(j) suppose m1 = 5 kg and m2 = 9 kg. what is the tension in the string?

The difference quotient evaluated in x = 2 gives:

[ f(2 + h) - f(2)]/h = h + 9

So the last option is the correct one.

Here we know the function:

f(x) = x^2 + 5x + 6

And we want to find the difference quotient:

[ f(2 + h) - f(2)]/h

Let's evaluate the function:

f(2 + h) = (2 + h)^2 + 5*(2 + h) + 6

            = 2^2 + h^2 + 4h + 10 + 5h + 6

            = h^2 + 9h + 20

f(2) = 2^2 + 5*2 + 6

f(2) = 4 + 10 +  6 = 20

Then we have:

[ f(2 + h) - f(2)]/h

[h^2 + 9h + 20 - 20]/h

[h^2 + 9h ]/h

Taking the quotient we get:

[h^2 + 9h ]/h = h + 9

So the correct option is the last one.

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Answer: \((\frac{\sqrt{3} }{2} ,-\frac{1}{2} )\)

Step-by-step explanation:

this forms a 30 degree reference angle

and this is in the 4th quadrant

When the angle is 30 degrees, the coordinates are:

\((\frac{\sqrt{3} }{2} ,-\frac{1}{2} )\)

The coordinates of the point on the unit circle will be ((√3) / 2, - 1/2).

The polar coordinate system in geometry is a two-dimensional latitude and longitude that uses the distance from a reference point and the angle from an optical axis are used to identify each point's location on a plane. This polar axis is the ray emanating from the pole in the direction of the point of comparison, which is referred to as the pole.

The cartesian coordinate is (x, y) and polar coordinate is (r, θ). Then the relation is given as,

x = r cos θ

y = r sin θ

The angle is 330° and the radius is one. Then we have

x = 1 x cos 330°

x = (√3) / 2

y = 1 x sin 330°

y = - 1/2

The coordinates of the point on the unit circle will be ((√3) / 2, - 1/2).

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The equation in x and y whose graph is the path of the particle is y = (x - 4)2 + 5. The velocity vector at t= 4 is v(4) = i + 8j.

A vector in mathematics is a quantity that not only expresses magnitude but also motion or position of an object in relation to another point or object. Euclidean vector, geometric vector, and spatial vector are other names for it.

In mathematics, a vector's magnitude is defined as the length of a segment of a directed line, and the vector's direction is indicated by the angle at which the vector is inclined.

Given r(t) as r(t) = x(t)i + y(t)j

Thus, this means that:

x = t+ 4         y = t2 + 5      

We see that we can solve t as:            

t = x - 4, thus:

y = (x - 4)2 + 5

v(t) is given by r'(t).

r'(t) = v(t) = i + 2tj                      

at t = 4:

v(4) = i + 8j

The acceleration is given by:  r"(t).

a(t) = r"(t) = 0i + 2j

The acceleration at t = 4 is:

a(4) = 0i + 2j

Hence, the equation in x and y whose graph is the path of the particle is y = (x - 4)2 + 5. The velocity vector at t= 4 is v(4) = i + 8j.

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High intensity fatigue involves the combination of impaired action potential firing from the alpha motor neuron and the buildup of H+ ions which accelerates the activity of the myosin ATPase.

High intensity fatigue occurs when the muscles are subjected to intense or prolonged activity, leading to a decrease in their ability to generate force. Several factors contribute to high intensity fatigue, and two of them are impaired action potential firing from the alpha motor neuron and the buildup of H+ ions. Impaired action potential firing from the alpha motor neuron refers to a decrease in the ability of the nerve impulses to differentiate stimulate muscle contraction.

This can result in reduced muscle activation and force production during high-intensity activities. Together, impaired action potential firing and the buildup of H+ ions contribute to high intensity fatigue by reducing muscle activation and interfering with the normal functioning of muscle fibers.

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Answer:

950.40

Step-by-step explanation:

The annual amount withheld for state tax would be $950.40.

Given that, gross pay $23760 married with 3 dependents state income tax rate 4%,

We need to calculate, amount withheld annually for state tax.

To calculate the annual amount withheld for state tax, we need to multiply the gross pay by the state income tax rate.

Here's the calculation:

Annual state tax withheld = Gross pay x State income tax rate

Gross pay = $23,760

State income tax rate = 4% (0.04)

Annual state tax withheld = $23,760 x 0.04 = $950.40

Therefore, the annual amount withheld for state tax would be $950.40.

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Complete question =

Find the amount withheld annually for state tax.  Gross pay $23760 married with 3 dependents state income tax rate 4%

Answer: 21450

Step-by-step explanation:

That is the initial price.

The line cross the y axis at 21450.

The correct option is (C)

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

Elise is buying a new car selling for $21,450.

The rate of depreciation on this type of car is 8% per year.

Using f(x) = A \((1+r)^x\)

A= $21,450.  and r = -8% (depreciated)

So, f(x) = A \((1+r)^x\)

f(x) = 21450 \((1- 8/100)^x\)

= 21450 x \((0.92)^x\)

Thus, the line cross the y axis at

= 21450 ( initial point)

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It would take 5040 cubic inches of water to completely fill the aquarium.

We know that the formula for the volume of cuboid :

V = length × width × height

Let us assume that l represents the length of the aquarium, w represent the width and h represents the height.

Here, l = 20 inches

w = 14 inches

and h = 18 inches

Using the formula for the volume of cuboid, the volume of aquarium would be,

V = l × w × h

V = 20 × 14 × 18

V = 5040 cu.in.

Therefore, it would take 5040 cu.in. of water.

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The rectangle with a perimeter of 100 inches that has maximum area has dimensions of 25 inches by 25 inches, resulting in a maximum area of 625 square inches.

This is achieved by dividing the perimeter equally into four sides, creating a square shape. To find the dimensions of the rectangle with maximum area, we consider the perimeter of the rectangle, which is given as 100 inches. Let's assume the length of the rectangle is L inches, and the width is W inches. The perimeter of a rectangle is given by the equation P = 2L + 2W. Since we are given that the perimeter is 100 inches, we have 2L + 2W = 100. Simplifying this equation, we get L + W = 50. To find the dimensions that maximize the area, we need to find the values of L and W that satisfy this equation and result in the largest possible area. One way to maximize the area is by making the rectangle a square, where all sides are equal. In this case, L = W. Substituting this into the equation L + W = 50, we get 2L = 50, which gives L = 25. Therefore, the dimensions of the rectangle with maximum area are 25 inches by 25 inches. The area of this rectangle is calculated by multiplying the length and width, giving us 25 * 25 = 625 square inches. Hence, the maximum area for a rectangle with a perimeter of 100 inches is 625 square inches.

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Answer:

6. What is the area of a circle you drew?

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

because all the orher ones are wrong and not correct.

Answer: The order of rotational symmetry of a shape is the number of times it can be rotated around a full circle and still look the same. If the triangle is rotated a full 360°, it never looks the same except when it arrives back at its original starting position.

Step-by-step explanation:

The order of rotational symmetry of this drawing is 4.

Each point in a figure is transformed into a rotation by rotating it a certain amount of degrees around another point.

As this is not a regular octagon, the appearance after a 45° rotation is different:

It must be rotated 90 degrees before it appears the same.

As a result, it maintains its appearance following rotations of 90, 180, 270, and 360 degrees, when it returns to its initial position.

As a result, the rotational symmetry order is 4.

The image is given in the image below.

Therefore, the order of symmetry is 4.

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The complete question:

What is the order of rotational symmetry of this drawing?

The drawing image is given in the image below.

The simplified sum of the expression ∑+1=−1 (2 − 1) is 2.

The given expression is the sum of (2 - 1) from i = -1 to n, where n = 1. Therefore, the expression can be simplified as follows:

∑+1=−1 (2 − 1) = (2 - 1) + (2 - 1) = 1 + 1 = 2

In this case, the value of n is 1, which means that the summation will only be performed for i = -1. The expression inside the summation is (2 - 1), which equals 1. Thus, the summation is equal to 1.

Adding 1 to the result of the summation gives:

∑+1=−1 (2 − 1) + 1 = 1 + 1 = 2

Therefore, the simplified sum of the expression ∑+1=−1 (2 − 1) is 2.

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Answer:

HL

Step-by-step explanation:

By the reflexive property of congruence, NL is congruent to NL. Note that NL is a leg shared by both triangles. Next, we can see that the two hypotenuses of the triangles are marked as congruent. This is enough information to prove that NKL is congruent to NJL by the HL congruence theorem.

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To solve this problem, we need to use trigonometry and the concept of distance, speed, and time.

a. We can use the Law of Cosines to find the distance between the boat and the lighthouse the second time. Let's call this distance "d". We know that the boat sailed for 3 hours at a speed of 16 mph, so it covered a distance of 3 x 16 = 48 miles. We also know the two bearings of the lighthouse, which form a triangle with the boat's position at the two times. We can use the included angle between the bearings (N10°E and N38°E), which is 28 degrees, and the side opposite to it (48 miles), to find the distance between the boat and the lighthouse using the Law of Cosines:

d^2 = 48^2 + x^2 - 2(48)(x)cos(28)
where x is the distance between the two bearings, which is what we want to find. Solving for x, we get:

x ≈ 36.6 miles

Therefore, the boat is about 36.6 miles from the lighthouse the second time.

b. To find how close the boat will approach the lighthouse if it follows the same course and speed, we need to draw a diagram and use some trigonometry. Let's call the closest distance between the boat and the lighthouse "y". We know that the boat will sail for a certain time, t, and cover a distance of 16t miles. We also know the bearing of the lighthouse, which is N38°E. We can use the right triangle formed by the boat's position, the lighthouse, and the closest approach point, to find y using trigonometry:

tan(38) = y/(16t)
y = 16t tan(38)

Therefore, the closest distance between the boat and the lighthouse will depend on the time it takes the boat to reach the lighthouse. If we want to know how close the boat will get after, say, 6 hours, we can substitute t = 6 in the above equation and get:

y ≈ 66.1 miles (rounded to the nearest tenth of a mile)

Therefore, if the boat follows the same course and speed, it will get as close as about 66.1 miles to the lighthouse.

1. Boat's speed: 16 miles per hour
2. First bearing of the lighthouse: N10°E
3. Time passed: 3 hours
4. Second bearing of the lighthouse: N38°E

a. To find the distance between the ship and the lighthouse the second time, we can use the Law of Sines.

First, we can calculate the distance traveled by the ship during the 3-hour period: 16 miles per hour * 3 hours = 48 miles.

Now, let's use the angle difference (38° - 10° = 28°) and form a triangle with the distance traveled (48 miles) and the two bearings:

sin(28°) / x = sin(10°) / 48 miles

By solving for x, we get the distance between the ship and the lighthouse the second time:

x ≈ 20.7 miles (rounded to the nearest tenth)

b. To find the closest approach to the lighthouse, we can use the Law of Cosines with the same triangle:

c^2 = a^2 + b^2 - 2ab*cos(C)

Where a = 48 miles, b = 20.7 miles, and angle C = 28°

c^2 ≈ 48^2 + 20.7^2 - 2(48)(20.7)cos(28°)

Solving for c, we find the closest approach:

c ≈ 18.9 miles (rounded to the nearest tenth)

So, the answers are:
a. The ship is about 20.7 miles from the lighthouse the second time.
b. The closest approach to the lighthouse will be approximately 18.9 miles.

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The probability that Isaiah makes a penalty kick is the likelihood of making the kick

The probability that Isaiah makes both penalty kicks is 35%

From the sample space, there are 7 occurrences where Isaiah makes both penalty kicks, and there are 20 occurrences in all

So, the probability (p) that Isaiah makes both penalty kicks is:

p = 7/20

Evaluate the quotient

p = 0.35

Express as percentage

p = 35%

Hence, the probability that Isaiah makes both penalty kicks is 35%

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Answer: -1536

Step-by-step explanation:

1: 4(3+3) (3+1) (3+5) (3-5)

2: 4(6) (4) (8) (-2)

3: 24 (4) (8) (-2)

4: 96 (8) (-2)

5: 768 (-2)

= -1536

An easement enabling its holder to prevent the possessor of the land subject to the easement from doing certain acts or exercising certain rights of ownership is known as a negative easement.

A negative easement grants the holder the right to restrict or prohibit specific activities on the land, even though the possessor of the land would otherwise have the legal right to engage in those activities. It imposes limitations on the use or enjoyment of the land by the possessor.

For example, a negative easement may prohibit the landowner from building any structures that would obstruct the view of the neighboring property or from engaging in any activities that would cause excessive noise or pollution. The holder of the negative easement, such as a neighboring property owner or a conservation organization, can enforce these restrictions to protect their interests or preserve certain conditions.

Negative easements are typically established through legal agreements or by court decisions. They serve to balance the rights of the landowner with the interests of the easement holder, allowing for the protection of specific rights or conditions associated with the land.

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The option that shows trigonometric functions of the same angle is:

Option C: cosY = 8 / 17, cotY = 8 / 15, secY = 17 / 8

The three primary trigonometric ratios are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

Here,

cosY = 8/17, cotY = 8/15, secY = 17 / 8

We know that in trigonometric ratios that:

cosY = 1 / SecY

Thus:

8 / 17 = 1 / secY

secY = 17 / 8

Now, using pythagoras theorem, we have:

P = √[17² - 8²]

P = 15

Thus:

Cot Y = 8 / 15

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The fact that the ratio of 0.75 to 0.375 is a small whole number is an illustration of "Law of Multiple Proportions."

When two elements combine to form and over one compound, the weights with one element which combine with such a fixed weight of the second are in a ratio of small whole numbers, according to the law of multiple proportions.

Some key features regarding the Law of Multiple Proportions are-

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The complete question is-

Carbon monoxide can be broken down into carbon and oxygen in a mass ratio of 3:4 or 0.75. Carbon dioxide can be broken down into carbon and oxygen in a mass ratio of 3:8 or 0.375. The fact that the ratio of 0.75 to 0.375 is a small whole number is an illustration of

The solution set of the equation x/3 = 8/(x + 2) when calculated is x = -6 or x = 4

Given the following equation

x/3 = 8/(x + 2)

Cross multiply

x(x + 2) = 24

To find the solution set of x(x + 2) = 24, we need to solve for x by simplifying the left-hand side of the equation and then factoring it.

x(x + 2) = 24

Expanding the left-hand side, we get:

x² + 2x = 24

Subtracting 24 from both sides, we get:

x² + 2x - 24 = 0

Now we can factor the quadratic expression on the left-hand side:

(x + 6)(x - 4) = 0

Using the zero product property, we know that the product of two factors is zero if and only if at least one of the factors is zero.

Therefore, we can set each factor equal to zero and solve for x:

x + 6 = 0 or x - 4 = 0

Solving for x, we get:

x = -6 or x = 4

So, the solution set is { -6, 4 }.

These are the values of x that make the equation true when plugged in.

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Answer:

Its walking at 3/5 miles per hour

A CR less than or equal to 0.1 is considered acceptable, indicating a consistent set of judgments in comparing the criteria. If the CR is greater than 0.1, it is advised to revise the pairwise comparisons to improve consistency.

The Consistency Ratio (CR) in the context of the GEAR Matrix (which is related to bikes, not fruit) measures the level of consistency in judgments made when comparing criteria in a decision-making process, such as the Analytic Hierarchy Process (AHP). To calculate the CR for the Criteria in the GEAR Matrix, follow these steps:

1. Determine the pairwise comparison matrix by comparing the importance of each criterion against the others.
2. Calculate the weights of each criterion by normalizing the columns and finding the average for each row.
3. Multiply the pairwise comparison matrix by the weight vector to obtain a new vector.
4. Divide each element of the new vector by its corresponding weight to obtain the Consistency Vector.
5. Calculate the average of the Consistency Vector to get the Consistency Index (CI).
6. Divide the CI by the Random Index (RI) for the specific matrix size (this value can be found in AHP literature) to obtain the Consistency Ratio (CR).

A CR less than or equal to 0.1 is considered acceptable, indicating a consistent set of judgments in comparing the criteria. If the CR is greater than 0.1, it is advised to revise the pairwise comparisons to improve consistency.

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Answer:

Step-by-step explanation:

0.04

All the numbers that show 4% as an equivalent fraction, decimal or percent from the listed options are:

Percent counts the number compared to 100.

So, if we have a%, that means for each 100, there are 'a' parts. If we divide each of them with 100, we get:

For each 1, there are a/100 parts.

Thus, 50% = 50/100 = 0.50 (in decimal)

For this case, the percent we have is 4%

That shows that for each 100 items, we have 4 of them. This can be written in fraction as 4/100

Solving this division, we get the result in decimal as 0.04

Thus, all the numbers that show 4% as an equivalent fraction, decimal or percent from the listed options are:

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The stress function satisfies the conditions of compatibility for a two-dimensional problem.

Given stress function is 50x² - 60xy - 70y²

To determine whether the stress function satisfies the conditions of compatibility for a two-dimensional problem, it is required to find the strains and then check for compatibility equations.

Strain components are given as,

εx = ∂υ/∂x + (du/dx)

εy = ∂υ/∂y + (du/dy)

γxy = ∂υ/∂y + (du/dx)

Here,

υ = 50x² - 60xy - 70y²

du/dx = 100x - 60

ydu/dy = -60x - 140y

∂υ/∂x = 100x - 60y

∂υ/∂y = -60x - 140y

∂²υ/∂y² = -140

∂²υ/∂x² = 100

Now,εx = 100x - 60

yεy = -140y - 60

xγxy = -60y - 60x

Taking derivative of εy w.r.t x,

∂(εy)/∂x = -60

Similarly, taking derivative of εx w.r.t y,

∂(εx)/∂y = -60

∴ The stress function satisfies the conditions of compatibility for a two-dimensional problem.

Stress components are given as,

σx = (C11εx + C12εy)

σy = (C21εx + C22εy)

τxy = (C44γxy)

Here,C11 = C22 = 100, C12 = C21 = -60 and C44 = 0

Therefore,

σx = 100(100x - 60y) - 60(-140y - 60x)

= 19600x - 8800

yσy = -60(100x - 60y) + 100(-140y - 60x)

= -19600y + 8800x

τxy = 0

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Answer:

(0, 4/3)

Step-by-step explanation:

2x +3y =4

3y =4 -2x

y = 4/3 - 2/3x

y = -2/3x + 4/3

y = -2/3(0) + 4/3

y = 4/3

-----------

or just plug in 0 for x from the start

2(0) + 3y = 4

3y = 4

y = 4/3

Answer:

The correct answer is:

6 inches by 6 inches

Step-by-step explanation:

Given that

Area of Enlarged photo = 256 square inches

Let x be the side of original photo

then the equation for area of new enlarged photo will be:

\((x+10)^2 = 256\)

We have to solve the given equation to find the side length of original photo

Taking square root on both sides

\(\sqrt{(x+10)^2} = \sqrt{256}\\x+10 = 16\)

Subtracting 10 from both sides

\(x+10-10 = 16-10\\x = 6\)

So the side length of original photo is 6 inches. The dimensions will be 6 inches by 6 inches.

Hence,

The correct answer is:

6 inches by 6 inches

Answer:

Its B on edge 2021

Step-by-step explanation:

Just took a test

Step-by-step explanation:

a=bx + cx

2

2*a=x(b+c)*2

2

2a = x(b+c)

(b+c) (b+c)

2a = x

(b+c)

There are 504 multiple ways to go about doing something. the probability that perhaps a specific event (or group of events) would happen.

either as a range between 0 and 100% or even as a percentage on either a line plot between 0 (impossibility) to 1 (certainty).

THE PROCEDURE IS HERE.

The three airports will each receive a fleet of nine taxis.

Three people travel to airport A, five to airport B, and one to airport C.

There are several different methods that this can be done, including:

(9C3) (6C5) (1C1)

(84) (6) (1) (1)

= 504

The result is that this could be done in 504 different ways.

Based on the probability equation, the likelihood that a will take place is related to the ratio of favorable outcomes to all outcomes. Amount of favorable outcomes/Total Number of outcomes determines the probability that an event will occur, P(E).

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Answer:

I gave you the answer

Step-by-step explanation:

I hope