Oct 16, 10:30:54 AM
A rocket is shot into the air. The function f (x) = -16x2 + 64x + 8 gives the
height of the rocket (in feet) as a function of the rockets horizontal distance from
where it was initially shot.
a. What was the initial height of the rocket when it was shot?
b. What is the maximum height the rocket reaches in the air?
a. The initial height of the rocket was
feet.
b. The maximum height the rocket reaches is
feet.

Answers

Answer 1

Answer:

A) 8 feet.

B) 72 feet

Step-by-step explanation:

We have the function [tex]f(x)=-16x^2+64x+8[/tex] which gives the height of the rocket (in feet) as a function of the rocket's horizontal distance.

Part A)

We want to find the initial height of the rocket when it was shot.

At the initial height, the rocket has not moved anywhere. So, the horizontal distance will be 0.

Therefore, to find the initial height, we will substitute 0 into our function. This yields:

[tex]f(0)=-16(0)^2+64(0)+8[/tex]

Evaluate:

[tex]f(0)=8[/tex]

Therefore, the initial height was 8 feet.

Part B)

Notice that our function is a quadratic.

Therefore, the maximum height will be given by the vertex of our quadratic.

To find the vertex, we use:

[tex](-\frac{b}{2a},f(-\frac{b}{2a}))[/tex]

Let's label our coefficients. We have [tex]-16x^2+64x+8[/tex]

Therefore, a=-16, b=64, and c=8.

Substitute them into the vertex formula to find the x-coordinate:

[tex]x=-\frac{64}{2(-16)}\\\Rightarrow x=64/32=2[/tex]

Now, to find the maximum height, substitute 2 back into our function f(x):

[tex]f(2)=-16(2)^2+64(2)+8[/tex]

Evaluate:

[tex]f(2)=-16(4)+64(2)+8\\\Rightarrow f(2)=-64+128+8\\\Rightarrow f(2)=72\text{ feet}[/tex]

Therefore, the rocket reaches a maximum height of 72 feet.


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Because: i looked it up

Answer: y=x10

Step-by-step explanation:

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In order to compare the durability of four different brands of golf balls (ALPHA, BEST, CENTURY, and DIVOT), the National Golf Association randomly selects five balls of each brand and places each ball into a machine that exerts the force produced by a 250-yard drive. The number of simulated drives needed to crack or chip each ball is recorded. The results are given in the following table.
Alpha Best Century Divot
281 270 218 364
220 334 244 302
274 307 225 325
242 290 273 337
251 331 249 355
Provide the EXCEL printout of ONEWAY ANOVA using either DATA ANALYSIS or PTSTAT2 to determine whether the mean number of stimulated drives differs by brand of golf ball.
Use the ANOVA printout to write-up the six step hypothesis testing procedure for determining whether the average number of simulated drives differs by brand of golf ball. What is the p-value for this problem and what does it mean? Assume alpha =.05.

Answers

Answer:

As our computed test statistic falls in critical region, so we reject our null hypothesis. Also p-value=0.0009 is less than significance level, so we reject our null hypothesis and conclude that the average number of simulated drives differs by brand of golf ball at 5% significance level.

Step-by-step explanation:

Excel output print out

Anova: Single Factor      

     

SUMMARY      

Groups Count Sum Average Variance  

Alpha 5 1268 253.6 609.3  

Best 5 1532 306.4 740.3  

Century 5 1209 241.8 469.7  

Divot 5 1583 316.6 1235.3  

     

     

ANOVA      

Source of Variation SS df MS F P-value F crit

Between Groups 20960.4 3 6986.8 9.149217573 0.000925804 3.238871517

Within Groups 12218.4 16 763.65    

     

Total 33178.8 19    

The six steps of hypothesis are

1. Null hypothesis: The average number of simulated drives are same by brand of golf ball

Alternative hypothesis: The average number of simulated drives differs by brand of golf ball

2. Significance level: α=0.05

3. Test statistic: F-ratio for one way anova

4. Computations

F=9.149

5. Critical region: F>3.239

6. Conclusion:

As our computed test statistic falls in critical region, so we reject our null hypothesis. Also p-value=0.0009 is less than significance level, so we reject our null hypothesis and conclude that the average number of simulated drives differs by brand of golf ball at 5% significance level.

how to factor g2 − 32g + 256

Answers

Answer:

Using the snowflake method, you have to find the factors of 256 that add up to get 32.

The result will look like this:

(g-16)(g-16)

Answer:

[tex](g-16)^2[/tex]

Step-by-step explanation:

[tex]g^2-32g + 256[/tex]

To factor it you should remember that

[tex](a-b)^2 = a^2 -2ab+b^2[/tex]

It is easy to seee that

[tex]32 = 2 \cdot 16[/tex]

and

[tex]256 = 16^2[/tex]

Therefore

[tex]g^2-32g + 256 = g^2 - (2\cdot 16)g+ 16^2 = (g-16)^2[/tex]

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Answers

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The equation of a circle is (x−2)2+(y+6)2=100. Find the equation of a circle that is externally tangent to the given circle and has a center at (18, −6).

Answers

Answer:

(x-18)^2+(y+6)^=36

Step-by-step explanation:

circle basic equation is (x-h)^2+(y-k)^2=r^2

center is (18,-6) it is also externally tangent

so

(x-18)^2+(y+6)^2=36 answer

The equation of a circle that is externally tangent to the given circle and has a center at (18, −6) is [tex](x-18)^2+(y+6)^=36[/tex]

What is an equation of a circle?

A circle can be characterized by its center's location and its radius's length. Let the center of the considered circle be at (h,k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

Given that the circle basic equation is [tex](x-2)^2+(y+6)^2=100[/tex]

The center is (18,-6) it is also externally tangent;

Therefore,

[tex](x-18)^2+(y+6)^2=36[/tex]

Therefore, the equation of a circle that is externally tangent to the circle is; [tex](x-18)^2+(y+6)^2=36[/tex]

Learn more about equation of a circle here:

https://brainly.com/question/10165274

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Answers

Answer:

Slope = -2

Step-by-step explanation:

Equation in slope intercept form:

y = -2x + 3

Meaning slope equals -2

Eight more than.twice an number is four less than the same number

Answers

Answer:

2x+8=x-4

Step-by-step explanation:

I think that's right, let me know if it's wrong and I'll delete

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Answers

Answer:

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Step-by-step explanation:

22-8=14

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

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Answers

Answer:

The answer is 14 students.

Step-by-step explanation:

70% of 20 = 14

IMPLAYER
Every day after ser daily walk, Dena drinks 1.06 liters of water. Which decimal is equivalent to 1.06?
A 1.6
O
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Answers

Answer:

C. 1.060

Explanation:

r Which decimal is equivalent to 1.06? Well, if you look at it, c. 1.060 is just 1.06 with a zero added at the end... And we all know zeros have no value. So you can technically just take off the zero at the end and have 1.06. But this is a multiple-choice so you don't get to choose whether or not to take the zero off. So yeah, the answer is c.

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Answer:

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STEP BY STEP EXPLANATION:

drops

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I think the answer is B
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Steven put together 2,494 pieces of a puzzle. About how many pieces did he put together?

Answers

Answer:

2,494

Step-by-step explanation:

if he put 2,494pieces together you repeated the same question

There are 8 dinner rolls in a package.

How many packages will be needed to feed 100 people if each person has 2 dinner rolls? Enter the correct answer to complete the statement.

They will need
packages.

Answers

Answer: 25 packages

Step-by-step explanation: 100x2=200 / 200/8=25

Answer:

100x2 = 200 dinner rolls

200 ÷ 8 = 25 packages

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Answers

Answer:

Point a is correct.

Step-by-step explanation:

hope I helped.

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Required:
Formulate your null and alternative hypotheses by selecting the appropriate values in the blue dropdown menus that follow.

Answers

Answer:

The null hypothesis is  [tex]H_o : \mu = 28.1[/tex]

 The alternative hypothesis is  [tex]H_a : \mu < 28.1[/tex]

Step-by-step explanation:

From the question we are told that

   The population mean at 1960 - 1962 is  [tex]\mu_1 = 25.0[/tex]

    The population mean at 1999- 2002 is  [tex]\mu_2 = 28.1[/tex]

     The sample size is  n=  1034

     The sample mean is  [tex]M = 28.9[/tex]

 The null hypothesis is  [tex]H_o : \mu = 28.1[/tex]

 The alternative hypothesis is  [tex]H_a : \mu < 28.1[/tex]

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Answers

Answer:

3x²-1

Step-by-step explanation:

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g(x) = 3x-1

[g·f](x)

g(f(x))

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What is the interquartile range (IQR) of the salaries?
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Answers

Answer:

First you order the data from least to greatest

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next you Calculate the median of both the lower and upper half of the data

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Step-by-step explanation:

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Answers

Answer:

She had 16 feet of ribbon

Step-by-step explanation:

Answer:

16 ft of ribon

Step-by-step explanation:

divide 6 by 3 and get 2. there is 2 ft for every 8th of the ribbon so 2×8=16

hope it helped

One of the dog treats in Shelley’s shop is 8 inches long and 3.2 inches wide. She wants to make a miniature version that has proportional dimensions. If the miniature treat will be 3 inches long, how wide should it be?

Answers

Answer:

1.2in

Step-by-step explanation:

Answer:

(1) 1.2 inches

insert two arithmetic means between 15 and 36​

Answers

Answer: a_1 = 15

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a_n = a_1 + (n - 1)d

36 = 15 + (4 - 1)d

21 = 3d

7 = d

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Answers

Answer:

take a look ...........

Alex needs to bisect ∠ABC using a compass and straightedge. He starts by performing the following steps. Step 1: Place the compass on vertex B of the angle. Step 2: Draw an arc that intersects both sides of the angle. Step 3: Label these intersections as point D and point E . Step 4: Place the compass at point D and draw an arc in the interior of the angle. What are the next steps Alex should take in his construction?

Answers

Answer:

Step 5: Without changing the length of the compass place it on point E and draw an arc in the interior of the angle.

Step 6: Draw a straight line with the straight edge that goes from the vertex and thru the intersection of both arcs.

Step-by-step explanation:

To bisect and angle is to split it prefectly in half, making for example a 90º angle into two 45º angles, in order to do this you will just need to use your compass and draw an arc that will pass over both sides of the angle, after that you put it in the intersections of the arc and the sides and just draw arcs that fit inside the angle from there where both arcs created from the intersections of the precious arc meet that's the middle of the angle, so now you just draw a straight line from the vertex to the intersection of both arcs and you just have bisected an angle.

Please help (click picture)

Answers

Answer:check photo

Step-by-step explanation:

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