21' 9" - 13' 1"

feet
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Inches

Answer:

  62,400 J

Step-by-step explanation:

As the problem statement tells you, the work done to lift the mass is the product of the force applied and the distance the mass is lifted. Here, the force decreases as the height of the mass increases.

For x meters of exposed cable, the force required to lift it is 3x newtons. The force required to lift the object is 1500 newtons, so the total force required to lift the masses an incremental distance (dx) is (3x +1500) newtons.

The work done lifting the mass that distance is the product of force and distance. The total work done is the integral of the incremental work over the total of distance lifted:

  [tex]\displaystyle W = \int_0^{40}(3x+1500)\,dx[/tex]

The value of the integral is ...

  [tex]\displaystyle W=\left.\left(\dfrac{3}{2}x^2+1500x\right)\right|_{x=0}^{x=40}=40\left(\dfrac{1}{2}(3\cdot40)+1500\right)=62\,400\qquad\text{joules}[/tex]

The work done to lift the cable and weight is 62,400 joules.

__

Additional comment

One reason for writing the integral evaluation this way is to demonstrate that the total of work done is that required to lift the weight (1500 N, 40 m) and that required to lift the center of mass of the cable (120 N, 20 m).

This will generally be the case for "disappearing mass" or "increasing distance" problems. Pumping from a pool is a similar kind of problem with a similar kind of solution.

Effectively, you're doing work on the center of mass of the system, moving it from its initial position to the top of the building.

Answer:

Step-by-step explanation:

The equation for h = f(t) will be, ⁣[tex]\rm h(t)=7.5sin({\pi}t-\frac{\pi}{2})+12.5[/tex].

A connection between independent variables and the dependent variable is defined by the function. Functions help to represent graphs and equations.

The given data in the problem is;

Ferris wheel diameter,d= 15 meters

The platform is 5 m above the ground.

The Ferris wheel function is;

h(t) = A sin(Bt + C) + D

Here,

A is Amplitude

D is the midline

B is period

C is a phase shift

t is the time

The amplitude of the function is half of the diameter;

A = d/2

A=15 m /2

A = 7.5 m

The value of the mid-line is found as;

Mid-line =  amplitude  + distance from the mid-line;

D= 7.5 + 5

D = 12.5

From the given data, the wheel completes 1 full revolution in 2 minutes

The period of the wheel is T.

B = 2

The phase shift is found as;

[tex]\rm \frac{C}{\pi}=\frac{-1}{2}\\\\ {C}=\frac{-\pi}{2}[/tex]

The Ferris wheel function is;

h(t) = A sin(Bt + C) + D

Substitute the obtained values we get;

[tex]\rm h(t)=7.5sin({\pi}t-\frac{\pi}{2})+12.5[/tex]

Hence, the equation for h = f(t) will be, ⁣[tex]\rm h(t)=7.5sin({\pi}t-\frac{\pi}{2})+12.5[/tex].

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Answer:

The answer is B. [tex]y = x^2 + 6x + 5[/tex]

Step-by-step explanation:

Because [tex]y = (x + 3)^2 - 4 = x^2 + 6x + 9 - 4 = x^2 + 6x + 5[/tex]

So the answer in this question is B.

Answer:

-2

Step-by-step explanation:

you will group the like terms and add and subtract the remaining digits

Answer:

I can help you, just tell me what it is.

Step-by-step explanation:

Step 1: Tell me the problem

Step 2: Wait for a response.

Answer:

yes it can help in some ways I think

The true statements are:

The marked up price of chicken before 10pm is $6

The 50% mark down is taken off the marked up price

Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.

Price after the mark up= (1 + mark up) x initial price

1.50 x 4 = $6

Price after the mark down = (1 - percentage mark down) x price after mark up

0.50 x $6 = $3

Here are the options:

The marked up price of chicken before 10pm is 6

The 50% mark down is taken off the marked up price

The chickens sell for $4 after 10pm

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4 pounds of fertilizer is mixed to make a mix of 80 pounds of soil.

The relationship between two things is called Ratio. It is written in p:q form.

It is given that

For 10 pounds of soil , farmer mixes 8 ounces of fertilizer.

=8/16 = 0.5 pounds of fertiliser

The ratio is 10 : 0.5

Suppose he mixes x pounds of fertilizer for 80 pounds of soil

to determine x

The ratio is 80 : x

As they are in Proportion

10 / 0.5 = 80 /x

x = 80 * 0.5 /10

x = 4 pounds

Therefore 4 pounds of fertilizer is mixed to make a mix of 80 pounds of soil.

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Answer:

z=2

Step-by-step explanation:

We are given that a line has a slope of 3.

The line passes through the points (-10, z) and (-8, 8)

We want to find the value of z.

To do that, we can calculate the slope.

The slope can be calculated using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points

Even though we already have 2 points, let's label their values to avoid any confusion.

[tex]x_1=-10\\y_1=z\\x_2=-8\\y_2=8[/tex]

Now substitute those values into the formula, and set it equal to 3. Remember that the formula uses subtraction.

[tex]\frac{8-z}{-8--10}[/tex] = 3

We can simplify this first.

[tex]\frac{8-z}{-8+10}[/tex] = 3

[tex]\frac{8-z}{2}[/tex] = 3

We can multiply both sides by 2 to clear the fraction and make it easier to calculate.

2([tex]\frac{8-z}{2}[/tex])  = 2(3)

Multiply.

8 - z = 6

Subtract 8 from both sides

-z = - 2

Multiply both sides by -1.

-1(-z) = -1(-2)

Multiply.

z = 2

Answer:

2nd answer option

Step-by-step explanation:

the domain is the interval or set of valid x values. the range is the same for valid y values.

so, what is the smallest x value we see in the functional graph ?

x = 0

there is no functional value for any x smaller than that.

and then the function goes on and on to the right in all eternity. that means it goes to infinity.

so, domain = [0, infinity)

please consider the round bracket at the end, because "infinity" is not a number.

now for the range and the y values.

in this case I start to ask for the largest y value.

y = 4

for no x value do we get a larger y value.

but it goes down and down in all eternity, going also to infinity, but -infinity (down is negative for y).

so, the range = (-infinity, 4]

"-infinity" is also not a number and therefore not included (hence the round bracket).

The interest based on the information given is $2564.

From the information given, the following can be deduced:

Principal = $36900

Time = 178 days

Rate = 14.25%

The simple interest will be:

= (PRT)/100

= (36900 × 14.25 × 178/365)/100

= $2564

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Answer:

  H.  99 ft²

Step-by-step explanation:

Area is proportional to the number of tiles.

The total area of the bathroom is 6×9 = 54 tiles. Of these, 12 are shaded. The proportion can be written as ...

  total area / shaded area = total tiles / shaded tiles

  total area / (22 ft²) = 54/12 . . . . . use given numbers

  total area = (22 ft²)×(54/12) = 99 ft² . . . . . multiply by 22 ft²

The total floor area of the bathroom is 99 square feet.

Answer:

gradient: 1.5

Explanation:

Take two points from the graph: (2, 0), (0, -3)

[tex]\sf gradient : \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

So here given:

Inserting values

[tex]\rightarrow \sf gradient : \dfrac{-3-0}{0-2} = \dfrac{-3}{-2} = 1.5[/tex]

Using it's concept, it is found that the period of the function is of 20 units.

The period of a function is given by the distance between it's repetitions.

Looking at the graph, the distance between the repetitions is of 20 units, which is the period of the function.

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The y-intercept of the function is  -9,25

The function is given as:

[tex]y = -5(.8)^{x - 1} - 3[/tex]

See attachment for the graph of the function

From the graph, we have the following highlights:

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[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\large{\textsf{\textbf{\underline{\underline{Answer : \:}}}}}}[/tex]

[tex] \bold{ \blue{Answer:} \sf{x = \sqrt{2} - 3, - \sqrt{2 } - 3 }}[/tex]

[tex]\bold{Step \: \: by \: \: step \: \: explanation }[/tex]

1: The expression x² + 6x + 7 fits the form a x²+ bx + c Let's complete the square, where:

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{a = 1} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf{ b = 6} \\ \sf{c = 7}[/tex]

2: Enter the constant k, which is 9 in our case.

[tex] \sf{x {}^{2} + 6x {}^{} + 9 - 9 + 7}[/tex]

3: Use Sum Square (a + b) ² = a² + 2ab + b².

[tex] \sf{(x + 3) {}^{2} - 9 + 7}[/tex]

4: Simplify

[tex] \sf{(x + 3) { }^{2} - 2}[/tex]

5: Substitute the above back into the original equation.

[tex] \sf{( x + 3) {}^{2} - 2 = 0}[/tex]

6: Add 22 to both sides.

[tex] \sf{(x + 3) {}^{2} = 2}[/tex]

7: Take the square root of both sides.

[tex] \sf{x + 3 = ± \sqrt{2}} [/tex]

8: Divide the problem into these 2 equations.

[tex]\sf{x + 3 = \sqrt{2} } \\ \: \: \: \: \: \sf{x + 3 = - \sqrt{2} }[/tex]

9: Solve the 1st equation:

[tex] \sf{ x + 3 = \sqrt{2} } \\ \sf{x = \sqrt{2} - 3 }[/tex]

10: Solve the 2nd equation.

[tex] \sf{ x + 3 = - \sqrt{2} } \\ \sf{x = - \sqrt{2} - 3 } [/tex]

11: Collect all the solutions.

[tex] \sf{x = \sqrt{2} - 3, - \sqrt{2} - 3 }[/tex]

I hope I've helped : )

Answer:

a=30,b=60,c=105

Step-by-step explanation:

a = 30 vertical angle therom

b = 180-120 = 60 using triangle sum therom

c = 180-75 = 105 because a line is always 180 degrees

The original dimensions of the metal sheet are 22 inches by 52 inch

The volume is defined as the space occupied by any object in three dimensions. For a rectangular box, the volume will be calculated by multiplying the length, width, and height of the object.

If the Width of the metal = x

The length is 30 inches longer than its width= x+30

If Squares with sides 6 in long are cut from the four corners and the flaps are folded.

The length of the pre-folded box =x+30-12=(x+18)inch

The width of the pre-folded box = (x-6-6)inch = (x-12) inch

The height of the flap= 6 inch

The volume of the box = 2400-inch cubed

Volume of a Cuboid = LWH

6(x-12)(x+18)=2400

6x²+36x-1296=2400

6x²+36x-1296-2400=0

6x²+36x-3696=0

6(x-22)(28+x)=0

x-22=0 or x+28=0

Therefore the original dimensions of the metal sheet are 22 inches by 52 inch

The complete question with correct data is given below:-

A rectangular piece of metal is 30 in longer than it is wide. Squares with sides 6 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 2400 incubated​what were the original dimensions of the piece of​ metal?

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Answer:

it's

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32.36

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Answer:

The money multiplier is the ratio of money supply to the money base. The money base is the sum of currency in circulation and reserves held by commercial banks.

The reserve rate is the percentage of deposits that commercial banks must hold in reserve.

If the reserve rate is 4%, the money multiplier is 10.

Step-by-step explanation:

The solution is about a distance-time graph. The interpretation of the graph is that it took the family 6 hours to travel a distance of 360 miles. Note that the distance is plotted on y-axis and time on the x-axis.

A distance time graph is a simple graph that shows the relationship between the time travelled the distance covered while doing do.

The slope-intercept form is

y= mx+b−⋯(1)

The y-intercept is 360

⇒b = 360; and m = −60

Substituting the value of m = −60

and b = 360

in (1) above,

⇒y = −60x  +360

The x-intercept is

y = 0,

⇒0= −60x+360

hence, x=6

The y-intercept is

x=0

⇒y=−60(0)+360

⇒y=360

In conclusion, the x - intercept is the time in hours between Cincinnati and St. Loui: and

The  y - intercept is the distance between Cincinnati and St. Louis.

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Alex had $444.231 in the beginning.

Two or more expressions with an Equal sign is called as Equation.

Let, x = the money Tierra had in the beginning

y = the money Nico had in the beginning

z = the money Alex had in the beginning

Tierra, Nico and Alex had $865 altogether

x + y + z = 865

Tierra spent 2/5 of her money and now she has: x - (2/5)x = 3x/5 left

Nico spent $40 and now has y - 40 left

Alex spent twice as much as Tierra and now has z - 2(2/5)x = z - 4x/5 left

the three friends had the same amount of money left

3x/5 = y - 40

y - 40 = z - 4x/5

by solving the system of equations

x + y + x = 865

3x/5 = y - 40

y - 40 = z - 4x/5

we find

x= $317.308

y = $230.385

z = $444.231

Alex had $444.231 in the beginning.

Hence, Alex had $444.231 in the beginning.

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The largest possible area of the forest is 2500 km^2

The perimeter is given as:

P = 200 km

The shape that will give the largest possible area for the forest is a square, and the area is calculated as:

A = (P/4)^2

This gives

A = (200/4)^2

Evaluate

A = 2500 km^2

Hence, the largest possible area of the forest is 2500 km^2

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The fraction of pizza each of her friends get if they split it evenly is 1/8

Number of pizza each friend gets = Quantity of pizza Elaine has ÷ Number of Elaine friends

= 5/8 ÷ 5

= 5/8 × 1/5

= (5 × 1) / (8 × 5)

= 5/40

= 1/8

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A. The exponential growth function that models the data is: [tex]A(t) = 5.89{0.0106t}[/tex]

B. Using the function, the population will be 11 million by 2059.

The function is given by:

[tex]A(t) = A(0)e^{kt}[/tex]

In which:

Item a:

We have that:

A(0) = 5.89, A(50) = 10.

We use this to find k, hence:

[tex]A(t) = A(0)e^{kt}[/tex]

[tex]10 = 5.89e^{50k}[/tex]

[tex]e^{50k} = \frac{10}{5.89}[/tex]

[tex]\ln{e^{50k}} = \ln{\frac{10}{5.89}}[/tex]

[tex]50k = \ln{\frac{10}{5.89}}[/tex]

[tex]k = \frac{\ln{\frac{10}{5.89}}}{50}[/tex]

k = 0.0106.

Hence the equation is:

[tex]A(t) = 5.89{0.0106t}[/tex]

Item b:

We have to solve for t when A(t) = 11, hence:

[tex]A(t) = A(0)e^{kt}[/tex]

[tex]11 = 5.89e^{0.0106t}[/tex]

[tex]e^{0.0106t} = \frac{11}{5.89}[/tex]

[tex]\ln{e^{0.0106t}} = \ln{\frac{11}{5.89}}[/tex]

[tex]0.0106t = \ln{\frac{11}{5.89}}[/tex]

[tex]t = \frac{\ln{\frac{11}{5.89}}}{0.0106}[/tex]

t = 58.9

Rounding up, the population will be of 11 million in 2059.

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Answer: 6 triangles

Step-by-step explanation:

hope this helps :)