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stellarik [79]
2 years ago
6

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.
Mathematics
2 answers:
ratelena [41]2 years ago
6 0
This is the quadratic function:
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.
lakkis [162]2 years ago
5 0
<h2><em><u>Answer: 400 ft.</u></em></h2><h2><em><u>For Plato</u></em></h2>

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kodGreya [7K]
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A) is technically the same as B), but B) expresses correct function notation.

B) 5 = 5(1) ⇒ 5 = 5
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C) I'm not sure what you mean y=5^5=x, but I'm going to use y=5^{x} because it's close to what you wrote:
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6 0
3 years ago
Suppose y varies directly as x, and y=14 when x=4. What is the value of y when x=9
Katena32 [7]

Given :-

  • y varies directly as x, and y=14 when x=4.

To Find :-

  • the value of y when x=9 .

Solution :-

<u>A</u><u>c</u><u>c</u><u>o</u><u>r</u><u>d</u><u>i</u><u>n</u><u>g</u><u> </u><u>t</u><u>o</u><u> </u><u>Q</u><u>u</u><u>e</u><u>s</u><u>t</u><u>i</u><u>o</u><u>n</u><u> </u><u>,</u>

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<u>When</u><u> </u><u>y</u><u> </u><u>=</u><u> </u><u>1</u><u>4</u><u> </u><u>a</u><u>n</u><u>d</u><u> </u><u>x</u><u> </u><u>=</u><u> </u><u>4</u><u> </u><u>,</u>

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<u>W</u><u>h</u><u>e</u><u>n</u><u> </u><u>x</u><u> </u><u>=</u><u> </u><u>9</u><u> </u><u>,</u>

  • y = 7/2*9
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BigorU [14]

Answer:

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Step-by-step explanation:

Blue = 6

White = 7

Gray = 8

Total socks = 6+7+8 =21

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Pr(blue) = 6/21

Divide both by 3 to make the fraction to the lowest term.

Pr(blue) = 2/7

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