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Vikentia [17]
3 years ago
11

A football thrown by a quarterback follows a path given by hx=-0.0095x2+x+7, where h is the height of the ball in feet and x is

the horizontal distance the ball has traveled in feet. If any height less than 10 feet can be caught or knocked down, at what distances from the quarterback can the ball be knocked down?
Mathematics
1 answer:
Wewaii [24]3 years ago
7 0

Answer:

The ball can be knocked down at a horizontal distance of 3.09 feet or 102.17 feet from the marshal.

Step-by-step explanation:

We have the function that represents the height h (x) of the ball h(x) = -0.0095x^2 + x + 7

Where x is the horizontal distance of the ball.

We want to find the horizontal distance the ball is at (horizontal distance between the field marshal and the ball) when it is at a height of 10 feet.

To do this, we must do h (x) = 10

10 = -0.0095x^2 + x + 7\\0 = -0.0095x^2 + x -3

Now we must solve the second degree equation. For this we use the formula of the resolvent:

\frac{-b + \sqrt{b ^ 2 - 4 * a * c}}{2a}

       and

\frac{-b - \sqrt{b ^ 2 - 4 * a * c}}{2a}


\frac{-1 + \sqrt{1 ^ 2 - 4 * (- 0.0095)(-3)}} {2 (-0.0095)} = 3.09 ft

  and

\frac{-1 - \sqrt{1 ^ 2 - 4 * (- 0.0095)(-3)}} {2 (-0.0095)} = 102.17ft


Then, the ball can be knocked down at a horizontal distance of 3.09 feet or 102.17 feet from the marshal.

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katrin2010 [14]

Answer:

1st problem: b) A=2500(1.01)^{12t}

2nd problem:  c) A=2500e^{.12t}

Step-by-step explanation:

1st problem:

The formula/equation you want to use is:

A=P(1+\frac{r}{n})^{nt}

where

t=number of years

A=amount he will owe in t years

P=principal (initial amount)

r=rate

n=number of times the interest is compounded per year t.

We are given:

P=2500

r=12%=.12

n=12 (since there are 12 months in a year and the interest is being compounded per month)

A=2500(1+\frac{.12}{12})^{12t}

Time to clean up the inside of the ( ).

A=2500(1+.01)^{12t}

A=2500(1.01)^{12t}

----------------------------------------------------

2nd Problem:

Compounded continuously problems use base as e.

A=Pe^{rt}

P is still the principal

r is still the rate

t is still the number of years

A is still the amount.

You are given:

P=2500

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Let's plug that information in:

A=2500e^{.12t}.

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3 years ago
How does the order of the numbers affect the product in multiplication problems
GalinKa [24]

Answer:

Uneffected.

Step-by-step explanation:

The order of the numbers doesn't affect the product in multiplication problems.

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We can write it as : 2×5×2

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Also,

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Step-by-step explanation:

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Answer:

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IgorC [24]

Answer:

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Step-by-step explanation:

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