a rock is launched from a canon. it's height, h(x), can be represented by a quadratic function in terms of time, x, in seconds. After 1 second, the Rock is 58 ft in the air; after 2 seconds, it is 112 feet in the air. find the height, in feet, of the rock after 10 seconds in the air.
Answers
h(x)=ax²+bx+c
We have two points:
(1,58)
(2,112)
Now, we calculate this quadratic funtion.
we assume that h(0)=0
Therefore:
a(0)²+b(0)+c=0
c=0
(1,58)
a(1)²+b(1)=58
a+b=58 (1)
(2,112)
a(2)²+b(2)=112
4a+2b=112
2a+b=56 (1)
With the equations (1) and (2) we make a system of equations:
a+b=58
2a+b=56
we can solve this system of equations by reduction method.
-(a+b=58)
2a+b=56
---------------------
a=-2
-2(a+b=58)
2a+b=56
-------------------
-b=-60 ⇒ b=60
The function is:
h(x)=ax²+bx+c
h(x)=-2x²+60x
Now find the height, in feet, of the rock after 10 seconds in the air.
h(10)=-2(10)²+60(10)
h(10)=-200+600=400
Answer: 400 ft.
Answer: 400 ft.
For Plato
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Step by Step:
8w^2+2w-3
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Solve exponents first:
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Y = -5x – 1
A) One
B) None
C) Infinite
D) Two
Answers
lets do that!
x + 5 = -5x - 1 now add +1 to both sides of the equation
+ 1 = +1 it cancels out on the right side and we solve on the left
*****************
x + 6 = -5x Now lets subtract that(1x) from both sides
-1x = -1x ( if x stands alone, theres always an imaginary 1 right by it)
************** now -5 - 1 = -6 so its -6x
6 = -6x Now divide both sides by -6 to isolate x to be alone
÷-6 = ÷6 It cancels out on the right side and we solve on the left
************ 6 ÷ -6 = 0 so lets see what we have
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I hope this helps!
and dont forget 2
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Answers
The lateral area of a regular pentagonal pyramid has a slant height of 14 in is 210 inch^2.
We have given that ,
The lateral area of a regular pentagonal pyramid that has a slant height of 14 in. and a base side length of 6 in.
What is the pentagonal pyramid?
A pentagonal pyramid is a pyramid with a pentagonal base upon which are erected five triangular faces that meet at a point. Like any pyramid, it is self-dual. The regular pentagonal pyramid has a base that is a regular pentagon and lateral faces that are equilateral triangles.
The question ask to choose among the following choices that contain the value of the lateral area of a regular pentagonal pyramid that has a slant height of 14 in and a base side length of 6 in.
Base on my calculation, the answer would be A.
210 inch^2.
To learn more about the pyramid visit:
#SPJ5
Answers
2x + 3y = 1
y = x - 8
2x + 3y = 1
2x + 3(x-8) = 1
2x + 3x - 24 = 1
5x = 1 + 24
5x = 25
5x/5 = 25/5
x = 5
y = x - 8
y = 5 - 8
y = -3
x = 5 ; y = -3
2x + 3y = 1
2(5) + 3(-3) = 1
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Answers
18/30 =3/5 =60/100 =60%
(b) {x | x > 3 or x < -3}
(c) {x | x | x > 3}
(d) {x | x < -3}
please show how you got the answer. thank you!
Answers
-9 -9 to remove 9 deduct it from both sides
- x² < -9
÷ -1 ÷-1 to remove the negative sign, divide both sides by -1
x² < 9
√x² < √9 to remove the exponent of 2, find the square root of both sides.
x < 3 Choice A.
To check:
9 - x² < 0
9 - 3² < 0
9 - 9 < 0
0 < 0
The solution is (b) {x | x > 3 or x < -3}