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What is the solution to this equation? (1/4)^x+1 =32

Answer:

a) 112 ft.

b) 256 ft. and 3 seconds

c) 7 seconds

Step-by-step explanation:

a) The model rocket is lauched from a platform. To find the height of the platform, we need to find h when t = 0, because the rocket starts from the platform when no time has elapsed:

[tex]h=-16t^2+96t+112[/tex]

[tex]h=-16*0+96+0+112\\\\h=112[/tex]

Therefore, the height of the platform is [tex]\fbox{112}[/tex] ft.

b) If you learned calculus before, we can find the maximum height easily. We take the derivative of h and set it equal to 0. Remember, the derivative of a function is simply the slope of it at an instantaneous point. At the maximum point of a function, it's slope equals to 0.

[tex]h=-16t^2+96t+112\\h'=-32t+96+0\\h'=-32t+96[/tex]

Ok! Let's set the derivative of h to 0!

[tex]0=-32t+96\\-96=-32t\\t=3[/tex]

We now know how long it takes for the rocket to reach maximum point (t represents seconds), but we also need to find the maximum height. We can simply plug our t=3 into the function of h, because t=3 is the point where the rocket reaches maximum height:

[tex]h(3)=-16(3)^2+96*3+112\\h(3)=-144+288+112\\h(3)=256[/tex]

The maximum height of the rocket is [tex]\fbox{256}[/tex] ft and the rocket takes [tex]\fbox{3}[/tex] seconds to reach the height.

c) The rocket reaches the ground when h equals 0. We can set up the equation to solve for it:

[tex]h=-16t^2+96t+112\\0=-16t^2+96t+112\\0=-16(t+1)(t-7)\\0=(t+1)(t-7)\\t=-1, t=7[/tex]

However, time can never be negative.

Therefore, it takes the rocket [tex]\fbox{7}[/tex] seconds to reach the ground.

I hope this helps! Let me know if you have any questions :)

9514 1404 393

Answer:

  about 33.4°

Step-by-step explanation:

There are many ways to work this problem. A solution using a geometry program is shown in the attachment. The ship must turn about 33.4° to the north.

__

Another way to work this is to redraw the diagram so the initial starting point is left of the origin on the x-axis. Then the ship's direction can be considered to be straight to the right along the x-axis. The origin is the ship's turning point. The ship's destination can be considered to be 350∠22° from the initial position of the ship. The location of that destination relative to the origin represents the turn the ship must make.

At 18 mph for 7 h, the ship has traveled 126 miles.

Using the above method, the ship's destination relative to the origin is ...

  (-126, 0) +(350)(cos(22°), sin(22°)) = (198.514, 131.112)

Then the angle the ship must turn is ...

  arctan(131.112/198.514) ≈ 33.44°

The ship must turn about 33.4° to the north to head directly to Barcelona.

Answer:

-14c

Step-by-step explanation:

I’m using the actual values 1F = -17C so just times that by 5.4

Answer:

750 ft²

Step-by-step explanation:

.Given :

Charge per ft² = 50¢ = $0.5

Total cost = ((charge per ft² * number of ft²) + cost of paint)

Given that :

Paint cost = $100

Total cost = $475

Number of ft² = x

Plugging values into the equation :

475 = (( 0.5 * x) + 100)

475 = 0.5x + 100

475 - 100 = 0.5x

375 = 0.5x

x = 375 / 0.5

x = 750 ft²

Answer:

o ye}x+3 and 3x –y> 2 system of linear inequalities is represented by the graph.

PLEASE LET ME KNOW IF ¡ AM WRONG!

The system of linear inequalities represented by the graph is

y ≥ (1/3)x + 3 and 3x - y  > 2

Option A is the correct answer.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =≤

Greater than and equal = ≥

We have,

We see that,

When we graph,

y ≥ (1/3)x + 3 and 3x - y  > 2 we get the graph shown.

y ≥ (1/3)x + 3

This inequality is positive on the y-axis.

3x - y  > 2

3x > 2 + y

This inequality is positive on the x-axis.

Thus,

The system of linear inequalities represented by the graph is

y ≥ (1/3)x + 3 and 3x - y  > 2

Learn more about inequalities here:

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Answer:

y = 658.3 ft

Step-by-step explanation:

Alternate angles are equal. Therefore,

Reference angle (θ) = 28°

Length of side Opposite to reference angle = 350 ft

Adjacent side = y

Apply TOA, which is:

Tan θ = Opp,/Adj

Substitute

Tan 28 = 350/y

y*tan 28 = 350

y = 350/tan 28

y = 658.3 ft (nearest tenth)

Answer:

Below in bold.

Step-by-step explanation:

One way to do these is to square both sides:

(x + 4)^2 < 4x^2

x^2 + 8x + 16 < 4x^2

3x^2 - 8x - 16 > 0

Let this = 0:

3x^2 - 8x - 16 = 0

(3x + 4)(x - 4) = 0

x = -4/3, 4.

So the critical  points are -4/3 and 4.

Make a table:

                      x < - 4/3           -4/3 +< x  <= 4            x > 4

3x + 4                  <0                        > 0                        > 0

x - 4                     <0                        < 0                       > 0

(3x+4)(x-4)           >0                        <0                         > 0

So the solution is   x < -4/3 or x > 4

or in  interval notation:

(-∞, -4/3) U (4, ∞)

Answer:

See image below for answer:)

Step-by-step explanation:

FYI you can use the app photo math, you just take a pic of the problem and it gives you the answer and explains the steps and it is free.

Answer:

20

Step-by-step explanation:

Answer:

I think the answer is C

Step-by-step explanation:

Complete question :

Complete the expressions Write each answer as a number, a variable, or the product of a number and a variable 7(9r + 2) = 7 . 9r + 7 . ___ = ___ +

Answer:

2 ; 63r ; 14

Step-by-step explanation:

Given :

7(9r + 2)

Opening the bracket :

7*9r + 7*2 - - - - (1)

Taking the product

63r + 14 - - - - (2)

Now filling the blanks :

First blank corresponds to 2 (from (1))

Second blank corresponds to 63r (from (2))

Third blank should be 14

Answer:

7x

Step-by-step explanation:

its simple you just add them

Answer:

[tex]g(x) = -\frac{1}{2}\tan{x}[/tex]

Step-by-step explanation:

Tangent function:

The tangent function is:

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

Horizontally compressed by a factor of 1/2

Horizontally compressing by a factor of 1/2 is multiplying by 1/2. So

[tex]g(x) = \frac{1}{2}\tan{x}[/tex]

Reflected over the x-axis.

Reflecting a function over the x-axis is the same as multiplying it by -1. Then g is given by:

[tex]g(x) = -\frac{1}{2}\tan{x}[/tex]

Step-by-step explanation:

(7-11)+(-3+51)

(-4)+(48)

44 ans

Answer:

44

Step-by-step explanation:

7-11= -4

-3+51=48

-4+48=44

Answer:

what is the following

Step-by-step explanation:

Answer:

$180

Step-by-step explanation:

$600/$100 = 6

$600 es 6 veces $100.

Por vender $600 gana 6 veces mas que por vender $100.

6 * $30 = $180

Respuesta: $180

Answer:

$325.50, mentioned methods below.

Step-by-step explanation:

55% means it increases by 55%.  an increase of 50% is basically taking half of the original amount .  So a 50% increase of 4 would be 4 + .5*4 = 4+2 = 6

So for 210 that's 210 + .55*210 = 325.50

You could also factor to make it a little simpler.

210 + .55*210 = 325.50

210(1 + .55) = 325.50

210*1.55 = 325.50

.55 = 55/100 = 11/20

what are the suggestions?

Answer:

what are the options

Step-by-step explanation:

Answer:

53

Step-by-step explanation:

By taking the number "41" and minus it with "35" and you'll get 12. Take the number "12" and plus with "41" and you'll get the answer.

the population variance is 144 and the population standard deviation is 12.

To find the population variance and standard deviation for the given data set, follow these steps:

Step 1: Find the mean (average) of the data set.

Step 2: Subtract the mean from each data point to find the differences.

Step 3: Square each difference.

Step 4: Calculate the sum of the squared differences.

Step 5: Divide the sum of squared differences by the total number of data points to find the variance.

Step 6: Take the square root of the variance to find the standard deviation.

Given data set: 8, 17, 29, 35, 41

Step 1: Find the mean (average):

Mean = (8 + 17 + 29 + 35 + 41) / 5

Mean = 130 / 5

Mean = 26

Step 2: Find the differences from the mean:

Differences: (8 - 26) = -18, (17 - 26) = -9, (29 - 26) = 3, (35 - 26) = 9, (41 - 26) = 15

Step 3: Square each difference:

Squared differences: [tex](-18)^2 = 324, (-9)^2 = 81, 3^2 = 9, 9^2 = 81, 15^2 = 225[/tex]

Step 4: Calculate the sum of squared differences:

Sum of squared differences = 324 + 81 + 9 + 81 + 225 = 720

Step 5: Calculate the variance:

Variance = Sum of squared differences / Number of data points

Variance = 720 / 5

Variance = 144

Step 6: Calculate the standard deviation:

Standard deviation = √Variance

Standard deviation = √144

Standard deviation = 12

So, the population variance is 144 and the population standard deviation is 12.

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Answer:

tanx=30/27

tanx=10/9

x=48

Answer:

25

Step-by-step explanation:

The length of side EF in Cory's project is 25 inches. Thus, the correct answer is option b.

To determine the length of side EF in Cory's project, we can use the concept of proportionality between corresponding lengths in Cory's design and project.

We are given that the length ML in Cory's design corresponds to the length DC in Cory's project, and ML is 8 inches while DC is 40 inches. Using this information, we can set up the proportion:

ML / DC = NH / EF

Plugging in the known values, we have:

8 / 40 = 5 / EF

To solve for EF, we can cross-multiply:

8 * EF = 40 * 5

8EF = 200

Dividing both sides by 8:

EF = 200 / 8

EF = 25

Therefore, the length of side EF in Cory's project is 25 inches.

Thus, the correct answer is option b: 25 inches.

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Answer:

s = 22.5 m

Step-by-step explanation:

the equation for the speed change of a coach moving along a straight section of the road and starting braking at a speed of 20 m / s has the form v (t) = 25-5t. Using integral calculus, determine the coach's braking distance.

v (t) = 25 - 5 t

at t = 0 , v = 20 m/s

Let the distance is s.

[tex]s =\int v(t) dt\\\\s =\int (25 - 5t)dt\\\\s= 25 t - 2.5 t^2 \\[/tex]

Let at t = t, the v = 20

So,

20 = 25 - 5 t

t = 1 s

So, s = 25 x 1 - 2.5 x 1 = 22.5 m

Answer:

Miki had 288 stickers and Ken had 252 stickers.

Step-by-step explanation:

This question is solved using a system of equations.

I am going to say that:

Miki has x stickers.

Ken has y stickers.

The ratio of the number of Miki's stickers to the number of Ken's stickers was 8:7.

This means that [tex]\frac{x}{y} = \frac{8}{7}[/tex], that is: [tex]7x = 8y[/tex], or [tex]x = \frac{8y}{7}[/tex]

After Miki gave Ken 18 of her stickers, they had the same number of stickers.

This means that:

[tex]x - 18 = y + 18[/tex]

[tex]x - y = 36[/tex]

Since [tex]x = \frac{8y}{7}[/tex]

[tex]\frac{8y}{7} - y = 36[/tex]

[tex]\frac{8y}{7} - \frac{7y}{7} = 36[/tex]

[tex]\frac{y}{7} = 36[/tex]

[tex]y = 36*7 = 252[/tex]

And

[tex]x - y = 36[/tex]

[tex]x = 36 + y = 36 + 252 = 288[/tex]

Miki had 288 stickers and Ken had 252 stickers.

Answer:

its for sure C

Step-by-step explanation:

Answer:

1/2

If you divide both numbers by 5, you would get 1/2

Answer:

D) [tex]222[/tex] [tex]km^2[/tex]

Step-by-step explanation:

------------------------------

Let's find the surface area of the rectangular prism.

Multiply 7 times 9 for the front side and 7 times 9 again for the back side.

[tex]7*9=63[/tex]

[tex]7*9=63[/tex]

---------->>>>

Multiply 7 times 3 for the left side and 7 times 3 again for the right side.

[tex]7*3=21[/tex]

[tex]7*3=21[/tex]

---------->>>>

Multiply 3 times 9 for the top side and again for the bottom side.

[tex]3*9=27[/tex]

[tex]3*9=27[/tex]

---------->>>>

Now, let's add all these sums.

[tex]63+63+21+21+27+27=[/tex]

[tex]126+42+54=[/tex]

[tex]168+54=[/tex]

[tex]=222[/tex]

------------------------------

Hope this is helpful.

Answer:

a.5years=300 rabbits

b. 50 years(multiply 50 by 300)

Step-by-step explanation:

hope this is helpful

Answer:

x=6

Step-by-step explanation:

Answer:

Interval Notation:

(6,∞)

Inequality Form:

x>6

there ya go

Answer:

Step-by-step explanation:

a1=5

d=2-5=-3

[tex]a_{n}=5+(n-1)(3)\\a_{n}=5+3n-3\\a_{n}=3n+2[/tex]