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Answer:

[tex]\sf\longmapsto \: x = 4[/tex]

Step-by-step explanation:

[tex]\sf\longmapsto \: 4x = 16[/tex]

[tex]\sf\longmapsto \: x = \frac{16}{4} [/tex]

[tex]\sf\longmapsto \: x = 4[/tex]

Using polar/cylindrical coordinates, we take

x = r cos(t )

y = r sin(t )

z = z

so that

dV = dx dy dz = r dr dt dz

The solid is given by the set

D = {(x, y, z) : x ² + y ² ≤ 1 and 0 ≤ z ≤ 4 - 2x - y}

or in cylindrical coordinates,

D = {(r, t, z) : 0 ≤ r ≤ 1, 0 ≤ t ≤ 2π, and 0 ≤ z ≤ 4 - 2r cos(t ) - r sin(t )}

Then the volume of the solid is

[tex]\displaystyle \iiint_D \mathrm dV = \iiint_Dr\,\mathrm dr\,\mathrm dt\,\mathrm dz \\\\ = \int_0^{2\pi} \int_0^1 \int_0^{4-2r\cos(t)-r\sin(t)} r\,\mathrm dz\,\mathrm dr\,\mathrm d t \\\\ = \int_0^{2\pi}\int_0^1 (4r-2r^2\cos(t)-r^2\sin(t))\,\mathrm dr\,\mathrm dt \\\\ = \int_0^{2\pi} \left(2 - \frac23 \cos(t) - \frac13 \sin(t)\right) \,\mathrm dt \\\\ = \boxed{4\pi}[/tex]

The volume of the given solid below the plane 2x + y + z = 4 and above the disk x2 + y2 ≤ 1 is 4π.

The volume of the solid in polar coordinates can be calculated by the double integral in polar coordinates.

[tex]V = \iint_R f(x,y) \,dA.\\[/tex]

Similarly, by polar coordinates,

x = r cost

y = r sint

z = z

we get, dV = dx dy dz = r dr dt dz

The solid is given

D = {(x, y, z) : x ² + y ² ≤ 1 and 0 ≤ z ≤ 4 - 2x - y}

or in polar coordinates,

D = {(r, t, z) : 0 ≤ r ≤ 1, 0 ≤ t ≤ 2π, and 0 ≤ z ≤ 4 - 2r cos(t ) - r sin(t )}

The volume of the solid is

[tex]\rm \int \int\int\ dV = \int \int\int\ rdr dt dz\\ \rm = \int\limits^{2\pi}_0\int\limits^1_0 \int\limits^{4-2rcost-rsint}_0 rdr dt dz\\\rm =\int\limits^{2\pi}_0\int\limits^1_0 {4r-2r^{2} cost-r^{2} sint} dr dt\\\rm =\int\limits^{2\pi}_0( 2-2/3cost-1/3sint) dt\\\rm =4\pi[/tex]

Hence, The volume of the given solid below the plane 2x + y + z = 4 and above the disk x2 + y2 ≤ 1 is 4π.

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9514 1404 393

Answer:

  b.  60

Step-by-step explanation:

The list of factors is 2, 3, 5, 7. The list of common factors is 2, 3, 5. The lowest exponents on those factor are ...

  2^2 × 3^1 × 5^1 = 60

The GCF of 720 and 2100 is 60.

_____

Additional comment

You can verify this using Euclid's method of finding the GCF.

  2100/720 = 2 r 660

  720/660 = 1 r 60

  660/60 = 11 r 0 . . . . 60 is the GCF

Find the remainder from the division. If it is zero, the divisor is the GCF. If it is non-zero, replace the largest number with the remainder, and repeat.

Answer:

Yes

Step-by-step explanation:

( x, y ) = ( 3, - 10 )

Here,

x = 3

y = - 10

y = - 4x + 2

- 10 = - 4 ( 3 ) + 2

- 10 = - 12 + 2

- 10 = - 10

LHS = RHS

Therefore,

( 3, - 10 ) a solution to the function y = - 4x + 2.

Answer:

Bro can you send your question

Answer:

whate your questions bro

Answer:

point a is start with positive but point b start with negative

Answer:

It would take 40 times to match the amount of money

Answer:

6 hours will have past if it's then -2°C

Since the value of y varies directly with x, the value of x when y equals 9 is [tex]\frac{9}{13}[/tex]

Given the following data:

To find the value of x when y = 9:

This is a direction proportion exercise and you're required to solve for the value of x when the value of y is equal to 9.

First of all, we would determine the constant of proportionality (k) for the mathematical expression.

[tex]y = kx\\\\15 = 195k\\\\k = \frac{195}{15}[/tex]

k = 13

Now, we can find x:

[tex]y = kx\\\\9 = 13x\\\\x = \frac{9}{13}[/tex]

Therefore, the value of x when y equals 9 is [tex]\frac{9}{13}[/tex]

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The average speed of the runner is 12.7 mph and 20.4 km/h

Given that the runner ran 26.2 mile in 2hr and 4 minutes, we start of by converting the time from  hours and minutes into minutes and finally hours, since hours is what we need. So, we have

2hr = 120mins

+ 4 mins = 124 mins

124 mins ÷ 60 hour/mins = 2.06 hours.

This means that the runner finished the race in 2.06 hours.

If we are to find the average speed in mile per hour, we have

Average speed = distance ran ÷ time taken

Average speed = 26.2 ÷ 2.06

Average speed = 12.7 mph

From the speed in mph, we can directly convert it to km/hr by saying

1 mph = 1.609 km/h

12.7 mph = 12.7 * 1.609 = 20.4 km/hr

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answer: -4 1/2

explanation:

Answer:

786 rounded to the nearest ten is 770.

Step-by-step explanation:

To round to the nearest 10, look at the units digit. if the units digit is 5 or more, round up. If the units digit is 4 or less, round down.

(7 hot dogs)/(4 minutes) = (23 hot dogs)/(x minutes)

7/4 = 23/x

7x = 4*23 .... cross multiplication

7x = 92

x = 92/7

x = 13.142857 approximately

x = 13.1

Answer:

68.42105263157895

Step-by-step explanation:

Answer:

68.42

Step-by-step explanation:

Answer:

12.87, 12.5  is closer to 13

12.08, 12.13  is closer to 12

Step-by-step explanation:

Least to Greatest:

12

13

Answer:

The answer is 78.5

Step-by-step explanation:

Work Shown:

f(x) = -x-5

f(4) = -4-5

f(4) = -9

Explanation: Replace every copy of x with 4. Then use PEMDAS to simplify.

It is observed that point (18, 206) does not lie on the line. Then the correct option is D.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The equation is given below.

y = 12x

Where 'y' represents the number of gallons of water in the pool and 'x' represents the number of minutes the water runs.

The equation is drawn below.

From the chart, it is seen that point (18, 206) doesn't lie on the line. Then the right choice is D.

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Answer:

c. 1.3452 x 10^4

Step-by-step explanation:

Answer:

3rd option is correct.

Step-by-step explanation:

The diagonal length of a square is [tex]\sqrt{2}[/tex] times the side lengths of the square. Squares have 90 degree angles, so we know that this triangle is half a square, making both side lengths 12.

Answer:

x=(-k-h)/r

Step-by-step explanation:

rx+h=-k

subtract h from both sides.

rx=-k-h

divide both sides by r.

x=(-k-h)/r

Answer: E

Step-by-step explanation:

The graph D has a x-intercept = −1  and y-intercept = 5

The given parameters are:

x-intercept = −1

y-intercept = 5

The above means that the graph crosses the x-axis at -1, and it crosses the y-axis at -5

From the list of options, the graph that satisfies the above highlights is graph D

Hence, the graph D has a x-intercept = −1  and y-intercept = 5

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