gained in cubic feet gained by the lake
= 624,305,840,400 0.9167
= 572,282,434,719.5 cubic feet
c.) the percentage change in the lake volume over that year
= 572,282,434,719.5 cubic feet / 173,693,585,360,000 cubic feet
= 0.0033
= 0.33%
Step-by-step explanation:
i) acres to square feet : 1 acre = 43560 square feet
therefore 14,332,090 acres = 624,305,840,400 square feet
ii) 1 mile = 5280 feet
1 cubic mile = 5280 5280
5280 = 147,197,952,000 cubic feet
therefore 1180 cubic miles = 173,693,585,360,000 cubic feet
a.) depth of the lake = (volume of the lake) / area of lake
= 173,693,585,360,000 / 624,305,840,400 = 278.22 feet
b.) 11 inches = 0.9167 feet
Water gained in cubic feet gained by the lake
= 624,305,840,400 0.9167 = 572,282,434,719.5 cubic feet
c.) the percentage change in the lake volume over that year
= 572,282,434,719.5 cubic feet / 173,693,585,360,000 cubic feet
= 0.0033
= 0.33%