Decomposition of 1,980

(a) Given the position function

x(t) = (B m/s²) t² + 5 m

it's clear that the object accelerates at B m/s² (differentiate x(t) twice with respect to t), so that the force exerted on the object is

F(t) = (2 kg) (B m/s²) = 2B N

(b) Recall the work-energy theorem: the total work performed on an object is equal to the change in the object's kinetic energy. The object is displaced by

∆x = x(5 s) - x(0 s)

∆x = ((B m/s²) (5 s)² + 5 m) - ((B m/s²) (0 s)² + 5 m)

∆x = 25B m

Then the work W performed by F (provided there are no other forces acting in the direction of the object's motion) is

W = (2B N) (25B m) = 50B² J = 200 J

Solve for B :

50B² = 200

B² = 4

B = ± √4 = ± 2

Since the change in kinetic energy and hence work performed by F is positive, the sign of B must also be positive, so B = 2 and the object accelerates at 2 m/s².

(c) We found in part (b) that the object is displaced 25B m, and with B = 2 that comes out to ∆x = 50 m.

Answer:

Domain: [0 , ∞)

Range: (-∞ , 4]

Step-by-step explanation:

For domain, look along the x axis.

The graph starts from x = 0 and it's ending point isn't given in the graph as it continues moving along the positive x axis.

Hence, it's ending point must be ∞

Domain of a function is:

[minimum point in x, maximum point in x]

=> [0, ∞)

"),(" is used for infinity.

"],[" for points that lie within the domain of the function.

For range, look along the y axis.

The graph starts at y = 4, and continues moving downwards till infinity.

Range:

[minimum in y, maximum in y]

=> (-∞, 4]

Answer:

lol in your head , literally

Step-by-step explanation:

After one of your limbs is amputated, you may feel as if the limb is still there. This is called phantom sensation. You may feel: Pain in your limb even though it is physically not there.

Answer:

The nerve in your leg.

Explanation:

It's not your leg that will hurt but the nerve in your leg that'll hurt. So wherever the leg is cut, the nerves must be cut as well, but another thing is when  one of your limbs is amputated, you may feel like the limb is still there. That's called phantom sensation. You might feel pain in your "limb" even though it's not physically there.

[tex]\huge \bf༆ Answer ༄[/tex]

Let's solve ~

Hence, the required power in fractional form is ~

It's a function because we don't have any repeated x coordinates. Any given x input value leads to exactly one y output value.

The domain is {-3,-2,-1,0,1} which is the set of all x inputs.

The range is {-6, -1, 0, 3, 15} which is the set of y outputs.

Answer:

its 1.944

Step-by-step explanation:

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. The formula used to calculate percentage is: (value/total value)×100%.

Explanation:

Divide the side length for B over the corresponding side length for A.

scale factor = B/A = 7/(2.5) = 2.8

Let's now convert this to a fraction

2.8 = 2 + 0.8 = 2 + 8/10 = 20/10 + 8/10 = (20+8)/10 = 28/10

Then reduce that fraction

28/10 = (14*2)/(5*2) = 14/5

Note that 14/5 = 2.8

Answer:

What's the question lol

Answer:

The equation of a line which contains the point (2, 5) and is parallel to the line y = 3x + 5 is

y = 3x - 1

A line is parallel to another when they both have the same slope.

The two equations above have a common slope of 3.

I hope this helped. Have a good new year!

Answer:

2

Step-by-step explanation:

5 feet + 12 inches = 2 yards

Therefore

5 feet + 12 inches = yard(2)

I solving for (s)

hope that helps

Answer: For Y the rate of change is +4

For the rate of x its +5

Step-by-step explanation:

Answer:

It is B

Step-by-step explanation:

Answer:

107

Step-by-step explanation:

Answer:

The answer is 105

Step-by-step explanation:

hope its help:)

Step-by-step explanation:

B

D

A

с

2

2-1

1

2

3 4 5

2 1

2

2 4 5

A

B

2-1

1

2

B

5 4 3 2 1

1

2 3 4 5

Answer:

ddd

Step-by-step explanation:

The given equation above written in the form AX = b will be;

[tex]\left[\begin{array}{ccc}1&2\\2&3\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}11\\18\\\end{array}\right][/tex]

Given the system of equation;

This equation can be represented in matrix form as [tex]AX = b[/tex]

where:

The given equation above written in the form AX = b will be;

[tex]\left[\begin{array}{ccc}1&2\\2&3\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}11\\18\\\end{array}\right][/tex]

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Answer:

2x^2 + 11x – 1

Step-by-step explanation:

The Formula of the relation is M = 8AT.

The mass of the metal sheet is 960 g.

The expression below shows the variation between the mass of the sheet (M), Area of the Sheet(A), and thickness (T).

Proportionality:

Removing the proportionality sign,

Where:

make K the subject of the equation:

From the question,

Given:

Susbtitute into equation 1

Formula:

Hence the formula of the relation is M = 8AT

If,

Substitute these values into equation 2

Hence,  the mass of the metal sheet is 960 g

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Answer:

......

Step-by-step explanation:

Answer:

x + (4x-20) = 180

by linear pair

therefore x= 70

Applying the definition of linear pair, the value of x is: D. 40.

Therefore:

x + (4x - 20°) = 180°

5x - 20 = 180

5x = 180 + 20

5x = 200

x = 40

Therefore, applying the definition of linear pair, the value of x is: D. 40.

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Answer:

300kms

Step-by-step explanation:

900÷300 is 300. so then i think it would be 300kms

Answer: neither statement is correct

Step-by-step explanation:

on Khan Academy

The statement by Tom "A player will most likely get 17.5 " is correct based on expected value .

Expected value (also known as EV, expectation, average, or mean value) is a long-run average value of random variables. It also indicates the probability-weighted average of all possible values. Expected value is a commonly used financial concept.

According to the question

Tom and Rosie are designing a game.

In each turn, a player rolls five 6-sided dice and adds the numbers showing on each face to determine how many points they get that turn.  

let X represent the sum in a given turn

the expected value of X is E(X)=17.5

As

expected value is also called mean value  

i.e

highest value of sum = 6+6+6+6+6

                                   = 30

Lowest value of sum = 1+1+1+1+1

                                   = 5

Therefore,

Mean = [tex]\frac{30+5}{2}[/tex]

          = 17.5

Now,

Tom says, "A player will most likely get 17.5

This statement is correct as per expected value which is mean value and it is 17.5 .

Rosie says, "Over 100 turns, we can expect a total of about 175

This statement is incorrect as per expected value as

expected value = 17.5

when 100 turn will happen it will

17.5 * 100

= 1750

Hence, The statement by Tom "A player will most likely get 17.5 " is correct based on expected value .

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Answer:

The answer is to the problem is 18.

The answer is C, 4 to the 21st over 5 to the 6th power.

Answer:

[tex]slope = \frac{20 - 16}{5 - 3} [/tex]

[tex] = \frac{4}{2} [/tex]

[tex] = 2 \: is \: the \: answer[/tex]

The slope of the equation is 2.

The slope of an equation shows a gradient line that measures the steepness of the line.

It can be expressed by using the formula:

[tex]\mathbf{slope = \dfrac{\Delta y}{\Delta x}}[/tex]

[tex]\mathbf{slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

From the parameters given;

[tex]\mathbf{slope = \dfrac{20-16}{5-3}}[/tex]

[tex]\mathbf{slope = \dfrac{4}{2}}[/tex]

slope = 2

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32

Divide 192 by 6, to find the amount of baseball cards Nick has.

192 ÷ 6 = 32

32 · 6 = 192

192 ÷ 6 = 32

Nick has 32 baseball cards, which is 6 times less than Juan's amount.

Considering the definition of equation, for a value of n of 10 the cost and revenue are equal.

A first degree equation is a mathematical equality with one or more unknowns.

Solving an equation consists of finding the value that the unknown must take so that equality is fulfilled.

The steps to solve an equation are as follows:

The cost C in dollars of producing a certain item is represented by the equation C = [tex]\frac{n}{2}[/tex]+ 20, where n represents the number of items produced.

The revenue R, in dollars, from selling n items is represented by the equation R=2n+ 5.

The cost and revenue are equal. Then:

[tex]\frac{n}{2}[/tex]+ 20= 2n+ 5

Solving:

When a term passes to the other side of equality, its sign changes (if it is positive it becomes negative and vice versa):

20 -5= 2n - [tex]\frac{n}{2}[/tex]

15= [tex]\frac{3}{2}n[/tex]

The X is cleared. Since the term in front of it is multiplying, it goes to the other side of the equation by dividing.

15 ÷[tex]\frac{3}{2}[/tex]= n

10= n

Finally, for a value of n of 10 the cost and revenue are equal.

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The volume of the solid of revolution is [tex]\frac{16\pi}{3}[/tex] cubic units.

First, we determine the limits between the two curves. ([tex]f(x) = 4\cdot x -2[/tex], [tex]g(x) = x^{2}+1[/tex])

[tex]f(x) = g(x)[/tex] (1)

[tex]4\cdot x - 2 = x^{2}+1[/tex]

[tex]x^{2}-4\cdot x +3 = 0[/tex]

[tex](x-1)\cdot (x-3) = 0[/tex]

The lower and upper bounds are 1 and 3, respectively. It is to notice that [tex]f(x) > g(x)[/tex] for [tex]x \in (1, 3)[/tex]. Thus, we determine the volume of the solid of revolution by shell method, that is to say:

[tex]V = 2\pi \int\limits^a_b {x\cdot |f(x) - g(x) |} \, dx[/tex] (2)

If we know that [tex]a = 3[/tex], [tex]b = 1[/tex], [tex]f(x) = 4\cdot x - 2[/tex] and [tex]g(x) = x^{2}+1[/tex], then the volume of the solid of revolution is:

[tex]V = 2\pi \int\limits^3_1 {|4\cdot x^{2}-2\cdot x -x^{3}-x|} \, dx[/tex]

[tex]V = 2\pi\int\limits^3_1 {(4\cdot x^{2}-x^{3}-3\cdot x)} \, dx[/tex]

[tex]V = 8\pi \int\limits^3_1 {x^{2}} \, dx - 2\pi \int\limits^3_1 {x^{3}} \, dx -6\pi \int\limits^3_1 {x} \, dx[/tex]

[tex]V = 8\pi\cdot \left(\frac{3^{3}}{3}-\frac{1^{3}}{3} \right)-2\pi \cdot \left(\frac{3^{4}}{4}-\frac{1^{4}}{4} \right) - 6\pi\cdot \left(\frac{3^{2}}{2}-\frac{1^{2}}{2} \right)[/tex]

[tex]V = \frac{208\pi}{3} - 40\pi -24\pi[/tex]

[tex]V = \frac{16\pi}{3}[/tex]

The volume of the solid of revolution is [tex]\frac{16\pi}{3}[/tex] cubic units.

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