i need help ill give uh 15?

S casts a "shadow" on the x-y plane given by the set

[tex]S' = \left\{(x,y) ~:~ -1 \le x \le 1 \text{ and } x^2 \le y \le 1\right\}[/tex]

Each cross section is a square whose side length is determined by the vertical distance between y = 1 and y = x², which is |1 - x²|. But since -1 ≤ x ≤ 1, this distance simplifies to 1 - x².

The volume of an infinitesimally thin section is then (1 - x²)² ∆x (where ∆x represents its thickness), and so the volume of S is

[tex]\displaystyle \int_{-1}^1 (1-x^2)^2 \, dx = \int_{-1}^1 (1 - 2x^2 + x^4) \, dx[/tex]

The integrand is even, so this integral is equal to twice the integral over [0, 1] :

[tex]\displaystyle \int_{-1}^1 (1-x^2)^2 \, dx = 2 \int_0^1 (1 - 2x^2 + x^4) \, dx = 2 \left(1 - \frac23 + \frac15\right) = \boxed{\frac{16}{15}}[/tex]

Answer:

1. Answer is 35

2. Answer is 13

Step-by-step explanation:

All you have to do is multiply 5 on both sides for number 1 and multiply by 2 on both sides for number 2.

Answer:

13

Step-by-step explanation:

pythagorean theorum

a^2+b^2=c^2

12^2+5^2=c^2

144+25=c^2

c^2=169

c=13

The length of the triangle's other leg is approximately 10.908.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

We can use the Pythagorean theorem to solve for the length of the other leg of the right triangle.

The Pythagorean theorem states that for any right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides (the legs).

That is, for a right triangle with legs a and b and hypotenuse c:

c² = a² + b²

In this case,

We know that the hypotenuse has a length of 12 and one of the legs has a length of 5.

Let's denote the length of the other leg as "x".

So we can set up the equation:

12² = 5² + x²

Simplifying, we get:

144 = 25 + x^2

Subtracting 25 from both sides, we get:

119 = x²

Taking the square root of both sides, we get:

x ≈ 10.908

Therefore,

The length of the triangle's other leg is approximately 10.908.

Learn more about triangles here:

https://brainly.com/question/25950519

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(5×3)-4 = 11

hope it helps...!!!

Answer:

(5*3)-4=11

Step-by-step explanation:

because when you multiply 5*3=15, then subtract 4 from it, it gives you 11. There are no other options becuase 5*4-3=17 and 4*3-5=16 and 5*4+3=23 and 4*3+5=17.

Answer:

Step-by-step explanation:

The total possble combinations = 5 * 5 = 25 ways.

The number of ways to get exactly 12

= 2,10  3,9  4,8  5,7  = 4 ways.

The ways to get > 12

= 3,10  4,9  4,10  5,8  5,9  5,10  =  6 ways.

So the number of ways to get < 12 = 25 - 4 - 6 = 15 ways.

Expected value

= 4(0) + 6(x) + 15(-6)

I have written x as you have not said how much he gets if he wins.

Answer:

−$2.40

Step-by-step explanation:

correct on khan

=======================================================

Explanation:

Take note that the x and y coordinate of this vector are the same.

This leads to a 45-45-90 reference triangle. If the vector was in the first quadrant (the northeast), then the answer would be 45 degrees.

However, we need to add on 180 so we get to the third quadrant instead where x and y are both negative. This gets us to 180+45 = 225 degrees

---------------

If you wanted to use a calculator, then you would compute the value of [tex]\tan^{-1}(b/a)[/tex] where <a,b> is the vector in question.

Since a = b in this case, we have b/a = 1 and the arctangent of this is 45 degrees. The adjustment of adding on 180 still applies like from before.

Answer:

27

step by step explanation

if you are calculating for the area of the figure, divide the shape into two figures and you will get two rectangles

for shape 1

length=3 width=5

for shape2

length 7-3=4

width=3

area of shape1. =3×5=15

area of shape2. =4×3=12

area of the shape= 12+15 = 27

Answer:

read step by step

Step-by-step explanation:

6 is +4.

19, 23, 27, 31

7 is all perfect square numbers

25, 36, 49, 64

8 is x2.

32, 64, 128, 256

9 is each number multiplied by the next. ex: 1x2=2, 2x3+6, 3x4=12

so the next few would be 30, 42, 56, 72

Problem 5

Apply the Law of Sines

s/sin(S) = r/sin(R)

s/sin(78) = 10/sin(48)

s = sin(78)*10/sin(48)

s = 13.162274

=============================================================

Problem 6

Use the Law of Sines here as well.

x/sin(X) = y/sin(Y)

x/sin(53) = 6/sin(22)

x = sin(53)*6/sin(22)

x = 12.791588

Answer:

Sine Rule

[tex]\sf \dfrac{a}{sinA}=\dfrac{b}{sinB}=\dfrac{c}{sinB}[/tex]

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

Question 5

[tex]\sf \implies \dfrac{s}{sin(78)}=\dfrac{10}{sin(48)}[/tex]

[tex]\sf \implies s=\dfrac{10sin(78)}{sin(48)}[/tex]

[tex]\sf \implies s=13.16227426[/tex]

s = 13.2 (nearest tenth)

Question 6

[tex]\sf \implies \dfrac{x}{sin(53)}=\dfrac{6}{sin(22)}[/tex]

[tex]\sf \implies x=\dfrac{6sin(53)}{sin(22)}[/tex]

[tex]\sf \implies x=12.79158761[/tex]

x = 12.8 (nearest tenth)

Answer:

8, 4, 0, -3, -5

(greatest to least order)

-Answer: C-

Step-by-step explanation:

8 is positive so its greatest

-5 is negative but it is farthest away from 0 so it is least

The value of the $6000 annuity given annual compounding is $124,836.12.

The value of the annuity can be determining using this formula: amount deposited x annuity factor

Annuity factor = {[(1+r)^n] - 1} / r

Where:

$6000 x [(1.155^10) - 1/0.155] = $124,836.12

To learn more about annuities, please check: https://brainly.com/question/24108530

Answer:

[tex]64\pi[/tex]

Step-by-step explanation:

[tex]2\pi {(4)}^{2} + 2\pi \: 4 \ast4 \\ \\ = 2\pi \ast16 + 2\pi \ast16 \\ \\ = 32\pi + 32\pi \\ \\ = 64\pi[/tex]

Answer:

64π

Step-by-step explanation:

2π(4²) + 2π(4)(4) <== exponents first

2π(16) + 2π(16) <== multiply

32π + 32π <== add

64π <== final answer

Note: 4 * 4 can also be written as 4²

Hope this helps!

Answer:

b = 0.62

Step-by-step explanation:

Hello!

We can look at the y-values of the function to find our multiplier. A multiplier will determine if the graph decays or grows in an exponential function, and by how much.

When x is 0, we can see the y-value is around 3, but as x approaches 1, the y-value comes to around 2.

We can find the multiplier by dividing the current term by the previous term.

This number is closest to 0.62, so the approximation is 0.62.

2/3

0.6666..

Approximation is 0.62 (b)

Hope this helped! Stay healthy!♡

Answer:

The correct answer would be 8 14/15 miles.

Step-by-step explanation:

You have to get the fractions 5 2/6 and 3 3/5 to a common denominator (30) getting you the fractions 10/30 and 18/30. 10/30+18/30 is 28/30 which can simplify to 14/15. 5+3 = 8 getting you the answer of 8 14/15

Answer:

7 steps.

Step-by-step explanation:

Since the monkey is sitting on the first step already you can subtract 9 by 1 to find the amount of steps left.

9-1 = 8 steps left

The monkey jumps 3 steps down

8-3= 5 steps

Then jumps 2 steps up

5 + 2 = 7 steps

The monkey has 7 more steps until he reaches the water level.

Answer:

GH = 15

Step-by-step explanation:

In a trapezoid, the length of the median is one-half the sum of the lengths of the bases. Therefore:

[tex]9x - 3 = \frac{1}{2} (19 + 5x + 1)[/tex]

[tex]18x - 6 = 5x + 20[/tex]

[tex]13x = 26[/tex]

[tex]x = 2[/tex]

[tex]9(2) - 3 = 18 - 3 = 15[/tex]

Answer:

81

Step-by-step explanation:

[tex] {x}^{2} + 18x + {(( \frac{1}{2})(18)) }^{2} [/tex]

[tex] {x}^{2} + 18x + {9}^{2} [/tex]

[tex] {x}^{2} + 18x + 81[/tex]

[tex] {(x + 9)}^{2} [/tex]

Answer:

  1/14

Step-by-step explanation:

In the given geometry, we have similar triangles:

  ΔCEF ~ ΔBEA ~ ΔDAF

This lets us write the relations for corresponding sides ...

  CF/CE = DF/DA

where DF = CF -CD

We can rearrange this relation to give the value we're looking for as follows.

__

Making the substutition for DF, and multiplying by CE, we have ...

  CF = CE(CF -CD)/DA

Both DA and CD are sides of the rhombus, so are both 14 cm in length. Multiplying by DA and making the number substitution, we have ...

  DA·CF = CE·CF -CE·CD

  14·CF = CE·CF -14·CE . . . . substitute 14 for DA and CD

  14(CF +CE) = CE·CF . . . . . add 14·CE

  (CF +CE)/(CE·CF) = 1/14 . . . . divide by 14·CE·CF

  1/CE +1/CF = 1/14 . . . . . . . . . simplify

Answer:

  YZ = 28

Step-by-step explanation:

A proportion involving the known and unknown sides is ...

  TR/ST = ZY/SZ

__

This proportion uses SZ, which is not shown on the diagram. The length of SZ can be found from ...

  SZ +ZT = ST . . . . . . . segment sum theorem

  SZ + 5 = 40 . . . . with given values

  SZ = 35 . . . . . subtract 5

__

So, the proportion with values filled in is ...

  (3x -7)/40 = (2x +2)/35

  7(3x -7) = 8(2x +2) . . . . . . . multiply by 280

  21x -49 = 16x +16 . . . . . . . eliminate parentheses

  5x = 65 . . . . . . . . . . add 49 -16x

  x = 13 . . . . . . . . divide by 5

  YZ = 2x +2 = 2(13) +2

  YZ = 28

_____

Additional comment

RT = 3x -7 = 3(13) -7 = 32

Answer:

Multiply each measure of ingredients by 3.5

Step-by-step explanation:

This recipe makes 10 flapjacks. We want to be able to make 35 flapjacks.

Divide 35 by 10 to find the ratio of these 2 numbers.

35 / 10 = 3.5

Now we can multiply the measures by this number to find out how much of each ingredient we need.

140 * 3.5 = 490

120 * 3.5 = 420

100 * 3.5 = 350

240 * 3.5 = 840

50 * 3.5 = 175

Answer:

Recipe: Makes 35 flapjacks

490 g Margarine

420 g sugar

350 ml syrup

840 g oats

200 g raisins

Answer:

600.

Well, to divide these numbers, we can use certain strategy that fits with out logic. For example, we know that 56 divided by 7 can be done mentally, because it's a simple division that can be immediately solved.

So, 56 divided by 7 is 8, then we add the two zeros to the quotient, because we isolated the first to digit to make the division easier and then we have to add back those zeros.

Therefore the division results in 600.

There are several operations that can be done by using certain strategy, like separating the number in easier parts like we did this time.

Answer:

Hi there!

[tex]\:\mathsf{a^2\:-\:5a\:+\:6\:=\:0}[/tex]

=> By splitting the middle term

=> [tex]\:\mathsf{a^2\:-\:2a\:-\:3a\:+\:6\:=\:0}[/tex]

=> [tex]\:\mathsf{a(a\:-\:2)\:-\:3(a\:-\:2)\:=\:0}[/tex]

=> [tex]\:\mathsf{(a\:-\:2)\:-\:(a\:-\:3)\:=\:0}[/tex]

=> [tex]\:\sf{a\:=\:2\: and\: a\:=\:3}[/tex]

[tex]\:\mathsf{Hope\:this\:helps\:you!\::)}[/tex]

Thank you!

Answer:

[tex]a = 3 \: \: \: and \: \: a = 2[/tex]

Step-by-step explanation:

⬇

[tex]a^{2} - 3a - 2a + 6 = 0[/tex]

⬇

[tex]a \: (a - 3) \: \: (a - 2)[/tex]

⬇

[tex]{}\ a - 3 = 0 \\ a = 2{}[/tex]

Answer:

100cm

Step-by-step explanation:

divide the shape into smaller shapes then find the area of each and add them together

Answer:

[tex]Y=\frac{2}{3} x +5[/tex]

Hope This Helped! :) Please Mark Brainliest!

Answer:

C, D, E

Step-by-step explanation:

15 * .15 = 2.25

50 * .05=  2.5

100 * .10= 10

100 * .05= 5

200 * .03= 6

Answer:

45 fireflies

Step-by-step explanation:

Because,

Sheri caught 70 and Robert caught 35.

150-35-70= 35

35+10 is equal to 45.

Following the rules given is the right answer

Answer:

305,080.0809

Step-by-step explanation:

3 x 100,000 : digit 3 is in the hundred thousands place

5 x 1000 : digit 5 is in the thousands place

8 x 10 : digit 8 is in the tens place

8 x 1/100 : digit 8 is in the hundredths place which means it is the second number after the decimal

9 x 1/10,000 : digit 9 is in the ten thousandths place which means it is the fourth number after the decimal

we get the following number:

305080.0809