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2 years ago

61-63 Sketch the region bounded by the given curves and find the area of the region.

1 answer:

8 0

The area of the region is 0.193 square units for the region bounded by the curves and find the area of the region.

<h3>What is integration?</h3>

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

To find the area of the bounded region by the curves(refer to attached picture):

$\rm A= \int\limits^2_1 {(\frac{1}{x}-\frac{1}{x^2}) } \, dx$

After solving:

A = 0.193 square units

Thus, the area of the region is 0.193 square units for the region bounded by the curves and find the area of the region.

Learn more about integration here:

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739 is closer to ___ than it is to _____

Marizza181 [45]

700 because if it was 750 it would be closer to 800 but it is under 50

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3 years ago

The combined area of a square and a rectangle is 225 square yards. the length of the rectangle is 8 times the width of the recta

snow_lady [41]

Answer:

The rectangle: L = 40 yards. W = 5 yards

The square: The length and width are both 5 yards.

Step-by-step explanation:

Let L and W be the length and width of the rectangle.

Let l and w be the length and width of the square.

Area for each is:

Rectangle: L*W

Square: l*w

We are told that L*W + l*w = 225 yards^2

We are also told that

L = 8W

and that

l = W

Since the sides of a square are all equal, w is also W: w=W

Summarizing and substituting:

L*W + l*w = 225 yards^2

(8W)*W + W*W = 225 yards^2

8W^2 + W^2 = 225 yards^2

9W^2 = 225 yards^2

W^2 = 25

W = 5 feet

---------------------

Therefore, since L = 8W , L = 40 yards. W = 5 yards for the rectangle.

The square: l=W, so l = 5 yards, and thus w=5 yards

--------------------------

Check:

Do a rectangle of 40' x 5' plus a square of 5' x 5' have a total combined area of 225 yards^2?

40yd x 5yd + 5yd x 5yd = 225 yards^2?

200 yd^2 + 25 yd^2 = 225 yards^2?

YES

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2 years ago

Check each equation whose graph is the line that

yanalaym [24]

Answer:

Points P ( 4 , - 7 ) and Q ( 1 , 5 ) belong to the equations:

1 ; 4 ; and 5

Step-by-step explanation:

Equations 1 ; 4 and 5 are the same equation

Equation 1 y = - 4*x + 9

Equation 4

y + 7 = - 4 * ( x - 4 ) ⇒ y + 7 = - 4*x + 16 ⇒ y = - 4*x - 7 + 16

y = -4*x + 9

Equation 5

4*x + y = 9 ⇒ y = - 4*x + 9

Now for the equation y = - 4*x + 9

P ( 4 , -7)

For x = 4 y = - 4*(4) + 9 ⇒ y = - 16 + 9 ⇒ y = - 7

Then point P is in the line y = - 4*x + 9

Point Q (1 , 5 )

For x = 1 y = - 4 * ( 1) + 9 ⇒ y = - 4 + 9 ⇒ y = 5

Point Q is in the line y = - 4*x + 9

Equation 2

y = - 4*x - 23

Point P ( 4 , - 7 )

For x = 4 y = 16 - 23 y = - 7

Point P is in the line

Point Q

For x = 1 y = - 4 *(1) - 23 ⇒ y = - 27

Then poin Q is not in the line

Equation 3

y - 1 = - 4 * ( x - 4 )

y - 1 = -4*x + 16 ⇒ y = - 4*x + 17

Point P ( 4 , - 7 )

For x = 4

y = - 16 + 17 ⇒ y = 1

Point P is not in the line

And Point Q ( 1 , 5 )

For x = 1

y = - 4* ( 1 ) + 17 ⇒ y = 13 Q is not in the line

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3 years ago

Which law would you use to simplify the expression (x^4)^9?

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The Power of a Power Rule. In this case, you basically multiply the two exponents together, and simplify (x^4)^9 to equal x^36

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3 years ago

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Can the government offices be represented as a function of the ministers' names?

Marina86 [1]

Answer and explanation:

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Therefore if government office y is a function of minister's name x then a government office would hold a particular value, example be named after the minister's name because it is dependent on the minister's name x

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3 years ago