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irakobra [83]
3 years ago
8

find real numbers a, b, and c so that the graph of the function y=ax^2+c contains the points (-1,6), (2,7), and (0,1)

Mathematics
1 answer:
Paraphin [41]3 years ago
5 0
This gives you three simultaneous equations:

6 = a + c
7 = 4a + c
1 = c
 
<u>c = 1
</u>
<u /><u />
If c =1,

6 = a + 1
<u>a = 5
</u>
<u /><u />
This doesn't work in the second equation, so the quadratic that goes through these points is not in the form y = ax^2 + bx + c
Was there supposed to be a b in the equation?




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a. To solve the first part, we are going to use the formula for the surface area of a sphere: A=4 \pi r^2
where
A is the surface area of the sphere
r is the radius of the sphere
We know from our problem that r=5ft; so lets replace that value in our formula:
A=4 \pi (5ft)^2
A=314.16ft^2

To solve the second part, we are going to use the formula for the volume of a sphere: V= \frac{4}{3}  \pi r^3
Where
V is the volume of the sphere
r is the radius 
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V= \frac{4}{3}  \pi (5ft)^3
V=523.6ft^3

We can conclude that the surface area of the sphere is 314.16 square feet and its volume is 523.6 cubic feet.

b. To solve the first part, we are going to use the formula for the surface area of a square pyramid: A=a^2+2a \sqrt{ \frac{a^2}{4} +h^2}
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A is the surface area
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We know form our problem that a=8ft and h=12ft, so lets replace those value sin our formula:
A=(8ft)^2+2(8ft) \sqrt{ \frac{(8ft)^2}{4} +(12ft)^2}
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To solve the second part, we are going to use the formula for the volume of a square pyramid: V=a^2 \frac{h}{3}
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h is the height of the pyramid
We know form our problem that a=8ft and h=12ft, so lets replace those value sin our formula:
V=(8ft)^2 \frac{(12ft)}{3}
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We can conclude that the surface area of our pyramid is 266.39 square feet and its volume is 256 cubic feet.

c. To solve the first part, we are going to use the formula for the surface area of a circular cone: A= \pi r(r+ \sqrt{h^2+r^2}
where
A is the surface area
r is the radius of the circular base
h is the height of the cone
We know form our problem that r=5ft and h=8ft, so lets replace those values in our formula:
A= \pi (5ft)[(5ft)+ \sqrt{(8ft)^2+(5ft)^2}]
A=226.73ft^2

To solve the second part, we are going to use the formula for the volume os a circular cone: V= \pi r^2 \frac{h}{3}
where
V is the volume
r is the radius of the circular base
h is the height of the cone 
We know form our problem that r=5ft and h=8ft, so lets replace those values in our formula:
V= \pi (5ft)^2 \frac{(8ft)}{3}
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We can conclude that the surface area of our cone is 226.73 square feet and its surface area is 209.44 cubic feet.

d. To solve the first part, we are going to use the formula for the surface area of a rectangular prism: A=2(wl+hl+hw)
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We know from our problem that w=6ft, l=10ft, and h=16ft, so lets replace those values in our formula:
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A=632ft^2

To solve the second part, we are going to use the formula for the volume of a rectangular prism: V=whl
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l is the length 
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V=(6ft)(16ft)(10ft)
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<span>We can conclude that there are 12 faces in on the four geometric shapes on the holes.
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Total vertices: 5 + 8 = 13 vertices

We can conclude that there are 0 vertices for the sphere and the cone; there are 5 vertices for the pyramid, and there are are 8 vertices for the solid (rectangular prism). We can also conclude that your boss will need 13 brackets for the vertices of the four figures.

7 0
3 years ago
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garik1379 [7]

Answer:

fourth option

Step-by-step explanation:

Given f(x) then f(x + a) represents a horizontal translation of f(x)

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f(x) = (x - 11)³ + 4

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Answer:

Step-by-step explanation

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Explanation:

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Answer:

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