How would knowing the slope of a linear function help determine whether a function is increasing or decreasing?

The inverse Laplace transform of G(s) is:

g(t) = (2/3) \(e^{-t}\) - (1/3) \(e^{-2t}\) - (1/3) \(e^{-3t}\)

The inverse Laplace transform of the function G(s) using the partial fraction expansion coefficients obtained from MATLAB, we need to express G(s) in terms of partial fractions.

G(s) = (2s³ + 5s² + 3s + 6) / (s³ + 6s² + 11s + 6)

The denominator of G(s) can be factored as:

s³ + 6s² + 11s + 6 = (s + 1)(s + 2)(s + 3)

Let's write G(s) in terms of partial fractions as follows:

G(s) = A / (s + 1) + B / (s + 2) + C / (s + 3)

To find the values of A, B, and C, we can multiply both sides of the equation by the denominator and equate the coefficients of like powers of s.

(2s³ + 5s² + 3s + 6) = A(s + 2)(s + 3) + B(s + 1)(s + 3) + C(s + 1)(s + 2)

Expanding the right side and collecting like terms, we have:

2s³ + 5s² + 3s + 6 = (A + B + C)s² + (5A + 4B + 3C)s + (6A + 3B + 2C)

Comparing the coefficients of like powers of s, we get the following equations:

A + B + C = 0

5A + 4B + 3C = 5

6A + 3B + 2C = 3

Solving these equations, we find:

A = 2/3

B = -1/3

C = -1/3

Therefore, the partial fraction expansion of G(s) becomes:

G(s) = (2/3) / (s + 1) - (1/3) / (s + 2) - (1/3) / (s + 3)

Now, we can use the linearity property and known Laplace transforms to find the inverse Laplace transform of each term.

Taking the inverse Laplace transform, we have:

g(t) = (2/3) \(e^{-t}\) - (1/3) \(e^{-2t}\) - (1/3) \(e^{-3t}\)

Therefore, the inverse Laplace transform of G(s) is:

g(t) = (2/3) \(e^{-t}\) - (1/3) \(e^{-2t}\) - (1/3) \(e^{-3t}\)

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Answer:

7+3^2(-5+1) divided by 2 is -11

Answer:

-11

Step-by-step explanation:

I am pretty sure -11 is correct

we know that a year has 12 months, so 1 year plus 8 more moths will be (12+8)/12 or 20/12 years, or 5/3 year.

\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$70000\\\ P=\textit{original amount deposited}\dotfill & \$60000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to \frac{20}{12}\dotfill &\frac{5}{3} \end{cases} \\\\\\ 70000=60000[1+(\frac{r}{100})(\frac{5}{3})]\implies \cfrac{70000}{60000}=1+(\frac{r}{100})(\frac{5}{3})\)

\(\cfrac{7}{6}=1+\cfrac{5r}{300}\implies \cfrac{7}{6}=1+\cfrac{r}{60}\implies \cfrac{7}{6}-1=\cfrac{r}{60}\implies \cfrac{1}{6}=\cfrac{r}{60} \\\\\\ \cfrac{60}{6}=r\implies 10=r\)

A simple difference is also called a marginal means difference. Option B

In experimental design and statistical analysis, a simple difference refers to the comparison of means between two groups or conditions. It represents the difference in average scores or values between the groups being compared. It is often used to assess the impact of an independent variable on a dependent variable by examining the variation in means between different levels of the independent variable.

The term "marginal means difference" emphasizes that the comparison is based on the average or marginal means of the groups being compared. It helps to distinguish it from other types of differences, such as interaction effects or main effects, which involve more complex comparisons or analyses in factorial designs.

Overall, a simple difference or marginal means difference is a straightforward way to evaluate the effect of an independent variable on a dependent variable by comparing the average values between different groups or conditions.

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The equation of the line passing through the points (0, 6) and (3, 0) is y = -2x + 6.

What is the slope of the equation?

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

To find the equation of the line passing through the points (0, 6) and (3, 0), we can use the two-point form:

y - y1 = m(x - x1)

where (x1, y1) is one of the given points, and m is the slope of the line.

To find the slope, we can use the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates of the given points, we get:

m = (0 - 6) / (3 - 0)

= -6 / 3

= -2

Substituting this value for m and the coordinates of one of the given points into the two-point form, we get:

y - 6 = -2(x - 0)

Combining like terms and multiplying through the parentheses, we get:

y = -2x + 6

Hence, the equation of the line passing through the points (0, 6) and (3, 0) is y = -2x + 6.

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Answer:

\(\frac{XM}{4y}=u\)

Step-by-step explanation:

First, multiply both sides by M.

X M = 4uy

Now, divide both sides by 4y.

\(\frac{XM}{4y} =\frac{4uy}{4y}\)

Therefore,

\(\frac{XM}{4y}=u\)

The correct option would be "None of these" since the projection is an ellipse and not any of the given options (2, 4, 16, or "This option").

To determine the projection of the region D onto the xy-plane, we need to find the intersection curve of the two paraboloids.

First, let's set the two equations equal to each other:

3x² + (12/24)y² = 16 - x²

Next, we simplify the equation:

4x² + (12/24)y² = 16

Multiplying both sides by 24 to eliminate the fraction:

96x² + 12y² = 384

Dividing both sides by 12 to simplify further:

8x² + y² = 32

Now, we can see that this equation represents an elliptical shape in the xy-plane. The equation of an ellipse centered at the origin is:

(x²/a²) + (y²/b²) = 1

Comparing this with our equation, we can deduce that a² = 4 and b² = 32. Taking the square root of both sides, we have a = 2 and b = √32 = 4√2.

So, the semi-major axis is 2 and the semi-minor axis is 4√2. The projection of region D onto the xy-plane is an ellipse with a major axis of length 4 and a minor axis of length 8√2.

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Answer:

x = 8°

y = 21°

Step-by-step explanation:

27 + 3y = 90

3y = 63

y = 21°

x + 8x + 18 = 90

9x = 72

x = 8°

Given :

A motorboat travels 9 miles downstream (with the current) in 30 minutes.

The return trip upstream (against the current) takes 90 minutes.

To Find :

The speed of stream and motorboat.

Solution :

Let, speed of stream is u and speed of motorboat is v.

Now, we know distance is same in both case.

Distance( downstream ) = speed × time

\(9 = ( v +u ) \times 0.5\\\\v + u = 18\)....1)

Distance( upstream ) = speed × time

\(9 = ( v- u ) \times 1.5\\\\v-u = 6\)....2)

Solving equation 1 and 2 , we get :

v = 12 miles/hour and u = 6 miles/hour

Hence, this is the required solution.

Answer:

The speed of the stream is 6 mph, and the speed of the boat is 12 mph.

Step-by-step explanation:

Downstream:

9 miles in 30 minutes (0.5 hour).

9 mi / 0.5 h = 18 mph

Upstream:

9 miles in 90 minutes (1.5 h).

9 mi / 1.5 h = 6 mph

Let s = speed of stream.

The speed of the stream adds to the speed of the boat downstream and is subtracted fromt he speed of the boat upstream.

Let speed of boat be b.

b + s = 18

b - s = 6

Add the equations.

2b = 24

b = 12

b + s = 18

12 + s = 18

s = 6

The speed of the stream is 6 mph, and the speed of the boat is 12 mph.

Answer:

its -10

Step-by-step explanation:

NO explain needed

y=-2x^2-8x-4

-2x^2-8x=4

divide by negative 2

x^2+4x=-2

complete the square

(x+2)^2=-2+4

(x+2)^2=2

x+2=±\(\sqrt{2}\)

x=-2±\(\sqrt{2}\)

nearest hundreths,

x=-0.59

x=-3.41

The number of seconds to reach Jane will be 2.25 seconds. Then the correct option is B.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The curve of the ball's path is given below.

d = -16t² + 32t + 9

The number of seconds to reach Jane is given as,

0 = -16t² + 32t + 9

16t² - 32t - 9 = 0

16t² - 36t + 4t - 9 = 0

4t(4t - 9) + 1(4t - 9) = 0

(4t - 9)(4t + 1) = 0

t = 9/4, -1/4

t = 2.25, -0.25

The number of seconds to reach Jane will be 2.25 seconds. Then the correct option is B.

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Answer:

The measure of angle WVX is 140°.

Step-by-step explanation:

Let x be the measure of angle WVX.

\( \frac{14}{9} \pi = 2x\)

\( x = \frac{7}{9} \pi( \frac{180}{\pi}) = 140 \: degrees\)

Answer:

angle = arc length/radius
in this case, the arc length is 14/9*\(\pi\) and the radius is 2. Upon multiplying these, you get 140.

so, the answer is 140 degrees.

The percent of the purchase price that is the price of the warranty is: b. 19%.

Using this formula

Purchase price percent=Total cost-Purchase price/Purchase price

Where:

Total cost=$512

Purchase price=$430

Let plug in the formula

Purchase price percent=$512-$430/$430

Purchase price percent=$82/$430

Purchase price percent=0.19×100

Purchase price percent=19%

Inconclusion the percent of the purchase price that is the price of the warranty is: b. 19%.

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The radius of convergence of the power series $\sum_{n=0}^\infty c_n x^n$ is $r$. To find the radius of convergence of the power series $\sum_{n=0}^\infty c_n x^{9n}$, we can rewrite the series as $\sum_{n=0}^\infty c_n (x^9)^n$.

Letting $y = x^9$, we obtain the power series $\sum_{n=0}^\infty c_n y^n$, which has the same coefficients as the original series. By the ratio test, the series $\sum_{n=0}^\infty c_n y^n$ has radius of convergence $R' = r^9$. Therefore, the radius of convergence of the power series $\sum_{n=0}^\infty c_n x^{9n}$ is $r^9$.

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The time taken for Montraie to travel a distance of 88 miles is 2 hours.

Speed is simply referred to as distance traveled per unit time.

It expressed mathematically as;

Speed = Distance ÷ time.

Given the data in the question;

First, we determine the speed of Montraie.

Speed = Distance ÷ time.

Speed =  220 miles ÷ 5 hours

Speed = 44 miles per hour.

Now, time spent in traveling a distance of 88 miles will be;

Speed = Distance ÷ time

Time = Distance / Speed

Time = 88 miles / 44 miles per hour

Time = 2 hours

Therefore, the elapsed time is 2 hours.

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If Montraie drove 220 miles in 5 hours. If he continued at the same rate, then it takes 2 hours to travel 88 miles.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that,

Montraie drove 220 miles in 5 hours.

We need to find how long it would take to reach 88 miles.

Let us form a equation based on given data.

Let x be the time to reach 88 miles.

We need to find value of x.

220/5=88/x

Apply cross multiplication

220x=440

x=440/220

x=2

Hence it takes 2 hours to travel 88 miles with same rate.

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Answers:

Domain:  \(\boldsymbol{(-\infty, \infty)}\)

Range:  \(\boldsymbol{(-\infty, \infty)}\)

=======================================================

Explanation:

domain = set of all possible x inputs

range = set of all possible y outputs

--------------

In this case, the domain is the set of all real numbers because the graph stretches forever to the left and right. There aren't any gaps, holes, jumps, etc to worry about. Any real number works as an input.

We can say x is between \(-\infty\) and \(\infty\) and write \(-\infty < x < \infty\)

That turns into the interval notation \((-\infty, \infty)\)

The curved parenthesis are always used with either infinity because we cannot reach them.

--------------

The range is the same story, but with the y values this time. The graph stretches forever upward and downward due to the arrow.

If it peaked at y = 4, then the range would be \((-\infty, 4]\), but instead the graph goes beyond y = 4 because of that upward arrow.

Answer:

90

Step-by-step explanation:

15+15=30

3x30=90

Therefore, the answer to what divided by 6 equals 15 is 90. You can prove this by taking 90 and dividing it by 6, and you will see that the answer is 15. Tip: For future reference, when you are presented with a problem like "What divided by 6 equals 15?", all you have to do is multiply the two known numbers together.

Therefore, n=90 is your correct answer

Answer:

C. 70 = 10x

E. 15x = 105

Step-by-step explanation:

x = 7

Using method of elimination;

A. X + 7 = 17

Substituting the value of x;

7 + 7 ≠ 17 (Incorrect option)

B. 7 = 17 - x

Substituting the value of x;

7 ≠ 17 - 7  (Incorrect option)

C. 70 = 10x

Substituting the value of x;

70 = 10 * 7  (Correct option)

D. X/35 = 5

Substituting the value of x;

7 / 35 ≠ 5  (Incorrect option)

E. 15x = 105

Substituting the value of x;

15 * 7 = 105  (Correct option)

Step-by-step explanation:

sorry need the graph but when you show graph I will definitely give you the right answer

Answer:

1: 1/2

2: 2

3: 1/2x+2

Answer:

0

Step-by-step explanation:

Answer:

undefined

Step-by-step explanation:

you cannot divide by Zero

The probability of Anna winning chances of buying 20 ticket out of 1500 tickets is  0.013.

Probability simply means possibility. It deals with how likely something is to happen.

Therefore,

p(A) = number of favorable outcomes to A / total number of outcome

Hence,

Number of ticket bought by Anna = 20

Total ticket sold = 1500

Therefore,

probability of the winning chances of Anna = 20 / 1500

probability of the winning chances of Anna = 2 / 150

probability of the winning chances of Anna = 1 / 75

probability of the winning chances of Anna  = 0.013

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Answer:

42.8

Step-by-step explanation:

Answer:

Hey there!

-x+2y=10

2y=x+10

y=1/2x+5

Thus, the y intercept is 5.

Hope this helps!

Answer:

(0,5)

Step-by-step explanation:

-x+2y=10

2y = x+10

y= (1/2)*x+ 5

The y-intercept is the number we add in the end of the equation wich is here (0,5)

Your joints and bones would first have to work harder to support your heavier weight.

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Answer:

27√2

Step-by-step explanation:

9√18

9√9√2

27√2

Answer:

45 degree line

Step-by-step explanation:

A distinguishing characteristic of a Keynesian cross diagram is the 45-degree line.

The Keynesian cross diagram is a simple graphical representation of the relationship between aggregate expenditure and real GDP in an economy. It shows the equilibrium level of real GDP where aggregate expenditure equals real GDP, and helps to illustrate the effects of changes in aggregate expenditure or other factors on the economy.

The 45-degree line in the Keynesian cross diagram represents the level of real GDP where aggregate expenditure equals real GDP, or where there is equilibrium in the economy. Points below the 45-degree line indicate that aggregate expenditure is less than real GDP, while points above the 45-degree line indicate that aggregate expenditure is greater than real GDP. The slope of the aggregate expenditure function determines the sensitivity of real GDP to changes in aggregate expenditure.

Answer:

f(1/2)=-1

Step-by-step explanation:

first plug f(1/2) in where you see an x: \(\frac{\sqrt{2(1/2)+3} }{6(1/2)-5}\)

then solve: \(\frac{\sqrt{1+3} }{3-5}\)

\(\frac{\sqrt{4} }{-2}\)

\(\frac{2}{-2}\)

-1