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Maslowich
2 years ago
6

(216/64) ^2/3 in its simplified form is equal to

Mathematics
1 answer:
LiRa [457]2 years ago
4 0

This answer should help.

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Find the equation of a line parallel to the line 2x-y-9=0 and passing through the point of intersection of the lines 5x+y+4=0 an
Cerrena [4.2K]

Answer:

y=2x-3

Step-by-step explanation:

1. Using the point of intersections, we use the substitution method to find the coordinates of the line parallel to 2x-y-9=0

5x+y+4=0

y= -4-5x

substituting the value of y in 2x+3y=1:

2x +3(-4-5x)=1\\\\2x-12-15x-1=0\\-13x=13x\\x= \frac{13}{-13}= -1

substituting x=-1 in y= -4-5x:

y= 1 (upon solving, you should get this)

(x,y)= (-1,1)

2. Using y=mx+c and making y the subject of the formula 2x-y-9=0 and using the coordinate we found earlier, we will find the equation of the parallel line. (We make y the subject of the formula to find the gradient)

2x-y-9=0\\2x-9=y\\y= 2x-9

y= mx+c\\

-1= 2 x 1 +c

-3=c

  • y= 2x-3

3 0
3 years ago
Which of the following equations is an example of inverse variation between the variables x and y?
Leni [432]

Answer:

C

Step-by-step explanation:

A and B are examples of direct variations because there is a nonzero constant k in each such that y=kx. A's k=1/12 while B's k=12.

D is not a direct or inverse variation because of the plus/minus constant.

C is an inverse variation because it has form y=k/x where k is nonzero. This k=12.

4 0
3 years ago
Read 2 more answers
The farm in queensland Australia,where the pirate battle was filmed is about 14800 kilometers away from Port Royal, Jamacia, whe
gogolik [260]
9196.2936 miles is the distance in miles
5 0
3 years ago
Graph the compound inequality on the number line.<br> X ≤4 or ≥ 7
notsponge [240]

Answer:

The number line is attached.

Step-by-step explanation:

The holes are filled in since they are both inclusive of the value they hold, and there are two separate lines since they are broken apart by "or".

4 0
2 years ago
Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the curves about the given
koban [17]


To start it off, we have to find where the 3 meet - to find when 3e^x and 3e^(-x) meet, we start off with dividing both sides to get e^x=e^(-x) and e^x=1/e^x, multiplying both sides by e^x to get e^(2x)=1 and x=0. Plugging in x=1 for both equations, we get 3e and 3/e respectively. Graphing it out, we can see that it forms a weird shape, but if you draw a line at y=3, we can have 2 separate shapes, making it super easy! We have x as the radius since it's about the y axis and the equations (from a certain point) as the height
We have 2 integrals - 2π(∫(from 3 to 3e) (x)(3e^x)) and  2π(∫(from 3/e to 3) (x)(e^(-x)). We then get 2π (∫3xe^x+∫3xe^(-x)) as added up they make the area between the curves.For ∫3xe^x,  For 3xe^x, which we can separate the 3 from and get xe^x, we use integration by parts to put x in for f and e^x as g in ∫fg'=fg-∫f'g, plugging it in to get xe^x-∫e^x, resulting in xe^x-e^x. Multiplying that by 3 (as we separated that earlier), we get 3xe^x-e^x 
For ∫3xe^(-x), we can use the same technique for separating the 3 out, but for ∫xe^(-x), we can use put x in for f and g' as e^(-x), resulting in g being -e^(-x) by using u substitution and making -x u. Next, we get (x)(-e^(-x))+∫(-e)^(-x), and ∫(-e)^(-x)=e^(-x) in the same way -e^(-x) being the integral of e^(-x) was found.
Adding it all up for this, we get 3(-xe^(-x)-e^(-x)) as our solved integral. 

Since 3xe^x-3e^x is just the solved integral and we need to find it on 3 to 3e, we plug in 3e for x and subtract it from plugging 3 into x to get ((9*e-3)*e^(3*e)-6*e^3). We need to multiply it by 2pi (since it's a cylindrical shell) to get (2pi(((9*e-3)*e^(3*e)-6*e^3))

For 3(-xe^(-x)-e^(-x)) , we can plug it in for 3 and 3/e (as the respective upper and lower bounds) to get 3*((e+3)*e^(-3*e^(-1)-1)-4*e^(-3)). Multiply that by 2pi to get 6pi*((e+3)*e^(-3*e^(-1)-1)-4*e^(-3)).
Add the two up to get 6pi*((e+3)*e^(-3*e^(-1)-1)-4*e^(-3))+(2pi(((9*e-3)*e^(3*e)-6*e^3)) in and it said

8 0
3 years ago
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