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ankoles [38]
3 years ago
6

HELP QUICKLY PLEASE!!!!!!!!!!!!!

Mathematics
1 answer:
Murljashka [212]3 years ago
6 0
X=0 is a vertical line, specifically it is the y-axis of the coordinate plane.

6y-5x=0

6y=5x

y=5x/6

and the third line is

3y=21-x

y=(21-x)/3

putting aside the first as it is a vertical line, we need to know when

y=(21-x)/3 is equal to the line y=5x/6 so

5x/6=(21-x)/3

15x/6=21-x

15x=126-6x

21x=126

x=42/7

x=6

so we know that the two sloped lines meet at x=6 or more specifically the point (6,5)

and when x=0 these two lines meet the x=0 line at (0,0) and (0,7)

So you have three points: (0,0),(0,7), and (6,5) forming a triangle.

The base of which is the vertical line from (0.0) to (0,7) which means the base is 7 units in length.  The height (in the x direction) is 6 units because the apex is at (6,5)

So the area of a triangle is just bh/2 and in our case is:

A=7*6/2=21 u^2

Now for the volume of this shape rotated about the y-axis....

We will have to do two integrations because of the way the lines are...

First note that we are rotating about the y axis thus x is the radius of revolution so we need our lines expressed in terms of y instead of x...

The top line was y=(21-x)/3...solving for x

x=21-3y and y varies from 5 to 7

The volume is the integral:

V=pSf(y)^2 dy

V=pS441+9y^2-126y dy

V=p[441y+3y^3-63y^2] for y=[5,7]

V=p(1029-1005)

V=24p   that is the top half volume...now for the lower half...

y=5x/6, x=6y/5, and y varies from 0 to 5

V=pS(6y/5)^2 dy

V=(36p/25)Sy^2 dy

V=(36p/25)(y^3/3)
  
V=(36p/25)(125/3)

V=60p

So the total volume is 60p+24p=84p

≈264 u^3
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Enter the values for m, n, and p that complete the difference:
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Answer:

p = 2

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m = 3

Step-by-step explanation:

In order to be able combine (either add or subtract) rational expressions we need to write them with a common (similar) denominator. For that reason we first find the Least Common Denominator of both fractions, that way understanding how to express the two fractions using equivalent fractions with like denominator that can be combined.

We see that the denominator of the first fraction contains the factor "x", therefore "x" has to be a factor of that least common denominator.

We also see that the second fraction  contains "2" as a factor, therefore 2 has to be a factor as well for our Least Common Denominator (LCD)

So the LCD we need is the product: 2*x which we write as 2x.

Now we write the first fraction as an equivalent one but with denominator "2x" by multiplying top and bottom by 2 (and thus not changing the actual value of the fraction): \frac{7}{x} =\frac{7*2}{x*2} =\frac{14}{2x}

Next we do the same with the second fraction, this time multiplying top and bottom by the factor "x":

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

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5 0
3 years ago
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Consider the following functions.G(x) = 4x2; f(x) = 8x(a)
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Answer:

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(b) Every function of the form 4x^2+C is an antiderivative of 8x

Step-by-step explanation:

A function <em>F </em>is an antiderivative of the function <em>f</em> if

F'(x)=f(x)

for all x in the domain of <em>f.</em>

(a) If f(x) = 8x, then G(x)=4x^2 is an antiderivative of <em>f </em>because

G'(x)=8x=f(x)

Therefore, G(x) is an antiderivative of f(x) because G'(x) = f(x) for all x.

Let F be an antiderivative of f. Then, for each constant C, the function F(x) + C is also an antiderivative of <em>f</em>.

(b) Because

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