A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot. y = -16x2 + 261x + 130

Answers

Answer 1

Answer

The highest height attained by the rocket = 1194.4 feet

Explanation

The height of the rocket, y, in feet as a function of the time, x in seconds as

y = -16x² + 261x + 130

We are then asked to find the maximum height reached by the rocket

To do this, we would use the differentiation analysis to obtain the maximum of this function.

At maximum point for any function,

The first derivative = (dy/dx) = 0

The second derivative = (d²y/dx²) < 0

y = -16x² + 261x + 130

First derivative

(dy/dx) = -32x + 261 = 0

32x = 261

Divide both sides by 32

(32x/32) = (261/32)

x = 8.15625 s

We can then substitute this value of x (time) into the equation to get the maximum height (y)

y = -16x² + 261x + 130

At x = 8.15625 s,

y = -16 (8.15625)² + 261 (8.15625) + 130

= -1064.39 + 2128.78 + 130

= 1194.39

= 1194.4 feet to the nearest tenth.

Hope this Helps!!!


Related Questions

matthew worked 20 hours ar $10 a hour. Taxes were 12%. How much money was left?

Answers

Step 1. calculate the totay pay (not including taxes)

Since he worked 20 hours with an hourly pay of $10, the total was:

[tex]20\times10=200[/tex]

Step 2. Calculate the taxes

We need to calculate the 12% of $200, to find the amount that he paid in taxes. For this, we divide $200 by 100 and multiply by 12%:

[tex]\frac{200}{100}\times12[/tex]

solving this operations we get:

[tex]\frac{200}{100}\times12=24[/tex]

He paid $24 in taxes

Step 3. Calculate the remaining amount

We substract $24 from the initial total amount $200:

[tex]200-24=176[/tex]

Answer:

How much money was left? $176

25. A group of students were asked how many movies they had watched the previous week. The results are shown below.Number of MoviesFrequency0818253547Find the mean and median for the number of movies watched per student. Round your answers to the nearest hundredth.Mean = Median =

Answers

Answer:

Explanation:

Given the results of the number of movies watched by the group of students and the frequency, we're asked to determine the mean and median for the number of movies watched per student.

We'll follow the below steps to solve for the mean and median;

1. Find the product of the number of movies and frequency;

[tex]\begin{gathered} 0\times8=0 \\ 1\times8=8 \\ 2\times5=10 \\ 3\times5=15 \\ 4\times7=28 \end{gathered}[/tex]

2. Find the sum of the product of the number of movies and frequency;

[tex]0+8+10+15+28=61[/tex]

3. Find the sum of the frequency;

[tex]8+8+5+5+7=33[/tex]

The mean can now be determined using the below formula;

[tex]\begin{gathered} \text{Mean}=\frac{\Sigma(f\cdot x)}{\Sigma f} \\ \text{where} \\ \Sigma(f\cdot x)=\text{ sum of the product of the number of movies and frequency} \\ \Sigma f=\text{ sum of the frequency} \end{gathered}[/tex]

Therefore, our mean is;

[tex]\text{Mean}=\frac{61}{33}=1.85[/tex]

We can go ahead and determine the median using the below formula;

[tex]undefined[/tex]

An empty tank is filled with water at a constant rate

Answers

Answer: D

Step-by-step explanation:

D is the answer because if you divide w by m, you get 16.5. Therefore 16.5 is the constant rate.

You put $400 in an account. The account earns $32 simple interest in 2 years what is the annual interest rate?

Answers

Answer

4 %

Explanation

Given:

Principal, P = $400

Interest, I = $32

Time,T = 2 years

What to find:

Annual interest rate, R

Step-by step solution:

The simple interest formula is given by:

[tex]I=\frac{\text{PRT}}{100}[/tex]

Substituting P = 400, I = 32, and T = 2 into the formula:

[tex]\begin{gathered} 32=\frac{400\times R\times2}{100} \\ 800R=3200 \\ R=\frac{3200}{800} \\ R=4\text{ \%} \end{gathered}[/tex]

In the gift shop of the History of Flight museum, Elisa bought a kit to make a model of a jet airplane. The actual plane is 18 feet long with a wingspan of 13.5 feet. If the finished model will be 10 inches long, what will the wingspan be?
3.75 in.
7.5 in.
24.3 in.
13.3 in.

Answers

Answer:

The answer is 24.3

Step-by-step explanation:

hope this helps you

How many kilometers could the red car travel in 12 hours? Write an equation to show your work.

Answers

The kilometers that the red car travel in 12 hours is 2604 kilometers.

What is an equation?

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

From the diagram, it should be noted that the red car has a speed of 217 km per hours.

Therefore, the distance traveled in 12 hours will be:

Distance = Speed × Time

= 217 × 12

= 2604 km

Learn more about equations on;

brainly.com/question/2972832

#SPJ1

7x +4 for x =9 The solution is ?

Answers

[tex]\begin{gathered} 7x+4 \\ \text{For x= 9} \\ 7(9)+4 \\ =63+4 \\ =67 \end{gathered}[/tex]

which statement is the contrapositive of the given statement statement if you play a sport then you wear a helmet

Answers

We will have that the contrapositive statement is:

*If you do not wear a helmet, then you do not play a sport.

Graph two full periods, highlighting the first period using bold marking and analyze each function.Y = 2 sin (1/2 (x + pi/2) ) + 1

Answers

Given

[tex]y=2\sin(\frac{1}{2}(x+\frac{\pi}{2}))+1[/tex]

Procedure

Period: 4pi

Interval length: In the graph 2 periods 8pi

Phase shift: -pi/2

1st Per. begins: -pi/2

1st Per. ends: 7pi/2

Amplitude: 2

Domain:

(-∞, ∞)

Range:

[-1,3]

y-intercep:

(0,2.414)

x-intercept:

[tex]x=\frac{11\pi}{6}+4\pi n,\frac{19\pi}{6}+4\pi n,\text{ for any integer of n }[/tex]

what isk + 6 greater than or equal to 19, if k = 11

Answers

what is

k + 6 greater than or equal to 19, if k = 11​

we have

[tex]\begin{gathered} k+6\ge19 \\ k\ge19-6 \\ k\ge13 \end{gathered}[/tex]

For k=11

we have

[tex]\begin{gathered} 11+6\ge19 \\ 17\ge19\text{ ----}\longrightarrow\text{ is not true} \\ \text{that means-}\longrightarrow\text{ the value of k is not a solution of the inequality} \end{gathered}[/tex]

Convert y+5=-(x+2) to the slope-Intercept (don’t put any spaces between numbers, variables, signs, or parentheses)

Answers

Given:

[tex]y+5=-(x+2)[/tex]

Required:

To find the slope-Intercept form of the given equation.

Explanation:

We know that, the slope intercept form can be represented as

[tex]y=mx+b[/tex]

Therefore, the given equation can be written as

[tex]\begin{gathered} y+5=-(x+2) \\ y+5=-x-2 \\ y=-x-2-5 \\ y=-x-7 \end{gathered}[/tex]

Final Answer:

The slope-Intercept form of the given equation is

[tex]y=-x-7[/tex]

what is 2*2?i dont know i in pweschool

Answers

[tex]2\times2=2+2=4[/tex]

2 x 2 is two times two

answer: 4

Find the domain of f(x) = 3x/x-1 and discuss the function behavior of f near any excluded x-values.

Answers

The domains are all real numbers except the the values that makes the denominator zero

x - 1 = 0

x=1

That is; the domain is all real numbers except x=1

Solve for X Geometry, Just need a quick over view!

Answers

The value of X = 11

Step - by - Step Explanation

What to find? The value of x

To find the value of X, take the ratio of the sides.

[tex]\frac{2x+6}{32}=\frac{52.5}{60}[/tex]

Cross -multiply.

[tex]60(2x+6)=52.5(32)[/tex][tex]60(2x+6)=1680[/tex]

Divide both-side of the equation by 60.

[tex]\frac{\cancel{60}(2x+6)}{\cancel{60}}=\frac{1680}{60}[/tex]

2x + 6 = 28

Subtract 6 from both-side of the equation.

2x + 6 - 6 = 28 - 6

2x =22

Divide both-side of the equation by 2.

[tex]\frac{\cancel{2}x}{\cancel{2}}=\frac{22}{2}[/tex]

x = 11

Hence, the value of X = 11

x-(7.65 + 3.18)=4 solve for x

Answers

Answer:

The value of x is;

[tex]x=14.83[/tex]

Explanation:

Given the equation;

[tex]x-(7.65+3.18)=4[/tex]

Solving for x;

[tex]\begin{gathered} x-(10.83)=4 \\ x=4+10.83 \\ x=14.83 \end{gathered}[/tex]

Therefore, the value of x is;

[tex]x=14.83[/tex]

what is 1/5 turned into a percent

Answers

[tex]\text{Let's recall that 1 divided by 5 is 0.2}[/tex][tex]\text{And 0.2 is 20\% or 0.2 }\cdot\text{ 100 = 20\%}[/tex]

What is the slope of the line through (-1, -7) and (3,9)? Choose 1 answerA. -1/4B. -4C. 4D. 1/4

Answers

Answer:

C. 4

Explanation:

Given the line that passes through points (-1,-7) and (3,9):

[tex]\begin{gathered} \text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =\frac{9-(-7)}{3-(-1)} \\ =\frac{9+7}{3+1} \\ =\frac{16}{4} \\ =4 \end{gathered}[/tex]

The slope of the line is 4.

The correct choice is C,

Which set of parametric equations represents the function y=x^2+4x-5? Select all that apply.

Answers

Solution

- The way to solve the equation is to take the expression for x i.e. x = 2t, and substitute into the expression for y(x).

- The result must be the corresponding y-value in terms of t.

- This is done below:

Option A:

[tex]\begin{gathered} x=2t \\ y(x)=x^2+4x-5 \\ \\ \text{ put }x(t)=2t \\ \\ y(x(t))=(2t)^2+4(2t)-5 \\ y(x(t))=y(t)=4t^2+8t-5 \\ \\ \therefore y(t)=4t^2+8t-5\text{ \lparen OPTION A\rparen} \end{gathered}[/tex]

Option B:

[tex]\begin{gathered} x=t+1 \\ y=x^2+4x-5 \\ \\ y(x(t))=y(t)=(t+1)^2+4(t+1)-5 \\ t^2+2t+1+4t+4-5 \\ y(t)=t^2+6t\text{ \lparen NOT IN THE OPTIONS\rparen} \end{gathered}[/tex]

Option C:

[tex]\begin{gathered} x=t-3 \\ y=x^2+4x-5 \\ \\ y(x(t))=(t-3)^2+4(t-3)-5 \\ =t^2-6t+9+4t-12-5 \\ =t^2-2t-8\text{ \lparen NOT IN THE OPTIONS\rparen} \end{gathered}[/tex]

Option D:

[tex]\begin{gathered} x=t^2 \\ y=x^2+4x-5 \\ \\ y(x(t))=(t^2)^2+4(t^2)-5 \\ =t^4+4t^2-5\text{ \lparen NOT IN THE OPTIONS\rparen} \end{gathered}[/tex]

Option E:

[tex]\begin{gathered} x=t+1 \\ y=x^2+4x-5 \\ \\ y(x(t))=(t+1)^2+4(t+1)-5 \\ =t^2+2t+1+4t+4-5 \\ =t^2+6t\text{ \lparen OPTION E IS CORRECT\rparen} \end{gathered}[/tex]

Final Answer

The answers are OPTIONS A AND E

Elena is organizing her craft supplies. She estimatesthat her jars will fit 1,000 buttons or 50 large beads.They actually fit 677 buttons or 22 large beads. DoesElena's estimate about the buttons or her estimateabout the large beads have less percent error? To thenearest percent, how much less?

Answers

Step 1

Given;

[tex]\begin{gathered} Elena-\text{ estimates her jar will take 1000 buttons or 50 large beads} \\ Her\text{ Jar actually takes 677 buttons or 22 large beads} \end{gathered}[/tex]

Required; To find if Elena's estimates have percentage error, to which percent, and how much less

Step 2

State the formula for percentage error

[tex]\text{ \% error=}\frac{|Approximate-exact|}{exact}\times100[/tex][tex]Elena^{\prime}s\text{ estimate about the button has a percentage error }[/tex][tex]\begin{gathered} For\text{ buttons} \\ Approximate=1000 \\ Exact=677 \end{gathered}[/tex][tex]\text{ \%error=}\frac{|1000-677|}{677}\times100=47.71048744\text{\%}[/tex][tex]\begin{gathered} For\text{ large beads} \\ \operatorname{\%}\text{error=}\frac{\text{\lvert50-22\rvert}}{22}\times100 \end{gathered}[/tex][tex]\text{ \% error=}\frac{28}{22}\times100=127.272727...\text{\%}[/tex]

Percent errors tells you how big your errors are when you measure something in an experiment. Smaller values mean that you are close to the accepted or real value. For example, a 1% error means that you got very close to the accepted value, while 45% means that you were quite a long way off from the true value.

The percentage error for buttons with about 47.71% is less than that of the large beads which is about 127.273%.

How much less of the percentage error to the nearest percent will be;

[tex]\begin{gathered} =79.56223986 \\ \approx80\text{\%} \end{gathered}[/tex]

in this work today in my class want to know if am right 5w+2p for w=6 and p=2 evaluate this

Answers

Solution

For this case we have the following expression given:

5w +2p

And we have that w= 6 and p= 2

And replacing we got:

5*6 + 2*2

30 + 4= 34

A class of 20 students wants to form a committee to fundraise for cancer research. If the committee is formed with four students, how many possible committees can be made?A: 116,280B: 24C: 4,845D: 9,690

Answers

1) Since there are 20 students, and each committee is formed by 4 people.

The order does not matter, and there can't be repetition. Just one person can be, let's say president, VP, secretary, and treasurer.

2) So we can write, the possibilities on the numerator of people filling in and on the denominator the number of vacancies for that committee, we can set this Combination simply as:

[tex]\frac{20}{4}\times\frac{19}{3}\times\frac{18}{2}\times\frac{17}{1}=4845[/tex]

3) So there are 4845 possibilities to form a Committee with 20 people for 4 vacant lots.

What is the slope of the line containing (-2,5) and (4,-4)?A.3/2B.-3/2C. -2D. 2

Answers

Answer:

B.-3/2

Step-by-step explanation:

To find the slope, we need to take two points from a line. I am going to call them:

(x1,y1) and (x2,y2).

The slope is:

[tex]a=\frac{y2-y1}{x2-x1}[/tex]

In this question:

(x1,y1) = (-2,5)

(x2,y2) = (4, -4)

So

[tex]a=\frac{y2-y1}{x2-x1}=\frac{-4-5}{4-(-2)}=\frac{-9}{4+2}=-\frac{9}{6}=-\frac{3}{2}[/tex]

So the correct answer is:

B.-3/2

• The function (x) is a transformation of the square root parent function,f(x) = V. What function is h(x)?5nuA. h(x) = v=-4B. h(c) = V - 4O C. h(z) = y +4D. h(x) = 1 + 4

Answers

we are given the following function:

[tex]f(x)=\sqrt[]{x}[/tex]

The graph of h(x) is the same graph translated 4 units to the left, therefore it must be:

[tex]h(x)=f(x+4)[/tex]

Replacing x for x + 4 in f(x) we get:

[tex]h(x)=f(x+4)=\sqrt[]{x+4}[/tex]

Estimate the square root to the nearest whole numberV450question 1

Answers

We need to solve the next square root

[tex]\sqrt[]{450}=21.21[/tex]

The nearest whole number is 21

A student in MAT110 this semester has the following grades at the end of the semester, after two quizzes and one lab grade are dropped: Quiz average: 95 Lab average: 89 Tests: 52, 82, 88 Final Exam: 73 Question 1 of 5 20 Points Find the student's course average rounded to the nearest whole number. You'll need to consult your syllabus (and/or the feedback given) for weighting percentages and other grading information.Weights:Quiz = 25%Lab = 25%Test = 35%Final = 15%

Answers

The overall course average is the average weight of all the quizzes, tests, finals, labs.

First we need the average for all the information:

Quiz Average: 95 (given)

Lab Average: 89 (given)

Test Average >> we have to find by summing and dividing by number of tests

[tex]\text{average}=\frac{52+82+88}{3}=74[/tex]

Final Exam: 73 (1 exam, so this is the average).

Thus, the information we have:

Quiz Avg = 95

Lab Avg = 89

Test Avg = 74

Final Avg = 73

Now, we multiply the scores with the respective weightage(in decimal) and sum it. We get:

[tex]95\mleft(0.25\mright)+89\mleft(0.25\mright)+74\mleft(0.35\mright)+73\mleft(0.15\mright)=82.85[/tex]

Rounded to nearest whole number: 83

Answer:

Course Average = 83 (rounded to nearest whole number)

Lincoln Middle School plans to collect more than 2,000 cans of food in a food drive. So far, 668 cans have been collected. Write and solve an inequality to find numbers of cans the school can collect on each of the final 7 days of the drive to meet this goal.Which inequality represents the solution to this situation?

Answers

Inequalities

Let's call c the number of cans of food.

The school wants to collect more than 2,000 cans in a food drive.

668 cans have been collected so far.

The number of cans needed to reach the goal is 2,000 - 668.

These cans will be collected in 7 days, thus:

7c > 2,000 - 668

Operating

7c > 1,332

Dividing by 7:

c > 1,332 / 7

c > 190.29

This is the average number of cans needed to collect each day.

The first choice is correct

Find three consecutive odd integers that add to - 99

Answers

We will investigate how three consecutive odd numbers add up to a certain value.

We will assign a variable to the first odd number as follows:

[tex]1st\text{ : x}[/tex]

The next consecutive odd number will occur two integers ahead or two integers before the first odd number. We can choose either ( ahead or before ) and express second consecutive odd number in terms of first odd number as follows:

[tex]2nd\colon\text{ ( x + 2 ) OR ( x - 2 )}[/tex]

Similarly, the next consecutive odd number will occcur two integers ahead or two integer before the second odd number OR four integers ahead of for integers before the first odd number. We can choose either ( ahead or before ) and express the third consecutive odd number in terms of first or second odd number as follows:

[tex]3rd\colon\text{ ( x + 4 ) OR ( x - 4 )}[/tex]

We will now sum up all three consecutive odd numbers and equate the result to ( -99 ) as follows:

[tex]\begin{gathered} (\text{ x ) + ( x + 2 ) + ( x + 4 ) = -99} \\ OR \\ (\text{ x ) + ( x - 2 ) + ( x - 4 ) = -99} \end{gathered}[/tex]

Then we will solve both possibilities step by step.

[tex]\begin{gathered} 3x\text{ + 6 = -99} \\ OR \\ 3x\text{ - 6 = -99} \\ \end{gathered}[/tex]

Then,

[tex]\begin{gathered} 3x\text{ = -105} \\ OR \\ 3x\text{ = -93} \end{gathered}[/tex]

Next,

[tex]\begin{gathered} x\text{ = }\frac{-105}{3}\text{ = -35} \\ \\ OR \\ \\ x\text{ = }\frac{-93}{3}\text{ = -31 } \end{gathered}[/tex]

For each possibilitiy the three consecutive odd numbers would be:

[tex]\begin{gathered} x\text{ = -35 , x + 2 = -33 , x + 4 = -31} \\ OR \\ x\text{ = -31 , x - 2 = -33 , x - 4 = -35} \end{gathered}[/tex]

We see that both possibilities result in identical three consecutive odd numbers that would add up to a total of ( -99 ). Therefore, the three consecutive odd numbers are:

[tex]-31\text{ , -33 , -35 }\ldots\text{ Answer}[/tex]

The volume of the tent is 576 cubic feet and the area of the base is 36 square feet. what is the height of the tebt

Answers

The volume of a triangular prism is: B*h. Where B is the area and h is the height.

Replacing the values in the equation we have:

V = B*h

576 = (36)*h

576/36 = h (Dividing by 36 on both sides of the equation)

16 = h (Dividing)

The answer is 16 ft.

Lesson 6.02: Finn's fish store has 5 tanks of goldfish; each tank holds 40 fish. He collects andinspects 5 fish from each tank and finds that 4 fish have fin rot. Find the estimated numbergoldfish in the store that have fin rot. SHOW ALL WORK!

Answers

Answer:

Explanation:

We are told that of each 5 fish inspected in the tank, 4 have fin rot, therefore, the probability o getting a fin rot is

[tex]\frac{4}{5}\times100\%=80\%[/tex]

This means 80% of the fish in a tank have fin rot.

Now, for one tank 80% of 40 fish is

[tex]\frac{80\%}{100\%}\times40=32[/tex]

Now, since there are 5 fish tanks in the store and 32 fish in each have fin rot; therefore, the total number of fish that have fin rot will be

[tex]32fish\times5=160\text{fish}[/tex]

Hence, the estimated number of fish with fish rot in the store is 160.

The fire department is having a BBQ fundraiser. The hot dogs costs $1.50 each and cans ofsoda cost $0.75 each. The department uses the algebraic expression 1.50x+0.75y to calculatecustomers' total expenses.a. What does the x variable represent?b. What does the y variable represent?c. A family buys 7 hot dogs and 4 sodas. What are their total expenses?

Answers

a) As the expression represents the total expense for a family, the term 1.50x represents how much the familiy spends in hot dogs.

This term is the product of the price (1.50) and the number of hot dogs purchased (x).

Then, x is the number of hot dogs bought by the familiy.

b) In the same way, 0.75y represent how much the family spends in soda: 0.75 is the price and y represents the number of soda cans purchased by the family.

c) If a family buys x=7 hot dogs and y=4 sodas, we can calculate the expenses as:

[tex]\begin{gathered} E=1.50x+0.75y \\ E=1.50\cdot7+0.75\cdot4 \\ E=10.5+3 \\ E=13.5 \end{gathered}[/tex]

Their total expenses are $13.5.

Other Questions
I need help with this question... the correct answer choice Elaine drives her car 50 miles and has an average of a certain speed. If the average speed had been 4mph more, she could have traveled 58 miles in the same length of time. What was her average speed? Question 1Use the chart to answer the following question:In which of the following countries are falling water tables causing a scarcity of fresh water? The hydrologic cycle is an open system in which water is moved from one _________ to another through __________. sue is 17 years old and believe she is overweight . Which would be the best strategy for maintaining her health? What is the best estimation of the equation [-? Drag the numbers into the boxes. Numbers may beused once, twice, or not at all.1142011/21/8 Andrei gauged the level of exposure to his marketing campaign using the percentage of the target population exposed at least once to his advertisement, representing its. Let f(x) = (5)2+1. Which is equal to f(-3)? find the measure of arc DB mDB = __ degrees simply what would be the effect on the melting point of a sample if it were not dried completely after filtering the recrystallized sample? The figure shows the layout of a symmetrical pool in a water park. What is the area of this pool rounded to the tens place? Use the value = 3.14. The circumference of a circle is 22 ft. What is the area, in square feet? Express your answer in terms of \pi. many stores, restaurants, and theaters offer discounts for college students who show their school id. why are these discounts for college students effective price discrimination, and why would this benefit firms? choose one or more: a.college students have a higher sensitivity to price than other adults do. b.college students are an easily identifiable group as they can prove their status with their student id. c.college students often buy goods that no one else buys. d.these goods are often consumed at the point of sale, which makes resale difficult. Can you help me please?A. How can Marc provide proof that his mighty shot actually hung in the air for 15 seconds? Or is this just another one of his lies?B. How long did the ball actually hang in the air? Deion measure the volume of a sink basin by modeling it as a hemisphere. Deion measures its diameter to be 28 3/4 inches. Find the sinks volume in cubic inches. Round your answer to the nearest tenth if necessary. what type of angle is angle 98 degrees what four things influence the way a member of congress votes? Six less than x equals twenty-two. a $20,000 bond has annual coupons and is redeemable at the end of 14 years for $22,600. it has a base amount equal to $18710 when purchased to yield 4%. find its base amount if it were to be purchased to yield 5% Lindsey bought a picnic basket originally priced at $40 but on sale for 50% off. After 10% sales tax, what was the total cost?$