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Leya [2.2K]
3 years ago
13

PLS HELP Find an equation of the line with a y-intercept of -3 and an x-intercept of -4.5

Mathematics
1 answer:
kari74 [83]3 years ago
3 0

Answer:

y = - \frac{2}{3} x - 3

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 )

Calculate m using the slope formula

m = \frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }

with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (- 4.5, 0 ) ← coordinates of intercepts

m = \frac{0-(-3)}{-4.5-0} = \frac{0+3}{-4.5-0} = \frac{3}{-4.5} = - \frac{2}{3}

The line crosses the y- axis at (0, - 3 ) ⇒ c = - 3

y = - \frac{2}{3} x - 3 ← equation of line

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inessss [21]
Hello,

The answer is "Evan 2/3".

Reason:

2   2
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If you need anymore help feel free to ask me!

Hope this helps!

~Nonportrit
5 0
3 years ago
Find the center of mass of the wire that lies along the curve r and has density =4(1 sin4tcos4t)
dolphi86 [110]

The mass of the wire is found to be 40π√2 units.

<h3>How to find the mass?</h3>

To calculate the mass of the wire which runs along the curve r ( t ) with the density function δ=5.

The general formula is,

Mass = \int_a^b \delta\left|r^{\prime}(t)\right| d t

To find, we must differentiate this same given curve r ( t ) with respect to t to estimate |r'(t)|.

The given integration limits in this case are a = 0, b = 2π.

Now, as per the question;

The equation of the curve is given as;

r(t) = (4cost)i + (4sint)j + 4tk

Now, differentiate this same given curve r ( t ) with respect to t.

\begin{aligned}\left|r^{\prime}(t)\right| &=\sqrt{(-4 \sin t)^2+(4 \cos t)^2+4^2} \\&=\sqrt{16 \sin ^2 t+16 \cos ^2 t+16} \\&=\sqrt{16\left(\sin t^2+\cos ^2 t\right)+16}\end{aligned}

Further simplifying;

\begin{aligned}&=\sqrt{16(1)+16} \\&=\sqrt{16+16} \\&=\sqrt{32} \\\left|r^{\prime}(t)\right| &=4 \sqrt{2}\end{aligned}

Now, use integration to find the mass of the wire;

       \begin{aligned}&=\int_a^b \delta\left|r^{\prime}(t)\right| d t \\&=\int_0^{2 \pi} 54 \sqrt{2} d t \\&=20 \sqrt{2} \int_0^{2 \pi} d t \\&=20 \sqrt{2}[t]_0^{2 \pi} \\&=20 \sqrt{2}[2 \pi-0] \\&=40 \pi \sqrt{2}\end{aligned}

Therefore, the mass of the wire is estimated as 40π√2 units.

To know more about density function, here

brainly.com/question/27846146

#SPJ4

The complete question is-

Find the mass of the wire that lies along the curve r and has density δ.

r(t) = (4cost)i + (4sint)j + 4tk, 0≤t≤2π; δ=5

5 0
1 year ago
Point Q(2, −1) is rotated 90° clockwise about the origin.
kumpel [21]
(1,-2) hope this helps you :)
6 0
3 years ago
If a fair coin is tossed 6 times, what is the probability, to the nearest thousandth, of getting exactly 6 tails?
xxTIMURxx [149]
<h2>Answer:</h2>

\frac{1}{64}

<h2>Step-by-step explanation:</h2>

The\ probability\ of\ tails\ per\ flip\ is\ \frac{1}{2}

so\ the\ probability\ of\ getting\ six

tails\ is

\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{64}

The\ probability\ of\ getting\ tails\ every

time\ you\ multiply\ them\ is\ the

probobility\ of\ getting\ tails\ all\ six

times?

<em>I hope this helps you</em>

<em>:)</em>

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2 years ago
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leva [86]
3(4m-2)-2(m+5)
Distribute 3 into the equation
12m-6 than do the same with -2
-2m-10
combine like terms
10m-16
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