A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 40 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(t) = -16t²+40t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at ___ second(s) after launch.
(Simplify your answer.)

The number of hours at which both companies' rental costs will be the same is nearly 6 hours.

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign. It shows that the expressions displayed on the left and right sides have an equal connection. To determine the value of an unknown variable that stands in for an unknown quantity, equations can be solved.

Let the number of hours = h The deposit price at the first canoe rental company = $10

Cost per hour to rent a canoe = $8.25/h

The total cost for rental for the first company is given by

C(A) = 10 + 8.25h

The deposit price at the second canoe rental company = $12.50

Cost per hour to rent a canoe = $7.85/h

The total cost for rental for the second company is given by

C(B) = 12.50 + 7.85h

The number of hours at which both company's rental costs will be the same is given as

C(A) = C(B)

10 + 8.25h = 12.50 + 7.85h

8.25h - 7.85h = 12.50 - 10

0.4h = 2.5

h = 2.5/0.4

h = 6.25

h ≈ 6 hours

To know more about equations, visit:

https://brainly.com/question/1529522

#SPJ13

The solution of the system of equations using substitution is, (2500, 5).

What is substitution method?

In the "by substitution" method, one of the equations is solved for one of the variables (you choose which one), which is then plugged back into the other equation where the chosen variable is "substituted" for and the second equation is then solved for. The first variable is then back-solved.

The equations are,

d = 200m + 1500             ..(1)

d = 500m                         ..(2)

Substitute d = 500m in equation (1),

500m = 200m + 1500

300m = 1500

      m = 5

Plug m = 5 in equation (2),

d = 500(5) = 2500

Hence, the solution of the system of equations using substitution is, (2500, 5).

To know more about the substitution method, click on the link

https://brainly.com/question/22340165

#SPJ1

Answer:

(x +5)/-16=-1 this is the answer

Answer:

the answer is 100...........

Answer:

C

Step-by-step explanation:

the directrix and focus are equidistant from the vertex

vertex = (0, 1 ) and focus = (0, - 2 ) then directrix is a horizontal line above the vertex with equation

y = 4

the focus and directrix are equidistant from any point (x, y ) on the curve.

using the distance formula

[tex]\sqrt{x-0)^2+(y-(-2))^2}[/tex] = | y - 4 |

[tex]\sqrt{x^2+(y+2)^2}[/tex] = | y - 4 | ( squaring both sides )

x² + (y + 2)² = (y - 4)²

x² + y² + 4y + 4 = y² - 8y + 16 ( subtract y² from both sides )

x² + 4y + 4 = - 8y + 16 ( add 8y to both sides )

x² + 12y + 4 = 16 ( subtract x² + 4 from both sides )

12y = - x² + 12 ( divide through by 12 )

y = - [tex]\frac{1}{12}[/tex] x² + 1

Answer: Y = -[tex]\frac{1}{12}[/tex][tex]x^{2}[/tex] + 1

Step-by-step explanation: Correct on Edmentum

A. The equation that represents the situation is $9.98 = c + $2.47

B. The solution using a related equation $.7.51

C. The solution of the equation represents the initial cost of the toy before the increment of price.

Equation:

Basically, the equation means the mathematical statement that is made up of two expressions connected by an equal sign.

Given,

Because it is popular, a store owner increases the cost of a toy by $2.47. The new cost of the toy is $9.98.

Here we need to find the following:

A. The equation that represents the situation

B. The solution using a related equation

C. The solution of the equation represent.

Here we know that the new cost of the toy is equal to the original cost of the toy plus the amount by which cost was increased.

So, the equation is written as,

=> New cost of the toy = original cost + amount of increase

=> $9.98 = c + $2.47

Here we need to determine the value of c, make c the subject of the formula by combining similar terms

So, the equation is rewritten as,

=> c = $9.98 - $2.47

=> c = $7.51

Therefore, the initial cost of the toy is $.7,51

To know more about Equation here.

https://brainly.com/question/10413253

#SPJ1

By using natural logarithm properties we will see that the solutions of the two equations are:

17) x = 3.11

19) p = 2.02

Here we will use the property of natural logarithms:

Ln( a^x) = x*ln(a)

17) We have the exponential equation:

5^(x - 2) = 6

If we apply the natural logarithm in both sides, we will get:

ln( 5^(x - 2)) = ln(6)

(x - 2)*ln(5) = ln(6)

(x - 2) = ln(6)/ln(5)

x = ln(6)/ln(5) + 2

x = 3.11

19) Now the exponential equation is:

7^p = 51

We will do the exact same thing, apply the natural logarithm in both sides:

ln(7^p) = ln(51)

p*ln(7) = ln(51)

p = ln(51)/ln(7) = 2.02

Learn more about exponential equations:

https://brainly.com/question/11832081

#SPJ1

Answer:

1. [tex]\frac{4}{27}[/tex]

2. D

Step-by-step explanation:

1. [tex]3^{-2} * 1 * 4^3 * 3^{-1}*4^{-2[/tex]

= [tex]3^{-3} * 4^1[/tex]

= [tex]\frac{4^1}{3^3}[/tex]

= [tex]\frac{4}{27}[/tex]

2. Remember the rule that 1/a^b is equal a^-b, in this case, [tex]\frac{1}{2^3}[/tex] is the same as [tex]2^{-3}[/tex], now 6 + (-3) = 3 -- which will be the exponent. [tex]2^3[/tex] is correct.

The value of x is x = -3.

What is solving an equation?

Finding an equation's solutions, or the values that satisfy the condition given by the equation, is known as solving an equation in mathematics. Solutions often consist of two expressions connected by an equals sign. One or more variables are marked as unknowns in order to find a solution.

Consider the given equation,

27 = (1/3)^x

This equation can be written as,

[tex]27 = \frac{1^x}{3^x}[/tex]

Here 1^x

1[tex]27 = \frac{1}{3^x}[/tex]

Take 3^x on numerator.

[tex]27 = 3^-^x[/tex]

Now 27 can be written as,  [tex]27 = (3)(3)(3) = 3^3[/tex]

⇒ [tex]3^3 = 3^-^x[/tex]

Applying the exponent rule: [tex]a^b=a^c[/tex] ⇒ b = c

So we get,

3 = -x

Multiply both sides by -1.

-3 = x

x = -3

Hence the value of x is x = 3.

To know more about the solving an equation, click on the link

https://brainly.com/question/22688504

#SPJ1

Answer: 6/10

Step-by-step explanation: Six parts are shaded and even though the shaded parts are not touching each other, they will still count as shaded. 4 parts are not shaded and there is a total of 10 parts so the answer would be 6/10.

Hoped This Helped!

Answer:

If it is asking for the fraction of shaded parts the answer is A

If it is asking for the fraction of non-shaded parts the answer is B

Step-by-step explanation:

I would most likely go with A, because I have very rarely gotten a question asking for the non-shaded parts.

Answer:

5n + 12p + 12m

Step-by-step explanation:

Perimeter means you are adding up all three sides.

4m + 3n + 8m + 10p + 2p + 2n

= 2n+3n + 10p+2p + 4m+8m

Combine like terms.

= 5n + 12p + 12m

The true equations are 24 over 2 squared equals 50 minus 6 squared minus 8 and  56 divided by 8 plus 3 squared equals 2 times 2 cubed.

The equation one is given as

39- 3(6) = 6(10/4)+4

After solving we get,

39 - 18 = 15 +4

21 = 19

Which is not a true equation.

2nd equation we have

24/(2^2)=50 -6^2-8

24/4 = 50 -36 -8

6 = 50 - 44

6 = 6

which is a true equation.

3rd equation we have

56/8+3^2= 2(2^3)

7 +9 = 2(8)

16 = 16

which is true equation.

4th equation, we have

8^2-5^2 = 4^2-7

16-10 = 16-7

6 = 9

Which is not a true equation.

To know more about true equation,

https://brainly.com/question/25510910

#SPJ1

Answer:

D)

Can you please mark me as "Brainliest"

The total surface area of the cylinder is 175.84 squared inches

The surface area of a cylinder can be defined as the amount of space covered by the flat surface of the bases of the cylinder and the curved surface of the cylinder. The total surface area of the cylinder includes the area of the 2 bases of the cylinder which are in the shape of a circle and the area of the curved surface.

The formula is given as

A = 2πrh + 2πr²

We can substitute the values into the equation and solve

A = 2(3.14 * 4 * 3) + 2(3.14 * 4²)

A = 175.84 in²

The cylinder has a surface area of 175.84 in²

Learn more on surface area of a cylinder here;

https://brainly.com/question/27440983

#SPJ1

Answer: 175.84

Step-by-step explanation:

Answer:

Take a look at the attachments...

Hope this helps! :)

For the given equation, c = 11.5t where t is the number of tickets to watch movie and c is the total cost to watch movie then table representing the equation is given by

option B:

Number of tickets :     1             2

Cost in dollars      :    $11.50      $23

As given in the question,

Given equation to represents the total cost to watch a movie related to number of tickets of movie.

c = 11.5t

Where t is the number of tickets to watch movie and c is the total cost to watch movie.

Table which represents the given situation is given by:

Option A:

Number of tickets cannot be in decimals that is 0.09 and 0.17.

Incorrect.

Option B.

Number of ticket  = 1

cost 'c' = 11.5(1)

          = $11.5

when t = 2

c = 11.5(2)

  = $23

Correct.

Option C:

Number of tickets cannot be in decimals that is 11.5.

Option D:

when t = 1

c = $0.09 is incorrect.

Therefore, For the given equation, c = 11.5t where t is the number of tickets to watch movie and c is the total cost to watch movie then table representing the equation is given by

option B:

Number of tickets :     1               2

Cost in dollars      :    $11.50      $23

Learn more about equation here

brainly.com/question/10413253

#SPJ1

Answer: 16720yd

Step-by-step explanation:

Henry biked 9.5 miles to the park. How far is this in yards?

5280 ÷ 3 x 9.5 = 16720yd

x>1

below is the graph.

any questions in the comments:

The minimum number of nickels that Jaxson could have is 9.

Given that, Jaxson has some pennies and some nickels.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Let the number of pennies be P and the number of nickels be N.

So, P + N > 13

Therefore

P×0.01 + N×0.05 ≥ 0.33

Because he has at most, $0.33

If  P = 4

4×0.01 + N0.05 ≥ 0.33

∵ $0.33 - $0.04 = $0.29

N×0.05≥ 0.29

N = 0.29/0.05 = 5.8

The number of nickels that he might have is 9.6, but because he cannot have 0.6 of a nickel, we have to round the figure down to 9.

Now that we also know that he had at least 15 coins in total, we can use that equation to get the smallest possible number for N.

4 +  N  > 13

N > 13 - 4

N> 9

So we have the range:

9 < N ≤ 5.8

Therefore, the minimum number of nickels that Jaxson could have is 9.

To learn more about the inequalities visit:

https://brainly.com/question/20383699.

#SPJ1

y=−1/2x+1/2

Step-by-step explanation:

Answer: 33 1/3 percent

Step-by-step explanation:

First, we need to find the volume of the tennis ball can, which is a cylinder.

The formula for the volume of a cylinder is pi r^2 h.

The radius of a tennis ball is 3.2 cm, so the radius of the cylinder would be 3.2 cm as well.

The height is equivalent to the height of three tennis balls, which is the diameter of 3 tennis balls. The diameter of one tennis ball is 6.4 cm, and we can multiply this by 6 to get 38.4 as our height.

We can plug in these values to our equation for the volume of the cylinder.

pi * 3.2^2 * 38.4

The volume of the cylinder is 393.216 pi.

Now, we need to find the volume of one tennis ball and multiply that by six.

The volume of a sphere is 4/3 pi r^3

We know our radius, 3.2, so we just have to substitute that into the equation.

4/3 pi 3.2^3 = 4/3 * pi * 32.768 = 43.69 and 2/3 pi for the volume of one tennis ball. If we multiply this by six, we get the volume of all the tennis balls, which is 43.6 and 2/3 *3 = 262.144 pi.

Now we have to find the percentage of the cylinder not occupied, so we can find one percent of the container and divide that by 262.144 pi.

1% of 393.216 = 3.93216

262.144 divided by this = 66 and 2/3, so 33 and 1/3 percent of the can is not occupied. The answer depends on how many places to round to, or whether or not to keep the answer as a fraction.

The most important to determine before allowing employees to access the server remotely is B. security method of allowing connections.

What is a computer network?

Computer networking refers to the interconnection of computing devices that can exchange data and share resources. These networked devices use a set of rules known as communications protocols to transmit data over physical or wireless networks.

A computer network is a collection of computers that share resources that are located on or provided by network nodes. To communicate with one another, the computers use common communication protocols over digital interconnections.

Local-area networks (LANs) and wide-area networks (WANs) are the two basic network types (WANs). LANs connect computers and peripheral devices in a constrained physical area, such as a business office, laboratory, or college campus, using data-transmitting links (wires, Ethernet cables, fiber optics, Wi-Fi).

In this case, it should be noted that the security method that's used for allowing the connection is important. Based on the information illustrated, the correct option is B.

Learn more about network here:

brainly.com/question/1027666

#SPJ1

The derivative of the function is  [tex]\frac{dy}{dx}=\frac{9x^2(x^3-4)^2}{1+(x^3-4)^6}[/tex].

The chain rule is a method for calculating the derivative of composite functions, which are created by joining one or more functions.

The given function is y = tan⁻¹(x³ -4)³.

The derivative of tan⁻¹(x) is 1/(1+x²).

Use the above fact and the chain rule to differentiate the function as follows:

[tex]y = \tan^{-1}(x^3-4)^3\\\\\frac{dy}{dx} = \frac{1}{1+((x^3-4)^3)^2}\cdot\frac{d}{dx}(x^3-4)^3\\\\=\frac{1}{1+(x^3-4)^6}\cdot3(x^3-4)^2\cdot3x^2\\\\=\frac{9x^2(x^3-4)^2}{1+(x^3-4)^6}[/tex]

Hence, the derivative of the function is  [tex]\frac{dy}{dx}=\frac{9x^2(x^3-4)^2}{1+(x^3-4)^6}[/tex].

Learn more about the chain rule:

https://brainly.com/question/29498741

#SPJ1

Answer:  64.95/5= C, C= 12.99

Step-by-step explanation:

If you want to figure out what the cost of 1 book you must divide the total cost of the books ($64.95) by how many books Jamal bought (5).

So the equation should look like this 64.95/5=C. Each book is $12.99.

Hope this helped!

In 2014, the predicted population of Boca Raton will be 100000.

Given that the population function of Boca Raton is,

p(n) = 74760+1940n

So when the population of Boca Raton is 100000, then

p(n) = 100000

So,

100000 = 74760+1940n

1940n = 100000-74760

1940n = 25240

n = 25240/1940 = 14 (approximately)

So, the year in which the predicted population of Boca Raton reach 100000 is = 2000+14 = 2014

To know more about Population Function refer to:

https://brainly.com/question/25896797

#SPJ1

Answer:

shsjsjsjsjshsh#6#7#7##+-##6#3

The value of expression when r = 0.1 , n = 12 and t = 2 is,

⇒ 24.192

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ (1 + r/n) nt

Now, We can put r = 0.1 , n = 12 and t = 2 in above equation as;

⇒ (1 + r/n) nt

⇒ (1 + 0.1/12) 12 x 2

⇒ (1 + 0.008) 24

⇒ 1.008 x 24

⇒ 24.192

Thus, The value of expression when r = 0.1 , n = 12 and t = 2 is,

⇒ 24.192

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ2

The function F(x) = -3x² + 18x + 3 has a maximum value of 30 at x = 3

From the question, we have the following equation that can be used in our computation:

F(x) = -3x² + 18x + 3

A quadratic function is represented as

F(x) = ax² + bx + 3

By comparison, we have

a = -3

For a quadratic function to have a maximum value, the value of a must be less than 0

This means that the function has a maximum value because -3 is less than 0

Solving further, we have

F(x) = -3x² + 18x + 3

Differentiate and set to 0

-6x + 18 = 0

So, we have

x = 3

Substitute x = 3 in F(x)

F(3) = -3(3)² + 18(3) + 3

Evaluate

F(3) = 30

This represents the maximum value

Read more about quadratic functions at

brainly.com/question/1214333

#SPJ1

Answer:

64 marbles

Step-by-step explanation:

hope it helped :)