A toy rocket is shot vertically into the air from a launching pad 3 feet above the ground with an initial velocity of 168 feet per second. The height​ h, in​ feet, of the rocket above the ground at t seconds after launch is given by the function h=−16t2+168t+3. How long will it take the rocket to reach its maximum​ height? What is the maximum​ height?

Answers

Answer 1

In linear equation,

The rocket will be reach its maximum​ height at t= 3 seconds.

The maximum height  'h' = 75

What in mathematics is a linear equation?

An algebraic equation B. y=mx+b (where m is the slope and b is the y-intercept) containing simple constants and first-order (linear) components, such as the following, is called a linear equation. The above is sometimes called a "linear equation in two variables" where x and y are variables.

                                  An equation with only one variable is called a univariate linear equation. It contains the expression Ax + B = 0. where A and B are any two real numbers and x is an ambiguous variable with only one possible value.  

Given the function 'h' = − 16t² +168t +3 ...(i)

Differentiating equation (i) with respective to 't' we get

  dh/dt = - 32t + 168

     - 32t + 168 = 0

             -32t = -168

                   t = 5.25

Again Differentiating equation (ii) with respective to 't' we get

       d²h/dt² = -32 (1)  < 0

The maximum height at t= 3

The rocket will be reach its maximum​ height at t= 3 second

The maximum height  

                       h = -16 (3)² + 168 (3) + 3

                             =   75

The rocket will be reach its maximum​ height at t= 3 seconds

The maximum height  'h' = 75

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Related Questions

Leo has a bag of dimes and quarters. He has a total of 29 coins worth $4.70. Let x represent the number of dimes and y represent the number of quarters. Which system of equations would be used to find out how many dimes and quarters Leo has?

{x+y=290.1x+0.25y=4.7

{y=x+29x+y=4.7

{x=29−yx+y=4.7

{x+y=4.70.1x+0.25y=29

(60 points)

Answers

Answer:

x+y=29

0.1x+0.25y=4.7

Step-by-step explanation:

- x+y=29 (x is the number of dimes and y is the number of quarters. there is a total of 29 coins)

- Each dime is $0.1 and each quarter is $0.25.

- By multiplying the number of dimes by $0.1 and multiplying the number of quarters by $0.25, you will get the total amount of money, which is $4.7. - - Therefore, the answer is:

x+y=29

0.1x+0.25y=4.7

Hope this helps! :) I also took the K12 quiz, here is proof that this is right:

Leo has a bag of dimes and quarters. He has a total of 29 coins worth $4.70. Let x represent the number

The diagram below is an oblique, or slanted, rectangular prism. Not all angles shown are 90 degrees. Complete the following sentence.

The diagram below is an oblique, or slanted, rectangular prism. Not all angles shown are 90 degrees.

Answers

Answer:

Oblique rectangular prism

exercise 5.3.9. assume f and g are as described in theorem 5.3.6, but now add the assumption that f and g are differentiable at a, and f′ and g′ are continuous at a with g′(a)

Answers

To prove the 0/0 case of L'Hospital's Rule under the stronger hypothesis, where f and g are differentiable at a, and f' and g' are continuous at a with g'(a) ≠ 0:

The given functions in the form of a limit:

  lim(x → a) f(x)/g(x)

Applying  the Mean Value Theorem to f(x) and g(x) within the interval [a, x]:

  f(x) - f(a) = f'(c)(x - a), where c is between a and x

  g(x) - g(a) = g'(d)(x - a), where d is between a and x

Rearranging the equation:

  f(x) = f(a) + f'(c)(x - a)

  g(x) = g(a) + g'(d)(x - a)

lim(x → a) [f(a) + f'(c)(x - a)]/[g(a) + g'(d)(x - a)]

Dividing the numerator and denominator by (x - a):

  lim(x → a) [f(a)/(x - a) + f'(c)][g(a)/(x - a) + g'(d)]

Taking the limit as x approaches a:

  lim(x → a) [f(a)/(x - a) + f'(c)][g(a)/(x - a) + g'(d)] = f(a)/a + f'(c)g(a)/a + f(a)g'(d)/a + f'(c)g'(d)

Since f(a)/a and g(a)/a are constants, their limits as x approaches a are simply f(a)/a and g(a)/a respectively. Also, f'(c) and g'(d) are continuous at a.

Therefore, taking the limit as x approaches a, the expression simplifies to:

  f(a)/a + f'(a)g(a)/a + f(a)g'(a)/a + f'(a)g'(a)

  f(a)g'(a) + f'(a)g(a)/a

Divide the expression by g'(a):

  [f(a)g'(a) + f'(a)g(a)]/g'(a)

This gives us the final form of the expression, which is the derivative of f(x) divided by the derivative of g(x):

  [f(a)g'(a) + f'(a)g(a)]/g'(a) = [f'(a)g(a) + f(a)g'(a)]/g'(a)

On comparing the statement of L'Hospital's Rule, we can see that the 0/0 case holds true under the given stronger hypothesis.

Therefore, we have proven the 0/0 case of L'Hospital's Rule under the stronger hypothesis where f and g are differentiable at a, and f' and g' are continuous at a with g'(a) ≠ 0.

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The complete question is:

Assume f and g are as described in Theorem 5.3.6, but now add the assumption that f and

g are differentiable at a, and f ′ and g′ are continuous at a with g′(a) 6 = 0. Find a short proof

for the 0/0 case of L’Hospital’s Rule under this stronger hypothesis.

Hewwo!
\( \underline{ \underline{ \bf{Question}}} : \) In a circle of radius 5 cm , AB and CD are two parallel chords of length 8 cm and 6 cm respectively. Calculate the distance between the chords , if they are :
i. on the same side of the centre
ii. on the opposite side of the centre
*Show your workings!

Answers

Answer:

AB=8cm⇒AE=4cmCD=6m⇒CF=3cmIn△AEDAE=4cm,AO=5cmOE=(AO)2−(AE)2=52−42=3cmIn△OFCCF=3cm,CO=5cmOF=OC2−CF2=52−32=4cm

∴ Distance between the chords=4cm−3cm=1cm

Answer:

I) 1 cm

II) 7 cm

Step-by-step explanation:

We are given a circle with a radius of 5 cm. AB and CD are two parallel chords of length 8cm and 6cm respectively. And we want to calculate the length of the chords if they are:

I) On the same side of the center.

Please refer to the first figure.

In it, O is the center, AB measures 8 and CD measures 6.

To find the distance between the two chords, we essentially need to find KJ, which is OJ - OK.

We will construct a segment from O to K and from K to J. This is perpendicular to the chords. Therefore, by the Perpendicular Bisector Theorem, it also bisects the chords.

ΔAOK is a right triangle. Therefore:

\(AO^2=OK^2+KA^2\)

AO is simply the radius.

KA is half the length of AB since OK perpendicularly bisects the chord.

Therefore:

\((5)^2=OK^2+(4)^2\)

So:

\(25=OK^2+16\Rightarrow OK^2=9\Rightarrow OK=3\)

Likewise, ΔCOJ is also a right triangle. Therefore:

\(CO^2=OJ^2+JC^2\)

CO is the radius, and JC will be half the length of CD. Thus:

\((5)^2=OJ^2+(3)^2\Rightarrow OJ^2=16\Rightarrow OJ=4\)

Therefore, the distance KJ between the two chords are:

\(KJ= OJ-OK=4-3=1\text{ cm}\)

II) On opposite sides of the center.

Please refer to the second figure.

Again, O is the center, AB measures 8, and CD measures 6.

Likewise, segments OK and OJ are perpendicular bisectors of AB and CD, respectively.

And to find the distance, we essentially need to find JK or OJ + OK.

ΔKOB is a right triangle. Thus:

\(OB^2=OK^2+KB^2\)

OB is the radius, and KB is half of AB:

\((5)^2=OK^2+(4)^2\Rightarrow OK=3\)

ΔJOD is also a right triangle. Thus:

\(OD^2=OJ^2+JD^2\)

OD is the radius and JD is half of CD:

\((5)^2=OJ^2+(3)^2\Rightarrow OJ=4\)

Therefore, the distance between the two chords are:

\(JK=OJ+OK=4+3=7\text{ cm}\)

Hewwo! [tex] \underline{ \underline{ \bf{Question}}} : [/tex] In a circle of radius 5 cm , AB and CD
Hewwo! [tex] \underline{ \underline{ \bf{Question}}} : [/tex] In a circle of radius 5 cm , AB and CD

If a rectangle has a length of 3.5 meters and a width of 6.5 meters, what is the perimeter?

Answers

Answer:

20 meters it asking my to write more stuff but I don't know

What’s the answer for 350÷10*3

Answers

35/5, 11.repeating decimals of 6, 11 2/3

One of the tables shows a proportional relationship.

Graph the line representing the proportional relationship from this table.

Keyboard Instructions
Initial graph state
The horizontal axis goes from -10.8 to 10.8 with ticks spaced every 1 unit(s).
The vertical axis goes from -10.8 to 10.8 with ticks spaced every 1 unit(s).
x 1 2 3 5
y 2 3 4 6


x 2 4 6 8
y 0 2 3 4


x 0 2 4 6
y 1 3 5 7


x −2 1 2 3
y −6 3 6 9

Answers

Two variables are primarily linked when there is a proportionate relationship, which means that as 1 variable rises or falls, the other rises or falls at the same rate.

What factors determine if one relationship is proportional?

The ratios between both the two variables should be considered in order to determine whether a relationship is proportional. The relation is proportional if the ratio remains constant. The relationship is indeed not proportional if the ratio shifts.

What are the two proportional relationships principles?

When two or more items are directly proportionate or change in size according to equivalent ratios, the relationship is said to be proportional. This proportional relationship can be expressed using the formula y = kx.

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Answer:

Two variables are primarily linked when there is a proportionate relationship, which means that as 1 variable rises or falls, the other rises or falls at the same rate.

What factors determine if one relationship is proportional?

The ratios between both the two variables should be considered in order to determine whether a relationship is proportional. The relation is proportional if the ratio remains constant. The relationship is indeed not proportional if the ratio shifts.

What are the two proportional relationships principles?

When two or more items are directly proportionate or change in size according to equivalent ratios, the relationship is said to be proportional. This proportional relationship can be expressed using the formula y = kx.

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Step-by-step explanation:

Is there a proportional relationship between time and the cost of the cell phone plan?

Answers

Answer:

no

Step-by-step explanation:

If a random sample of five households is selected, is it valid to use the Central Limit Theorem to describe the sampling distribution of the sample mean? Explain.

Answers

Yes, it is valid to use the Central Limit Theorem (CLT) to describe the sampling distribution of the sample mean, even for a random sample of five households. Although a sample size of five is relatively small, the CLT still applies as long as the sample is random and independent.

  The Central Limit Theorem is a fundamental concept in statistics that states that, under certain conditions, the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.

While a sample size of five may be considered small, the CLT still holds for this case. The key consideration is that the sample is selected randomly and each observation is independent of the others. As long as these conditions are met, the CLT can be applied, even for small sample sizes.

In practice, larger sample sizes are generally preferred to ensure better approximation to the normal distribution. However, the CLT provides a theoretical foundation for the validity of using the normal distribution as an approximation for the sampling distribution of the sample mean, even with relatively small sample sizes like five households.

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You have attempts remaining Mr. Wutz owns hot dog business named 'Wutz upDogs.' The daily profit function, dollars; when hot = dogs= are sold given (65' 7)(s? by P(e) Evaluate P' (6). P'(5) dollars per hot Jop

Answers

The value of P'(5) = 65 and  P'(6) = 65.

Mr. Wutz owns a hot dog business called 'Wutz upDogs.' The daily profit function is given by P(x) = 65x + 7, where x is the number of hot dogs sold.

To evaluate P'(6), the derivative of P(x) at x = 6, we need to use the power rule for derivatives. The power rule states that d/dx(xn) = nxn-1. Therefore, P'(6) = 65(6)1 = 65 dollars per hot dog.

To evaluate P'(5), the derivative of P(x) at x = 5, we use the same power rule. Therefore, P'(5) = 65(5)1 = 65 dollars per hot dog.

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Find EF. Please help!

Find EF. Please help!

Answers

Answer:

EF = 7 + 39 = 46

Step-by-step explanation:

EF = FG

x + 39 = 7x - 3

39 + 3 = 7x - x

42 = 6x

x = 42/6

x = 7

hope this helps :)

Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.

Answers

Therefore , on solving the provided question we can say that inequality will be  x < 2.2727272727 .

What is inequality?

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two variables values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality.

Here,

Given :

the inequality will be

=> 3(2x – 5) < 5(2 – x)

=> 6x - 15 < 10-5x

=> 11x < 25

=> x < 2.2727272727

Thus ,

x < 2.27

Therefore , on solving the provided question we can say that inequality will be  x < 2.2727272727 .

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The complete question is " Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left. "

Enter the slope-intercept equation of the line shown below.​

Enter the slope-intercept equation of the line shown below.

Answers

Answer:

m=3

Step-by-step explanation:

Go up 3 and across one to find the slope from the points given.

Answer:

m=3

Step-by-step explanation:

Give the other guy brainliest :)

Which diagram best represents the relationship among integers, rational numbers, and whole
numbers?

Which diagram best represents the relationship among integers, rational numbers, and wholenumbers?

Answers

Answer:

Step-by-step explanation:

I think it the choice of A and D

What are the domain and range of the logarithmic
function f(x) = log7X? Use the inverse function to
justify your answers.

Answers

Answer:

The domain of f is x > 0.

The range of f is all real numbers.

The domain of the inverse function is all real numbers.

The range of the inverse function is y > 0.

The domain of f is the same as the

range of the inverse function.

The range of f is the same as the

the domain of the inverse function.

Step-by-step explanation:

this is the sample answer, make sure you rewrite in your own words!

The domain and the range of a function are the set of input and output values of the function

The domain and the range of the function are set of real numbers greater than 0

The function is given as:

\(f(x) = log_7(x)\)

The above function is a logarithmic function.

From the properties of a logarithmic function, we have:

The x-values are always greater than 0The y-values are always greater than 0

This means that, the domain and the range of the function are set of real numbers greater than 0

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helppppp this is very hard

helppppp this is very hard

Answers

Answer: \(135cm^{3}\)  

Step-by-step explanation:

1: Cut the shape into two rectangular prisms.

2: First prism is 7 x 3 x 5 = 105

3: Second prism is 5 x 2 x 3 = 30

4: Add the first prism to the second prism

   105 + 30 = \(135cm^{3}\)

I hope this helped!

Answer:

135 cm³

Step-by-step explanation:

find the volume of the two parallelepipeds and add them

5*2*3 + 7*3*5 =

30 + 105 =

135 cm³

U/3=-8. What does U stand for? Need answer within 5 minutes pls

Answers

Answer:

-24

Step-by-step explanation:

\( \frac{u}{3} = - 8\)

\( \frac{u}{3} \times 3 = - 8 \times 3\)

\(u = - 24\)

Rewrite the equation 6x + 2y = 10 in slope-intercept form.

Answers

Y=3x+5 I'm pretty sure that's the answer

Select the graph that would represent the best presentation of the solution set. 4x-2<10

Answers

The solution set for the inequality 4x - 2 < 10 is x < 3.

What is inequality?

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
To solve the inequality 4x - 2 < 10, we need to isolate the variable x on one side of the inequality sign.

First, we add 2 to both sides of the inequality to get:

4x - 2 + 2 < 10 + 2

Simplifying, we get:

4x < 12

Next, we divide both sides of the inequality by 4 (since 4 is positive and we are not multiplying or dividing by a negative number) to get:

x < 3

Therefore, the solution set for the inequality 4x - 2 < 10 is x < 3.

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Select the graph that would represent the best presentation of the solution set. 4x-2&lt;10

Helppp!!!!!!!!!!!!!!!!!!!!!

Helppp!!!!!!!!!!!!!!!!!!!!!

Answers

The value of x is equal to 15°

How to determine the value of x?

In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

By substituting the given parameters, we have the following:

3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.

3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.

23x + 15 = 360°.

23x = 360 - 15

23x = 345

x = 345/23

x = 15°.

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A recipe for pizza sauce calls for 11 cans of tomatoes and 44 teaspoons of oregano. How many teaspoons of oregano would you need for a single can of tomatoes?

Answers

Answer:

One can of tomatoes needs 4 teaspoons of oregano.

Step-by-step explanation:

\(\frac{11}{44}\) = \(\frac{1}{x}\)  Cross multiply and solve for x

11x = 44  Divide both sides by 11

x = 4

One can of tomatoes needs 4 teaspoons of oregano.

The following table shows the salary of 7 people in an office last year. Name Income Andy £9500 Bevan £30000 Cheryl £11250 Deva £72000 Elliott £12750 Frankie £29500 Grace £11000 a) Work out the mean income to 2 DP. b) Deva was given a large bonus for 30 years service. Excluding Deva's income, what was the mean income for the remaining 6 workers to 2 DP?

Answers

a) The mean income to 2 DP is £23714.28. b. If Deva's income is excluded, then the mean income will be £16,500.

What is addition?

The addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.

a.

Andy = £9500

Bevan = £25000

Cheryl = £11250

Elliott = £12750

Frankie = £29500

Grace = £11000

Deva = £72000

Total Income = £166,000

To get the mean Income, we will divide the total income by 6 which is the number of people.

= £166,000/7

= £23714.28

b. If Deva's income is excluded, there'll be 6 people left.

Total income = £99000

Mean income = £99,000/6

= £16,500

a) The mean income to 2 DP is £23714.28. b. If Deva's income is excluded, then the mean income will be £16,500.

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There are 42 runners in a race.   How many different ways can the runners finish first, second, and third?

Answers

Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

A teacher claims that the relationship between
number of hours studied for a test and test score can be
described by g(x) = 45 + 9x, where x represents the
number of hours studied. Graph this function

Answers

The graph representing the given function g(x) = 45 + 9x is as drawn in the attachment.

How to draw a Linear Equation Graph?

We are given the equation of line as;

g(x) = 45 + 9x

Where;

x represents the number of hours studied.

g(x) represents the test score

Thus, to plot this graph, we need to input some x values and find their corresponding g(x) values

At x = -10;

g(x) = 45 + 9(-10)

g(x) = -45

At x = -1;

g(x) = 45 + 9(-1)

g(x) = 35

At x = 0;

g(x) = 45 + 9(0)

g(x) = 45

At x = 1;

g(x) = 45 + 9(1)

g(x) = 54

At x = 2;

g(x) = 45 + 9(2)

g(x) = 63

At x = 3;

g(x) = 45 + 9(3)

g(x) = 72

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A teacher claims that the relationship betweennumber of hours studied for a test and test score can bedescribed

Sam has 30.00 in his checking account and earns 8.00 per week as a allowance how many weeks will it take Sam to earn 78.00

Answers

It will take Sam 6 weeks

Answer:

6 weeks

Step-by-step explanation:

end goal = $76

how much he has in the bank = $30

how much he earnes per week = $8

first, subtract 30 from 78 to figure out how much he has left to ear:

$78 - $30 = $48

then take the difference and divide it by 8 since he earned $8 per week:

48 ÷ 8 = 6

It will take him 6 remaining weeks to complete his end goal.

A, B and C lie on a straight line.
Given that angle
y
= 135° and angle
z
= 103°, work out
x
.

Answers

Answer:

x = 42

Step-by-step explanation:

a striaght line = 180°

z + y + x = 180

103 + 135 + x = 180

138 + x = 180

subtract 138 from both sides

138 - 138 + x = 180 - 138

x = 42

Answer:

what shape it is

Step-by-step explanation:

wat is the shape

help if you can asap pls!!!!!

help if you can asap pls!!!!!

Answers

The relationship between DE and AC, considering the triangle midsegment theorem, is given as follows:

DE is half of AC.DE and AC are parallel.

What is the triangle midsegment theorem?

The triangle midsegment theorem states that the midsegment of the triangle divided the length of the midsegment of the triangle is half the length of the base of the triangle, and that the midsegment and the base are parallel.

The parameters for this problem are given as follows:

Midsegment of DE.Base of AC.

Hence the correct statements are given as follows:

DE is half of AC.DE and AC are parallel.

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Find the area of the shaded segment of the circle

Find the area of the shaded segment of the circle

Answers

The area of the shaded segment of the circle is 55.9 cm².

Given that a sector in the circle having the central angle = 90° with the radius = 14 cm.

We need to find the area of the segment which is shaded.

So, for finding the same, we will find the area of the sector and then the right triangle formed by the radii and the chord.

Area of the sector = 1/4 × π × radius²

= 1/4 × 3.14 × 14²

= 153.86 cm²

Area of the triangle = 1/2 × base × height

= 1/2 × 14 × 14

= 98 cm²

Area of the segment = 153.86 - 98 ≈ 55.9 cm²

Hence, the area of the shaded segment of the circle is 55.9 cm².

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i think it’s #1 but what’s the work?

i think its #1 but whats the work?

Answers

You have to divide first then subtract
You correct the answer is 1

Because sin^-1(-2/5)=-23.578
Plug in cot theta = -2.29
which is approximately equal to 1

So you are right option 1 is correct



2. What is the center of dilation and the scale factor of the dilation of ABCD to EFGH?

2. What is the center of dilation and the scale factor of the dilation of ABCD to EFGH?

Answers

Answer:

The center of dilation of ABCD to EFGH is (0, 0), and the scale factor is 4/3

Other Questions
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