What is the value of y?

16
50
130
164

Answer:

b.

[tex]V = \pi \cdot \int\limits^a_b {\left([f(x)]^2 - [g(x)]^2} \right) \, dx[/tex]

(c)

[tex]V = \pi \cdot \int\limits^3_1 {\left([arcos(y - 2)]^2 - [arcsine(x)]^2 - (-1)^2} \right) \, dx[/tex]

Step-by-step explanation:

b. The volume of solid formed is given by the washers formula as follows;

[tex]V = \pi \cdot \int\limits^a_b {\left([f(x)]^2 - [g(x)]^2} \right) \, dx[/tex]

Therefore, we have, the integral expression whose solution is the volume formed by rotating 'R', about the equations y = 2 + cos(x) and y = csc(x) in the first quadrant on the interval, 0 ≤ x ≤ π, V is given as follows;

[tex]V = \pi \cdot \int\limits^\pi_0 {\left([2 + cox(x)]^2 - [csc(x)]^2} \right) \, dx[/tex]

(c)  We have;

x = arcos(y - 2), x = arcsin(1/y)

At x = 0, y = 2 + cos(0) = 3

csc(0) = ∞

At x = π, y = 2 + cos(π) = 2 + -1 = 1

csc(π) = ∞

Therefore, we get;

[tex]V = \pi \cdot \int\limits^3_1 {\left([arcos(y - 2)]^2 - [arcsine(x)]^2 - (-1)^2} \right) \, dx[/tex]

B) An equation that involves integral expressions whose solution is the volume of the solid generated when R is revolved around the x-axis is;

[tex]V = \pi \int\limits^\pi _0 ({[2 + cos(x)]^{2} - [csc(x)]^{2}}) \, dx[/tex]

C) An equation involving integral expressions whose solution is the volume of the solid generated when R is revolved around the line x= -1 is;

[tex]V = \pi \int\limits^\pi _0 ({[cos^{-1} (y - 2)]^{2} - [sin^{-1}(x)]^{2} - (-1)^{2} }) \, dx[/tex]

B) The volume of solid formed is gotten from applying the washers formula;

[tex]V = \pi \int\limits^a_b ({[f(x)]^{2} - [g(x)]^{2}}) \, dx[/tex]

This means that the integral expression whose solution is the volume formed by rotating R about the equations y = 2 + cos(x) and y = csc(x) in the first quadrant on the interval, 0 ≤ x ≤ π, V is expressed as;

[tex]V = \pi \int\limits^\pi _0 ({[2 + cos(x)]^{2} - [csc(x)]^{2}}) \, dx[/tex]

C) From answer above, we have;

x = cos⁻¹(y - 2), x = sin⁻¹(1/y)

Now,

At x = 0; y = 2 + cos(0) = 3

csc(0) = 1/0 = ∞

Also,

At x = π; y = 2 + cos(π)

y = 2 + (-1)

y = 1

Also, csc(π) = ∞

Thus, we have;

[tex]V = \pi \int\limits^\pi _0 ({[cos^{-1} (y - 2)]^{2} - [sin^{-1}(x)]^{2} - (-1)^{2} }) \, dx[/tex]

Read more about finding the integral volume of solid at; https://brainly.com/question/21036176

Answer:

True

Step-by-step explanation:

A system of equations can be solved by Translating the system of equations into a matrix by following theses steps

write out the resulting answer in form of equations.

Answer:

Part A;

$79

Part B;

The amount Stella would have saved in 'w' weeks = 15 + 8·w

Step-by-step explanation:

Part A

The amount of money Stella already has = $15

The amount she can save per week = $8

The total amount of money, 'A', Stella would have after 8 weeks is given as follows;

A = The amount Stella already has + The amount she can save per week × The number of weeks of savings

Therefore;

A = 15 + 8 × 8 = 79

The amount Stella would have after 8 weeks, A = $79

Part B

The expression that represents the amount of money Stella would have saved in w weeks is given as follows;

A = The initial amount Stella has + The amount she can save per week × w (number of weeks)

∴ A = 15 + 8·w.

Answer:

Find the answers below

Step-by-step explanation:

Using m<X as the reference angle

Opposite YZ = 7

Adjacent  XY = 10

Hypotenuse XZ = √149

Using the SOH CAH TOA identity

sinX = opp/hyp

sinX =YZ/XZ

sinX = 7/√149

For cos X

cos X = adj/hyp

cos X =10/√149

Using m<Z as reference angle;

Opposite XY = 10

Adjacent  YZ = 7

Hypotenuse XZ = √149

Using the SOH CAH TOA identity

sinZ = opp/hyp

sinZ =10/√149

sinZ = 7/√149

For cos Z

cosZ = 7/√149

Answer:

5 loaves

Step-by-step explanation:

13 1/3 divided by 2 2/3 is 5 so the answer is 5 loaves.

Rewrite the fractions as improper fractions then divide the total amount used by the amount per loaf:

13 1/3 = 40/3

2 2/3 = 8/3

40/3 / 8/3

When dividing by a fraction flip the fraction over and multiply

40/3 x 3/8 = (40 x3) /( 3 x 8) = 120/24 = 5

She made 5 loaves of bread.

6,000 + 700 + 30 + 8 is the expanded from.

Answer:

A. i think

Step-by-step explanation:

Answer:

4, -16, 64, -256

the common ratio is -4

Step-by-step explanation:

Answer:

98 m³

Step-by-step explanation:

For similar shapes

The ratio of the cube of the corresponding length of similar shapes is equal to the ratio of their volume.

Applying,

L³/L'³ = V/V'............... Equation 1

Where, L = Length of the smaller prism, L' = Length of the larger prism, V = Volume of the smaller prism, V' = Volume of the larger prism

From the question,

Given: L = 5 m, L' = 7 m, V = 50 m³

Substitute these values into equation 1

5²/7² = 50/V'

25/49 = 50/V'

V' = (50×49)/25

V' = 98 m³

Answer: 137.2

Step-by-step explanation:

I'm just making the correct answer an actual answer instead of a comment so it's easier to see

Answer:

2,457

Step-by-step explanation:

The thousands place is when you move four spaces to the left starting from the first number. In this case, that number was seven, and to round, you need to round it up or down depending if the number to the left of the 4th number is greater or less than 5. In this case, that number was 3, so that 3 and the rest of the remaining numbers turn into 0's, making the rounded number 2,457.

I hope this information was of any use to you.

Answer:

2,457,000

Hope that this helps!

Answer:

410

Step-by-step explanation:

Inputs are x's

Substitute the 18 where you see the x

y = 23(18) - 4

y= 414 - 4

y = 410

Answer:

9x^2 + 27x + 18

Step-by-step explanation:

(9x + 9)(x + 2)

=9x(x + 2) +9(x + 2)

=9x^2 + 18x + 9x + 18

=9x^2 + 27x + 18

Step-by-step explanation:

The area of a circle = pi r^2

d = 2r Divide by 2 to get the radius

r = d/2

The diameter = 2.8 cm

r = d/2

r = 2.8/2

r = 1.4

The area of the circle = pi * r^1

The area of the circle = 3.14 * 1.4^2

The area of the circle = 6.1544

But you are working with a semic circle

The area of a semicircle is 1/2 that of a circle

Area of semicircle = 1/2 6.1544 = 3.0772 =3.08 when rounded

Answer:

it is 12

Step-by-step explanation:

for n= 36 divided by 3.

Answer:

1/2

Step-by-step explanation:

These two triangles are similar, so there is a scale factor. The heights and the bottom sides of each triangle are similar, figure A has a bottom length of 6, and figure B has a bottom length of 3. To get from A to B, you multiply by 1/2. So the scale factor is 1/2.

Answer:

6/5

Step-by-step explanation:

2x+3=ky

ky=2x+3

y=(2x+3)/k

y=2x/k + 3/k - > equation 1

y=mx + c - >equation 2

Comparing equation 1 and 2,

2/k=m

2/k=5/3

6/5=k

k=6/5

Answer:yes, base = 9. No, the exponent is not variable. yes, base =9/10.

Step-by-step explanation:

Answer:

∠a=∠b

Step-by-step explanation:

Alternate exterior angles are congruent

Answer:

Step-by-step explanation:

20000000000+3000000000+900000000+60000+8000+400+7

Step-by-step explanation:

everything can be found in the picture

Answer:

x=50, y=20

Step-by-step explanation:

50-20=30, 50+20=70

Answer:

option alphabet c is the answer

Answer:

B

Step-by-step explanation:

An experiment is a study carried out in a controlled environment where the person undertaking the research hopes to understand cause and effect between the independent and dependent variables. An example of a experiment is the palovian experiment

The independent variable is the variable that the person carrying out an experiment changes or manipulates. the independent variable usually have a direct effect on the dependent variable

The dependent variable is the variable that is being measured in an experiment. It is usually affected by the independent variable

Observational study is the study where the researcher observes and measures cause and effect between independent and dependent variables without trying  to control or influence the population

Answer with Step-by-step explanation:

We are given that

[tex]g(x)=(x^2-3x-10)(x^2+2x^2-5x+4)[/tex]

x=-1

Using property of limit

[tex]\lim_{x\rightarrow -1}g(x)=\lim_{x\rightarrow -1}(x^2-3x-10)(3x^2-5x+4)[/tex]

=[tex](1+3-10)(3+5+4)[/tex]

=[tex](-6)(12)[/tex]

=[tex]-72[/tex]

[tex]g(-1)=(1+3-10)(1+2+5+4)[/tex]

[tex]g(-1)=(-6)(12)=-72[/tex]

[tex]\lim_{x\rightarrow -1}g(x)=g(-1)[/tex]

Hence, the function is continuous at x=-1

Answer:

hundredths

Step-by-step explanation:

Numbers after the decimal start with

tenth

hundredth

Answer:

90 or -270

Step-by-step explanation:

Answer:

i think the answer is c cuz theres 36 number cards

Answer:

Height = 6000 m

Step-by-step explanation:

[tex]Volume = length \times breadth \times height \\\\480000 = 10 \times 8 \times height\\\\480000 = 80 \times height\\\\height = \frac{480000}{80} = 6000 \ m[/tex]

Answer:

16π

Step-by-step explanation:

The circle touches the X-axis and center at (3,4), the coordinate is representing as (x, y), so the radio will be r = y (circle touches the X-axis), and the formula of circle area is π * r^2, so:

π * 4^2 is equal to 16π

[tex]\underline \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]

[tex] \huge\underline{\sf{\red{Problem:}}}[/tex]

7.) Detemine the value of [tex] \sf{ {3a}^{2} -b.}[/tex]

[tex] \huge\underline{\sf{\red{Given:}}}[/tex]

[tex]\quad\quad\quad\quad\sf{a = 2}[/tex]

[tex]\quad\quad\quad\quad\sf{b = - 1}[/tex]

[tex]\quad\quad\quad\quad\sf{c = - 3}[/tex]

[tex] \huge\underline{\sf{\red{Solution:}}}[/tex]

[tex]\quad\quad\quad\quad\sf{⟶{3a}^{2} - b}[/tex]

[tex]\quad \quad \quad \quad \sf{⟶{(3)( 2)}^{2} -( - 1)}[/tex]

[tex]\quad \quad \quad \quad \sf{⟶3(4)-( - 1)}[/tex]

[tex]\quad \quad \quad \quad \sf{⟶12-( - 1)}[/tex]

[tex]\quad \quad \quad \quad \sf{⟶12 + 1 }[/tex]

[tex]\quad \quad \quad \quad ⟶ \boxed{ \sf{ 13}}[/tex]

[tex]\huge\underline{\sf{\red{Answer:}}}[/tex]

[tex]\huge\quad \quad \underline{ \boxed{ \sf{ \red{\:13}}}}[/tex]

8.) Find the value of [tex] \sf{ {a}^{3} {b}^{3} - abc.}[/tex]

[tex] \huge\underline{\sf{\red{Solution:}}}[/tex]

[tex]\quad\quad\quad\quad\sf{⟶ {a}^{3} {b}^{3} - abc}[/tex]

[tex]\quad\quad\quad\quad\sf{⟶{(2)}^{3} {( - 1)}^{3} - (2)( - 1)( - 3)}[/tex]

[tex]\quad\quad\quad\quad\sf{⟶{(8)}{( - 1)} - ( - 2)( - 3)}[/tex]

[tex]\quad\quad\quad\quad\sf{⟶{( - 8)} - ( 6)}[/tex]

[tex]\quad\quad\quad\quad ⟶\boxed{\sf{ - 14}}[/tex]

[tex]\huge\underline{\sf{\red{Answer:}}}[/tex]

[tex]\huge\quad \quad \underline{ \boxed{ \sf{ \red{-14}}}}[/tex]

[tex]\underline \bold{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]

#CarryOnLearning

[tex]\sf{\red{✍︎ C.Rose❀}}[/tex]

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Answer:

3(3x - 10)(9x² + 30x + 100)

Step-by-step explanation:

Given

81x³ - 3000 ← factor out 3 from each term

= 3(27x³ - 1000 )← a difference of cubes which factors in general as

a³ - b³ = (a - b)(a² + ab + b²) , then

27x³ - 1000

= (3x)³ - 10³

= (3x - 10)((3x)² + (3x)(10) + 10²)

= (3x - 10)(9x² + 30x + 100)

Then

81x³ - 3000 = 3(3x - 10)(9x² + 30x + 100) ← in factored form