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3 years ago

Find the equation of this line y = [?]x + [ ] Please help

Mathematics

1 answer:

larisa [96]3 years ago

5 0

<h2>Writing an Equation of a Line in Slope-Intercept Form</h2><h3>Answer:</h3>

$y = [ -2 ] x + [ 1 ]\\$

<h3>Step-by-step explanation:</h3>

<em>Please refer to my answer from this Question to know more about Slope-Intercept Form: <u>brainly.com/question/24599351</u></em>

We must first find the slope.

<em>Please refer to my Answer from this Questions to know more about Slopes of a Line:</em>

<em><u>brainly.com/question/24640665</u></em>
<em><u>brainly.com/question/24638053</u></em>

We can see the marked points, $(0,1)$ and $(4, -7)$ , are on the line.

Solving for the slope:

$m = \frac{y_2 -y_1}{x_2 -x_1} \\ m = \frac{-7 -1}{4 -0} \\ m = \frac{-8}{4} \\ m = -2$

Now we can now solve for the $y$ -intercept.

<em>Please refer to the second paragraph of my Answer from this Question to know more about y-intercepts: <u>brainly.com/question/24606058</u></em>

We can see that the line intersected the $y$ -axis at $(0,1)$ so $b = 1$ .

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On a coordinate plane, 5 trapezoids are shown. Trapezoid L M N P is in quadrant 2 and has points (negative 2, 3), (negative 2, 6

blondinia [14]

Answer: C

Step-by-step explanation:

Reflecting over the x axis, the image of a point in Quadrant 2 is a point in Quadrant 3.

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2 years ago

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How do I show my work for solving the radius of a circle if the area is 78.5 cm^2

SIZIF [17.4K]

9514 1404 393

Answer:

radius = 5 cm

Step-by-step explanation:

The point of "show your work" is to have to do exactly that. If you know the answer to the problem, you are being requested to show how you got it. If you got it by using a web calculator, then show your input and its result.

If you worked the problem yourself, you probably did it by filling in numbers in the equation for the area of a circle:

A = πr²

78.5 = 3.14×r²

Dividing both sides by 3.14 gives the square of the radius:

78.4/3.14 = r² = 25

Taking the positive square root gives the radius:

r = √25 = 5

The area is in square centimeters, so the radius is in centimeters:

radius = 5 cm

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2 years ago

The fastest speed a table tennis ball has been hit about 13.07 times as fast as the speed for the fastest swimming. What is the

Marrrta [24]

Given there is no speed given for the fastest swimming, the tennis ball is 13.07 times f(Fastest Swimming), or 13.07f.

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3 years ago

Read 2 more answers

Calculus 3 help please.

Reptile [31]

I assume each path $C$ is oriented positively/counterclockwise.

(a) Parameterize $C$ by

$\begin{cases} x(t) = 4\cos(t) \\ y(t) = 4\sin(t)\end{cases} \implies \begin{cases} x'(t) = -4\sin(t) \\ y'(t) = 4\cos(t) \end{cases}$

with $-\frac\pi2\le t\le\frac\pi2$ . Then the line element is

$ds = \sqrt{x'(t)^2 + y'(t)^2} \, dt = \sqrt{16(\sin^2(t)+\cos^2(t))} \, dt = 4\,dt$

and the integral reduces to

$\displaystyle \int_C xy^4 \, ds = \int_{-\pi/2}^{\pi/2} (4\cos(t)) (4\sin(t))^4 (4\,dt) = 4^6 \int_{-\pi/2}^{\pi/2} \cos(t) \sin^4(t) \, dt$

The integrand is symmetric about $t=0$ , so

$\displaystyle 4^6 \int_{-\pi/2}^{\pi/2} \cos(t) \sin^4(t) \, dt = 2^{13} \int_0^{\pi/2} \cos(t) \sin^4(t) \,dt$

Substitute $u=\sin(t)$ and $du=\cos(t)\,dt$ . Then we get

$\displaystyle 2^{13} \int_0^{\pi/2} \cos(t) \sin^4(t) \, dt = 2^{13} \int_0^1 u^4 \, du = \frac{2^{13}}5 (1^5 - 0^5) = \boxed{\frac{8192}5}$

(b) Parameterize $C$ by

$\begin{cases} x(t) = 2(1-t) + 5t = 3t - 2 \\ y(t) = 0(1-t) + 4t = 4t \end{cases} \implies \begin{cases} x'(t) = 3 \\ y'(t) = 4 \end{cases}$

with $0\le t\le1$ . Then

$ds = \sqrt{3^2+4^2} \, dt = 5\,dt$

and

$\displaystyle \int_C x e^y \, ds = \int_0^1 (3t-2) e^{4t} (5\,dt) = 5 \int_0^1 (3t - 2) e^{4t} \, dt$

Integrate by parts with

$u = 3t-2 \implies du = 3\,dt \\\\ dv = e^{4t} \, dt \implies v = \frac14 e^{4t}$

$\displaystyle \int u\,dv = uv - \int v\,du$

$\implies \displaystyle 5 \int_0^1 (3t-2) e^{4t} \,dt = \frac54 (3t-2) e^{4t} \bigg|_{t=0}^{t=1} - \frac{15}4 \int_0^1 e^{4t} \,dt \\\\ ~~~~~~~~ = \frac54 (e^4 + 2) - \frac{15}{16} e^{4t} \bigg|_{t=0}^{t=1} \\\\ ~~~~~~~~ = \frac54 (e^4 + 2) - \frac{15}{16} (e^4 - 1) = \boxed{\frac{5e^4 + 55}{16}}$

$\begin{cases} x(t) = 3(1-t)+t = -2t+3 \\ y(t) = (1-t)+2t = t+1 \\ z(t) = 2(1-t)+5t = 3t+2 \end{cases} \implies \begin{cases} x'(t) = -2 \\ y'(t) = 1 \\ z'(t) = 3 \end{cases}$

with $0\le t\le1$ . Then

$ds = \sqrt{(-2)^2 + 1^2 + 3^2} \, dt = \sqrt{14} \, dt$

and

$\displaystyle \int_C y^2 z \, ds = \int_0^1 (t+1)^2 (3t+2) \left(\sqrt{14}\,ds\right) \\\\ ~~~~~~~~ = \sqrt{14} \int_0^1 \left(3t^3 + 8t^2 + 7t + 2\right) \, dt \\\\ ~~~~~~~~ = \sqrt{14} \left(\frac34 t^4 + \frac83 t^3 + \frac72 t^2 + 2t\right) \bigg|_{t=0}^{t=1} \\\\ ~~~~~~~~ = \sqrt{14} \left(\frac34 + \frac83 + \frac72 + 2\right) = \boxed{\frac{107\sqrt{14}}{12}}$