The base of a solid is bounded by x^2 + y^2 = 16. Cross sections perpendicular to the x-axis are right isosceles triangles with one leg located in the base. Which definite integral represents the volume of this solid?

[tex]\textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{(x+4)^2}{400}~~ + ~~\cfrac{(y+3)^2}{144}~~ = ~~1\implies \cfrac{[x-(-4)]^2}{20^2}~~ + ~~\cfrac{[y-(-3)]^2}{12^2}~~ = ~~1 \\\\\\ \begin{cases} h=-4\\ k=-3\\ a=20\\ b=12 \end{cases}\qquad \qquad c=\sqrt{20^2-12^2}\implies c=\sqrt{256}\implies \boxed{c=16} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{center}{(-4,-3)}\qquad vertices \begin{cases} (\stackrel{-4-20}{-24}~~,~~-3)\\\\ (\stackrel{-4+20}{16}~~,~~-3) \end{cases}\qquad foci \begin{cases} (\stackrel{-4-16}{-20}~~,~~-3)\\\\ (\stackrel{-4+16}{12}~~,~~-3) \end{cases}[/tex]

Answer:

It makes a right traiangle.

Step-by-step explanation:

Graph the points and you will see that it makes a right triangle.

The figure formed by the vertices A(3,5), B(3,1), and C(0,1) is a right-angled triangle.

In this triangle, side BC is the shortest side with a length of 3 units, side AB is the longest side with a length of 4 units, and side AC has a length of 5 units.

The right angle is formed between side BC and side AC at point C (0,1).

Here, we have to identify the figure with the given vertices A (3,5), B (3,1), and C (0,1), we can plot these points on a coordinate plane.

Let's plot the points A(3,5), B(3,1), and C(0,1) on a Cartesian coordinate plane.

A(3,5): This point is located at x-coordinate 3 and y-coordinate 5.

B(3,1): This point is located at x-coordinate 3 and y-coordinate 1.

C(0,1): This point is located at x-coordinate 0 and y-coordinate 1.

Since point A and point B share the same x-coordinate (x = 3), they lie on a vertical line. Point C has a different x-coordinate, so we need to connect it with the others to complete the figure.

The figure formed by connecting the points A, B, and C is a right-angled triangle.

To calculate the distances between the vertices, we'll use the distance formula:

Distance between two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by:

Distance = √[tex]((x_2 - x_1)^2 + (y_2 - y_1)^2)[/tex]

Let's calculate the distances:

Distance between A(3,5) and B(3,1):

Distance_AB = √[tex]((3 - 3)^2 + (1 - 5)^2)[/tex]

Distance_AB = √(0 + 16)

Distance_AB = √16

Distance_AB = 4 units

Distance between A(3,5) and C(0,1):

Distance_AC = √[tex]((0 - 3)^2 + (1 - 5)^2)[/tex]

Distance_AC = √[tex]((-3)^2 + (-4)^2)[/tex]

Distance_AC = √(9 + 16)

Distance_AC = √25

Distance_AC = 5 units

Distance between B(3,1) and C(0,1):

Distance_BC = √[tex]((0 - 3)^2 + (1 - 1)^2)[/tex]

Distance_BC = √[tex]((-3)^2 + 0^2)[/tex]

Distance_BC = √9

Distance_BC = 3 units

As we calculated, the distances between the vertices of the figure are:

AB = 4 units

AC = 5 units

BC = 3 units

Based on the distances, we can determine that the figure formed by the vertices A(3,5), B(3,1), and C(0,1) is a right-angled triangle.

In this triangle, side BC is the shortest side with a length of 3 units, side AB is the longest side with a length of 4 units, and side AC has a length of 5 units.

The right angle is formed between side BC and side AC at point C (0,1).

To learn more on triangle click:

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Answer:

[tex]2x^{6}y^{2} }[/tex]

Step-by-step explanation:

Just Simplifying the Fraction.

we get,

[tex]=\frac{12x^{9} y^{4} }{6x^{3}y^{2} } \\\\=2x^{9-3} y^{4-2} \\=2x^{6} y^{2}[/tex]

[tex]-4x^2+16 & =0\\\\\implies -4(x^2-4) & =0 \\\\\implies x^2-4 =0\\ \\\implies x^2-2^2 =0\\\\\implies (x+2)(x-2)=0\\\\\implies x=2,~~x = -2[/tex]

Answer:

Answer:

Expression equivalent to (k + k)(4) is 28.

Step-by-step explanation:

Given:

k(x) = 5x - 6

We need to find an expression equivalent to (k + k)(4)

First, we find,

(k + k)(x) = k(x) + k(x)

            = ( 5x - 6 ) + ( 5x - 6 )

            = 5x - 6 + 5x - 6

            = 5x + 5x - 6 - 6

            = 10x - 12

Now, (k + k)(4) = 10(4) - 12 = 40 - 12 = 28

Therefore, the Expression equivalent to (k + k)(4) is 28.

Answer:

4π

Step-by-step explanation:

since the shaded in area is the tile and the radius is 2 and we only need the SHADED IN area 2^2 is 4 therefore 4pi is the correct answer

Answer:

-12x²

Step-by-step explanation:

Given expression:

[tex]-5x^{2} -7x^{2}[/tex]

Since both terms in the expression have common terms, we can subtract the terms by combining like terms.

[tex]\implies x^{2} (-5 -7)[/tex]

[tex]\implies x^{2} (-12)[/tex]

[tex]\implies -12x^{2}[/tex]

We are given that:

Circumference = 19.4 cm

Formula:

2πr = Circumference

Rewrite the equation:

The "r" variable represents the radius of the circle. Thus, we need to isolate it on one side to determine the radius. This can be done with the four mathematical operations (+  -  ×  ÷). Since the "÷" is included, we can divide both sides by 2π to isolate the "r" variable.

Divide both sides by 2π:

Substitute the radius as 22/7:

Answer: 15840

Step-by-step explanation: multiply the length value by 5280

Answer:

15840 feet

Step-by-step explanation:

5280 (feet per mile) times 3 (the amount of miles Ashlynn runs every morning) is 15840

Answer:

(B) No

Step-by-step explanation:

If I remember correctly a solution is a point that is on the shaded area or on a solid line, the point 3,-3 is not on the shaded region and not on a solid line. Even if it was on the line in this problem it wouldn't be a solution because it is a dotted line. Hope this helps!

Answer: 0.9

Step-by-step explanation: All you need to just keep your decimal (0.9) as it is since 4 and 2 are below 5 then you don't need to round it higher. I hope this helped!

0.942

the nearest tenth of 0.942

to round to the nearest tenth, if the number in hundredths place is 5 or more you'll have to round up, if not keep it as it is and remove all the digits in the right side.

=0.9

hence, the nearest tenth of 0.942 is 0.9

Step-by-step explanation:

[tex]5 {x}^{2} - 4 {y}^{2} + 80 = 0[/tex]

[tex]5 {x}^{2} - 4 {y}^{2} = - 80[/tex]

[tex] - \frac{ 5{x}^{2} }{16} + \frac{ {y}^{2} }{20} = 1[/tex]

[tex] \frac{ {y}^{2} }{20} - \frac{5 {x}^{2} }{16} = 1[/tex]

To find foci,

[tex]c = \sqrt{ {a}^{2} + b {}^{2} } [/tex]

so

[tex]c = \sqrt{20 + 16} [/tex]

[tex]c = \sqrt{36} [/tex]

[tex]c = ±6[/tex]

Since the y term has a greater denomiator, our foci is

(0,6) and (0,-6)

Answer:

x=15

Step-by-step explanation:

A line is 180 degrees

We know that 8x+19=139

8x+19=139

subtract 19 from both sides to isolate x

8x=120

divide both sides by 8

8x/8=120/8

x=15

Answer:

domain x   [0,4]     range y  [0,64]

Step-by-step explanation:

Answer:

Interpolation is used to predict values that exist within a data set, and extrapolation is used to predict values that fall outside of a data set and use known values to predict unknown values. Often, interpolation is more reliable than extrapolation, but both types of prediction can be valuable for different purposes

Answer:

  (b)  y = -7x -27

Step-by-step explanation:

When x and y in the equation y = f(x) are replaced by (x-h) and (y-k), the function graph is translated h units right and k units up. The translated function can be written as ...

  y -k = f(x -h)

  y = f(x -h) +k . . . . . . add k

__

Your function is ...

  y = -7x

and you want to translate it by (h, k) = (-5, 8). That makes it ...

  y' = -7(x -(-5)) +8 = -7x -35 +8

  y' = -7x -27

Answer:

He can make eight 3-pancake servings.

Step-by-step explanation:

6 eggs make 12 pancakes.

12 eggs make 24 pancakes.

24 divided by 3 is 8.

Answer:

I think it would be fine if they notified you but only if they used me for a good reason.

On the other hand...

no matter if it's on the agreement if it is inappropriate on your part it is illegal and you can complain.

Answer:

30 cm

Step-by-step explanation:

just times it by three because theres three sides

Answer:

8 x 10^5

Step-by-step explanation:

Answer:

x = 28

Step-by-step explanation:

Supplementary angles mean that both angles are equal to 180. So, the equation becomes 3x + 96 = 180. Solving for x, we get 28.

Answer:

The value of x is 28

Step-by-step explanation:

Given :

Now,

Supplementary angles are a pair of angles that make sum of 180° .

Therefore, The sum of given angles will be equal to 180°.

i.e. one angle + other angle = 180°

Substituting the values of angles , we get..

[tex]⇢3x + 96 = 180[/tex]

[tex]⇢3x = 180 - 96[/tex]

[tex]⇢3x = 84[/tex]

[tex]⇢x = \frac{84}{3} [/tex]

Answer:

10 Quarts

Step-by-step explanation:

First, convert 1/2 gallons into quarts. 1/2x4=2. Then convert 1 1/4 to quarts. 1 1/4x4=5. Finally, add it all togher. 2+5+3=10. So, the answer is 10 quarts.

Answer:

No, -14 is not greater than 9

Step-by-step explanation:

because -14 is a negative interger making the postive a higher/greater number

Answer:

3, 7

Step-by-step explanation:

3, 3, 3, 4, 4, 6, 7, 7, 7

3 and 7