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2 years ago

The equation representa Function A and the graph represents Function B

Mathematics

1 answer:

worty [1.4K]2 years ago

3 0

Answer:

D) Slope of Funcation B = - Slope of Function A

Step-by-step explanation:

The equation for the line is:

y=mx+b

Where m is the slope and b is the y-intercept

In this question, we are only interested in the slope.

For function A, we can see that the equation is f(x) = -2x + 1

Going back to the equation, we can see that -2 is the slope

Now for function B, we need to find the slope by looking at the graph.

To do this, you need to remember that the slope is y/x, or rise over run. (This is saying that every time the y happens, the x also happens. For example, if the slope is 1/2, every time the line goes up 1 unit, it goes to the right 2 units)

So for the function, we can see that when you move to the right 1 unit (run), you also move up 2 units (rise), so the slope would be

Comparing the slope of both the functions

Function A is -2

and

Function B is 2

So the answer is D

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(5) Find the Laplace transform of the following time functions: (a) f(t) = 20.5 + 10t + t 2 + δ(t), where δ(t) is the unit impul

Aloiza [94]

Answer

(a) $F(s) = \frac{20.5}{s} - \frac{10}{s^2} - \frac{2}{s^3}$

(b) $F(s) = \frac{-1}{s + 1} - \frac{4}{s + 4} - \frac{4}{9(s + 1)^2}$

Step-by-step explanation:

(a) $f(t) = 20.5 + 10t + t^2 +$ δ(t)

where δ(t) = unit impulse function

The Laplace transform of function f(t) is given as:

$F(s) = \int\limits^a_0 f(s)e^{-st} \, dt$

where a = ∞

=> $F(s) = \int\limits^a_0 {(20.5 + 10t + t^2 + d(t))e^{-st} \, dt$

where d(t) = δ(t)

=> $F(s) = \int\limits^a_0 {(20.5e^{-st} + 10te^{-st} + t^2e^{-st} + d(t)e^{-st}) \, dt$

Integrating, we have:

=> $F(s) = (20.5\frac{e^{-st}}{s} - 10\frac{(t + 1)e^{-st}}{s^2} - \frac{(st(st + 2) + 2)e^{-st}}{s^3} )\left \{ {{a} \atop {0}} \right.$

Inputting the boundary conditions t = a = ∞, t = 0:

$F(s) = \frac{20.5}{s} - \frac{10}{s^2} - \frac{2}{s^3}$

(b) $f(t) = e^{-t} + 4e^{-4t} + te^{-3t}$

The Laplace transform of function f(t) is given as:

$F(s) = \int\limits^a_0 (e^{-t} + 4e^{-4t} + te^{-3t} )e^{-st} \, dt$

$F(s) = \int\limits^a_0 (e^{-t}e^{-st} + 4e^{-4t}e^{-st} + te^{-3t}e^{-st} ) \, dt$

$F(s) = \int\limits^a_0 (e^{-t(1 + s)} + 4e^{-t(4 + s)} + te^{-t(3 + s)} ) \, dt$

Integrating, we have:

$F(s) = [\frac{-e^{-(s + 1)t}} {s + 1} - \frac{4e^{-(s + 4)}}{s + 4} - \frac{(3(s + 1)t + 1)e^{-3(s + 1)t})}{9(s + 1)^2}] \left \{ {{a} \atop {0}} \right.$

Inputting the boundary condition, t = a = ∞, t = 0:

$F(s) = \frac{-1}{s + 1} - \frac{4}{s + 4} - \frac{4}{9(s + 1)^2}$

3 0

3 years ago

In analyzing statistical data, which do you think is more likely: a correlation coefficient of 0.9 or a correlation coefficient

alex41 [277]

Answer:

Is this middle school math I believe tha answer is 0.9

Step-by-step explanation:

I did it before pretyy sure thats what it is

4 0

2 years ago

Find the zeros of the function.

Zigmanuir [339]

Answer:

x = 3, x = 4

Step-by-step explanation:

To find the zeros of the function, equate f(x) to zero, that is

(x - 3)(2x - 8) = 0

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3 ← smaller solution

2x - 8 = 0 ⇒ 2x = 8 ⇒ x = 4 ← larger solution

5 0

3 years ago

Find the mean mode median,range 5.4, 3, 4.2, 9, 2.1, 3, 4.2

RideAnS [48]

Range = 6.9
mode = 4.2
median= 3

7 0

3 years ago

A used-car dealer has a vehicle on the lot with a sticker price of $5999. If the

Digiron [165]

Answer:

$4999

Step-by-step explanation:

Let the cost of the car be x

Then considering 20% markup, the sticker price is:

x + 20% = 5999

Since 20% of x is 20/100x = 0.2x,

x+ 0.2x = 5999
1.2x = 5999
x = 5999/1.2
x ≈ $4999

So dealer paid $4999 for the car

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3 years ago