Help with this question

The height of the toy is an illustration of the height function

The given parameters are:

The function of the height is calculated as:

h(t) = -16t² + Vot + H

This gives

h(t) = -16t² + 200t + 50

Hence, the velocity function is h(t) = -16t² + 200t + 50

In (a), we have:

h(t) = -16t² + 200t + 50

Differentiate

h'(t) = -32t + 200

Set to 0

-32t + 200 = 0

Subtract 200 from both sides

-32t = -200

Divide both sides by -32

t = 6.25

Substitute 6.25 for t in h(t)

h(6.25) = -16 *6.25² + 200 * 6.25 + 50

h(6.25) = 675

Hence, the time to reach the maximum height is 6.25 seconds and the maximum height is 675 feet

This is represented as

h(t) >300

So, we have:

-16t² + 200t + 50 > 300

Subtract 300 from both sides

-16t² + 200t - 250 > 0

Using a graphical calculator, we have:

t = 11.09s and t = 1.41 s

Hence, the rocket will be at a height more than 300 at 11.09s and 1.41 s

This means that

h(t) = 0

So, we have:

-16t² + 200t + 50 = 0

Using a graphical calculator, we have:

t = 12.75

Hence, the rocket will hit the ground at 12.75s

Read more about height function at:

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f(x+1)

Answer:

(5, 5) and (6, 1)

Step-by-step explanation:

Solutions to the system of inequalities are any points that are in the overlapped shaded region.

For example (5, 5) and (6, 1)

Find the equations of the two lines.

Blue line

Two points on the line: (-5, 8)  and  (0, -7)

[tex]\implies \sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{-7-8}{0-(-5)}=-3[/tex]

Point-slope form of linear equation:  [tex]\sf y-y_1=m(x-x_1)[/tex]

(where m is the slope and (x₁, y₁) is a point on the line)

[tex]\implies \sf y-(-7)=-3(x-0)[/tex]

[tex]\implies \sf y=-3x-7[/tex]

As the shading is above the line, and the line is dashed:

[tex]\sf y > -3x-7[/tex]

Red line

Two points on the line:  (0, -9)  and  (2, 1)

[tex]\implies \sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{1-(-9)}{2-0}=5[/tex]

Point-slope form of linear equation:  [tex]\sf y-y_1=m(x-x_1)[/tex]

(where m is the slope and (x₁, y₁) is a point on the line)

[tex]\implies \sf y-(-9)=5(x-0)[/tex]

[tex]\implies \sf y=5x-9[/tex]

As the shading is below the line, and the line is solid:

[tex]\sf y\leq 5x-9[/tex]

[tex]\sf Inequality\:1: y > -3x-7[/tex]

[tex]\sf Inequality\:2:y\leq 5x-9[/tex]

Point (5, 5)

[tex]\sf Inequality\:1\implies -3(5)-7=-22 < 5\: \implies\:true[/tex]

[tex]\sf Inequality\:2\implies 5(5)-9=16 > 5\: \implies\:true[/tex]

Point (6, 1)

[tex]\sf Inequality\:1\implies -3(6)-7=-25 < 1\: \implies\:true[/tex]

[tex]\sf Inequality\:2\implies 5(6)-9=21 > 1\: \implies\:true[/tex]

Answer: question 1 equals 31 Over 8 or 3.875 .

question 2 equals 425 over 24 .

question 3 equals 41 over 6 or 6.83333333

question 4 equals 55 Over 14

Step-by-step explanation: hope it helps you .

Answer:

[tex]x=20\\\\m\angle B = 92^{\circ}\\\\m\angle C = 40^{\circ}[/tex]

Step by step explanation:

[tex]~~~m\angle A +m\anglee B + m\angle C =180^{\circ}\\\\\implies 48+6x-28+2x = 180\\\\\implies 8x +20 = 180\\\\\implies 8x = 180 -20 = 160\\\\\implies x = \dfrac{160}8=20\\\\\\m\angle B = (6x -28)^{\circ} = (6\cdot 20 -28)^{\circ}=92^{\circ}\\\\m\angle C = (2x)^{\circ} = (2\cdot 20)^{\circ}=40^{\circ}[/tex]

[tex]\textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ \theta =2\\ s=99 \end{cases}\implies 99 = r(2)\implies \cfrac{99}{2}=r\implies 49.5=r[/tex]

Answer:

56

Step-by-step explanation:

1) Add together all numbers. 30+45+50+75+80 = 280.

2) Divide result by amount of numbers. 280/5 = 56

3) You are welcome. :)

On an average, you sold 56 unit per, day.

A number that is calculated by adding quantities together and then dividing the total by the number of quantities.

Given that, Last week you sold 30, 45, 50, 75, and 80 units each day of the week.

To find the average, we will, first add together all numbers and then divide the result by the sum of numbers.

Therefore,

Adding together all numbers = 30+45+50+75+80 = 280.

Divide result by amount of numbers =  280/5 = 56

Hence, On an average, you sold 56 unit per, day.

For more references on average, click;

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#SPJ2

Answer: 10, And i dont know how to really explain but the answer is 10

Answer:

B. megalopolis

Step-by-step explanation:

Hope it helps you in your learning process.

Answer:

its A and D dont listen to the other person lol

W

Answer:

C) $0.28 per packet

Step-by-step explanation:

I divided them to find how much each packet costs

Each pack of watermelon costs $0.76
Each pack of tomato seed packet costs 0.48

Subtract and you have your answer!

0.76 - 0.48 = 0.28

Answer:

The answer is 65

Step-by-step explanation:

As تھ measure of angles of rectangle is 90

So 90-25 is equal to 65

Answer:

p = 1.26

Step-by-step explanation:

We know that the total weight (p) is going to be split equally (divided) by 3.

We also know that divided weight will be equal to 0.42 pounds.

p / 3 = 0.42

To solve:

multiply both sides by 3 to cancel the division by 3

p = 1.26

To test this you could divide 1.26 by 3 again to get 0.42

Answer:

4:7

Step-by-step explanation:

4:7 is the same as 4/7

Answer:

Step 1. Plot x and y-intercepts

Step 2. Draw a line through the points

m, rise over run = -1/2

b, y-intercept = (0, -2)

x-intercept = (-4, 0)

m, rise over run = -1/3

b, y-intercept = (0, -4)

x-intercept = (-12, 0)

Hope this helps! Good luck!

Answer:

48

Step-by-step explanation:

180 is the whole thing

So add 25 and 107 to make 132, then 180-132

Explanation:

The N stands for Pi so when you type in the answers to Khan Academy use the Pi symbol when theres an N! These are the common questions and common radius Khan Academy gives when they ask to find the radius of the circle.

Answers:

For 4 - 267.95  

For 1/4 - 1/48n  

For 1 - 4/3n    

For 9 - 972n

For 7 - 1372/3n

For 6 - 288n

For 3 - 36n

For 10 - 4000/3n

For 8 - 2048/3n

For 1/2 - 1/6n

For 5 - 500/3n

For 2 - 33.49

Step-by-step explanation:

I did the go math so all of these rights and the majority of the answers are the questions Khan Academy will ask you to find the radius of the circle.

f(x) = (2x³ + 1 + x²)/(x² + 9) as a sum of two functions g(x) and h(x), where g is an odd function and h is an even function is f(x) = 2x³/(x² + 9)  + (1 + x²)/(x² + 9).

To answer the questions, we need to know what functions are

A function is a mathematical expression that shows the relationship between two variables.

Since f(x) = (2x³ + 1 + x²)/(x² + 9).

Its odd part g(x) = [f(x) - f(-x)]/2

So, g(x) =  [f(x) - f(-x)]/2

= [(2x³ + 1 + x²)/(x² + 9) - (2(-x)³ + 1 + (-x)²)/((-x)² + 9)]/2

= [(2x³ + 1 + x²)/(x² + 9) - (-2x³ + 1 + x²)/(x² + 9)]/2  

= (2x³ + 1 + x² + 2x³ - 1 - x²)/2(x² + 9)  

= 4x³/2(x² + 9)  

g(x) = 2x³/(x² + 9)  

Its even part h(x) = [f(x) + f(-x)]/2

So, h(x) =  [f(x) + f(-x)]/2

= [(2x³ + 1 + x²)/(x² + 9) + (2(-x)³ + 1 + (-x)²)/((-x)² + 9)]/2

= [(2x³ + 1 + x²)/(x² + 9) + (-2x³ + 1 + x²)/(x² + 9)]/2  

= (2x³ + 1 + x² - 2x³ + 1 + x²)/2(x² + 9)  

= 2(1 + x²)/2(x² + 9)  

h(x) = (1 + x²)/(x² + 9)

So, f(x) = g(x) + h(x)

f(x) = 2x³/(x² + 9)  + (1 + x²)/(x² + 9)  

So, f(x) = (2x³ + 1 + x²)/(x² + 9) as a sum of two functions g(x) and h(x), where g is an odd function and h is an even function is f(x) = 2x³/(x² + 9)  + (1 + x²)/(x² + 9).

Learn more about odd and even functions here:

https://brainly.com/question/26322830

Answer:

[tex]g(x)=\frac{2x^{3} }{x^{2} -9}[/tex]

[tex]h(x)=\frac{x^{2}+1 }{x^{2} -9}[/tex]

Step-by-step explanation:

'x² - 9' is an even.

Break up the numerator into odd an even parts to get your answer.

'2x³' is odd and 'x² + 1' is even.

[tex]g(x)=\frac{2x^{3} }{x^{2} -9}[/tex]

[tex]h(x)=\frac{x^{2}+1 }{x^{2} -9}[/tex]

The value of x, y and z from the system of equation are -1, -8 and 5 respectively.

Data;

To solve this problem, we have to solve the system of equation using substitution method.

From equation (iii)

[tex]2z = 10\\z = 5[/tex]

let us substitute the value of z into equation (ii)

[tex]-3y + 7z = 59\\z = 5\\-3y + 7(5) = 59\\-3y + 35 = 59\\-3y = 59 - 35\\-3y = 24\\y = -8[/tex]

Let's substitute the value of x and y into equation (i)

[tex]-2x + 6y + 3z = -31\\y = -8, z = 5\\-2x + 6(-8) + 3(5) = -31\\-2x - 48 + 15 = -31\\-2x - 33 = -31\\-2x = -31 + 33\\-2x = 2\\x = -1[/tex]

From the calculation above, the value of x, y and z are -1, -8 and 5 respectively.

Learn more on system of equations here;

https://brainly.com/question/14323743

Answer:

1 hour=55 miles

Step-by-step explanation:

Answer:

55 mph

Step-by-step explanation:

605 miles/11 hours

605/11 mph

55 mph

Hope this helps!

=================================================

Explanation:

Refer to the figure below.

Focus on triangle ABF. Angle AFB = 40 is marked in red. Angle BAF = 90 is marked in blue. The missing angle is 180-90-40 = 50 which is angle ABF.

Inscribed angle ABF = 50 doubles to arc AC since this inscribed angle subtends the arc in question. I'm using the inscribed angle theorem.

arc AC = 2*(angle ABF) = 2*50 = 100 degrees

Note: We don't need the fact that angle AGD = 86

[tex]\begin{array}{lcccl} &\stackrel{solution}{gallons}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{gallons of }}{pure~alcohol}\\ \cline{2-4}&\\ \textit{25\% solution}&x&0.25&0.25x\\ \textit{5\% solution}&y&0.05&0.05y\\ \cline{2-4}&\\ mixture&20&0.08&1.6 \end{array}~\hfill \begin{cases} ~\hfill x + y &= 20\\\\ 0.25x+0.05y&=1.6 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{x+y=20\implies \underline{y = 20-x}} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{0.25x~~ + ~~0.05(\underline{20-x})~~ = ~~1.6}\implies 0.25x+1-0.05x=1.6 \\\\\\ 0.20x+1=1.6\implies 0.2x=0.6\implies x=\cfrac{0.6}{0.2}\implies \boxed{x=3}[/tex]

In a trapezoid, the segment at the midpoint is the average of the other two bases.

In other words: YZ = (QR + TS) / 2

5x + 1 = ( (2x + 7) + 19 ) / 2

2(5x + 1) = 2x + 26

10x + 2 = 2x + 26

8x = 24

x = 3

YZ = 5x + 1

YZ = 5(3) + 1

YZ = 15 + 1

YZ = 16

Hope this helps!

Answer:

$25.40

Step-by-step explanation:

Find the unit price. So what you do is just divide 304.80 by 12 to get the price of one which comes out to be $25.40

Using proportions, it is found that her discount is of $0.29664.

A proportion is a fraction of a total amount.

In this problem, the total amount she spent on gas is given by:

T = $45.23 + $102.34 + $13.67 + $34.56 + $48.72 + $52.12 = $296.64.

Considering that she receives ten cents off per gallon on gas for every $100 she spends, we apply the proportion to find that her discount is given by:

[tex]D = 0.1 \times \frac{296.64}{100} = 0.29664[/tex]

Her discount is of $0.29664.

More can be learned about proportions at https://brainly.com/question/24372153

-7 + 4(n-1).  Use this and plug in 10 for n, making it

-7 + 4(9)

-7+36

29

Answer:

circumference = 31.43 cm

Step-by-step explanation:

circumference = 2πr = 2 × 22/7 × 5 = 220/7

= 31.43 cm

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's find the circumference of given circle ~

[tex]\qquad \tt\dashrightarrow \:c =2 \pi r[/tex]

where,

now, let's calculate circumference ~

[tex]\qquad \tt  \dashrightarrow \:c = 2 \times \pi \times 5[/tex]

[tex]\qquad \tt  \dashrightarrow \:c = 10 \pi \: \: cm[/tex]

Now, let's plug in approximate value of pi :

[tex]\qquad \tt  \dashrightarrow \:c = 10\times 3.14 \: \: [/tex]

[tex]\qquad \tt \dashrightarrow \:c = 31.4\: \: cm[/tex]

We have been provided with the total surface area of cube that is 150cm².

So here we will first find out the value of a side of cube.

★ Total surface area of cube :-

Here,

Putting the values,

6a² = 150cm²

a² = 150 / 6

a² = 50 / 2

a² = 25

a = √25

a = 5

Henceforth,

★ Finding out volume of cube :-

As we know that volume of cube is calculated by the formula :

Putting the values,

V = 5³

V = 5 × 5 × 5

V = 25 × 5

V = 125

Henceforth,