Solve the system, enter ur answer as an ordered triple.

Using the Chain Rule, we have: dy/dx = f'(g(x)) * g'(x) = 1 * 1 = 1.The derivative of y with respect to x is 1.

When we compose a function, it may be possible to write it in a variety of different ways. Differentiating such functions can result in different derivatives, but the Chain Rule indicates that the derivatives of the compositions should be the same regardless of how the function is written, if the function is continuous and differentiable.For instance, consider the function f(x) = sin(x²). It can be written as f(g(x)) where g(x) = x² and f(x) = sin(x). Furthermore, it can be written as f(h(x)) where h(x) = x² and f(x) = sin(x). These are both compositions of functions, but they are different compositions that lead to different derivatives.However, if the function is a composite of differentiable functions, the Chain Rule tells us that the derivative of a composite function is the derivative of the outer function multiplied by the derivative of the inner function.

To find dy/dx if y = x using the Chain Rule with y as a composite of the following functions, we must first rewrite y as a composite function: y = f(g(x)) where g(x) = x and f(x) = x. This composite function can be written in a variety of different ways, such as y = f(h(x)) where h(x) = x and f(x) = x, or y = f(k(x)) where k(x) = x and f(x) = x. However, regardless of how we write it, the Chain Rule tells us that the derivative of y is equal to the derivative of the outer function (f(x) = x) multiplied by the derivative of the inner function (g(x) = x).

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Statement 1, 2 and 3 are correct about using the distributive property.

Expanding is the same as using the distributive property. Factoring means going from ab + ac to a(b + c).Factoring can only be done when an expression has two terms.

Statement 1: Expanding is the same as using the distributive property. The distributive property states that a(b + c) = ab + ac. When we expand an expression, we are multiplying everything out. So, expanding an expression is the same as using the distributive property. Therefore, this statement is correct.

Statement 2: Factoring means going from ab + ac to a(b + c).When we factor an expression, we are essentially undoing the distributive property. In other words, we are going from a common factor in the two terms to a product. This is exactly what happens when we factor ab + ac to a(b + c). Therefore, this statement is correct.

Statement 3: Factoring can only be done when an expression has two terms. Factoring is the process of breaking down an expression into simpler factors. However, in order to do that, the expression needs to have two or more terms. If the expression only has one term, then we cannot factor it. Therefore, this statement is correct.

Statement 4: Factoring can only be done when an expression has plus signs. This statement is incorrect. Factoring can be done when an expression has either plus signs or minus signs. For example, we can factor x² - 4 to (x + 2)(x - 2). Therefore, this statement is incorrect.

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Answer:

\( P(X=3)\)

And we can use the probability mass function and we got:

\(P(X=3)=(3C3)(0.45)^3 (1-0.45)^{3-3}=0.091\)

Then the probability that all three have a smart phone is 0.091

Step-by-step explanation:

Let X the random variable of interest "number of students with smartphone", on this case we now that:

\(X \sim Binom(n=3, p=0452)\)

The probability mass function for the Binomial distribution is given as:

\(P(X)=(nCx)(p)^x (1-p)^{n-x}\)

Where (nCx) means combinatory and it's given by this formula:

\(nCx=\frac{n!}{(n-x)! x!}\)

And we want to find this probability:

\( P(X=3)\)

And we can use the probability mass function and we got:

\(P(X=3)=(3C3)(0.45)^3 (1-0.45)^{3-3}=0.091\)

Then the probability that all three have a smart phone is 0.091

(a) The differential equation

\(y' + \dfrac14 y = 3 + 2 \cos(2x)\)

is linear, so we can use the integrating factor method. We have I.F.

\(\mu = \displaystyle \exp\left(\int \frac{dx}4\right) = e^{x/4}\)

so that multiplying both sides by \(\mu\) gives

\(e^{x/4} y' + \dfrac14 e^{x/4} y = 3e^{x/4} + 2 e^{x/4} \cos(2x)\)

\(\left(e^{x/4} y\right)' = 3e^{x/4} + 2 e^{x/4} \cos(2x)\)

Integrate both sides. (Integrate by parts twice on the right side; I'll omit the details.)

\(e^{x/4} y = 12 e^{x/4} + \dfrac8{65} e^{x/4} (8\sin(2x) + \cos(2x)) + C\)

Solve for \(y\).

\(y = 12 + \dfrac8{65} (\sin(2x) + \cos(2x)) + Ce^{-x/4}\)

Given that \(y(0)=0\), we find

\(0 = 12 + \dfrac8{65} (\sin(0) + \cos(0)) + Ce^0 \implies C = -\dfrac{788}{65}\)

and the particular solution to the initial value problem is

\(\boxed{y = 12 + \dfrac8{65} (\sin(2x) + \cos(2x)) - \dfrac{788}{65} e^{-x/4}}\)

As \(x\) gets large, the exponential term will converge to 0. We have

\(\sin(2x) + \cos(2x) = \sqrt2 \sin\left(2x + \dfrac\pi4\right)\)

which means the trigonometric terms will oscillate between \(\pm\sqrt2\). So overall, the solution will oscillate between \(12\pm\sqrt2\) for large \(x\).

(b) We want the smallest \(x\) such that \(y=12\), i.e.

\(0 = \dfrac8{65} (\sin(2x) + \cos(2x)) - \dfrac{788}{65} e^{-x/4}\)

\(\dfrac{788}{65} e^{-x/4} = \dfrac{8\sqrt2}{65} \sin\left(2x + \dfrac\pi4\right)\)

\(\dfrac{197}{\sqrt2} e^{-x/4} = \sin\left(2x + \dfrac\pi4\right)\)

Using a calculator, the smallest solution seems to be around \(\boxed{x\approx21.909}\)

Answer:

j

Step-by-step explanation:

j

Answer:

1 5/12

Step-by-step explanation:

You can do the opposite of this problem to get the answer. 2/3 + 3/4 = 1 5/12. You can confirm this answer by doing 1 5/12 - 3/4. Therefore, 1 5/12 is your answer.

Answer:

$127975, $182875

Step-by-step explanation:

Let the salary in state A be x. Then, the salary in state B is x+54900.

\(x+x+54900=310850 \\ \\ 2x=255950 \\ \\ x=127975 \\ \\ x+54900=182875\)

Answer:

O (5,-3.5)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The formula for the volume of a rectangular prism is V = lwh, where V is the volume, l is the length, w is the width, and h is the height.

We know that V = 5,890.625 cm^3, h = 14.5 cm, and l = 25 cm.

Substituting these values into the formula, we get:

5,890.625 = 25w(14.5)

5,890.625 = 362.5w

w = 16.25

Therefore, the width of the rectangular prism is 16.25 cm.

Answer:

It's A

Step-by-step explanation:
well all you have to do is divide like 5,890.625 dvided by 14.5 then divide again by 25 them bam you got 16.25

Using it's concept, the standard deviation of the data is of 3.742.

For this data-set, the mean is:

M = (1 + 4 + 4 + 4 + 4 + 6 + 5)/7 = 4.

Hence the standard deviation is:

\(S = \sqrt{\frac{(1 - 4)^2 + (4 - 4)^2 + (4 - 4)^2 + (4 - 4)^2 + (4 - 4)^2 + (6 - 4)^2 + (5 - 4)^2}{7}} = 3.742\)

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Answer:

Please find attached pdf

Step-by-step explanation:

Answer:

5150

Step-by-step explanation:

Answer: v(t) = 5,000(1.03)t

Step-by-step explanation:

The width of the room is 5 meters and its length is 20 meters.

A rectangle is a plane figure with four straight sides and four right angles, especially one with unequal adjacent sides, in contrast to a square.

The Perimeter of rectangle is -

P = 2(x + y)

The Area of rectangle is -

A = xy

We can write -

P = 2x + 2y

Py = 2xy + 2y²

Py = 2A + 2y²

2y² - Py + 2A = 0

y = ± (P² - 16A)/4

Given is a rectangular room is 4 times as long as it is wide. Its perimeter is 50.

Perimeter of the room -

2(x + y) = 50

and

x = 4y

Then, the perimeter of the room -

2(x + y) = 50

2(5y) = 50

5y = 25

y = 5 m

Then -

x = 20 m

Hence, the width of the room is 5 meters and its length is 20 meters.

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The height of the hill is approximately 25.73 ft. Where v0 is the initial velocity (108 ft/s), g is the acceleration due to gravity \((-32.2 ft/s^2)\),

To find the height of the hill, we can use the formula for the vertical position of an object under constant acceleration:

h = h0 + v0t + 1/2at^2

where h is the final height, h0 is the initial height, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity (-32.2 ft/s^2).

In this case, we are given that the initial height h0 is 3 ft, the initial velocity v0 is 108 ft/s, and the time t is 9.5 s. We want to find the height of the hill, which we can denote as h_hill. The final height is the height of the plain, which we can denote as h_plain and assume is zero.

At the highest point of its trajectory, the arrow will have zero vertical velocity, since it will have stopped rising and just started to fall. So we can set the velocity to zero and solve for the time it takes for that to occur. Using the formula for velocity under constant acceleration:

v = v0 + at

we can solve for t when v = 0, h0 = 3 ft, v0 = 108 ft/s, and a = -32.2 ft/s^2:

0 = 108 - 32.2t

t = 108/32.2 ≈ 3.35 s

Thus, it takes the arrow approximately 3.35 s to reach the top of its trajectory.

Using the formula for the height of an object at a given time, we can find the height of the hill by subtracting the height of the arrow at the top of its trajectory from the initial height:

h_hill = h0 + v0t + 1/2at^2 - h_top

where h_top is the height of the arrow at the top of its trajectory. We can find h_top using the formula for the height of an object at the maximum height of its trajectory:

h_top = h0 + v0^2/2a

Plugging in the given values, we get:

h_top = 3 + (108^2)/(2*(-32.2)) ≈ 196.78 ft

Plugging this into the first equation, we get:

h_hill = 3 + 108(3.35) + 1/2(-32.2)(3.35)^2 - 196.78

h_hill ≈ 25.73 ft

If the arrow is launched at t0, the equation describing velocity as a function of time would be:

v(t) = v0 - gt

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Answer:

the answer is .5 I think I'm sorry if I'm wrong

Answer:

x > 0.5

Step-by-step explanation:

Let the number be x.

6 + 5x > x + 8

4x > 2

x > 0.5

This is a question on inequalities. If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)

Answer:

-5, 10, 12, 14, 15, 20, 25

Answer:

a) Equilibrium point : [ 947, 53 ]

b) N = 947 is stable equilibrium, N = 53  is unstable equilibrium

c) N0, the population will not go extinct

Step-by-step explanation:

a)

Given that;

r = 2, k = 1000, H = 100

dN/dT = R(1 - N/k)N - H

so we substitute

dN/dt = 2( 1 - N/1000)N - 100

now for equilibrium solution, dN/dt = 0

so

2( 1 - N/1000)N - 100 = 0

((1000 - N)/1000)N = 50

N^2 - 1000N + 50000 = 0

N = 1000 ± √(-1000)² - 4(1)(50000)) / 2(1)

N = 947.213 OR 52.786

approximately

N = 947 OR 53

Therefore Equilibrium point : [ 947, 53 ]

b)

g(N) = 2( 1 - N/1000)N - 100

= 2N - N²/500 - 100

g'(N) = 2 - N/250

SO AT 947

g'(N) = g'(947) =  2 - 947/250 = -1.788 which is less than (<) 0

so N = 947 is stable equilibrium

now AT 53

g'(N) = g"(53) = 2 - 53/250 = 1.788 which is greater than (>) 0

so N = 53  is unstable equilibrium

The capacity k=1000

If the population is less than 53 then the population will become extinct but since the capacity is equal to 1000 then the population will not go extinct.

ANSWER

25s²

EXPLANATION

The area of a square with side length a is the square of its side length:

The values of all angles \( \angle \: GAL, \angle \: LAO, \angle CAO, \: angle \: KAC\) are 71°, 90°, 90°, 90° respectively.

Given angle GAK is 19°.

It is clear that angle KAL is equal to 90°.

So,

\( \angle KAL = {90}^{o} \)

Now,

\( \angle \: KAL = \angle KAG+ \angle \: GAL\)

So,

\( \angle \: GAL = {90}^{o} - {19}^{o} \\ = {71}^{o} \)

Now,

\( \angle \: KAO = 180°\)

Now

\( \angle \: KAL + \angle \: LAO = {180}^{o} \\ \angle \: LAO = {180}^{o} - {90}^{o} \\ \angle \: LAO = {90}^{o} \)

Again,

\( \angle \: CAO = {180}^{o} - \angle \: LAO \\ \angle \: CAO = {180}^{o} - {90}^{o} = {90}^{o} \)

Similarly,

\( \angle \: KAC = \angle \: KAO - \angle \: CAO \\ \angle \: KAC = {180}^{o} - {90}^{o} \\ = {90}^{o} \)

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Answer:

Given equations are,

5x+2y=−2        (1)

3x−5y=17.4      (2)

Multiply equation (1) by 5 and equation (2) by 2, we get,

5(5x+2y)=5×−2

∴25x+10y=−10          (3)

2(3x−5y)=2×17.4

∴6x−10y=34.8          (4)

Adding equations (3) and (4), we get,

31x=24.8

∴x=

31

24.8

​

Put this value in equation (1), we get,

5(

31

24.8

​

)+2y=−2

∴

31

124

​

+2y=−2

∴2y=−2−

31

124

​

∴2y=

31

−186

​

∴y=

31

−93

​

Step-by-step explanation:

The value of angle ABE is 52°

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted by triangle ABC.

The interior angles of a triangle are the inside angles formed where two sides of the triangle meet.

The sum of interior angle in a triangle is 180°

Angle EBD = 180-(90+27)

= 180-117

= 63°

angle ABE + EBD = ABD

ABE = ABD - EBD

ABE = 115-63

= 52°

Therefore the value of angle ABE is 52°

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Answer:

The answer is: 4y(2x+y)

Step-by-step explanation:

Answer:

106

Step-by-step explanation:

174-68=106

Answer:

Step-by-step explanation:

To calculate the amount of money Nathaniel needs to deposit today to fund this gift for his descendants, we can use the present value formula for a perpetuity:

Present Value = Annual Payment / Discount Rate

In this case, the annual payment is R380 000 and the discount rate (expected rate of return) is 6.45% in decimals, or 0.0645 as a fraction. So we can plug these values into the formula:

Present Value = R380 000 / 0.0645

This gives us a present value of approximately R5,899,225.68. Therefore, Nathaniel would need to deposit R5,899,225.68 today into the trust fund to provide R380 000 a year forever for his descendants, assuming a 6.45% expected rate of return.

Answer: D. slides the graph 1 unit right

Step-by-step explanation:

See attached image.

According to the Empirical Rule, 99.7% of the measures fall within 3 standard deviations of the mean in the normal distribution.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

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Answer:

B or D

Step-by-step explanation:

I would go with D

Answer:

x=12

Step-by-step explanation:

x-4/2=10

x-2=10

+2. +2

x=12

Answer:

Hey

Step-by-step explanation:

Where is the question