Which angles are congruent to each other?

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) 728

2) 274.89

Step-by-step explanation:

Find the volume and surface formulas for each shape attached.

I'll do a couple for you. For rest just use the formulas and input the values and solve.

1) It is a pyramid.

V  = 1/3 * b * h, where b is the area of base, which is a rectangle so,

b = l * w

so,

V = 1/3 * l * w * h

V = 1/3 * 8 * 21 * 13

V = 1/3 * 2184

V = 2184 / 3

V = 728

2) It is a cylinder

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

V = π * 5^2 * 3.5

V = π * 25 * 3.5

V = 87.5 π

V = 274.89

Step-by-step explanation:

the scaling ratio is 12/20 = 3/5.

this always applies only to one-dimensional distances, lengths.

the perimeter is calculated as the sum of individual lengths. so while each length is scaled by the same ratio, also the sum is then scaled by that ratio.

p_old = a + b + c

p_new = ra + rb + rc = r(a + b + c) = r×p_old

so, the ratio for the perimeter is also 3/5.

for the area this is a bit different, as an area is always calculated by multiplying 2 lengths (other unscaled factors can be ignored for that consideration of relative change), and that means the scaling ratio has to be multiplied in twice.

a_old = a × b

a_new = ra × rb = r² × a×b = r² × a_old

so, the ratio for the area is

(3/5)² = 9/25

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:

Por 1 kg: $1.15

Por 2 kg: $2.30

Por 5 kg: $5.75

Por 10 kg: $11.50

Lo siento si esta respuesta no es correcta, si lo es o no, por favor dímelo en los comentarios!

Step-by-step explanation:

Primero, divida $ 3.45 por 3, lo que le dará $ 1.15.

Luego, multiplique $ 1.15 a 1, 2, 5 y 10.

(Respondí esto usando un traductor, por lo que mi gramática podría estar un poco desviada. ¡Espero que esto ayude!)

Answer:

Well, there is no picture so theres no way to know what it could be. All I can do is guess.

B

(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:

-lukelaws

did i help?

Answer:

The answer would be 17

Step-by-step explanation:

Answer:

x = 17

Step-by-step explanation:

Pythagorean Theorem: a^2 + b^2 = c^2

15^2 + 8^2 = c^2 (15^2 = 225 and 8^2 = 64)

225 + 64 = 289

[tex]\sqrt{289}[/tex] = 17

Answer:

Step-by-step explanation:

First box: (3/4)*b

Second box (3/4 * -8)

third box (3/4b)

fourth box: -6

5th box: 12

Answer:

95% of 28 is 26.6

Step-by-step explanation:

28 * 0.95 = 26.6

Answer:

HOPE IT HELPS!

MARK AS BRAINLIAST.

Answer:

Step-by-step explanation:

Answer:

(2 , 2) is the solution

Step-by-step explanation:

7x - 4y = 6

-6x + 7y = 2

49x - 28y = 42

-24x + 28y = 8

25x = 50

therefore

x = 2

7x - 4y = 6

7×2 - 4y = 6

14 - 4y = 6

14 - 6 = 4y

8 = 4y

8 ÷ 4 = 4y ÷ 4

2 = y

therefore

x = 2

y = 2

hope this will helpful to you....

Answer:

10.1

Step-by-step explanation:

 292.9

   29

                                 29     ×  10

               2929

                290    This is the same as: 2929 / 290  or  2929 ÷ 290

                               = 10.1

WELL UNDERSTOOD????

There is a probability of 22.66% that their average catch is less than 31.5 pounds

The z score is used to determine by how many standard deviations the raw score is above or belaw the mean. It is given by:

z = (raw score  - mean)/ (standard deviation ÷ √sample)

Given that, mean = 32, std = 4, sample = 36, hence:

For 31.5:

z = (31.5 - 32) / (4 ÷√36) = -0.75

P(z < -0.75) = 0.2266

There is a probability of 22.66% that their average catch is less than 31.5 pounds

Find out more on z score at: https://brainly.com/question/25638875

Answer:

its 2 all of those are in the 2 time tables unwelcome

The inequality in the total amount of purchase is the greater than inequality

The inequality to find the additional amounts x you can spend to get free delivery is 24.00 + x > y

The given parameters are:

Small pizza = $4.50

Salad = $3.75

The cost of two small pizzas and four salads is:

Total = 2 * 4.50 + 4* 3.75

Evaluate

Total = 24.00

Let the amount to get free delivery be y.

So, the inequality would be:

24.00 + x > y

Read more abput inequalities at:

https://brainly.com/question/11234618

Answer:

the anwer is a so 0

Step-by-step explanation:

the number that showed up the most is 0 so median is 0

Answer:

648 cubic centimeters

Step-by-step explanation:

6×9×12=648

Answer:

648 cubic centimeters

Step-by-step explanation:

All you need to do is multiply all of the measures that they show you.

6 x 9 x 12 which equals 648

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

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

The required equation is :

[tex]\qquad \rm \dashrightarrow \:y =a \cos(bx) + k[/tex]

Now, let's find the required values :

period (p) = 6

[distance between any successive Crest or trough]

a = - 4 (flipped)

b = 2π/p = 2π/6 = π/3

k = -2

Distance of starting position from origin = k

Now, plug in the values ~

[tex]\qquad \rm  \dashrightarrow \: - 4 \cos( \frac{\pi}{3} x) - 2[/tex]

Answer:

36

Step-by-step explanation:
36 x 3.14 = 113.04

Since to find a diameter from the area, you need to divide by 3.14

113.04 divided by 3.14 = 36


But since its already there you can just figure out that 36 is the diameter and you don't have to do any calculating

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.

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

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.

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)

Take some points

As here < sign present line will be dashed and shading should be done below the line

So

Graph attached

Answer:

Given inequality

[tex]\sf 2x + 3y < 6[/tex]

Rearrange to make y the subject

[tex]\sf \implies 2x + 3y < 6[/tex]

Subtract 2x from both sides:

[tex]\sf \implies 3y < -2x + 6[/tex]

Divide both sides by 3:

[tex]\sf \implies y < -\dfrac23x + 2[/tex]

When graphing inequalities

If the inequality sign is < or > then the line of the graph should be dashed.

If the inequality sign is ≤ or ≥ then the line of the graph should be solid.

If y < (less than) then the shading is below the line.

If y > (more than) then the shading is above the line.

Therefore, as the inequality is y < the line should be dashed and the shading should be below the dashed line.

To plot the line, substitute x = 0 and x = 3 into the equation:

[tex]\sf \implies -\dfrac23(0) + 2=2[/tex]

[tex]\sf \implies -\dfrac23(3) + 2=0[/tex]

Therefore, plot points (0, 2) and (3, 0).  Draw a dashed straight line through the points.  Shade below the dashed line.

The expected squash seed packets is its mean or average value

You should expect 47 squash seed packets in the next 94 seed packets

The given parameters are:

The expected squash seed packets is calculated as:

E(x) = x/n * N

This gives

E(x) = 22/44 * 94

Evaluate the product

E(x) = 47

Hence, you should expect 47 squash seed packets in the next 94 seed packets

Read more about expected values at:

https://brainly.com/question/15858152

Answer:

Step-by-step explanation:

Since all graphs pass throught the origin, they all have the form of:

The coefficient of each graph's equation can be calculated based on the given pairs of points.

Each of them calculated for you and attached below.

In short: y = 4(L)

0)

What is the greatest side length Sarah could make with 48 inches of yarn?

divide both sides by 4

→ the greatest side length she could make is 12 inch.

1)

Inches on one side       ||   2     ||    3    ||     4      ||     5      ||   6

Inches of yarn needed ||   8     ||   12    ||   16     ||    20      ||   24

2)

pattern: