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Vikentia [17]
3 years ago
6

Why did he let (y) equals to (1/2 sec t) ? And how did (-1) & (- √2/2) become (2π/3) & (3π/4) ?!!

Mathematics
1 answer:
Diano4ka-milaya [45]3 years ago
7 0
Just to go into more detail than I did in our PMs and the comments on your last question...

You have to keep in mind that the limits of integration, the interval \left(-1,-\dfrac{\sqrt2}2\right), only apply to the original variable of integration (y).

When you make the substitution y=\dfrac12\sec t, you not only change the variable but also its domain. To find out what the new domain is is a matter of plugging in every value in the y-interval into the substitution relation to find the new t-interval domain for the new variable (t).

After replacing y and the differential \mathrm dy with the new variable t and differential \mathrm dt, you saw that you could reduce the integral to -1. This is a continuous function, so the new domain can be constructed just by considering the endpoints of the y-interval and transforming them into the t-domain.

When y=-1, you have -1=\dfrac12\sec t\implies t=\arcsec(-2)=\dfrac{2\pi}3.

When y=-\dfrac{\sqrt2}2, you have -\dfrac{\sqrt2}2=\dfrac12\sec t\implies t=\arcsec(-\sqrt2)=\dfrac{3\pi}4.

Geometrically, this substitution allows you to transform the area as in the image below. Naturally it's a lot easier to find the area under the curve in the second graph than it is in the first.

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tekilochka [14]

Answer:

3.5 inches

Step-by-step explanation:

create a proportion:

inches / miles = inches / miles

let 'x' = distance in inches

<u>1/4</u> = <u> x </u>

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18x = 252(1/4)

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5 0
3 years ago
Question 7 )
soldier1979 [14.2K]

<em>Answer:</em>

<u>Tony</u> has 45 dollars  

<u>Milan</u> has 15 dollars

<u>Lucy</u> has 25 dollars

<em>Explanation:</em>

<u>Let </u><u><em>x</em></u><u> represent the amount of money Milan has in his wallet.</u>

TONY: 3x

MILAN: x

LUCY: x+10

<u>Lucy, Milan, and Tony have a total of $85 in their wallets. Hence, the following equation.</u>

<u />

3x+x+x+10=85

5x+10=85

5x=75

x=75/5

x=15

Tony has 45 dollars (3*15=45)

Milan has 15 dollars (x=15)

Lucy has 25 dollars (10+15=25)

7 0
3 years ago
Where does the line y = -4x + 9 cross the y-axis?
Zanzabum

Answer:

slope is -4 y-axis is 9

Step-by-step explanation:

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3 years ago
What is an equation of the line that passes through the point (5,4)(5,4) and is parallel to the line 6x-5y=156x−5y=15?
Westkost [7]

Answer:

7x+y=0

x+6y=5

x+y=0

Step-by-step explanation:

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3 years ago
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