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The position of a ball after it is kicked can be determined by using the function f left parenthesis x right parenthesis equals

Citrus2011 [14]

Answer:

When kicked, the height of the ball is 1 feet. The highest point for the ball's trajectory is 12 feet.

Step-by-step explanation:

We are given that the height is given by $f(x)=-0.11x^2+2.2x+1$ . The distance between the ball to the point where it was kicked is 0 right at the moment the ball was kicked. So, the height of the ball, when it was kicked is f(0) = -0.11*0 + 2.2*0 +1 = 1.

To determine the highest point, we will proceed as follows. Given a parabola of the form x^2+bx + c, we can complete the square by adding and substracting the factor b^2/4. So, we get that

$x^2+bx+c = x^2+bx+\frac{b^2}{4} - \frac{b^2}{4} +c = (x+\frac{b}{2})^2+c-\frac{b^2}{4}$ .

In this scenario, the highest/lowest points is $c-\frac{b^2}{4}[/tex} (It depends on the coefficient that multiplies x^2. If it is positive, then it is the lowest point, and it is the highest otherwise). Then, we can proceed as follows. [tex] f(x) = -0.11x^2+2.2x+1 = -0.11(x^2-20x)+1$

We will complete the square for $x^2-20x$ . In this case b=-20, so

$f(x) = -0.11(x^2-20x+\frac{400}{4}-\frac{400}{4})+1 = -0.11(x^2-20x+100-100)+1$

We can distribute -0.11 to the number -100, so we can take it out of the parenthesis, then

$f(x) = -0.11(x^2-20x+100)+1+100*0.11 = -0.11(x^2-20x+100)+1+11 = -0.11(x-10)^2+12$

So, the highest point in the ball's trajectory is 12 feet.

5 0

4 years ago

Read 2 more answers

Find the volume of the prism. 6 m 20 m 26 m The volume of the prism is m?

Masja [62]

Step-by-step explanation:

To find the volume, you need to do length x width x height.

In this case, we are going to do 6 x 20 x 26.

You get 3,120 m^3.

Hope you found this helpful!

3 0

3 years ago

Suppose x has a distribution with μ = 10 and σ = 9. (a) If a random sample of size n = 43 is drawn, find μx, σ x and P(10 ≤ x ≤

JulsSmile [24]

Answer:

P(10 ≤ x ≤ 12) = 0.4274

Step-by-step explanation:

Population mean = u = 10

Population Standard Deviation = $\sigma$ = 9

Sample size = n = 43

Sample mean( $\mu_{x}$ ) is equal to the population mean. So,

Sample mean = $\mu_{x}$ = 10

Sample standard deviation( $\sigma_{x}$ ) is equal to population standard deviation divided by square root of sample size. So,

Sample standard deviation = $\sigma_{x}$ = $\frac{9}{\sqrt{43}}=1.372$

We have to find the probability that for a random sample of n = 43, the value lies between 10 and 12 i.e. P(10 ≤ x ≤ 12)

P(10 ≤ x ≤ 12) = P(x ≤ 12) - P( x ≤ 10)

We can find P(x ≤ 12 ) and P(x ≤ 10) by converting these values to z scores.

The formula for z score is:

$z=\frac{x-\mu_{x}}{\sigma_{x}}$

For x =12, we get:

$z=\frac{12-10}{1.3725}=1.457$

For x =10, we get:

$z=\frac{10-10}{1.3725}=0$

So,

P(x ≤ 12) - P( x ≤ 10) = P(z ≤ 1.457) - P(z ≤ 0)

From the z table,

P(z ≤ 1.457) = 0.9274

P(z ≤ 0) = 0.5

So,

P(x ≤ 12) - P( x ≤ 10) = P(z ≤ 1.458) - P(z ≤ 0) = 0.9274 - 0.5 = 0.4274

So,

P(10 ≤ x ≤ 12) = P(x ≤ 12) - P( x ≤ 10) = 0.4274

Therefore,

The probability that for a random sample of size 43, the mean lies between 10 and 12 is 0.4274.

8 0

3 years ago

Find the area of the shaded square, PQRS.

Tanya [424]

Answer:

22

Step-by-step explanation:

3 0

3 years ago

I NEED HELP WITH THIS ONE TOO!

oee [108]

4 × ( 4 + 9 ) = 2 × ( 2 + x )

4 × 13 = 2 × ( 2 + x )

2 × 2 × 13 = 2 × ( 2 + x )

2 × 26 = 2 × ( 2 + x )

Divide both sides by 2

2 × 26 ÷ 2 = 2 × ( 2 + x ) ÷ 2

26 = 2 + x

Subtract both sides 2

26 - 2 = 2 - 2 + x

x = 24

6 0

3 years ago