Part B
Now that you know the missing side length, is triangle BCD a right triangle? Give you
reason.

Parameterize S by the vector function

[tex]\vec s(u,v) = \left\langle 4 \cos(u) \sin(v), 4 \sin(u) \sin(v), 4 \cos(v) \right\rangle[/tex]

with 0 ≤ u ≤ π/2 and 0 ≤ v ≤ π/2.

Compute the outward-pointing normal vector to S :

[tex]\vec n = \dfrac{\partial\vec s}{\partial v} \times \dfrac{\partial \vec s}{\partial u} = \left\langle 16 \cos(u) \sin^2(v), 16 \sin(u) \sin^2(v), 16 \cos(v) \sin(v) \right\rangle[/tex]

The integral of the field over S is then

[tex]\displaystyle \iint_S \vec f \cdot d\vec s = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \vec f(\vec s) \cdot \vec n \, du \, dv[/tex]

[tex]\displaystyle = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \left\langle 8 \cos(u) \sin(v), -12 \cos(v), 12 \sin(u) \sin(v) \right\rangle \cdot \vec n \, du \, dv[/tex]

[tex]\displaystyle = 128 \int_0^{\frac\pi2} \int_0^{\frac\pi2} \cos^2(u) \sin^3(v) \, du \, dv = \boxed{\frac{64\pi}3}[/tex]

Answer:

Step-by-step explanation:

~1

Given Polynomial:

To Find:

Solution:

Substitute x = -2 onto the given polynomial,as we need to find f(-2),so x = -2.

Simplify using PEMDAS,then.

Hence, f(6) = -14

[tex] \rule{225pt}{2pt}[/tex]

~2

Given polynomial:

To Find:

Solution:

g(x) = -4x-1

Substitute x = 7 onto the given polynomial,as we need to find g(7),so x = 7.

Simplify using PEMDAS.

Hence, g(7) = -29.

[tex] \rule{225pt}{2pt}[/tex]

Step-by-step explanation:

first you should check whether the sequence is arithmetic and geometric .as you see the sequence is arithmetic with the common difference of -16384.

Answer:

Parabola in vertex form: y = a(x - h)2 + k

Vertex: (h, k) = (3, 2) and (x, y) = (13, 8)

y = a(x - h)2 + k

y = a(x - 3)2 + 2 <== with substitution (h, k) = (3, 2)

8 = a(13 - 3)2 + 2 <== with substitution (x, y) = (13, 8)

8 = a(10)2 + 2

100a = 8 - 2 ==> 100a = 6 ==> a = 6/100 ==> a = 3/50

Parabola in vertex form: y = a(x - h)2 + k

y = (3/50)(x - 3)2 + 2  (Final Answer - Parabola in vertex form)

Step-by-step explanation:

Answer:

Hi,

Step-by-step explanation:

Parabola has the equation:

y=k*(x-5)²+8

if x=3, y=-2: -2=k*(-2)²+8 ==> 4k=-10==> k=-5/2

So y=-5/2(x-5)²+8

Answer:

Herman is wrong.  Latoya got the better deal.

Step-by-step explanation:

Latoya bought 8 pounds of potatoes for $18.

    ► 18 / 8 = $2.25 per pound

Herman bought 6 pounds of potatoes for $15.

    ► 15 / 6 = $2.50 per pound

Cheaper per pound is better!

The possible values of N from the given probability parameters is; N equals 15 or 21

We are told that;

Number of pens in the box = N

Let the number of red pens be x

Thus; number of black pens = x + 3

Thus;

x + x + 3 = N

x = (N - 3)/2

The probability that she will take a black pen followed by a red pen is;

P(she will take a black pen followed by a red pen) = (x + 3)/N * x/(N - 1)

Plugging in he relevant values and solving for N gives ;

Solving for N gives N equals 15 or 21

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Answer:

500π in^3

Step-by-step explanation:

The radius is half the diameter, so the radius is 5 in. Since the height is four times that, the height is 20 in.

The equation for the volume of a cylinder is:

[tex]V = \pi r^{2}h[/tex]

We can plug in the radius and height:

[tex]V = \pi \times (5)^{2} \times 20\\V = \pi \times 25 \times 20\\V = 500\pi in^{3}[/tex]

Answer: 17

Step-by-step explanation:

Don't forget about PEMDAS. (parentheses, exponents, multiplication, division, addition, subtraction)

Start with parentheses

(3+13-10)... 13+3= 16, 16-10=6 ...

so (3+13-10)=6

Now we have...

6 + 14 / 2 + 4

No exponents so we go on.

no multiplication so we go on

Now division...

14 / 2 = 7 because 7 x 2 = 14

Now we have...

6 + 7 + 4

now we do addition, addition is commutative so you can add it in any order you want

6 + 7 = 13, 13 + 4 = 17

therefore, the answer is 17

Answer:

f(g(2)) = 4

Step-by-step explanation:

find g(2) then substitute the value obtained into f(x)

locate x = 2 on the x- axis, go vertically up to meet g(x) at (2, 5 )

locate x = 5 on the x- axis, go vertically up to meet f(x) at (5, 4 )

then f(g(2)) = 4

Answer:

a

Step-by-step explanation:

anything less than 18 is wrong

Answer:

the answer is 6 just add the radius of both circle

Answer:

OP is 6

Step-by-step explanation:

Because we av being given d parameters

4 is d radius of the first circle and 2 is d radius of the second circle so automatically d answer is 6

A circle has a center, radius, diameter and points in a plane. Depending on the context, the definition of a circle must contain at least one of the following terms:

Center

Radius

Diameter

Points in a plane

The complete question is as follows:-

James defines a circle as "the set of all the points equidistant from a given point." His statement is not precise enough

because he should specify that

A circle includes its diameter

The set of points is in a plane

A circle includes its radius

The set of points is collinear

A circle is a two-dimensional geometry on the plane having a center point and the circular line is drawn equidistant from the center point.

Based on James' definition of a circle, he needed to specify that the points are in a plane (option c).

As presented in his definition "the set of all the points" can be interpreted in several ways. Some of which are:

the set of points on a line

the set of points in a plane

the set of points in a region

Etc

Of these numerous possible interpretations, James should have specified that the set of points is in a plane

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Answer: 453.592 grams

Step-by-step explanation:

I searched it up online. But if you're going to use this to calculate. Use 454 grams.

Answer:

453.592 rounded would be 454* grams witch is equal to 1 pound

Step-by-step explanation:

1 pound is equivalent to __453.592 or just say 454*__ grams.

Had to fix that hehehe

Hope This Helped

Answer:

You will be 55

Step-by-step explanation:

Answer:

3 and 4

Step-by-step explanation:

given that the difference is 7, two numbers that add up to 7 are 3 and 4.

if the "d"iameter of the pie is 30, then its radius must be half that, or 15.

[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=15\\ \theta =42 \end{cases}\implies \begin{array}{llll} A=\cfrac{(42)\pi (15)^2}{360}\implies A=\cfrac{105\pi }{4} \\\\\\ \stackrel{using~\pi =3.14}{A\approx 82.43} \end{array}[/tex]

Answer: A.) y=4+x

Step-by-step explanation:

To solve this problem, we just have to substitute the values into the exponential equations and solve.

In the given exponential equation, we simply need to plug in the values of x from 0 to 5

[tex]y = 4(3)^x[/tex]

when x = 0

[tex]y = 4(3)^x\\y = 4(3)^0\\y = 4[/tex]

when x = 1

[tex]y = 4(3)^x\\y = 4(3)^1\\y = 12\\[/tex]

when x = 2

[tex]y = 4(3)^2\\y = 36[/tex]

when x = 3

[tex]y = 4(3)^3\\y = 108[/tex]

when x = 4

[tex]y = 4(3)^4\\y = 324[/tex]

when x = 5

[tex]y = 4(3)^5\\y = 972[/tex]

From the calculations above, the value of y when x is from 0 to 5 are

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Since the paper representing her desk is 1 1/4 inches by 2 1/4 inches, the actual dimensions of her desk are D: 2 ¹/₂ ft by 4 ¹/₂ ft

To answer the question, we need to know what scale is

A scale is the ratio of two dimension and it is given on a scale drawing.

Given that Chelsea makes a scale drawing of the room and cuts out pieces of paper to represent her furniture, and the paper representing her desk is 1 1/4 inches by 2 1/4 inches.

Since on the scale, we have 1/2 in = 1 foot ⇒ 1 in = 2 ft

So, the actual dimensions of her desk are

1 ¹/₄ in by 2 ¹/₄ in = 5/4 in by 9/4 in

= 5/4 × 1 in by 9/4 × 1 in

= 5/4 × 2 ft by 9/4 × 2 ft

= 5/2 ft by 9/2 ft

= 2 ¹/₂ ft by 4 ¹/₂ ft

So, the actual dimensions of her desk are D: 2 ¹/₂ ft by 4 ¹/₂ ft

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[tex] \sqrt{12} + 1 - \sqrt{5} \\ = \sqrt{4} \times \sqrt{3} + 1 - \sqrt{5} \\ = 2 \sqrt{3} + 1 - \sqrt{5} [/tex]

Answer:

66

Step-by-step explanation:

6(n² + 2)

6(3² + 2)

6(9 + 2)

6(11)

66

The probability that she will NOT take out an orange, then an apple, and finally a grapefruit in that order is 0.2917.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

A.) The probability that she will NOT randomly take out two oranges in a row,

Probability = 1 - (5/12)² = 0.8264

B.) The probability that she will NOT randomly take out two grapefruits in a row,

Probability = 1 - (4/12)² = 0.8264 = 0.8889

C.) The probability that she will NOT randomly take out two apples in a row,

Probability = 1 - (3/12)² = 0.8264 = 0.9375

D.) The probability that she will NOT take out an orange, then an apple, and finally a grapefruit in that order,

Probability = (7/12) × (9/12) × (8/12) = 0.2917

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The number of winners that Heather can expect is 300.

The first step is to determine the total number of winners to the total number of players using the information in the table.

Ratio = 180 / 450 = 0.40

Number of winners if there are 750 players = 0.40 x 750 = 300 winners

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Answer:

the value is 14

Step-by-step explanation:

because im just trying to get points

Answer:

Sides other than hypotenuse of an isosceles triangle are equal.

Let the other two sides be x each.

Using pythagoras theorem

x

2

+x

2

=(5

2

)

2

2x

2

=50

⇒x

2

=25

⇒x=5cm

So the other two sides are 5cm each.