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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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(3x+1)/(3x+2) = (x+2)/(x-5)
jonny [76]

Answer:

x = -9/22 or -0.409 to the nearest thousandth.

Step-by-step explanation:

Cross multiplying we get:

(3x + 1)(x - 5) = (3x + 2)(x + 2)

3x^2 - 14x - 5 = 3x^2 +8x + 4

3x^2 - 3x^2 - 14x - 8x = 4 + 5

-22x = 9

x = -9/22

6 0
2 years ago
A sample of 15 commuters in Chicago showed the average of the commuting times was 33.2 minutes. If s = 8.3 minutes, find the 95%
OleMash [197]

Answer:

The 95% confidence interval of the true mean.

(29.4261 ,36.9739)

Step-by-step explanation:

<u>Step :- (i)</u>

Given sample size 'n' =15

sample of the mean x⁻ = 33.2

The standard deviation of the sample 'S' = 8.3

<u>95% of confidence intervals</u>

<u></u>(x^{-} - t_{\alpha } \frac{S}{\sqrt{n} } ,x^{-} + t_{\alpha }\frac{S}{\sqrt{n} } )<u></u>

<u>Step:-(ii)</u>

<u>The degrees of freedom γ=n-1 = 15-1=14</u>

The tabulated value t = 1.761 at 0.05 level of significance.

now substitute all possible values, we get

(33.2 - 1.761\frac{8.3}{\sqrt{15} } ,33.2+ 1.761\frac{8}{\sqrt{15} } )

After calculation , we get

(33.2-3.7739 , 33.2+3.7739

(29.4261 ,36.9739)

<u>Conclusion</u>:-

the 95% confidence interval of the true mean.

(29.4261 ,36.9739)

8 0
3 years ago
What is bigger 1/5 or .29
n200080 [17]
.29 is bigger.

If you convert 1/5 to a decimal (or simply solve it!) you will end up with .2 or .20
Which is obviously smaller than .29
3 0
3 years ago
Read 2 more answers
Someone please help.
Alexxandr [17]

Hi there!

f(x)+f(x+1)=4f(x)

There are 3 parts to this equation:

f(x)

f(x+1)

4f(x)

We must first determine these three parts separately.

<u>1) f(x)</u>

We're given that  f(x)=3^x:

⇒ f(x)=3^x:

<u>2) f(x+1)</u>

Now, we must find f(x+1). To do so, add 1 to x in the original function f(x)=3^x:

⇒ f(x+1)=3^x^+^1

<u>3) 4f(x)</u>

To find 4f(x), multiply the original function f(x)=3^x by 4:

4f(x)=4*3^x:

<u>4) Put it all together</u>

Now, plug each of the three parts into the equation f(x)+f(x+1)=4f(x):

f(x)+f(x+1)=4f(x)

3^x+3^x^+^1=4*3^x\\3^x+3^x*3=4*3^x

Factor the left side

3^x*(1+3)=4*3^x

Divide both sides by 3^x

1+3=4\\4=4

Because this equation is true, f(x)+f(x+1)=4f(x) is therefore true.

I hope this helps!

3 0
3 years ago
What is the measure of
irinina [24]
Than answer you looking for is I think B
8 0
2 years ago
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