which expression is equivalent to (4^2)(4^5)

By apply the cylindrical shells method proved that the volume of the cone is V = [tex]\frac{1}{3}[/tex]πr²h.

Given that,

Consider an upright cone that was generated by rotating the triangular plane region shown in the image about the y-axis. It has a base radius of r and a height of h.

We have to apply the cylindrical shells method to confirm that the volume of the cone is V = [tex]\frac{1}{3}[/tex]πr²h

We know that,

By using the disk method,

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

Differentiating on both the sides,

dV = π[f(x)]² dx

Integrating on both sides with the limits 0 to h

[tex]\int\limits^h_0 { dV }= \int\limits^h_0 {\pi[f(x)]^2 }dx[/tex]

V = [tex]\int\limits^h_0 {\pi \frac{r^2x^2}{h^2} } \, dx[/tex]

V = [tex]\pi \frac{r^2}{h^2}\int\limits^h_0 {x^2 } \, dx[/tex]

V = [tex]\pi \frac{r^2}{h^2}[\frac{x^3}{3}]^h_0[/tex]

V = [tex]\pi \frac{r^2}{h^2}[\frac{h^3}{3}][/tex]

V = [tex]\frac{1}{3}[/tex]πr²h

Therefore, By apply the cylindrical shells method proved that the volume of the cone is V = [tex]\frac{1}{3}[/tex]πr²h.

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Answer:

11

Step-by-step explanation:

you subtract 3 every time, so 14-3 = 11

Answer:

Step-by-step explanation:

x = 5

The value of x in the given angle is 5.

A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent. A circle is also known as the location of points that are evenly spaced apart from the centre. The radius of a circle is measured from the centre to the edge.

Labelling the figure,

We have,

Measure of complete angle of circle = 360 degree

∠ABC = 360 - (81 + 74)

          =  205 degree

Now from figure,

∠APE = (205 - 81 )/2

          = 62 degree

Since we know that,

∠APE = 17x - 23

Therefore,

17x - 23 = 62

17x = 85

  x = 5 degree,

Hence,

Required value is 5.

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Answer:

4 times 10 to the negative seventh power

Step-by-step explanation:

We can see that the decimal has 6 zeros before it, and then it’s 4.

since there are 7 digits after the decimal point, we put 10 to the negative seventh power.

that gives us 0.0000001

to get 0.0000004, we need to multiply ten to the negative seventh power (0.0000001) by 4

The answer is a. which is 4 x 10‐⁷

Let the calories of a cheeseburger be C, and the calories of a small order of fries be F. Using this notation: Two cheeseburgers and one small order of fries contain a total of 1400 calories. Calories in 2 cheeseburgers + Calories in 1 small order of fries = 14002C + F = 1400. Three cheeseburgers and two small orders of fries contain a total of 2260 calories. Calories in 3 cheeseburgers + Calories in 2 small orders of fries = 22603C + 2F = 2260. We can solve for C and F by solving these two equations for C and F using the method of elimination.

Let's double the first equation and subtract the second equation: 4C + 2F = 2800  -(3C + 2F = 2260). 1C = 540  C = 540. Calories in a cheeseburger = C = 540. Substituting this value of C into either of the two equations and solving for F gives us:2C + F = 14002(540) + F = 1400. F = 320. Calories in a small order of fries = F = 320. Therefore, two cheeseburgers contain 2C = 2(540) = 1080 calories, and one small order of fries contains F = 320 calories. Three cheeseburgers contain 3C = 3(540) = 1620 calories, and two small orders of fries contain 2F = 2(320) = 640 calories.

Answer: Calories in a cheeseburger = C = 540Calories in a small order of fries = F = 320. Calories in two cheeseburgers = 2C = 2(540) = 1080. Calories in three cheeseburgers = 3C = 3(540) = 1620. Calories in one small order of fries = F = 320Calories in two small orders of fries = 2F = 2(320) = 640.

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Answer: 1.7

Step-by-step explanation: We can use the pythagorean theorem!

A² + B² = C²

1² + B² = 2²

1 + B² = 4

4 - 1 = B²

3 = B²

√3 = B

1.7 = B

Hope this helps :)

The value of x is: 75°

360° - 128° - 85° - 72° = 75°

Answer:

x and y are proportional. Two quantities are proportional if there is a constant ratio between them. In this case, the ratio between y and x is always 16:

4/0.25=16

8/0.5=16

12/0.75=16

Since the ratio between y and x is always the same, x and y are proportional.

Step-by-step explanation:

The characteristic polynomial for matrix A is (1-x)(2²), and the real eigenvalues for matrix A are 1 and 2.The characteristic polynomial for the matrix A can be written as (1-x)(2²), where x is the eigenvalue.

The real eigenvalues for matrix A can be found by setting the characteristic polynomial equal to zero and solving for x. Since the characteristic polynomial is a product of linear factors, the eigenvalues are the values of x that make each factor equal to zero.

In this case, we have two factors: (1-x) and (2²). Setting each factor equal to zero, we find that x = 1 and x = 2 are the real eigenvalues for matrix A.

To summarize, the characteristic polynomial for matrix A is (1-x)(2²), and the real eigenvalues are 1 and 2. The characteristic polynomial captures the relationship between the eigenvalues and the matrix A, while the real eigenvalues represent the values for which the matrix A has corresponding eigenvectors.

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Answer:

21

Step-by-step explanation:

We know that the sqaure root of 121 = 11.

So, A - 10 = 11

=> A = 21

Answer:

a = -1 or a = 21

Step-by-step explanation:

take square root of each side to get:

a - 10 = [tex]\sqrt{121}[/tex]

a - 10 = 11;  a = 21

a - 10 = -11;  a = -1

Answer:i don’t know yet give me a sec

Step-by-step explanation:

Answer:

12.56 cubic feet (ft^3)

Step-by-step explanation:

Area of the circular face of the cylinder = (pi)r^2, or (3.14)(2)^2.

This ends up being equal to 12.56. Multiply this by the height of the cylinder, 1, and you get 12.56, your final answer.

I would appreciate Brainliest, but no worries.

Answer:

−

8

n

+

24

Step-by-step explanation:

Answer:

I D K

Step-by-step explanation:

Answer:

14.6

Step-by-step explanation:

Sin (59) = x/17

17*sin (59) = x

17*0.857=14.57

The value of x in the triangle is x = 14.581

We have,

From  the triangle,

using the sin function.

Now,

sin = perpendicular/hypotenuse

So,

sin 59 = x/17

Now,

To solve for x in the equation sin(59°) = x/17, we can use the properties of trigonometric functions and algebraic manipulation.

First, let's isolate x by multiplying both sides of the equation by 17:

17 x sin(59°) = x

Using a calculator to evaluate sin(59°), we find:

17 x 0.857167 = x

Therefore,

The value of x is x = 14.581

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The sample proportion of households without fiber cable can be calculated by subtracting the proportion of households with fiber cable from 1.

In this case, out of the 491 households surveyed, 343 households have internet fiber cable. To find the proportion of households without fiber cable, we subtract the proportion of households with fiber cable (343/491) from 1. The proportion of households without fiber cable is 1 - (343/491). Simplifying this expression, we get (491 - 343)/491 = 148/491.

Therefore, the sample proportion of households without fiber cable is 148/491, which is approximately 0.3012 or 30.12%. This means that in the surveyed sample, around 30.12% of households do not have internet fiber cable. It's important to note that this proportion represents the sample and not the entire population, as it is based on the households surveyed.

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Probability that "sample-proportion" of "households-spending" more than $125 per-week is less than 0.29 is 0.8340.

In order to calculate the probability that the sample-proportion of households spending more than $125 a week is less than 0.29, we use the sampling-distribution of sample-proportions, assuming the sample was selected using simple random sampling.

The Population-proportion (p) is = 0.27

Sample-size (n) is = 467,

Sample-proportion (p') is = 0.29,

To calculate the probability, we find the z-score corresponding to the sample proportion and then find the probability,

The formula to calculate the z-score is:

z = (p' - p)/√((p × (1 - p))/n),

Substituting the values,

We get,

z = (0.29 - 0.27)/√((0.27 × (1 - 0.27))/467),

z = 0.02/√((0.27 × 0.73) / 467),

z ≈ 0.97

We know that the probability associated with a z-score of 0.97 is 0.8340.

Therefore, the required probability is 0.8340.

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Answer:

Less than

Step-by-step explanation:

To see how 3/4 compares to 3/8, give em the same denominator. The simplest way is to multiply 3/4 by 2. Multiply each the numerator and denominator by 2. That gives you 6/8. She needs 6/8 but only has 3/8, so less than a pizza.

The equation of the curve as, (y - a) = (b - a) (x - nt) / (a - nt) which is a straight line passing through the two given points, A(nt, a) and B(a, b).

Given: Two points A (e.g., a) and B (a, b) are traversed by the curve whose equation is Sin(x) – y Cos(x) = y (a Solution: (sin x - y cos x) = y Taking y to the left, we get (sin x) = (y y cos x) Again, we can write y as (y) = (sin x) / (1 cos x) Simplifying this even further, we get (y) = (sin x / 2) / (cos x/2) Substituting the values of x = nt A( eg, a) and B( a, b), we get the condition in the structure, y - a = (b - a) (x - ex.)/( a​​​​-ex.)

Tackling the above condition, we get the condition bend which is a straight line going through two given focuses A (eg, a) and B(a, b). As a result, we obtain a curve in the form of an equation (y - a) = (b - a) (x - nt) / (a) - nt), which is a straight line that runs through the two points A(eg, a) and B(a, b) that have been given to us.

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Answer:

-5.5

Step-by-step explanation:

-6x - 27 = 6

+ 27 +27

-6x = 33

÷-6 ÷-6

x = - 5.5

I am pretty sure the awnser is -5.5  because -6 Multiplied by -5.5 Is 33. 33 minus 27 is 6

Answer: No

Step-by-step explanation: Because if you substitute the 2 for x and 3 for y it is not equal

To solve the given initial value problem using the method of Laplace transforms, we need to perform the following steps:

Step 1: Take the Laplace transform of both sides of the given differential equation.

Step 2: Solve for the Laplace transform of y.

Step 3: Take the inverse Laplace transform to obtain y.

Step 4: Use the initial conditions to find the constants in the solution obtained in Step 3.1.

Taking the Laplace transform of both sides of the given differential equation: L{y" - 12y' + 72y} = L{40e⁴}L{y" - 12y' + 72y} = 40L{e⁴}.

Taking Laplace transform of y" term L{y"} - 12L{y'} + 72L{y} = 40L{e⁴}.

Using the Laplace transform property of derivatives,

we get:s²Y(s) - sy(0) - y'(0) - 12[sY(s) - y(0)] + 72Y(s) = 40/(s - 4)

Simplifying the above equation, we get: s²Y(s) - s - 10 - 12sY(s) + 12 + 72Y(s) = 40/(s - 4)⇒ s²Y(s) - 12sY(s) + 72Y(s) = 40/(s - 4) + s + 2

Using partial fraction decomposition, we can write the right-hand side of the above equation as:40/(s - 4) + s + 2 = [10/(s - 4)] - [10/(s - 4)²] + s + 2

Now, the given equation becomes:

s²Y(s) - 12sY(s) + 72Y(s) = [10/(s - 4)] - [10/(s - 4)²] + s + 2

Taking the Laplace transform of y(0) = 1 and y'(0) = 10, we get: Y(s) = (10s + 2 + 1)/[s² - 12s + 72]

Applying partial fraction decomposition to find Y(s),

we get: Y(s) = [3/(s - 6)] - [1/(s - 6)²] + [7/(s - 6)²] + [1/(s - 6)]

Taking the inverse Laplace transform of Y(s), we get: y(t) = [3e⁶t - 3te⁶t + 7te⁶t + e⁶t]

Using the initial conditions y(0) = 1 and y'(0) = 10, we get: y(0) = 1 = 1 + 0 + 0 + 1, y'(0) = 10 = 18 - 3 + 7 + 1

Therefore, the solution to the given initial value problem is: y(t) = [3e⁶t - 3te⁶t + 7te⁶t + e⁶t]

Answer: y(t) = [3e⁶t - 3te⁶t + 7te⁶t + e⁶t]

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9. H is a subspace of R3 as it contains a 2s vector [0, 2s, 0].

10. H is a subspace of R3 as it consists of the zero vector [0, 0, 0].

11. W is a subspace of R3 as it is spanned by the vectors [1,0,0] and [1,1,0].

12.W is a subspace of R4 as it is spanned by the vectors [1,2,0,0] and [0,-1,4,0].

9. To find a 2s vector v in R3 such that H is a subspace of R3, we can choose v = [0, 2s, 0]. This vector satisfies the condition of H being a subspace since it is of the form 2s, and any scalar multiple of v will also be of the form 2s, which is within H. Therefore, H is a subspace of R3.

0. Let H be the set of all vectors of the form [0, 0, 0]. To show that H is a subspace of R3, we can use the method from Exercise 9. By choosing v = [0, 0, 0],

we can see that H is closed under scalar multiplication and addition, as any scalar multiple or sum of the zero vector will still result in the zero vector. Therefore, H is a subspace of R3.

11. Let W be the set of all vectors of the form [b, c, 0], where b and c are arbitrary. To show that W is a subspace of R3, we need to find vectors u and v such that W is spanned by (u, v).

We can choose u = [1, 0, 0] and v = [0, 1, 0]. Any vector in W can be expressed as a linear combination of u and v, and therefore W is spanned by (u, v). This shows that W is a subspace of R3.

12. Let W be the set of all vectors of the form [s, 2s - t, 4t] in R4. To show that W is a subspace of R4, we can use the method from Exercise 11. By choosing u = [1, 2, 0, 0] and v = [0, -1, 4, 0],

we can observe that any vector in W can be expressed as a linear combination of u and v. Hence, W is spanned by (u, v), indicating that W is a subspace of R4.

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Answer:

Supplementary angles

Step-by-step explanation:

AEB and BEC form a straight line.

They add to 180 degrees

AEB+ BEC

150+30

180

That means that they are supplementary angles

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Step-by-step explanation:

Answer:

11 square units

Step-by-step explanation:

Find the diagram attached

First we need to find the side length of the square with known areas.

Area of a square = L²

L is the side length of the square

For the green square

44 = L²

Lg = √44

For the purple square

Ap = Lp²

33 = Lp²

Lp = √33

Get the length (L) of the unknown square using pythagoras theorem;

Lg² = L²+Lp²

(√44)² = L²+(√33)²

44 = L²+33

L² = 44-33

L² = 11

Since Al = L²

Hence the area of the square adjacent to the third side of the triangle is 11 square units

Answer:

y = -2x  + 7

Step-by-step explanation:

When 2 lines are perpendicular, the relationship between their slopes m1 and m2 may be stated as

m1m2 = -1

Given the line

y = 1/2 x + 8

Comparing with the general equation of a line y = mx + c where m is the slope and c is the intercept

m = m1 = 1/2

Hence the slope of the perpendicular line m2

= -1/1/2

= -2

Given that the line passes through the points (1,5)

using the equation

y - y1 = m (x - x1)

y - 5 = -2(x - 1)

y = -2x +2 + 5

y = -2x  + 7

Answer:

C. 52 degrees

Step-by-step explanation:

Vertical angles share the same angle of measure.

Answer:

$7

Step-by-step explanation:

The amount max keeps for spending = 1/2(total allowance - amount he spends on snacks)

total allowance = $17

amount he spends on snacks = $3

Amount he would have for  his college fund and spending money. = $17 - $3 = $14

Since he splits the amount equally between his college fund and spending money, the amount he would have for spending can be determined by dividing 14 by 2

$14/2 = $7