Let R be the region in the first quadrant bounded by the
graph of y = x² and the line y = 4.
(a) Find the area of the region R.
(b) A solid S has base R. Each cross-section of this solid
perpendicular to the y-axis is a semicircle, with its
diameter in R. Find the volume of the solid S.
(c) Another solid is formed by revolving R about the line
y = 7. Find the volume of this new solid.

Answer:

Your question is unclear as to which product you're looking for, the dot product or the cross product, so I'll answer for both.

The i and j notations for vectors refer to their coordinates, e.g. a vector that is 2i+3j is one that moves 2 units in the x-direction and 3 units in the y-direction. This can also be notated as (2, 3), and that's the notation I'll be using in this answer to keep things simple.

In order to get either product, we have to do the subtraction in parentheses first:3v - 4w = 3 * (2, -2) - 4 * (0, -2). When multiplying a vector by a scalar number, you just multiply the coordinates by the scalar, so this becomes (6, -6) - (0, -8). Performing this subtraction by subtracting corresponding coordinates, we get 3v - 4w) = (6, 2). Also, 5u = 5 * (-3, 2) = (-15, 10).

Now, the dot product of two vectors is a scalar quantity. The dot product of the two vectors (-15, 10) • (6, 2) is the sum of the products of the corresponding coordinates. This is -15 * 6 + 10 * 2, which is -90 + 20, and that is -70.

Step-by-step explanation:

Answer

she has a 3 out of 11 percent chance aka 3/11

Step-by-step explanation:

There is 1 red meaning there is less of a chance to get that one unless she is lucky same goes with purple! She has 2 brown flip flops so there is more of a chance she may get that one, but 4 pairs of pink flip flops meaning she is more likely to pick pink on Tuesday then Monday. but the answer can be 3/7 if I do not count the others flip flops... but hopefully this helps...

Answer:

the 30th term of the given linear sequence is -63.

Step-by-step explanation:

The given sequence is in arithmetic progression whose difference is given by:

-7 - (-5) = d

d = -2

The nth term in the arithmetic progression is given by the formula:

where 'n' is the number of terms, 'a' is the first term,  is the nth term, and 'd' is the difference.

Now, substitute the known terms in the above formula.

So, the 30th term of the given linear sequence is -63.

ANSWER:

x° = 24°

y° = 72°

Analysis on picture hope it helps

Answer:

Step-by-step explanation:

The slope of a line on a graph is found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

Ernest used (x1, y1) = (15, 450) and (x2, y2) = (60, 900) to fill values into this formula. In doing so, he got ...

  m = (900 -450)/(60 -15) = 450/45 = 10

This is an appropriate use of the formula, so gave Ernest the correct answer.

Answer:

84

2 42

2 21

3 7

Step-by-step explanation:

It has total 12 factors of which 84 is the biggest factor and the prime factors of 84 are 2, 3 and 7. The Prime Factorization of 84 is 2^2 × 3 × 7

Answer:

in attachment

Step-by-step explanation:

Step-by-step explanation:

$70*8% ≈ 56

so, 70 - 56 = i14

ihopethishelps

Answer:

3

Step-by-step explanation:

share 30 in the ratio 1:9

1+9=10

30÷10 =3

3 in each part

20

y'all homeworks are easy lølllll

Answer:

As shown, a box-and-whisker plot is a way of summarizing a set of data measured on an interval scale. This type of graph is used to show the shape of the distribution, its central value, and its variability.

Explanation:

100% When I put this in

Answer:

5 mph

Step-by-step explanation:

1/2 mile in 1/10 of an hour

1 mile in 1/5 of an hour

5 miles in 1 hour

The probability that the person also buys cereal at least once a month, given that a randomly chosen person eats breakfast almost every day is 53/64

Random sample is the way to choose a number or sample in such a manner that each of the sample of the group has an equal probability to be chosen.

A survey asked about the number of people who eat breakfast almost every day (B) and the number of people who buy cereal at least once a month (C).

The results of the survey are shown in the Venn diagram as,

Therefore, for circle B, it can be given as,

[tex]n(B)=11+53=64[/tex]

Similarly, for the circle C,

[tex]n(C)=53+4=57[/tex]

As the intersection of circle B and C contains 53,

[tex]n(BC)=53[/tex]

Now the probability that the person also buys cereal at least once a month, given that a randomly chosen person eats breakfast almost every day,

[tex]P(C|B)=\dfrac{P(BC)}{P(B)}\\P(C|B)=\dfrac{n(BC)}{n(B)}\\P(C|B)=\dfrac{53}{64}[/tex]

Hence, the probability that the person also buys cereal at least once a month, given that a randomly chosen person eats breakfast almost every day is 53/64

Learn more about the random sample here;

https://brainly.com/question/17831271

Answer:

C or 53/64

Step-by-step explanation:

Ed2022

Answer:  A. x=-2y^2

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

I just did the test

Answer:

parallel

Step-by-step explanation:

if two lines are not parallel they will cross eventually at one point meaning they will have a point in common so they must be parallel

Answer:

5X²+16X+8=0

Step-by-step explanation:

5(X+2) (X+2)=4(X+3)

5(X²+2X+2X+4)=4(X+3)

5(X²+4X+4)=4(X+3)

5X²+20X+20=4X+12

5X²+20X-4X+20-12=0

5X²+16X+8=0

answer:

C. 16

explanation:

when x is 0, the y-intercept is 8

coordinates: (0,8) and (4,6)

slope:

[tex]\sf \frac{y2-y1}{x2-x1}[/tex]

[tex]\sf \frac{6-8}{4-0}[/tex]

[tex]\sf \frac{-2}{4}[/tex]

[tex]\sf -\frac{1}{2}[/tex]

equation:

[tex]\sf y = mx +b[/tex]    [ where m is slope and b is y-intercept ]

[tex]y = \sf -\frac{1}{2}x +8[/tex]

solve for x-intercept:

note: zeros of a function are the values of x when f(x) is equal to 0

[tex]y = \sf -\frac{1}{2}x +8[/tex]

[tex]0= \sf -\frac{1}{2}x +8[/tex]

[tex]-8= \sf -\frac{1}{2}x[/tex]

[tex]\sf x = -8 * -2[/tex]

[tex]\sf x = 16[/tex]

Answer:C 16.

Step-by-step explanation:

its 16

Answer:

5.83 or 6

Step-by-step explanation:

don't know for sure sorry! have a good day or night!

Answer: 5.83

Step-by-step explanation: Im a fifth grader I’m only taking an estimate

Answer:

Step-by-step explanation:

Hope it helps!!!

Answer:

Simple Interest: $3.44

Annually Compounded Interest: $3.51

Answer:

Joey is going to pay $687.5

In all Joey is going to pay $3437.5

Step-by-step explanation:

To get 687.5 you have to do $2750 x 0.05 x 5 years

That gets you 687.5

We are provided that [tex]{\sf \sin (64^{\circ})=p}[/tex] and we have to find the value of [tex]{\sf 8\sin (16^{\circ})\cdot \cos (16^{\circ})\cdot \cos (32^{\circ})}[/tex] . But let's recall a identity which is gonna be very helpful to do this question i.e

Now , coming back on the question ;

[tex]{:\implies \quad \sf 8\sin (16^{\circ})\cdot \cos (16^{\circ})\cdot \cos (32^{\circ})}[/tex]

[tex]{:\implies \quad \sf 4\{ 2\sin (16^{\circ})\cos (16^{\circ})\}\cos (32^{\circ})}[/tex]

Using the above identity ;

[tex]{:\implies \quad \sf 4\sin (32^{\circ})\cos (32^{\circ})}[/tex]

[tex]{:\implies \quad \sf 2\{2\sin (32^{\circ})\cos (32^{\circ})\}}[/tex]

Again using the same identity ;

[tex]{:\implies \quad \sf 2\sin (64^{\circ})}[/tex]

Putting the given value of [tex]{\sf \sin (64^{\circ})}[/tex]

[tex]{:\implies \quad \sf 2p}[/tex]

[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{8\sin (16^{\circ})\cdot \cos (16^{\circ})\cdot \cos (32^{\circ})=2p}}}[/tex]

Proof of the above identity :-

We know that ;

[tex]{\quad \boxed{\sf \sin (A\pm B)=\sin (A)\cos (B)\pm \cos (A)\sin (B)}}[/tex]

So ;

[tex]{:\implies \quad \sf \sin (A+ B)=\sin (A)\cos (B)+\cos (A)\sin (B)}[/tex]

Putting [tex]{\sf A=B=\theta}[/tex] ,

[tex]{:\implies \quad \sf \sin (\theta+ \theta)=\sin (\theta)\cos (\theta)+\cos (\theta)\sin (\theta)}[/tex]

[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{\sin (2\theta)=2\sin (\theta)\cos (\theta)}}}[/tex]

Hence , Proved :D

Answer:

d= 66

Step-by-step explanation:

1- Calculate diameter of the circle

Answer:

20 mins

Step-by-step explanation:

The answer is 20 minutes. If you look at the times it's 11:47 and 12:07. Notice the times end in 7. You would add ten minutes until you get the time, and in the end you have 20 mins.

Hope this helps!

Answer:

[tex]f(g(x)) = 2x - 1[/tex]

Step-by-step explanation:

learn composite functions

The volume of the dilated prism is calculated to be considering scale factor for the area as well as the height is 7558272 cm³.

The scale factor in the dilation of a mathematical object determines how much larger or smaller the image will be (compared to the original object).

Given that

The base area of prism = 8 cm²

Height of the prism = 6

Scale factor = 54

So enlarged area =( scale factor )² * previous area = 54²* 8 = 23328 cm²

Enlarged height = 54*6= 324 cm

Enlarged volume = enlarged area* enlarged height = 7558272 cm³

Thus, the volume of the dilated prism is 7558272 cm³.

To get more about dilation refer to:

https://brainly.com/question/25722260

Answer:

6/12 ≈ 1/2

Step-by-step explanation:

Q) 2/3 × 3/4 = ?

→ a = 2/3 × 3/4

→ a = (2 × 3)/(3 × 4)

→ a = 6/12

→ [ a = 1/2 ]

1/2

Multiply the numerators and the denominators of both fractions,

2  *  3

_____    

3  *  4

= 6/12

Simplify.

1/2

Answer:

76.92%

Step-by-step explanation:

Green: 5

Orange: 5

Yellow: 3

First: 5 + 5 + 3 = 13

Now we need to find the probablility of picking an orange or green marble.

We need to divide the number of green and orange marbles put together by the total, 13.

10/13 = 76.92%

You have a 76.92% chance of picking either a green or orange marble.

Have an amazing day!!

PLEASE RATE AND MARK BRAINLIEST!

Answer:

11/3

Step-by-step explanation:

let the 3rd no be x

(x-3)3 = 18

x-3 = 6

x = 9

keep solving the equation and the first term will be 11/3

Answer:

[tex]\huge\boxed{a^6b^3}[/tex]

Step-by-step explanation:

Because every term here is multiplied, simply count the number of 'a's and 'b's.

Hope it helps :) and let me know if you want me to elaborate.

The graph of the equation y = m^x passes through the point (1, m)

Given the equation of a graph expressed as y = m^x

We need to determine the coordinate point that lies on this graph.

If x = 1, substitute into the formula to have:

y =m^1

y = m

Hence the required coordinate will be (1, m)

Learn more on equation of graph here: https://brainly.com/question/24894997