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bixtya [17]
3 years ago
5

Write the equation of the line with an x-intercept at (0,2) and perpendicular to 3x+4y=12.

Mathematics
2 answers:
Deffense [45]3 years ago
8 0
The answer is y=4/3+2
juin [17]3 years ago
6 0

First you normalize 3x+4y=12 into y = -3/4 x + 3 (dividing by 4).

Then you observe that the slope of the line is -3/4 (it's always the factor with the x). A perpendicular line has the reciprocal slope. Reciprocal means inverted and negated. So -3/4 becomes +4/3.

The equation will thus look like y = 4/3 x + b. To find b, we fill in the given x intercept (0,2), (we get 2 = 4/3 * 0 + b). With x=0, b must be 2.

So the equation is: y = 4/3 x + 2

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"find the reduction formula for the integral" sin^n(18x)
dexar [7]
Let

I(n,a)=\displaystyle\int\sin^nax\,\mathrm dx
For demonstration on how to tackle this sort of problem, I'll only work through the case where n is odd. We can write

\displaystyle\int\sin^nax\,\mathrm dx=\int\sin^{n-2}ax\sin^2ax\,\mathrm dx=\int\sin^{n-2}ax(1-\cos^2ax)\,\mathrm dx
\implies I(n,a)=I(n-2,a)-\displaystyle\int\sin^{n-2}ax\cos^2ax\,\mathrm dx

For the remaining integral, we can integrate by parts, taking

u=\sin^{n-3}ax\implies\mathrm du=a(n-3)\sin^{n-4}ax\cos ax\,\mathrm dx\mathrm dv=\sin ax\cos^2ax\,\mathrm dx\implies v=-\dfrac1{3a}\cos^3ax

\implies\displaystyle\int\sin^{n-2}ax\cos^2ax\,\mathrm dx=-\dfrac1{3a}\sin^{n-3}ax\cos^3ax+\dfrac{a(n-3)}{3a}\int\sin^{n-4}ax\cos^4ax\,\mathrm dx

For this next integral, we rewrite the integrand

\sin^{n-4}ax\cos^4ax=\sin^{n-4}ax(1-\sin^2ax)^2=\sin^{n-4}ax-2\sin^{n-2}ax+\sin^nax
\implies\displaystyle\int\sin^{n-4}ax\cos^4ax\,\mathrm dx=I(n-4,a)-2I(n-2,a)+I(n,a)

So putting everything together, we found

I(n,a)=I(n-2,a)-\displaystyle\int\sin^{n-2}ax\cos^2ax\,\mathrm dx
I(n,a)=I(n-2,a)-\left(-\dfrac1{3a}\sin^{n-3}ax\cos^3ax+\dfrac{n-3}3\displaystyle\int\sin^{n-4}ax\cos^4ax\,\mathrm dx\right)
I(n,a)=I(n-2,a)-\dfrac{n-3}3\bigg(I(n-4,a)-2I(n-2,a)+I(n,a)\bigg)+\dfrac1{3a}\sin^{n-3}ax\cos^3ax
\dfrac n3I(n,a)=\dfrac{2n-3}3I(n-2,a)-\dfrac{n-3}3I(n-4,a)+\dfrac1{3a}\sin^{n-3}ax\cos^3ax

\implies I(n,a)=\dfrac{2n-3}nI(n-2,a)-\dfrac{n-3}nI(n-4,a)+\dfrac1{na}\sin^{n-3}ax\cos^3ax
7 0
2 years ago
An elevator is on the twentieth floor. It goes down 11 floors and then up five floors. What floor is the elevator on now?
love history [14]
The answer is -4

because when you minus 11 and 20 that will get you -9 and then you add 5 that get you the answer
8 0
2 years ago
A cylindrical metal tin has a diameter of 12 inches and a height of 4 inches.
Tanya [424]

Answer:

452.39

Step-by-step explanation:

5 0
3 years ago
-0.4a+3=7<br><img src="https://tex.z-dn.net/?f=%20-%200.4a%20%2B%203%20%3D%207" id="TexFormula1" title=" - 0.4a + 3 = 7" alt=" -
natali 33 [55]
Sorry if I'm wrong
a = 10
this what I did
7 - 3 = 4 ÷ 0.4 = 10
5 0
3 years ago
Suzie Chambers sells cars for a living. She earns $450 per week plus a commission of 5% on
Greeley [361]

Answer:

$930

Step-by-step explanation:

450 + 9600(.05)

450 + 480

$930

6 0
2 years ago
Read 2 more answers
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