A skydiver weighing 160 lb (including equipment) falls vertically downward from an altitude of 20,000 ft and opens the parachute after 18 s of free fall. Assume that the force of air resistance, which is directed opposite to the velocity, is of magnitude 0.7|v| when the parachute is closed and is of magnitude 14|v| when the parachute is open, where the velocity vis measured in ft/s. Assume that acceleration due to gravity has magnitude 32 ft/s; remember that weight is the product of mass and gravitational acceleration.

Required:
a. Find the speed of the skydiver when the parachute opens.
b. Find the distance fallen before the parachute opens.
c. What is the limiting velocity vL after the parachute opens?
d. Determine how long the sky diver is in the air after the parachute opens.
e. Plot the graph of velocity versus time from the beginning of the fall until the sky diver reaches the ground.

Step-by-step explanation:

It is given that, Katie walks 2 ft forward and 5 ft backwards. We need to find her displacement traveled.

The difference between final position and the initial position is equal to displacement. It is the shorted path covered.

Let forward is +x and backward is -x

Initial position of Katie = +2 ft

Final position of Katie = -5 ft

Displacement = final position - initial position

= -5 - 2

Displacement = -7 ft

So, her displacement is 7 feet in backward direction.

The value of x is  = -5, -3

Answer:

2.4/3

8 Feet of yarn

This is because we're asking of one third of the original amount so we divide it by three.

Answer:

[tex](x-3-2i)(x-3+2i)[/tex]

Steps:

[tex]8x^2-48x=-104[/tex]

[tex]8x^2-48x+104=0[/tex]

Divide both sides by 8

[tex]x^2-6x+13=0[/tex]

But we can't factor it.

Using the Quadratic Formula to calculate the roots:

[tex]$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$[/tex]

[tex]$x=\frac{-(-48)\pm \sqrt{(-48)^2-4\cdot 8\cdot 104}}{2\cdot 8}$[/tex]

[tex]$x=\frac{48\pm32i}{16}$[/tex]

[tex]x_1=3+2i\\x_2=3-2i[/tex]

The answer might be

[tex](x-(3+2i))(x-(3-2i))[/tex]

[tex](x-3-2i)(x-3+2i)[/tex]

Answer:

Pritam gets $22.50

Step-by-step explanation:

Ratios

Pritam =3

Sarah=6

Emily=4

The ratio between Sarah and Emily = 6:4

=3:2

If Sarah gets $15 more than Emily

Then,

Sarah gets $45

Emily gets $30.

The ratio between Pritam and Sarah = 3:6

= 1:2

Since Sarah gets $45,

Pritam gets half as much= $45 / 2

=$22.50

Answer:

3.935 x 10^5.

Step-by-step explanation:

There are five digits after the first 3 so  it will be 10^5.

The answer is 3.935 x 10^5.

393500 equals 3.935×10⁵

If we write xⁿ then we mean to say that x is multiplied n times.

The exponent of a number says how many times the number is multiplied by itself.

393500=3.935×100,000=3.935×10⁵

Hence, 393500=3.935×10⁵

Learn more about exponents here- https://brainly.com/question/5497425?referrer=searchResults

#SPJ2

Answer: 22 kph

Step-by-step explanation:

distance (d) = rate (r) x time (t)

UPSTREAM: d = 5 km,   r = *x - y,  y = 2 kph,   t = 2t

DOWNSTREAM: d = 3 k,  r = *x + y,   y = 2 kph,   t = t

*x is the speed in still water and y is the current of the water.

Upstream equation:       5 = 2t(x - 2)   -->    [tex]\dfrac{5}{2(x-2)}=t[/tex]

Downstream equation:  3 = t(x + 2)     -->    [tex]\dfrac{3}{x+2}=t[/tex]

Set the equations equal to each other to solve for x:

[tex]\dfrac{5}{2(x-2)}=\dfrac{3}{x+2}\\\\\\\text{Cross multiply:}\\5(x+2)=3\cdot2(x-2)\\\\\text{Distribute:}\\5x+10=6x-12\\\\\text{Isolate x:}\\10=x-12\\22=x[/tex]

Step-by-step explanation:

Step-by-step explanation:

distance (d) = rate (r) x time (t)

UPSTREAM: d = 5 km, r = *x - y, y = 2 kph, t = 2t

DOWNSTREAM: d = 3 k, r = *x + y, y = 2 kph, t = t

*x is the speed in still water and y is the current of the water.

Upstream equation: 5 = 2t(x - 2) --> \dfrac{5}{2(x-2)}=t

2(x−2)

5

=t

Downstream equation: 3 = t(x + 2) --> \dfrac{3}{x+2}=t

x+2

3

=t

Set the equations equal to each other to solve for x:

\begin{gathered}\dfrac{5}{2(x-2)}=\dfrac{3}{x+2}\\\\\\\text{Cross multiply:}\\5(x+2)=3\cdot2(x-2)\\\\\text{Distribute:}\\5x+10=6x-12\\\\\text{Isolate x:}\\10=x-12\\22=x\end{gathered}

2(x−2)

5

=

x+2

3

Cross multiply:

5(x+2)=3⋅2(x−2)

Distribute:

5x+10=6x−12

Isolate x:

10=x−12

22=x

Answer:

The +1 in f(x) is the y intercept

The +1 in g(x) is the y coordinate of the vertex

Step-by-step explanation:

For f(x), plugging in x = 0 leads to

f(x) = 2x^2+5x+1

f(0) = 2(0)^2+5(0)+1

f(0) = 1

Showing that (0,1) is the y intercept of f(x).

The same is not true for g(x)

g(x) = 2(x+5)^2+1

g(0) = 2(0+5)^2+1

g(0) = 51

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

The +1 for g(x) represents the y coordinate of the vertex. Recall that vertex form in general is

y = a(x-h)^2+k

with (h,k) being the vertex. This means we can quickly spot the vertex for g(x) without having to graph. The same cannot be said for f(x) as we need to complete the square to get f(x) into vertex form. Currently, f(x) is in standard form.

Answer:

x=3 15/16 hours together

Step-by-step explanation:

the painter paints 1/7 of the house in 1 hour

the assistant paints 1/9 of the house in 1 hour

x=# of hours it takes them together to paint the house

(1/7)x+(1/9)x=1 (job finished)

multiply both sides by the LCM which is 63

63(1/7)x+63(1/9)x=63(1)

9x+7x=63

16x=63

x=63/16

x=3 15/16 hours together

Answer:

Step-by-step explanation:

8/2

Numerator is bigger than denominator. So it is improper fraction and rational number

Rational numbers are any number that can be written in p/q form

Answer:

it should be improper fraction

Step-by-step explanation:

because the numerator is greater than the denominator.

Hope it helps :)

Answer:

1. 1/120

2. 7/24

Step-by-step explanation:

n = 10

Number of defective = 3

1. Probability of all defective =

(Number of defective/n) x (number of defective -1/n -1)...(number of defective -n/n-1)

=3/10 x 2/9 X 1/8

= 6/720

= 1/120

2. probability of none defective

Since 3 are defective, those that are not defective = 7

The probability is therefore:

7/10 x 6/9 x 5/8

= 210/720

= 7/24.

Systematic

Got it right on test

The information depicted is an example of cluster sampling.

From the information given, Farmer Joe separates his apple tree farm into 10 regions and then counts the number of apples that are produced in two of the regions and uses that estimate to predict the number of apples produced on the whole farm, this illustrates cluster sampling.

Cluster sampling is when researchers divide a population into smaller groups that are called clusters and then randomly select from the population.

Read related link on:

https://brainly.com/question/17255201

Answer:

316,912,650,057,057,350,374,175,801,344

Step-by-step explanation:

You can see that this sequence is geometric so you need to know the geometric sequence which is [tex]x_{n} =r^{n-1}[/tex] and if you plug in every thing you get [tex]x_{n}[/tex]=[tex]2^{99-1}[/tex] which would be [tex]2^{98}[/tex] which is 316,912,650,057,057,350,374,175,801,344

Answer:

(a) the time for the event of the highest 5% is 15.29 minutes.

(b) the time for the event of the lowest 50% is 12 minutes.

(c) the time for the event of the middle 95% is 8.08 minutes and 15.92 minutes.

(d) the time for the event of the lowest 80% is 13.68 minutes.

Step-by-step explanation:

We are given that the time required to cook a pizza at a neighborhood pizza joint is normally distributed with a mean of 12 minutes and a standard deviation of 2 minutes.

Let X = the time required to cook a pizza at a neighborhood pizza joint.

The z-score probability distribution for the normal distribution is given by;

                              Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean time = 12 minutes

           [tex]\sigma[/tex] = standard deviation = 2 minutes

(a) We have to find the time for the event of the highest 5%, that means;

           P(X > x) = 0.05     {where x is the required time}

           P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{x-12}{2}[/tex] ) = 0.05

           P(Z > [tex]\frac{x-12}{2}[/tex] ) = 0.05

Now, in the z table, the critical value of x that represents the top 5% of the area is given as 1.645, i.e;

                      [tex]\frac{x-12}{2}=1.645[/tex]

                      [tex]{x-12}=1.645\times 2[/tex]

                      x = 12 + 3.29 = 15.29 minutes.

Hence, the time for the event of the highest 5% is 15.29 minutes.

(b) We have to find the time for the event of the lowest 50%, that means;

           P(X < x) = 0.50     {where x is the required time}

           P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{x-12}{2}[/tex] ) = 0.50

           P(Z < [tex]\frac{x-12}{2}[/tex] ) = 0.50

Now, in the z table, the critical value of x that represents the lowest 50% of the area is given as 0, i.e;

                      [tex]\frac{x-12}{2}=0[/tex]

                      [tex]{x-12}=0[/tex]

                      x = 12 + 0 = 12 minutes.

Hence, the time for the event of the lowest 50% is 12 minutes.

(c) We have to find the time for the event of the middle 95%, that means we have to find the time for the event of 2.5% and above 97.5%;

Firstly, the time for the event of the lowest 2.5%, i.e;

           P(X < x) = 0.025     {where x is the required time}

           P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{x-12}{2}[/tex] ) = 0.025

           P(Z < [tex]\frac{x-12}{2}[/tex] ) = 0.025

Now, in the z table, the critical value of x that represents the lowest 2.5% of the area is given as -1.96, i.e;

                      [tex]\frac{x-12}{2}=-1.96[/tex]

                      [tex]{x-12}=-1.96 \times 2[/tex]

                      x = 12 - 3.92 = 8.08 minutes.

Firstly, the time for the event of the below 97.5%, i.e;

           P(X < x) = 0.975     {where x is the required time}

           P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{x-12}{2}[/tex] ) = 0.975

           P(Z < [tex]\frac{x-12}{2}[/tex] ) = 0.975

Now, in the z table, the critical value of x that represents the top 2.5% of the area is given as 1.96, i.e;

                      [tex]\frac{x-12}{2}=1.96[/tex]

                      [tex]{x-12}=1.96 \times 2[/tex]

                      x = 12 + 3.92 = 15.92 minutes.

Hence, the time for the event of the middle 95% is 8.08 minutes and 15.92 minutes.

(d) We have to find the time for the event of the lowest 80%, that means;

           P(X < x) = 0.80     {where x is the required time}

           P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{x-12}{2}[/tex] ) = 0.80

           P(Z < [tex]\frac{x-12}{2}[/tex] ) = 0.80

Now, in the z table, the critical value of x that represents the lowest 80% of the area is given as 0.8416, i.e;

                      [tex]\frac{x-12}{2}=0.8416[/tex]

                      [tex]{x-12}=0.8416 \times 2[/tex]

                      x = 12 + 1.68 = 13.68 minutes.

Hence, the time for the event of the lowest 80% is 13.68 minutes.

Answer:

The answer is "c"

Step-by-step explanation:

Answer:

b. The paint will not fill the tray by 5.22 in3.

Step-by-step explanation:

The computation is shown below:

First we have to determine the volume of tray by using the following equation

[tex]V = L \times W \times H[/tex]

Now transform this from dimensions to inches

Now  putting the values,

[tex]V = 10\times12\times (5\times(\frac{1}{2.54})) \\\\As\ 5 cm = 5 \times (\frac{1}{2.54})[/tex]

the volume would be equivalent to the

236.22 inches^3

Now 1 gallon is 231 inches^3

So, the remaining would be

= 236.22 - 231

= 5.22^3

Therefore the correct option is b.

Hence, all the other options are wrong

Answer:

Length of the diagonal = 20√3 units

Step-by-step explanation:

Given:

Side of square = 10√6 units

Find:

Length of the diagonal

Computation:

Using Pythagorean theorem.

Length of the diagonal = √2(a)²

Length of the diagonal = √2(10√6)²

Length of the diagonal = √1200

Length of the diagonal = 20√3 units

Answer:

The answer is

Step-by-step explanation:

Perimeter of a square = 4l

Area of a square = l²

where

l is the the length of one side

To find the area we must first find the length of the square using the perimeter

Perimeter = 128m

Substitute the value into the formula for finding the perimeter and find the length

That's

[tex]128 = 4l[/tex]

Divide both sides by 4

length = 32 m

So the area of the square is

A = 32²

We have the final answer as

Hope this helps you

Answer:

B

Step-by-step explanation:

To achieve an average of 95% on 4 tests, the sum of the scores Olivia gets must be 95 * 4 = 380. Right now, the sum of her scores is 89 + 98 + 96 = 283 so she must get at least a 380 - 283 = 97% on her last test.

Answer:

x = 1

Step-by-step explanation:

Given

3x + 5x = 8 ← collect like terms on left side

8x = 8 ( divide both sides by 8 )

x = 1

Answer:

Read Exp:

Step-by-step explanation:

1.) 4 is the Base and 8 is the Exponent.

2.) 9^4 = 9 x 9 x 9 x 9 = 6561.

3.) (-5)^2 = -5 x -5 = 25.

4.) 3^3 = 3 x 3 x 3 = 27.

5.) (1/2)^5 = 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 0.03125

Have to change it to a simplified fraction:

* 1/32

Answer:

Wednesday: 45 - 18

Thursday: 55 - 22

Step-by-step explanation:

18*2.5=45

55/5=11

11*2=22

Answer:

Trees Planted Unknown Value = 45

Trees Harvested Unknown Value = 22

Step-by-step explanation:

Plants : Harvest

= 5 : 2

= x : 18

= 5 * x : 2 * x

= 5 * x : 18 / 2

= 5 * x : 9

= 5 * x : x

= 5 * x : 2 * x

= 5 * 9 : 2 * 9

= 45 : 18

Trees planted value  = 45

Plants : Harvest

= 5 : 2

= 55 : y

= 5 * y : 2 * y

= 55 / 5 : 2 * y

= 11 : 2 * y

= y :  2 * y

= 5 * y : 2 * y

= 5 * 11 : 2 * 11

= 55 : 22

Trees harvested value  = 22

I really hope this helps! Tell me if I am incorrect!

Answer:

B. 0.36

Step-by-step explanation:

Given:

Right ∆ABC,

AB = 5

BC = 13.93

CA = 13

Required:

Value of sin C

SOLUTION:

[tex] sin(C) = \frac{opposite}{hypotenuse} [/tex]

Opposite = 5

Hypotenuse = 13.93

[tex] sin(C) = \frac{5}{13.93} [/tex]

[tex] sin(C) = 0.3589 [/tex]

[tex] sin(C) = 0.36 [/tex]

the answer would be B, 0.36

Answer:

Approximately

W=132.29

Step-by-step explanation:

W=k(TA√F)/R

T=78°F

R=5.6 inches

F=4

A=1000 square feet

W=$72

Solve for k

W=k(TA√F)/R

72=k(78*1000*√4)/5.6

72=k(78,000*2) / 5.6

72=k(156,000) / 5.6

72*5.6 =156,000k

403.2=156,000k

k=403.2/156,000

=0.002585

Solve for w when F=6, A=1500, T= 78, R=5.6 inches

W=k(TA√F)/R

W=0.002585(78*1500*√6) / 5.6

=0.002585(78*1500*2.4495) / 5.6

=0.002585(286,591.5) /5.6

=740.8390 / 5.6

=132.2927

W=132.2927

Approximately 132.29

Answer:

12,464 ft

Step-by-step explanation:

I assume that the elevation of the lake is the altitude at the surface of the water.

The surface of the lake is 922 ft above the deepest point of the lake.

11,542 ft + 922 ft = 12,464 ft

Answer:

6½ gallons

Step-by-step explanation:

Givem the cost of 1gallon of gas = $2.78. . If Cory buys $18 of gas, we are to find the number of gallons did he buy. To do that we will use the equality method as shown;

$2.78 ,= 1gallon

$18 = x gallon

Cross multiply

2.78 × x = 1×18

2.78x = 18

Divide through by 2.78

2.78x/2.78 = 18/2.78

.x = 6.5

Hence Cory buys about 6½ gallons of gas for $18

Answer:

A - x (x+3) = Area of the rectangle

B- 28 inches squared

Step-by-step explanation:

B- using the formula from A

x = 4

x + 3 = 4 +3 = 7

4 times 7 is 28

Answer: 28ins²

Step-by-step explanation:

From the question, let the width of the rectangle = xins.

Therefore, the breadth                                            = ( x + 3 )ins.

(A) The area of the rectangle which is L x B          = x( x+ 3 )

                                                                              = (x² + 3x)ins² . In polynomial.

(B) The area of the rectangle if the width is 4ins, that is if x = 4ins.To find the area, we substitute for x in the area above

                                                                             = 4² + 3 x 4

                                                                             = 16 + 12

                                                                             = 28ins²

Answer: D

Step-by-step explanation:

Irrational numbers cannot be expressed as a ratio of two integers.

Answer:

D only

Step-by-step explanation: