Using f(x) = 8x + 5 and g(x) = 7x - 2, find:g(f(6))

To find y(2), we first need to solve the given differential equation: dy/dx = 8y.

1. Separate variables: divide both sides by y and multiply both sides by dx. This gives us (1/y) dy = 8 dx.
2. Integrate both sides: ∫(1/y) dy = ∫8 dx.
3. The antiderivative of (1/y) is ln|y|, and the antiderivative of 8 is 8x. So we have ln|y| = 8x + C, where C is the integration constant.
4. Solve for y: y = e^(8x + C) = e^(8x) * e^C. Since e^C is also a constant, we can replace it with another constant, say k: y = k * e^(8x).
5. Use the initial condition y(0) = 10 to find the value of k: 10 = k * e^(8 * 0), so k = 10.
6. Plug in the value of k to get the final solution: y = 10 * e^(8x).


Now we can find y(2) by plugging in x = 2: y(2) = 10 * e^(8 * 2) = 10 * e^16.

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Answer:

The first one I'm pretty sure.

Step-by-step explanation:

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\(y=\dfrac{qx}{p}\\\\qx=py\\\\x=\dfrac{py}{q}\)

Answer:

\(x = \frac{yp}{q}\)

Step-by-step explanation:

the power series representation of 2x * cos(\(x^2\)) is:

\(2x * cos(x^2) = 2x - x^4/1! + x^8/2! - x^12/3! + ...\)

with an infinite radius of convergence.

To find the power series representation of 2x * cos(\(x^2\)) by differentiating the power series representation of sin(\(x^2\)), we'll start with the power series representation of sin(\(x^2\)) and differentiate it term by term.

The power series representation of sin(\(x^2\)) is:

sin(x^2) = x^2 - (x^2)^3/3! + (x^2)^5/5! - (x^2)^7/7! + ...

Differentiating term by term, we'll also multiply each term by 2x:

\(2x * cos(x^2) = 2x * (1 - (x^2)^2/2! + (x^2)^4/4! - (x^2)^6/6! + ...)\)

To simplify this expression, we'll distribute the 2x:

\(2x * cos(x^2) = 2x - 2x * (x^2)^2/2! + 2x * (x^2)^4/4! - 2x * (x^2)^6/6! + ...\)

Simplifying further:

\(2x * cos(x^2) = 2x - x^4/1! + x^8/2! - x^12/3! + ..\).

This gives us the power series representation of 2x * cos(\(x^2)\). Each term has an alternating sign and involves higher powers of x.

Now, let's discuss the radius of convergence. The power series representation of sin\((x^2\)) has an infinite radius of convergence because it converges for all x.

When we differentiate or multiply a power series by a polynomial, the radius of convergence remains the same. Therefore, the power series representation of 2x * cos(\(x^2\)) also has an infinite radius of convergence.

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Answer:

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Answer:

D. 702square inches

Step-by-step explanation:

1. V=78km^3

2. K=∛9

3. K^3=∛9^3

4.9 x 78=702

Rest of the Key for the test is here:

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Elena should choose the South Market to maximize her chance of buying both cherries and asparagus.

The study of random events or phenomena falls under the category of probability, which is a branch of mathematics. It is a scale between 0 and 1, with 0 denoting impossibility and 1 denoting certainty, used to convey the likelihood that an event will occur or not.

To determine which market Elena should choose to maximize her chance of buying both cherries and asparagus, we need to consider the probabilities of each market individually and calculate the probability of both events occurring together.

Given that the availability of cherries and the availability of asparagus are assumed to be independent, we can calculate the joint probability by multiplying the probabilities of each event.

Let's calculate the joint probability for each market:

North Market:

Probability of cherries = 0.96

Probability of asparagus = 0.5

Joint probability = Probability of cherries * Probability of asparagus = 0.96 * 0.5 = 0.48

South Market:

Probability of cherries = 0.8

Probability of asparagus = 0.65

Joint probability = Probability of cherries * Probability of asparagus = 0.8 * 0.65 = 0.52

Comparing the joint probabilities, we find that the joint probability of finding both cherries and asparagus is higher at the South Market (0.52) compared to the North Market (0.48).

Therefore, Elena should choose the South Market to maximize her chance of buying both cherries and asparagus.

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One concept that I have learnt in geometry is the congruency of triangles.

We know that in geometry, the core of the study is the shapes. We have studied several shapes and the properties of the shapes and there are a lot of concepts that have been discussed.

One of the important concepts of geometry that we have discussed is the congruency of the triangles. There are several reasons why we can say that the triangles are congruent such as;

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Answer:

h = C-50/30

Step-by-step explanation:

50+30h=C

50+30h-50=C-50

30h=C-50

30h/30 = c/30 - 50/30

h = C-50/30

The first step is converting both the velocity and the wind in vector form, as follows:

Then the true speed of the plane is given by the addition of these two vectors, as follows:

\(\vec{v_1} + \vec{v_2} = \sqrt{|v_1|^2 + |v_2|^2 + 2 \cdot |v_1| \cdot |v_2| \cdot \cos(\theta)}\)

The magnitudes of each vector are given as follows:

The angle between these two vectors is given as follows:

\(\theta = 100^\circ - 42^\circ = 58^\circ\)

Thus the resulting speed is obtained as follows:

\(\vec{v_1} + \vec{v_2} = \sqrt{180^2 + 30^2 + 2 \cdot 180 \cdot 30 \cdot \cos(58^\circ)} = 197.54\)

The resulting angle of the plane is then obtained as follows:

\(\angle = \arctan\left(\frac{|v_1| \cdot \sin(\theta) + |v_2| \cdot \sin(\theta_2)}{|v_1| \cdot \cos(\theta) + |v_2| \cdot \cos(\theta_2)}\right)\)

Hence:

\(\angle = \arctan\left(\frac{180 \cdot \sin(58^\circ) + 30 \cdot \sin(42^\circ)}{180 \cdot \cos(58^\circ) + 30 \cdot \cos(42^\circ)}\right)\)

\(\angle = 59.87^\circ\)

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Answer:

  197.5 km/h

Step-by-step explanation:

You want the resultant speed with an airplane at a speed of 180 km/h at 100° is acted upon by a wind at a speed of 30 km/h at 42°. Angles are bearings CW from north.

A vector calculator makes short work of this. The resultant speed is ...

  197.5 km/h at 92.6°

The law of cosines can be used to find the side opposite the known angle in the triangle with sides 30 km/h and 180 km/h. The known angle is ...

  180° -(100° -42°) = 122°

So, the resultant speed is ...

  c = √(a²+b²-2ab·cos(C))

  = √(30² +180² -2(30)(180)·cos(122°)) ≈ √39023.13

  c ≈ 197.543

The true speed of the plane is about 197.5 km/h.

__

Additional comment

You will notice that we used bearing angles directly in the calculator computation. As long as angles are consistently measured, it doesn't matter how they're measured.

When plotting the vectors on the Cartesian plane, we need to subtract the bearing angles from 90° to make them correspond to the vectors plotted on a map with north at the top.

A flow network with supplies is a directed capacitated graph where each edge has a capacity indicating the maximum flow that can pass through it. The flow in the network represents the movement of a certain resource (e.g., water, electricity, goods) from sources to sinks.

In a flow network with supplies, there may be multiple sources, which are nodes that generate the resource and have outgoing edges, and multiple sinks, which are nodes that consume the resource and have incoming edges.

The sources and sinks can have different supply or demand values, indicating the amount of resource they generate or consume.

The edges in the flow network have capacities that restrict the maximum flow that can pass through them. The capacity represents the limit on the amount of resource that can traverse the edge. The flow through an edge cannot exceed its capacity.

The objective in a flow network is to determine the maximum flow that can be sent from sources to sinks while respecting the capacities of the edges. This is typically solved using algorithms such as the Ford-Fulkerson algorithm or the Edmonds-Karp algorithm.

The concept of a flow network with supplies is important in various applications, such as transportation networks, communication networks, and supply chain management, where resources need to be efficiently distributed from multiple sources to multiple sinks, taking into account the capacity constraints of the network.

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Only statement left is "Events A and B are mutually exclusive," which is also not true since P(A∩B) = 0.1, which is greater than 0.

Thus, none of the statements is true.

None of the statements is true.

If events A and B were independent, then P(A∩B) = P(A)P(B) = 0.4, which is not equal to 0.1.

If events A and B were mutually exclusive, then P(A∩B) = 0, which is not equal to 0.1.

Therefore, neither of the first two statements is true.

Since P(A∪B) = P(A) + P(B) - P(A∩B), we have P(A∩B) = 0.4, which is not equal to 0.1. Therefore, the third statement is not true.

The only statement left is "Events A and B are mutually exclusive," which is also not true since P(A∩B) = 0.1, which is greater than 0.

Thus, none of the statements is true.

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Substitute 80 for C in the formula F = 9/5C +32 to obtain the temperature in fahrenheit.

Thus temperature in

18 ft is equal to 6 yards. A yard is one linear yards. "Yd" is the yard symbol. It is equivalent to three feet or 36 inches.

The majority of cloth is now sold by the linear yard. A linear yard is 36" long, with a width that varies depending on the cloth roll. Only the length of the material is considered when measuring in linear yards. To calculate square yards, multiply the length and width in yards. In a yard, there are 36 inches. The length of a yard of fabric is 36 inches. Calculating the amount of fabric required for a sewing job is a little more difficult than that, though. A yard of fabric is always one yard long, however the breadth varies depending on where you get it. Between 33 and 44 inches are the typical widths.

Add the conversion factor "0.33333333333278" to the number in feet.

So, 18 feet

= 18 × 0.33333333333278

= 5.99999999999 yards.

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Answer:

MN = 25

Step-by-step explanation:

If LN=45, then the addition of both quantities will be 45.

LN = 3x + 2 + x + 19

3x + 2 + x + 19 = 45

4x + 21 = 45

4x = 45 - 21 = 24

x = 6

Now that we found the value of "x", we can find the lenght of MN

MN = x + 19

MN = 6 + 19

MN = 25

Hope it was helpful ;)

Answer: MN = 25

Step-by-step explanation:

Since the length is already given we just add the equations equal to it.

45 =  3x + 2 + x + 19  Combine like terms

45 = 4x + 21               Subtract 21 from both sides

24 = 4x                       Divide by 4

x = 6

Now we plug x into the equation needed.

X + 19

6 + 19 = 25

Answer:

Step-by-step explanation:

that is 55/22 = 2.5 hrs

Answer: .two and a half hours.

Step-by-step explanation:

22/1 = 55/x

22x=55

X=2.5

Answer:

A) negative strong correlation B ) negative weak correlation C) no relationship

Step-by-step explanation:

draw a line if these points gather around a line there is a relationship . since the slope will be negative by drawing a straight . Line in the A and B graphs , we according to the will see if it is week and strong according point distribution that will have a negative correlation .C for ) dots scattered no relationship

Answer:

8

Step-by-step explanation:

\(x^2-2x \\x=4\\(4)^2-2(4)\\16-8\\8\)

Answer:

75

Step-by-step explanation:

322 = 2(86) + 2w

322 = 172 + 2w

322-172 = 172 +2w -172

150 = 2w

150/2 = 2w/2

w=75

we get that

as the figure are congruent we get

so the volume is

Answer:

the value of y = 5

Step-by-step explanation:

Answer: When you solve the equations and work them out, you get the answer of $4000.

Answer: Factoring a polynomial is the process of decomposing a polynomial into a product of two or more polynomials.

(1) Find the length of the curve whose equation is y=3+(1/2)cosh2x for 0≤x≤2Solution:The formula for the length of a curve is given by L=∫[a, b] (1+(y')^2)^(1/2) dx. Differentiating the given equation, we get: y' = sinh2xTherefore, (y')² = sinh²2x.Now, L=∫[a, b] (1+(y')²)^(1/2) dx= ∫[0, 2] (1+sinh²2x)^(1/2) dx= ∫[0, 2] (cosh²2x)^(1/2) dx= ∫[0, 2] cosh2x dx

Using the identity cosh2x

= (e^(2x)+e^(-2x))/2, we get:∫[0, 2] cosh2x dx

= 0.25[e^(4) - 1]Therefore, the length of the curve is 0.25[e^(4) - 1]

Answer)(2) Find the length of the curve whose equation is y

=ln(13cosx) for 0≤x≤π/3Solution:

The formula for the length of a curve is given by L=∫[a, b] (1+(y')^2)^(1/2) dx.

Differentiating the given equation, we get:

y' = -13tanx/sinxcosx Therefore,

(y')² = (13tanx/sinxcosx)². Now,

L=∫[a, b] (1+(y')²)^(1/2) dx

= ∫[0, π/3] (1 + (13tanx/sinxcosx)²)^(1/2) dx We know that

1+tan²x=sec²x

Hence, 1 + (13tanx/sinxcosx)²

= (13/sin²x)

Therefore, L=∫[0, π/3] ((13/sin²x)^(1/2) dx

= ∫[0, π/3] (13^(1/2)cosecx) dx

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2 + 7 < 18 inequalities represent the number of remaining hours Mr. Roy could be scheduled to work this week.

The term "inequality" in mathematics refers to a relationship among two expressions or values which are not similar to one another.

Both equations and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols " >, < , ≤ ,or ≥ ".

If x is 2, then 2+7 should equal 9, which is less than the amount Roy wanted to work, and would be the best option for him since he wanted to work for less than 18 hours.

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The complete question is as follows:

Mr. Roy is scheduled to work less than 18 hours this week. he has already worked 7 hours. if x is the remaining number of hours. Mr. Roy could work this week which inequalities represent the number of remaining hours Mr. Roy could be scheduled to work this week? select all that apply

A 2+7 > 18

B 2 + 7 < 18

C 2 +18 > 7

DI > 11

EI < 11

Based on the right triangle altitude theorem, the term that completes the equation is: a. YZ.

The right triangle altitude theorem state that when an altitude is drawn to from the vertex of a right triangle to intersect the opposite side perpendicularly, the length of the altitude would be equal to the geometric mean of the line segments that are formed by the altitude on the right triangle's hypotenuse.

In other words, the square of the length of the altitude equals the product of the line segments formed, according to the right triangle altitude theorem.

XZ = altitude

WY = hypotenuse

WZ and YZ are the line segments formed.

Therefore, the equation would be:

XZ² = (WZ)(YZ) [right triangle altitude theorem]

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Answer:

slope = \(\frac{2}{7}\)

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = \(\frac{2}{7}\) x + \(\frac{3}{4}\) ← is in slope- intercept form

with slope m = \(\frac{2}{7}\)