look at pic 10 pts will mark brainilest

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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well you see I'm supposed to answer this with 20 character so my bad for the long response, but I'd go with C

vvfvhrf uiiutgbvfbfd

Answer is

2, 4, 6, 8

Answer:

None of the option is correct.

The right answer is 18/7 or 2.57

Step-by-step explanation:

Answer:

Find the GCF of all the terms in the polynomial.

Express each term as a product of the GCF and another factor.

Use the distributive property to factor out the GCF.

Step-by-step explanation:

Answer:

f(-3)= 10(-3)^2 - 5(-3) - 3

       =90 + 15 -3

f(-3) = 102

Step-by-step explanation:

Answer:

153

Step-by-step explanation:

The formula is 3 mL of A to 5 mL of B.

Let's say the chemist uses just the numbers in the formula.

Add 3 mL of A to 5 mL of B.

3 mL + 5 mL = 8 mL

The chemist ends up with 8 mL of the drug.

He really want 408 mL.

408 mL is how many times greater than 8 mL?

408/8 = 51

He needs to use 51 times the numbers in the formula.

51 * 3 mL of A + 51 * 5 mL of B =

= 153 mL of A + 255 mL of B

= 408 mL of the drug

Answer: 153

Answer:

ST = 2x

Step-by-step explanation:

if not please elaborate on the question.

Answer:

A. 6.6 ft

Step-by-step explanation:

Answer:

This cinder block has gravitational potential energy.

This cinder block has 15 484 joules of potential energy

Step-by-step explanation:

PE = mass*gravity*height and g= 9.8 m/s^2

PE = 79 * 9.8 * 20

PE = 15 484

No of hours

[tex]\\ \sf\longmapsto 4(1)[/tex]

[tex]\\ \sf\longmapsto 4 hours[/tex]

None of the above

Answer: 33.125

Step-by-step explanation:

So you would do 200 divdied by 5 which is 40 then you would do 1,325 divided by 40 which is the anwser 33.125. If you did it another way let me know.

Answer:

[tex]13x + 7 = 9x - 33 + 4x \\ 7 + 33 = 13x - 13x \\ \\ 40 = 0 \\ \\ no[/tex]

Answer:

(0, −3)

(2, −2)

(1, −4)

(6, 1)

(−3, 0)

Step-by-step explanation:

try plugging them in, might seem tedious, but it's the best way to practice. if you plug in a pair and the left side of the equation is less than or equal to 6, it's the right answer.

Answer:

B.) Progressive

Step-by-step explanation:

Its schedule of marginal tax rates imposes a higher income tax rate on people with higher incomes, and a lower income tax rate on people with lower incomes. The percentage rate increases at intervals as taxable income increases.

Answer: the 15th day

Step-by-step explanation:

Skip count by both numbers until you reach the first number they have

   in common;

     3, 6, 9, 12, 15, 28, 21, 24, 27, 30

     5, 10, 15, 20, 25, 30, 35, 40

Answer:

true

Step-by-step explanation:

England claimed the colonies, so they ruled over them.

Answer:

31, 114 and 35

Step-by-step explanation:

I set up the equation as such:

(3x + 21) + (x + 4) + x = 180

then I combined like terms:

5x + 25 = 180

And then solving for x I get:

5x = 155

x = 31

And then plugged the solved x value into the terms to give:

(3(31) + 21) = 114

(31 + 4) = 35

alongside the found angle of 31.

Answer:

[tex]31^{\circ}, 35^{\circ}, 114^{\circ}[/tex]

Step-by-step explanation:

Let the first angle be [tex]x[/tex]. Then, the second angle is [tex](x+4)^{\circ}[/tex] and the third angle is [tex](3x+21)^{\circ}[/tex].

We know that the sum of the angles in a triangle will always be [tex]180^{\circ}[/tex]. So, we want to solve the equation for x: [tex](x)+(x+4)+(3x+21)=180[/tex].

Combining like terms on the left side gives [tex]5x+25=180[/tex].

Subtracting [tex]25[/tex] from both sides gives [tex]5x=155[/tex].

Dividing both sides by [tex]5[/tex] gives [tex]x=31[/tex].

So, the first angle is [tex]31^{\circ}[/tex].

The second angle is [tex]x+4=31+4=35[/tex], so the second angle is [tex]35^{\circ}[/tex].

The third angle is [tex]3x+21=3(31)+21=93+21=114[/tex], so the third angle is [tex]114^{\circ}[/tex].

So, the angles are [tex]\boxed{31^{\circ}, 35^{\circ}, 114^{\circ}}[/tex] and we're done!

The check that these angles work is left as an exercise to the reader.

Answer:

sorry bro I even don't know coz I am class 7

Answer:

it will look like this 4(a+3)-2/3

Step-by-step explanation:

look since the equation "a+3" replaced for the place of "x" in f(x), you replace it on the equation "4x- 2/3" and just solve

Answer:

Step-by-step explanation:

Id..k how to help u sorry

Answer:

the answer is infinity....

Answer:

D`

Step-by-step explanation:

The answer would be D because 40 is twice as much as 20. We also double the number of hours. So instead of having the ratio of 20:1 we have the ratio 40:2 (Miles : Hours)

lolol lfeofviponvfnfuibouigb

The least-squares regression line equation gives the line that approximate the relationship between the variables in the fuel efficiency data

The fuel efficiency when the speed is 60 mph is approximately 38.55 mpg.

Reason:

The given least-squares regression line equation is presented as follows;

ln(Fuel Efficiency) = 1.437 + 0.541 × ln(speed)

Required:

The value of the fuel efficiency for a speed of 60 mph.

Solution:

The general form of the least-squares regression line equation is [tex]\hat y[/tex] = a + b·x

Where, in the current question, we have;

[tex]\hat y[/tex] = The predicted value = ln(Fuel Efficiency)

a = The y-intercept = 1.437

b = The slope = 0.541

x = The input value = ln(speed)

When the speed = 60 mph, we have;

ln(Fuel Efficiency) = 1.437 + 0.541 × ln(60) = 3.65204040816

Therefore;

[tex]Fuel \ Efficiency = e^{(1.437 + 0.541 \times ln(60))} \approx 38.55[/tex]

The fuel efficiency when the speed is 60 mph ≈ 38.55 miles per gallon

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Answer:

the person above me is correct.

Step-by-step explanation: