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2 years ago

A line passes through the points (3,0) and (4,2). What is its equation in slope-intercept form?

Mathematics

1 answer:

N76 [4]2 years ago

3 0

Answer:

y = 2x - 6

Step-by-step explanation:

<h2>Slope intercept form:</h2>

Equation of the line:

$\sf \boxed{ y = mx +b}$

Here m is the slope and b is the y-intercept.

Step 1: Find the slope

(3 , 0) ⇒ x₁ = 3 & y₁ = 0

(4 , 2) ⇒ x₂ = 4 & y₂ = 2

$\sf \boxed{Slope=\dfrac{y_2-y_1}{x_2-x_1}}$

$\sf = \dfrac{2 -0}{4-3}\\\\= \dfrac{2}{1}\\\\=2$

Step2: Now, substitute the value of 'm' in the equation.

y = 2x + b

Step3: In the above equation plug in any point. Here, (3 ,0) is chosed.

0 = 2*3 + b

0 = 6 + b

-6 = b

Step4: Equation of the line:

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ehidna [41]

Answer:

Step-by-step explanation:

7 0

3 years ago

Find the mass of the lamina that occupies the region D = {(x, y) : 0 ≤ x ≤ 1, 0 ≤ y ≤ 1} with the density function ρ(x, y) = xye

Alona [7]

Answer:

The mass of the lamina is 1

Step-by-step explanation:

Let $\rho(x,y)$ be a continuous density function of a lamina in the plane region D,then the mass of the lamina is given by:

$m=\int\limits \int\limits_D \rho(x,y) \, dA$ .

From the question, the given density function is $\rho (x,y)=xye^{x+y}$ .

Again, the lamina occupies a rectangular region: D={(x, y) : 0 ≤ x ≤ 1, 0 ≤ y ≤ 1}.

The mass of the lamina can be found by evaluating the double integral:

$I=\int\limits^1_0\int\limits^1_0xye^{x+y}dydx$ .

Since D is a rectangular region, we can apply Fubini's Theorem to get:

$I=\int\limits^1_0(\int\limits^1_0xye^{x+y}dy)dx$ .

Let the inner integral be: $I_0=\int\limits^1_0xye^{x+y}dy$ , then

$I=\int\limits^1_0(I_0)dx$ .

The inner integral is evaluated using integration by parts.

Let $u=xy$ , the partial derivative of u wrt y is

$\implies du=xdy$

and

$dv=\int\limits e^{x+y} dy$ , integrating wrt y, we obtain

$v=\int\limits e^{x+y}$

Recall the integration by parts formula: $\int\limits udv=uv- \int\limits vdu$

This implies that:

$\int\limits xye^{x+y}dy=xye^{x+y}-\int\limits e^{x+y}\cdot xdy$

$\int\limits xye^{x+y}dy=xye^{x+y}-xe^{x+y}$

$I_0=\int\limits^1_0 xye^{x+y}dy$

We substitute the limits of integration and evaluate to get:

$I_0=xe^x$

This implies that:

$I=\int\limits^1_0(xe^x)dx$ .

$I=\int\limits^1_0xe^xdx$ .

We again apply integration by parts formula to get:

$\int\limits xe^xdx=e^x(x-1)$ .

$I=\int\limits^1_0xe^xdx=e^1(1-1)-e^0(0-1)$ .

$I=\int\limits^1_0xe^xdx=0-1(0-1)$ .

$I=\int\limits^1_0xe^xdx=0-1(-1)=1$ .

No unit is given, therefore the mass of the lamina is 1.

3 0

3 years ago

A random sample of 500 reports an average yearly income of $42,000 with a standard deviation of $1000. An estimate of the parame

Lorico [155]

Answer:

Step-by-step explanation:

Confidence Interval = mean + or - error margin

Mean = 42,000, error margin = width of estimate of the parameter ÷ 2 = 175 ÷ 2 = 87.50

We can be 95% confident that the population mean is 42,000 plus or minus 87.50

8 0

3 years ago

When CA= 3x-1 and SR=5x+4, what is CA?

avanturin [10]

Answer:

CA=17

Step-by-step explanation:

From given picture we see that A and C are the mid points of sides QR and QS respectively.

We know that line joining mid points of the two sides of triangle is always half of the length of the third side.

So that means:

2*CA=SR

2(3x-1)=5x+4

6x-2=5x+4

6x-5x=4+2

x=6

plug value of x into CA=3x-1

CA=3*6-1=18-1=17

Hence final answer is CA=17

8 0

3 years ago

Two common names for streets are FirstFirst Street and MainMain â€‹Street, with 14 comma 86614,866 streets bearing one of these

oksian1 [2.3K]

Answer: There are 7,677 streets named as " First Street" and 7, 189 streets named as "Main Street" .

Step-by-step explanation:

Let x be the number of streets named as First Street .

y be the number of streets named as Main Street.

AS per the given information, we have the following system of equations :

$x+y=14866-------------(1)\\\\x=488+y-------------(2)$

Substitute the value of x from (2) in (1) , we get

$488+y+y=14866\\\\ 2y =14866- 488\\\\ 2y=14378\\\\ y=7189$

Put value of y in (2), we get

$x=488+7189=7677$

Hence , there are 7,677 streets named as " First Street" and 7, 189 streets named as "Main Street" .

6 0

3 years ago