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2 years ago

12

restaurant etiquette dictates that you should leave a 15% tip for the server if the service is acceptable if that is the case ho

w much should you tip if your total is 24.00

1 answer:

zmey [24]2 years ago

3 0

Multiply .15 by 24 to get your answer. The answer would be 3.6 which is $3.60 as your tip

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Evaluate the triple integral ∭EzdV where E is the solid bounded by the cylinder y2+z2=81 and the planes x=0,y=9x and z=0 in the

dem82 [27]

Answer:

I = 91.125

Step-by-step explanation:

Given that:

$I = \int \int_E \int zdV$ where E is bounded by the cylinder $y^2 + z^2 = 81$ and the planes x = 0 , y = 9x and z = 0 in the first octant.

The initial activity to carry out is to determine the limits of the region

since curve z = 0 and $y^2 + z^2 = 81$

∴ $z^2 = 81 - y^2$

$z = \sqrt{81 - y^2}$

Thus, z lies between 0 to $\sqrt{81 - y^2}$

GIven curve x = 0 and y = 9x

$x =\dfrac{y}{9}$

As such,x lies between 0 to $\dfrac{y}{9}$

Given curve x = 0 , $x =\dfrac{y}{9}$ and z = 0, $y^2 + z^2 = 81$

y = 0 and

$y^2 = 81 \\ \\ y = \sqrt{81} \\ \\ y = 9$

∴ y lies between 0 and 9

Then $I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \int^{\sqrt{81-y^2}}_{z=0} \ zdzdxdy$

$I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{z^2}{2} \end {bmatrix} ^ {\sqrt {{81-y^2}}}_{0} \ dxdy$

$I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{(\sqrt{81 -y^2})^2 }{2}-0 \end {bmatrix} \ dxdy$

$I = \int^9_{y=0} \int^{\dfrac{y}{9}}_{x=0} \begin {bmatrix} \dfrac{{81 -y^2} }{2} \end {bmatrix} \ dxdy$

$I = \int^9_{y=0} \begin {bmatrix} \dfrac{{81x -xy^2} }{2} \end {bmatrix} ^{\dfrac{y}{9}}_{0} \ dy$

$I = \int^9_{y=0} \begin {bmatrix} \dfrac{{81(\dfrac{y}{9}) -(\dfrac{y}{9})y^2} }{2}-0 \end {bmatrix} \ dy$

$I = \int^9_{y=0} \begin {bmatrix} \dfrac{{81 \ y -y^3} }{18} \end {bmatrix} \ dy$

$I = \dfrac{1}{18} \int^9_{y=0} \begin {bmatrix} {81 \ y -y^3} \end {bmatrix} \ dy$

$I = \dfrac{1}{18} \begin {bmatrix} {81 \ \dfrac{y^2}{2} - \dfrac{y^4}{4}} \end {bmatrix}^9_0$

$I = \dfrac{1}{18} \begin {bmatrix} {40.5 \ (9^2) - \dfrac{9^4}{4}} \end {bmatrix}$

$I = \dfrac{1}{18} \begin {bmatrix} 3280.5 - 1640.25 \end {bmatrix}$

$I = \dfrac{1}{18} \begin {bmatrix} 1640.25 \end {bmatrix}$

I = 91.125

4 0

2 years ago

Using the digits 1, 3, 5, 7 at most once, you can make many three-digit numbers. What is the maximum possible sum of two such di

lyudmila [28]

Answer:

1504

Step-by-step explanation:

Given the digits :

1, 3, 5, 7

The maximum possible sum of two distinct three digit numbers formed from the digits above will be the sum of the the two hight possible three digit numbers that can be formed.

Highest three digit number = 753

Next highest = 751

The sum of these two. Values gives :

753 + 751 = 1504

3 0

2 years ago

A boat travels 8 miles north from point A to point B. Then it moves in the direction S 40°W and reaches point Finally, it turns

uysha [10]

Answer:

B.18. 44 miles

Step-by-step explanation:

We are given that

Distance between A and B=8 miles

Angle B=Angle BCQ=40 degree (Alternate interior angles)

Angle ACB=180-Angle ACP-Angle BCQ

Angle ACB=180-40-40=100 degree

In triangle ABC

Angle A+ Angle B +Angle C=180 degree using sum of angles of triangle property

Substitute the values

$\angle A+40+100=180$

$\angle A+140=180$

$\angle A=180-140$

$\angle A=40$ degree

Angle A=Angle B

When two angles are equal of a triangle then the triangle is isosceles triangle.

Therefore, triangle ABC is an isosceles triangle.

$\implies BC=AC$

Now, Sine law

$\frac{a}{sin A}=\frac{b}{sin B}=\frac{c}{sin C}$

Using the sine law

$\frac{BC}{sin 40}=\frac{AB}{sin 100}$

$\frac{BC}{sin 40}=\frac{8}{sin 100}$

$BC=\frac{8\times sin40}{sin 100}$

BC=5.22

AC=BC=5.22 miles

Now, total distance covered by the boat=AB+BC+AC

Total distance covered by the boat=8+5.22+5.22=18.44 miles

Hence, option B is correct.

4 0

2 years ago

Explain the rule for multiplying two negative integers. Use a number line or algebra tiles to illustrate three examples. Make a

Blizzard [7]

Multiplying two negative numbers would always give you a positive product

Example 1) -2 * -1 = 2

Example 2) -5 * -4 = 20

Example 3) -10 * -3 = 30

4 0

2 years ago

HELP ME PLEASED IT IS DUE TODAY AND NO LINKS

Alisiya [41]

Answer:

a

Step-by-step explanation:

city 2 has a wider range so it's less consistent

4 0

2 years ago

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