A movie features dangerous stunts including jumping from a helicopter, riding on the hood of a speeding car, and a number of other acrobatic stunts. The director has hired a stunt double to perform these stunts. In the filming of the helicopter scene, the stunt double is released from a height of 10,000m. Assume the only forces acting on the stunt double are gravity and air resistance. The force of air resistance is assumed to be proportional to the velocity with proportionality constant λ = 10. Assume the stunt double has a mass of 60kg and the force of gravity is −9.81m/s^2.

Required:
Construct a differential equation which models the velocity of the falling stunt double. Explain the reasoning behind how you constructed the model you chose to use. Discuss any potential shortcomings of your model. Describe any initial conditions associated with your model.

Answer:

(8 * x) + 2x = 60

8x + 2x = 60

10x = 60

/10   /10

x = 6

8 is a constant that is being multiplied by an unknown number which we will name x. It is then being added to two times the unknown number(x), so we multiply x by 2, which is 2x. The final product will be 60, so in the equation it'll then equal 60.

We consider "a number" to be a variable that withholds an unknown value, which is x (or any other variable you prefer).

Answer:

The number is 6

Step-by-step explanation:

Given :-

8N + 2N = 60

To Find :-

N

Solving :-

8N + 2N = 60

10N = 60

N = 6

Solution :-

The number is 6

The cost of 24 tickets for the students is $480.

The given expression is t(28-8) represents the total cost for t tickets.

Mrs. Price purchases 24 tickets for the students in her class. Evaluate the expression for t=24.

Substitute t=24 in the given expression t(28-8), we get

24(28-8)

= 24×20

= $480

Therefore, the cost of 24 tickets for the students is $480.

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Answer:

4b +8

Step-by-step explanation:

8b +8 - 4b

Combine like terms

8b -4b     +8

4b          +8

Step-by-step explanation:

That's the solution;

Final answer; y + 1 = 5 ( x + 2 )

Answer:

A F E.....???

Step-by-step explanation: i hope this helps!

Answer:

None of the above is necessarily true.

Step-by-step explanation:

I've attached an example of such a function to show this.

Answer:

104,000,027,571

Step-by-step explanation:

billions, millions, thousands, hundreds

Answer:

x ≈ 44.6°

Step-by-step explanation:

perimeter of a perfect circle: 2πr = 2π(9) = 18π

perimeter of the circle arc : 25 - 2(9) = 7

The central angle in a full circle is 360 degrees. In the segment of the circle is x degrees. The value of x is obtained using proportionality.

[tex] \frac{360}{x} = \frac{18\pi}{7} \\ \\ x = \frac{7 \times 360}{18\pi} = 44.56[/tex]

Answer:

Step-by-step explanation:

1. ⁷C₅ = ⁷C₂ = 7 x 6 / 2 = 21

2. ⁹C₈ = ⁹C₁ = 9

3. ¹²C₅ = 12 x 11 x 10 x 9 x 8 / 2 x 3 x 4 x 5

= 11 x 9 x 8 = 11 x 72 = 792

4. ²⁰C₁₇ = ²⁰C₃ = 20 x 19 x 18 / 2 x 3

= 19 x 3 = 57

5. ¹⁶C₁₃ = ¹⁶C₃ = 16 x 15 x 14 / 2 x 3

= 8 x 5 x 14 = 40 x 14 = 560

6. ⁷C₄ + ¹¹C₉ = ⁷C₃ + ¹¹C₂ = (7 x 6 x 5 / 2 x 3) + (11 x 10 / 2)

= 35 + 55 = 90

7. ⁷C₃ + ⁷C₄ + ⁷C₅ = 2(⁷C₃) + ⁷C₂ = (2 x 7 x 6 x 5 / 2 x 3) + (7 x 6 / 2)

= 70 + 21 = 91

Legit only this much I can do now.

Hope it is enough.

Answer:

1 mango = $1.50

Step-by-step explanation:

2 mangoes - $3

1 mango - $?

3 / 2 = 1.5

So:

1 mango = $1.50

Hope this helped!

(Let me know if I got something wrong!)

Answer: $1.50

Step-by-step explanation:

The total cost of mangoes cost $3.00, and the person bought two.

To find the cost per mango, you can divide 3 by 2.

3/2 is 1.5, so each mango costs $1.50

hope this helped :)

Answer:

Step-by-step explanation:

Comparing the difference with the average in absolute value

The smallest number is 2 indicating the closest to average score

Matching student is C

Answer:

1/3

Step-by-step explanation: hope this helps!

Answer:

t ≈ 13.26

Step-by-step explanation:

We are given;

x¯ = 20 minutes per day

μ = 17 minutes per day

sample standard deviation; s = 1.6 minutes

Sample size; n = 50

When σ is unknown, formula for test statistic is;

t = (x¯ - μ)/(s/√n)

t = (20 - 17)/(1.6/√50)

t = 3/0.2263

t ≈ 13.26

Answer:

11/8 or 1 3/8

Step-by-step explanation:

hope this helps

Answer:

The answer is the last one 5/12 > 3/8

Step-by-step explanation:

Convert the fractions to regular numbers so 5/12 just do 5 ÷ 12 and 3/8 do 3 ÷ 8 whatever side has the arrow opened to means that's should be the bigger number for example 2 > 1 is true because 2 is greater than 1 but 2 < 1 is false

Answer:

5/12>3/8

Step-by-step explanation:

you need a common denominator

you multiply 5/12 by 2 the top and the bottom to get 10/24

then you multiply 3/8 by 3 the top and the bottom to get 9/24

10/24>9/24

Answer:

She made $12.95 after four hours

Step-by-step explanation:

because 35 cents is written as .35 we have to remember to put the decimal in our answer two spots to the left so

1st hour: 6 × 35 = $2.10

2nd hour: 5 × 35 = $1.75

3rd hour: 11 × 35 = $3.85

4th hour: 15 × 35 = $5.25

Total: $12.95

Answer:

r=(1/t) (A/P-1) = 2.75%

The simple interest rate is 2.75%

Answer:

C) $46.80

Explanation:

The price of new shoes = $85

The amount paid for the shoes  = $ 40

The balance amount for the shoes = $85 - $40 = $ 45

The rate of interest = 8%  

The time period = 6 months = 0.5 years

Simple interest:

Simple interest =  = $1.8

So, Amount = Principal + Interest

or, Amount = $45 + $1.8 = $ 46.8

The balance amount owned in six months is $46.8

Answer:

$46.8

Step-by-step explanation:

i took the test

Answer:

Step-by-step explanation:

Formula

% =  (favorite sport/total surveyed) * 100

Givens

favorite sport = 25

Total surveyed = 75

Solution

% = (25/75) * 100

% = 0.33333 * 100

% = 33.3333... or 33 1/3

Answer: A

Answer:

x=19/3  x=6 1/3 x=6.333333333

Step-by-step explanation:

Answer:

a

[tex]\mu_x  =7.5 \ minutes [/tex]

b

[tex]\sigma_{x} = 4.33 \  minutes [/tex]

c

[tex]P(5 <  X  <  11 ) = 0.4 [/tex]

d

[tex]P(W = 4 ) =  0.228[/tex]

Step-by-step explanation:

From the question we are told that

  The  interval is [tex](w , y) =  (0 , 15)[/tex]

Considering question a

    Generally the mean waiting time is mathematically represented as

              [tex]\mu_x  = \frac{w + y}{2}[/tex]

=>          [tex]\mu_x  = \frac{0 + 15}{2}[/tex]

=>          [tex]\mu_x  =7.5 \ minutes [/tex]

Considering question b

Generally the standard deviation is mathematically represented as

      [tex]\sigma_{x} = \frac{y - w}{\sqrt{\sqrt{12} } }[/tex]

=>    [tex]\sigma_{x} = \frac{15 - 0}{\sqrt{\sqrt{12} } }[/tex]

=>    [tex]\sigma_{x} = 4.33 \  minutes [/tex]

Considering question c

Generally the probability density function for a random variable  X is  

     [tex]f(x) =  \left \{ {{ \frac{1}{y} \ \ \ \ \  0 <  X  <  y } \atop {0} \\ \ \ \  Otherwise} \right.[/tex]

=>       [tex]f(x) =  \left \{ {{ \frac{1}{15} \ \ \ \ \  0 <  X  <  15 } \atop {0} \\ \ \ \  Otherwise} \right.[/tex]

Generally the probability that the waiting time is between 5 and 11 minutes is mathematically represented as

     [tex]P(5 <  X  <  11 )= \int\limits^{11}_{5} {f(x)} \, dx[/tex]

=>    [tex]P(5 <  X  <  11 )= \int\limits^{11}_{5} {\frac{1}{15}} \, dx[/tex]

=>   [tex]P(5 <  X  <  11 ) =  \frac{1}{15}  x | \left \  11 } \atop {5}} \right.[/tex]

=>   [tex]P(5 <  X  <  11 ) =  \frac{1}{15} [ 11 - 5][/tex]

=>   [tex]P(5 <  X  <  11 ) = 0.4 [/tex]

Considering question d

      Generally the probability the  waiting time is less than 5 minutes is mathematically represented as

     [tex]P(X < 5) =  \int\limits^5_{-\infty} {\frac{1}{15} } \, dx[/tex]

Given that time cannot be negetive

     [tex]P(X < 5) =  \int\limits^5_{0} {\frac{1}{15} } \, dx[/tex]

    [tex]P(X < 5) = \frac{1}{15} *  x  | \left \  5 } \atop {0}} \right.[/tex]

    [tex]P(X < 5) =0.33.[/tex]  

Generally the probability that the waiting time is less than 5 minutes on exactly 4 of 10 mornings follows a binomial  distribution because  the number of trial is finite i.e 10  the probability of success is probability that the waiting time is less than 5 minutes and probability of failure is probability that the waiting time is not  less than 5 minutes(i.e there is  only two outcome )

Hence for a random variable K representing the number of times in the total of 10 mornings that the  waiting is less than 5 minutes then

    The probability the random variable(W) is exactly 4 is mathematically represented as

    [tex]P(W = 4 ) =  ^{10}C_4 * (0.33)^4 *  (1- p)^{10 -4}[/tex]

Here C denotes combination

So

     [tex]P(W = 4 ) =  0.228[/tex]

Answer:

8 percent to find this answer you can do 12 divided by 15 to get 0.8 percent which is 8

Answer:

-7

Step-by-step explanation:

21 divided by -3 = -7

-7 times -3 =21

Answer:

Image of the graph attached

Step-by-step explanation:

STEP 1: Write the given function

Taking the x in the given question to be an absolute value, the function is:

[tex]y = 3 |x| + 4[/tex]

STEP 2: Plot the given function

y = x

15 = 9

y = 21

9y = 315

y = 315/9

y = 35

Answer:

35

Step-by-step explanation:

y is propotional to x, means, if x changes, y changes.

Considering, y depends on x only. Introduce a constant.

y = kx

When x = 9, y = 15,

=> 15 = k(9) => 5/3 = k

When x = 21, note that k is constant.

=> y = kx = (5/3)*21

= 35

Answer:

where m represents the slope and

(

x

1

,

y

1

)

a point on the line

here

m

=

−

5

4

and

(

x

1

,

y

1

)

=

(

−

8

,

−

5

)

substituting these values into the equation.

y

−

(

−

5

)

=

−

5

4

(

x

−

(

−

8

)

)

⇒

y

+

5

=

−

5

4

(

x

+

8

)

←

in point-slope form

distributing and simplifying gives the equation in an alternative form.

y

+

5

=

−

5

4

x

−

10

⇒

y

=

−

5

4

x

−

15

←

in slope-intercept form

Answer link

Step-by-step explanation:

Answer:1

3,000 + 1,200 = 4,200

add value of items

2

35 / 100 = .35

divide percentage by 100 to get decimal

3

4,200 * .35 = $1,470

multiply value of items by decimal to find collateral

RESULT

$1,470

Step-by-step explanation:

The maximum amount that he could borrow from Broadway is $1,470.

Since The policy of the Broadway Pawnshop is to lend up to 35% of the value of a borrower’s collateral. John wants to use a $3,000 ring and a $1,200 necklace as collateral for a loan.

Here the total amount should be

= $3,000 + $1,200

= $4,200

And, there is 35%

So, the maximum amount should be

= 35% of $4,200

= $1,470

Hence, The maximum amount that he could borrow from Broadway is $1,470.

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Answer:

20%

Step-by-step explanation:

If you already know that 64 students equals 32% you can fill the gaming club in for 32%. Since 100% is the goal you can add 32+32+16 to get 80 and subtract that from 100 to get the remaining percent.

Answer:

45 Degrees

Step-by-step explanation:

CEA and DEB are equal and AEF and BEG are equal hence 25+20 is 45

Step-by step explanation:

             Statement                                              Reason                  

⇒ ∠AEC + ∠AEF = x

Substitute the values to find x.