A direct variation has a constant slope, i.e. (y/x)= constant.
Both of the given two points give a slope of (y/x)=14/2=28/4=7, so the equation of the function is
y/x=7, or simply
y=7x
Answer:
61 , 63 , 65 , 67
Step-by-step explanation:
Let the least even number be denoted by x. The sum of the four consecutive even numbers would be:
(x) + (x + 2) + (x + 4) (x + 6) = 256
First, simplify. Combine all like terms:
x + x + x + x + 2 + 4 + 6 = 256
4x + 12 = 256
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
First, subtract 12 from both sides of the equation:
4x + 12 (-12) = 256 (-12)
4x = 256 - 12
4x = 144
Next, divide 4 from both sides of the equation:
(4x)/4 = (144)/4
x = 144/4
x = 61
61 is your first number. Find the next 3 consecutive numbers:
x = 61
x + 2 = 63
x + 4 = 65
x + 6 = 67
Check:
61 + 63 + 65 + 67 = 256
256 = 256
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The sales tax is 2$ Hope this is the answer you're looking for.
we know that
the perimeter of the rectangle is equal to

where
P is the perimeter of the rectangle
W is the width of the rectangle
L s the length of the rectangle
In this problem

Substitute the values in the formula above


therefore
the answer is
the length of the longer side of the rectangle is equal to 
Answer:
Required volume is
unit.
Step-by-step explanation:
Given equations of curves,
,
substitute second in first we will get,

When
and
. Thus both curves intersect at the points (4,16),(-4,16). And thus
.
Considering width of the representative rectangle as
which is parallel to x-axis because of considering cylindrical shell. Therefore volume of the shell is given by,

Now,
Length of generating box=Length of
from line x=4(axis of revolution)=circumference of the shell=(4-x)
Width of box=
Hence,


![=2\pi\{144\big[x\big]_{-4}^{4}-18\big[x^2\big]_{-4}^{4}-\frac{8}{3}\big[x^3\big]_{-4}^{4}+\frac{1}{2}\big[x^4\big]_{-4}^{4}\}](https://tex.z-dn.net/?f=%3D2%5Cpi%5C%7B144%5Cbig%5Bx%5Cbig%5D_%7B-4%7D%5E%7B4%7D-18%5Cbig%5Bx%5E2%5Cbig%5D_%7B-4%7D%5E%7B4%7D-%5Cfrac%7B8%7D%7B3%7D%5Cbig%5Bx%5E3%5Cbig%5D_%7B-4%7D%5E%7B4%7D%2B%5Cfrac%7B1%7D%7B2%7D%5Cbig%5Bx%5E4%5Cbig%5D_%7B-4%7D%5E%7B4%7D%5C%7D)

which is required volume of generating area.