Use cylindrical coordinates.
Find the volume of the solid that is enclosed by the cone
z = \sqrt{x^2+y^2} and the sphere x2 + y2 + z2 = 32.

Answer:   [tex]\dfrac{3}{2}x^{2}-\dfrac{7}{x}+\dfrac{11}{2x^2}+C[/tex]

Step-by-step explanation:

[tex]\int {\dfrac{3x^4+7x-11}{x^3}} \, dx \\\\\\= \int \bigg({\dfrac{3x^4}{x^3}} +\dfrac{7x}{x^3}+\dfrac{-11}{x^3}\bigg)\, dx\\\\\\= \int \bigg(3x+7x^{-2}-11x^{-3}\bigg)\, dx\\\\\\=\dfrac{3x^{1+1}}{1+1}+\dfrac{7x^{-2+1}}{-2+1}+\dfrac{-11x^{-3+1}}{-3+1}+C\\\\\\=\dfrac{3x^{2}}{2}+\dfrac{7x^{-1}}{-1}+\dfrac{-11x^{-2}}{-2}+C\\\\\\=\large\boxed{\dfrac{3x^{2}}{2}-\dfrac{7}{x}+\dfrac{11}{2x^2}+C}[/tex]

Answer:

OK its that question

Answer:

The amount required is  [tex]l_t = 1586 \ m[/tex]

Step-by-step explanation:

From the question we are told that

   The length of one side is  [tex]l_1 = 435 \ m[/tex]

    The length  of the second side is  [tex]l_2 = 656 \ m[/tex]

     The angle between the line of sight of second and third side is  [tex]\theta = 49^o \\[/tex]

Generally using cosine rule the third side is evaluated as

     [tex]l_3^2 = l_1 ^2 + l_2^2 - 2 * l_1 * l_2 cos (\theta )[/tex]

=>    [tex]l_3^2 = 435 ^2 + 656^2 - 2 * 453* 656 cos (49)[/tex]

=>   [tex]l_3 = 495 \ m[/tex]

The total  amount of face required is  mathematically evaluated as

       [tex]l_t = l_1 + l_2 + l_3[/tex]

   [tex]l_t = 435 + 656 + 495[/tex]

   [tex]l_t = 1586 \ m[/tex]

Answer:

#1 Use Pythagorean theorem to solve DF

c²-b²=a²

5.83²-5²=a²

33.9889-25=a²

a²=8.9889

a=3.00 (rounded to nearest hundredth)

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

# Use Trigonometry to find the angles

angle D:90

angle E: tan E=3/5

                    E=tan^-1 (3/5)

                    E=30.96 (rounded to nearest hundredth)

angle F: tan F=5/3

                    F=tan^-1 (5/3)

                    F=59.04 (rounded to nearest hundredth)

Answer:

-8x + 12

Step-by-step explanation:

We can use the distributive property of multiplication which states that a(b + c) = a * b + a * c. Therefore:

-4(2x - 3)

= -4 * 2x - 4 * (-3)

= -8x + 12

Answer: -8x -12

Step-by-step explanation:

Multiply -4 by 2x getting -8x

Then Multiply -4 by 3 getting 12

Since you can't subtract 12 from -8x this is the simplest way

Answer:

Step-by-step explanation:

16

Answer:

f(g(x)) = 18x - 8

Step-by-step explanation:

f(x) = 3x + 7 and g(x) = 6x - 5

Substitute g(x) into f(x):

f(g(x)) = 3(6x - 5) + 7

Distribute the 3 from outside the parentheses:

f(g(x)) = (18x - 15) + 7

Combine like terms:

f(g(x)) = 18x - 8

Answer:

A

Step-by-step explanation:

The area of a circle is given by the formula:

[tex]A=\pi r^2[/tex]

Where A is the area and r is the radius.

Since we already know the area, we can plug it in and solve for r. Thus:

[tex]1808.64=\pi r^2\\[/tex]

Divide both sides by π. We can use 3.14 as an approximation. The πs on the right cancel out:

[tex]1808.64\div(3.14)=r^2\\r^2=576[/tex]

Take the square root of each side:

[tex]\sqrt{r^2}=\sqrt{576}[/tex]

The squares on the left cancel. The root of 576 is 24:

[tex]r=24[/tex]

Therefore, the radius is 24.

Answer:

I agree 24 miles

Step-by-step explanation:

the person above is correct

Answer: 504 ways

Step-by-step explanation:

given data:

no of people = 6

no of offices = 3

no of people in each office = 2

solution:

first we need to find the number of ways 6 people can be shared in 2 or pairs as this is a combination problem.

= 6C2

= 15 ways

ways to place a pair of 2 in 3 offices

= 15 * 3

= 45ways.

using the remaining 4 people we have 4C2 = 6 ways

in the remaining 2 offices

6 * 2 = 12ways

withour conditions

= 45 * 12

= 540ways

considering the constraint

= 4C2

= 6ways

shared in 3 offices

= 6 * 3

= 18 ways

remaining 2 offices

= 18 * 2

= 36 ways

Without constraints - With constraints

= 540 - 36

= 504ways

90 ways.

Given:

Six people are to be assigned in three offices, two people per office.

Thinking of this problem from the perspective of offices themselves picking persons, we get this:

Firstly out of 6 person, 2 person are chosen in [tex]^6C_2[/tex] ways.

Secondly, from rest of the 4 persons, 2 people are chosen in [tex]^4C_2[/tex] ways.

Then rest of the 2 persons are chosen from rest persons in [tex]^2C_2[/tex] ways.

Applying law of multiplication for number of ways:

Total number of ways = [tex]^6C_2 \times ^4C_2 \times ^2C_2 = 15 \times 6 \times 1 = 90[/tex]

For more information, refer this link below:

https://brainly.com/question/13003667

Answer:

2/(3x-2)²

Step-by-step explanation:

4x²-6x³-2x²+6x³/4x²-6x³-6x³+9x^4=

2x²/4x²-12x³+9x^4=

2x²/x²(4-12x+9x²)=

2/9x²-12x+4

2/(3x-2)²

We have the equation:

[tex]9x^2-12x+4=0[/tex]

so:

[tex]a=9\qquad b=-12\qquad c=4[/tex]

and:

[tex]\Delta=b^2-4ac=(-12)^2-4\cdot9\cdot4=144-144=\boxed{0}[/tex]

This equation has one solution.

Answer:

k=17

Step-by-step explanation:

k+10=27

k=27-10

k=17

Hi there! Hopefully this helps!

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

[tex]k + 10 = 27[/tex]

Subtract 10 from both sides.

[tex]k = 27 - 10[/tex]

Answer:

there are no zeros in f(x)

Step-by-step explanation:

[tex]f(x)=3x^2+9x+12\\\\f(x)=0\\\\0=3x^2+9x+12\\\\[/tex]

to know if the equation has real solutions we have to know if

[tex]b^2-4ac\geq 0[/tex]

a=3

b=9

c=12

[tex]9^2-4*3*12\\\\=81-144\\\\=-63[/tex]

so there aren't real solutions

hence there aren't any zeros in f(x)

Answer:

f(x) = 7/8 + n=0 = 7/8 so the answer you looking for would be: n=0

Answer:

  48/132

Step-by-step explanation:

The length of 1.5-inch screws is ...

  36 × 1.5 in = 54 in

The length of 2-inch screws is ...

  24 × 2 in = 48 in

The length of 2.5-inch screws is ...

  12 × 2.5 = 30 in

The total length of all screws is ...

  54 in + 48 in + 30 in = 132 in

Then the ratio of 2-in screw length to total screw length is ...

  2-in : total = 48 : 132

Answer:

36

Step-by-step explanation:

2 x 3 x 3 x 2 = 36

Answer:

87

Step-by-step explanation:

[tex]\frac{96+85+90+92+x}{5} = 90\\[/tex]

[tex]\frac{353+x}{5} = 90[/tex]

[tex]353+x= 5(90)\\[/tex]

[tex]353+x=450[/tex]

[tex]x=87[/tex]

Answer:

A.P. : 10, 20, 30, 40, 50

G.P. : 5, 10, 20, 40, 80 .

Step-by-step explanation:

It is given that fourth term of a sequence is 40.

It is not given that whether the sequence is A.P. or G.P.

We need to write two different sequences that satisfy the given condition.

For A.P.,

Required sequence : 10, 20, 30, 40, 50

Here, first term is 10, common difference is 10.

For G.P.,

Required sequence : 5, 10, 20, 40, 80

Here, first term is 5, common ratio is 2.

Therefore, the two sequences are 10, 20, 30, 40, 50  and 5, 10, 20, 40, 80 .

Answer:

-31

Step-by-step explanation:

-3 to the power of 2 means -3*-3 and since negative multiplied by negative is positive, that will give 9

9 + (2-6)(10)

9+-4(10)

9+ -40

9-40

-31

Answer:

$ 5.5

Step-by-step explanation:

$33 for 6 sandwiches.

For 1 sandwiche = ?

Now,

= 33 ÷ 6

= $5.5

Thus, the unit rate is $5.5

Answer:

[tex]\frac{3}{20}[/tex] or [tex]0.15[/tex] (they're the same thing)

Step-by-step explanation:

I hope this helps!

Answer:

9(x² + 5y⁴) (x² - 5y⁴)

Step-by-step explanation:

9x⁴ - 225y⁸

factor out a 9

9(x⁴ - 25y⁸)

factor (x⁴ - 25y⁸)

(x⁴ - 25y⁸)

x² • x² = x⁴

5y⁴ • -5y⁴ = -25y⁸

(x² + 5y⁴) (x² - 5y⁴)

↓

9(x² + 5y⁴) (x² - 5y⁴)

Answer:

C.

Step-by-step explanation:

"Two more than three times a number is seven"

Add 2 to 3n and set it equal to 7.

The equation that represents the mentioned condition will be 3n + 2 = 7. Then the correct option is C.

The expression is defined as the relations of the numbers and the variables combined together to form the equation by the use of mathematical algebraic symbols like equal greater than or less than.

From the statement, two more than three times a number is seven.

Let n be the number. The three times a number is then written as,

⇒ 3n

And the expression that is 2 more than 3n is written as follows:

⇒ 2 + 3n

The expression equals 7. The equation is then given as,

3n + 2 = 7

The equation that represents the mentioned condition will be 3n + 2 = 7. Then the correct option is C.

To know more about an expression follow

brainly.com/question/10606712

#SPJ2

Answer:

23

Step-by-step explanation:

Answer:

(4,3)

Step-by-step explanation:

Point V lies in the Ist quadrant . and the co-ordinates are (4,3)

Answer:

Friday needs 11 bikes

Step-by-step explanation:

Mean = (summation of all the numbers)/the total number of the given data

(summation of all the numbers)

= 3.5+5.5+0+5+x

(summation of all the numbers)

= 14+x

the total number of the given data

=5

Mean= 5

Mean= (summation of all the numbers)/the total number of the given data

5= (14+x)/5

25= 14+x

25-14=x

11= x

Answer:

- 4x^8 + 3x^4 + 3x^2 + 9x

Step-by-step explanation:

First simplify

Put in standard form

Answer:

Step-by-step explanation:

Hello, please consider the following.

We take y different from -5, as dividing by 0 is not allowed and we can compute as below.

[tex]\dfrac{y^2+3y-10}{3y+15}=\dfrac{(y+5)(y-2)}{3y+15}\\\\=\dfrac{(y+5)(y-2)}{3(y+5)}\\\\\large \boxed{\sf \bf \ \ =\dfrac{y-2}{3} \ \ }[/tex]

Thank you

Answer:

60

Step-by-step explanation:

1, Extand line y for which y intercepts CB at point K

2, line y is a straight line and thus KAB=180-110=70

3, AY parallel to CX thus angle CKA=130 which is a alternative angle of BCX (if you can't see then try to extend CX as well

4,BKA=180-130=50 as BC is a straight line

5, the sum of interior angle of a triangle is 180, and we have KAB and BKA, thus angle ABC = 180-KAB-BKA=180-70-50=60

Answer: 8

Step-by-step explanation: Think of the 32 in this problem as 32/1.

So rewriting, we have 1/4 × 32/1.

Now, the 4 and 32 cross-cancel to 1 and 8.

So we have 8/1 or just 8.