The triangular base of the given prism has an interior angle with a measure of 80° and an interior angle with a measure of 55°. What is the measure of the unknown angle?


A. 45°
B. 65°
C. 75°
D. 85°

The volume of the resulting solid is (26π/3) cubic units.

To find the volume of the solid generated by rotating the region bounded by the curves x = (y - 6)², x = 25, about the axis y = 1, we will integrate the cylindrical shells along the y-axis.

The limits of integration for y are from y = 1 to y = 11, as determined earlier.

The differential volume of a cylindrical shell is given by dV = 2πrh dy, where r is the distance from the axis of rotation to the curve, h is the height of the cylindrical shell, and dy is the thickness of the shell.

In this case, the radius of the cylindrical shell is r = 1, and the height of the cylindrical shell is h = x₁ - x₂ = 25 - (y - 6)².

Thus, the differential volume becomes dV = 2π(1)(25 - (y - 6)²) dy.

We can now integrate this differential volume over the range of y = 1 to y = 11 to find the total volume V:

V = ∫[1,11] 2π(25 - (y - 6)²) dy

Expanding and simplifying the integral:

V = 2π ∫[1,11] (25 - (y - 6)²) dy

V = 2π ∫[1,11] (25 - (y² - 12y + 36)) dy

V = 2π ∫[1,11] (25 - y² + 12y - 36) dy

V = 2π ∫[1,11] (-y² + 12y - 11) dy

Integrating the terms individually:

V = 2π [-y³/3 + 6y² - 11y] |[1,11]

V = 2π [-(11³/3) + 6(11²) - 11(11)] - [-(1³/3) + 6(1²) - 11(1)]

V = 2π [-1331/3 + 726 - 121] - [-1/3 + 6 - 11]

V = 2π [-1331/3 + 726 - 121 + 1/3 - 6 + 11]

V = 2π [-604/3 + 616 + 1/3]

V = 2π [13/3]

Simplifying further:

V = (26π/3)

Therefore, the volume of the resulting solid is (26π/3) cubic units.

To know more about volume, refer here:

https://brainly.com/question/2900556

#SPJ4

It is given that P = principal, R = rate of interest and T = time

Formula to find compound interest is:

A = P(1 + R/100)^T

where A = amount received after n years

P = principal amount invested

R = rate of interest

T = time for which the amount is invested

The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest.

It is thought that Italy in the 17th century is where the concept of "interest on interest" or compound interest first appeared. It will accelerate the growth of a total more quickly than simple interest, which is solely calculated on the principal sum.

Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.

Learn more about compound interest:

https://brainly.com/question/13155407

#SPJ9

Answer:

3

Step-by-step explanation:

15 - 2(7 - x) = 7

collect like terms

-2(7 - x) = 7 - 15

-2(7 - x) = -8

divide both sides by -2

7 - x = -8/-2

7 - x = 4

collect like terns

-x = 4 - 7

-x = -3

dividing both sides by -

x = 3

Answer:

Step-by-step explanation:

15-2(7-x)=7

15-14+2x=7

1+2x=7

2x=6

x=3

Answer:

The area is 81.27

Step-by-step explanation:

Sorry for the late response, but I hope I helped and I always appreciate brainliest!!! :)

If you ever need me to answer a question, feel free to ask!

Answer:

area = 130.5 in²

Step-by-step explanation:

area = 1/2(6)(8.7)(5) = 130.5 in²

The point on the plane 4x - y + 4z = 40 nearest the origin is (-3.048, -0.762, 6.467)

Given data ,

To find the point on the plane 4x - y + 4z = 40 nearest the origin, we need to minimize the distance between the origin and the point on the plane.

The normal vector to the plane 4x - y + 4z = 40 is given by (4,-1,4). To find the perpendicular distance from the origin to the plane, we need to project the vector from the origin to any point on the plane onto the normal vector. Let's choose the point (0,0,10) on the plane:

Vector from origin to (0,0,10) on the plane = <0-0, 0-0, 10-0> = <0,0,10>

Perpendicular distance from the origin to the plane = Projection of <0,0,10> onto (4,-1,4)

= (dot product of <0,0,10> and (4,-1,4)) / (magnitude of (4,-1,4))

= (0 + 0 + 40) / √(4^2 + (-1)^2 + 4^2)

= 40 / √(33)

To find the point on the plane nearest the origin, we need to scale the normal vector by this distance and subtract the result from any point on the plane. Let's use the point (0,0,10) again:

Point on the plane nearest the origin = (0,0,10) - [(40 / √(33)) / √(4^2 + (-1)^2 + 4^2)] * (4,-1,4)

= (0,0,10) - (40 / √(33)) * (4/9,-1/9,4/9)

= (0,0,10) - (160/9√(33), -40/9√(33), 160/9√(33))

= (-160/9√(33), -40/9√(33), 340/9√(33))

Hence , the point on the plane 4x - y + 4z = 40 nearest the origin is approximately (-3.048, -0.762, 6.467)

To learn more about distance between a point and plane click :

https://brainly.com/question/14442366

#SPJ1

Answer: I don't know if it's correct but maybe the answer will be something like

Step-by-step explanation: 0.18 = 9/50

3.596 = 899/250             and        0.2467 = 2467/10000

The curve that passes through (4, 5) and has a slope of 3√x at each point is given by y = (\(2x^{3/2}\) + 5 -  2\((4)^{3/2}\)

To find the curve that passes through (4, 5) and has a slope of 3√x at each point, we can integrate the derivative of y with respect to x, which gives us the original function y(x):

\(\frac{dy}{dx}\) = 3√x

Integrating both sides with respect to x, we get:

y = (\(2x^{3/2}\)) + C

where C is a constant of integration.

We can use the point (4, 5) to solve for C:

5 = 2\((4)^{3/2}\) + C

C = 5 - 2\((4)^{3/2}\)

Substituting this value of C, we get the final equation for the curve:

y =  (\(2x^{3/2}\)) + 5 -  2\((4)^{3/2}\)

Therefore, The curve that passes through (4, 5) and has a slope of 3√x at each point is given by y = (\(2x^{3/2}\) + 5 -  2\((4)^{3/2}\)

To know more about curve refer here

https://brainly.com/question/31114246#

#SPJ11

The maximum height of the ball is 9.8 feet.

The distance the ball travels horizontally before hitting the ground is 2.

The graph that model the parabolic path is given below.

Parabolic path is defined as the angle of trajectory of a projectile.

We have,

y = 0.4x² + 1.6x + 5 _____(1)

Where,

x = balls horizontal distance

y = height of the ball

To find the maximum height we need to differentiate y and set y = 0.

y' = 0

0.4 x (2x) + 1.6 + 0 = 0

0.8x + 1.6 = 0

-0.8x = -1.6

x = 1.6 / 0.8

x = 2

Now the maximum height of the ball is:

Put x = 2 in (1)

y = -0.4 x (2)² + 1.6 x (2) + 5

y = 0.4 x 4 + 3.2 + 5

y = 1.6 + 3.2 + 5

y = 9.8

The distance the ball travels horizontally before hitting the ground:

x = 2

The equation that models the​ ball's parabolic path is given below:

Thus,

The maximum height of the ball is 9.8 feet.

The distance the ball travels horizontally before hitting the ground is 2.

The graph that model the parabolic path is given below.

Learn more about parabolic here:

https://brainly.com/question/27927804?referrer=searchResults

#SPJ1

(a) With 10 rectangles using left endpoints, 5 rectangles are contributing negative area values to the estimated net area. This means that the function is below the x-axis in those intervals.

The remaining 5 rectangles are contributing positive area values, as the function is above the x-axis in those intervals.

When using midpoints, the number of positive and negative rectangles may not be the same. It depends on the behavior of the function within each subinterval. The use of midpoints can result in a different distribution of positive and negative rectangles compared to using left endpoints.

(b) The error when using midpoints with 10 subintervals can be determined by calculating the difference between the estimated net area using midpoints and the actual net area.

To calculate the error, we need to evaluate the definite integral of the function over the given interval and subtract the estimated net area using midpoints.

Error = Actual Net Area - Estimated Net Area using Midpoints

Since the exact values are not provided, the specific error value cannot be determined without further information or calculations.

Using left endpoints with 10 rectangles, 5 rectangles contribute negative area values and 5 contribute positive area values. When using midpoints, the distribution of positive and negative rectangles may differ. The error when using midpoints can be calculated by subtracting the estimated net area using midpoints from the actual net area, but the exact error value cannot be determined without further information or calculations.

To know more about rectangles , visit

https://brainly.com/question/2607596

#SPJ11

Answer:

x = 16

Step-by-step explanation:

To solve for x, use the Intersecting Secant-Tangent Theorem.

A tangent is a straight line that touches a circle at only one point.

A secant is a straight line that intersects a circle at two points.

If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the length of the tangent segment is equal to the product of the length of the secant segment and the length of the external secant segment.

From inspection of the given diagram:

Therefore, according to the Intersecting Secant-Tangent Theorem:

\(\begin{aligned}\textsf{(Tangent segment)}^2&=\textsf{(Secant segment)} \cdot \textsf{(External secant segment)}\\ 15^2&=(x+9) \cdot 9\end{aligned}\)

Solve the equation for x:

\(\implies 15^2=(x+9) \cdot 9\)

\(\implies 225=9x+81\)

\(\implies 225-81=9x+81-81\)

\(\implies 144=9x\)

\(\implies 9x=144\)

\(\implies 9x \div 9=144 \div 9\)

\(\implies x=16\)

Therefore, the value of x is 16.

a. To find the inverse function of f(x), we need to interchange the roles of x and y and solve for y. So, we have:

y = 1x - 3
x = 1y - 3
x + 3 = y
Therefore, the inverse function of f(x) is f^-1(x) = x + 3.
The domain of f^-1(x) is the range of f(x). Since f(x) = 1x - 3 is a linear function, its domain is all real numbers. Therefore, the range of f(x) is also all real numbers. In interval notation, we can write this as (-inf, inf).

The range of f^-1(x) is the domain of f(x). As we determined in part b, the domain of f(x) is all real numbers. Therefore, the range of f^-1(x) is also all real numbers. In interval notation, we can write this as (-inf, inf).
Hi! I'd be happy to help you with your question.
a. To find the inverse function of f(x) = 1x - 3, you can follow these steps:
1. Replace f(x) with y: y = 1x - 3
2. Swap x and y: x = 1y - 3
3. Solve for y: y = x + 3
So, the inverse function f^(-1)(x) = x + 3.
The domain of f^(-1) refers to the set of all possible x-values. Since the inverse function is a linear function with no restrictions, the domain of f^(-1) is all real numbers. In interval notation, this is written as (-∞, ∞).

c. The range of f^(-1) refers to the set of all possible y-values (output). Again, since it's a linear function with no restrictions, the range of f^(-1) is also all real numbers. In interval notation, this is written as (-∞, ∞).

To know more about Function  click here .

brainly.com/question/21145944

#SPJ11

Answer:

False

Step-by-step explanation:

numbers are integers, the integers are negative, zero and positive, 

while natural numbers are only positive, 

therefore the statement is false

 . False. Integers comprise negative and positive numbers (...- 3, -2, -1, 0, 1, 2, 3 ...) and natural numbers only comprise positive integers (0, 1, 2, 3 ...)  

The amount of water added in each step is the dilution factor minus 1 times the volume of material taken out. The final concentration of the series is the product of the dilution factors of each step.

In simple (linear) and serial dilutions, the volume of material taken out of the stock solution, the amount of water added, and the final concentration are important factors to consider. The answers will be provided in the following paragraphs.

In simple (linear) dilutions, a known volume of the stock solution is removed and diluted with water to achieve the desired final concentration. To calculate the volume of material taken out of the stock solution, subtract the desired final volume from the initial volume. The amount of water to be added is equal to the final volume minus the volume of material taken out. The final concentration is determined by dividing the initial concentration by the final volume.

For serial dilutions, a series of dilutions is performed, each using the previous dilution as the new stock solution. The volume of material taken out of each dilution is determined by the desired dilution factor, which represents the ratio of the final concentration to the initial concentration. The amount of water added in each step is the dilution factor minus 1 times the volume of material taken out. The final concentration of the series is the product of the dilution factors of each step.
It's important to specify the units at every step to ensure accurate calculations and dilution procedures.

Learn more about factor here:

https://brainly.com/question/14549998

#SPJ11

Answer:

10 x 10, 2 x 50

Step-by-step explanation:

Answer:

19. 13

20. 6

21. 12

Step-by-step explanation:

Answer:

The answer is E

Step-by-step explanation:

We first are going to look at our first term on the table(the number that comes up first) which is $75.

Then we have to find the common factor. So, you divide the second number by the first number( 88.50 divided by 75 which gets us 1.18).

Now, since we found the first term and the common factor, we are going to have to find the exponent for our f(x) equation.  

We know that she bought the painting in 2009! Now the problem is asking how much the painting will cost in 2030. So, you will subtract 2030-2009 which gets you 21! So 21 is your exponent!

Equation:   F(x)= 75(1.18) ^21

The answer that you get is:    $2424.28

Let me know if you have any questions!

:)

The value of the painting in 2030 would be $2424.28.

From the given table, it can be observed that the painting increases in value over the years. Increase in value of the painting from 2009 to 2010 = ($88.50 / $75) - 1 = 18%.

The formula for determining the future value of the painting is:

FV = P (1 + r)^nm

FV = Future value

P = Present value

R = interest rate

N = number of years

The value of the painting in 2030 = $75 x (1.18)^21 = $2424.28

To learn more about future value, please check: https://brainly.com/question/18760477

Answer:

324 square meters

Step-by-step explanation:

Hey there!

The surface area of a shape is the area of all the surfaces added up

The side surface area is 48 since 16 x 3 is 48. Since there are two side areas, we need to multiply 48 x 2 is 96

Now we need to do this for the other sides

the bottom and top areas are 96 square meters each so we multiply 96 by 2 which is 192

The front and back faces have an area of 18 square meters so we multiply 18 by 2 since there are two faces which are 36

Now we add all the values: 96+192+36 which is 324

So the surface area of the prism is 324 square meters

Answer:

33

Step-by-step explanation:

Measure of ∠MOP is equals to 71.7°.

" Supplementary angles are those angles whose sum is equals to 180°."

According to the question,

∠MOP = 3x - 3

∠MON = 4x + 9

As ∠MOP and ∠MON has common arm OM.

Therefore, ∠MOP and ∠MON are supplementary angles.

As per definition of supplementary angles we have

∠MON + ∠MOP = 180°

Substitute the value of ∠MOP and ∠MON  we get,

 4x + 9 + 3x - 3= 180°

⇒7x - 6 = 180°

⇒7x = 174

⇒ x = 24.9 (round off)

Substitute the value of x in measure of ∠MOP we get,

∠MOP = 3(24.9) -3

          = 71.7°

Hence, measure of ∠MOP is equals to 71.7°.

Learn more about supplementary angles here

https://brainly.com/question/18164299

#SPJ2

Cluster analysis is a valuable tool in data analysis that helps identify hidden patterns and group similar objects or data points.

It is useful in various fields, such as market research, image analysis, customer segmentation, and anomaly detection. By clustering data, we can gain insights, make predictions, and improve decision-making. Hierarchical clustering is a specific approach to cluster analysis. It organizes data points into a hierarchy of clusters, where each cluster can contain subclusters. This method allows for a hierarchical structure that captures different levels of similarity or dissimilarity between data points.

For example, in customer segmentation, hierarchical clustering can group customers based on similar attributes like demographics, purchase history, and behavior. In image analysis, it can be used to segment images into meaningful regions or objects based on their visual characteristics. Hierarchical clustering offers a flexible and interpretable way to analyze complex datasets and discover underlying structures.

To learn more about data points click here: brainly.com/question/17148634

#SPJ11

Step-by-step explanation:

1 . when we collect like terms we only focus on the variables and the power of the variable I f exist so in this question the answer is 8x^2 because both have the same variable and same power or exponent.

2. one term is monomial

two terms is binomial

3. b

4. -9

5. c

Answer:

$96.

Step-by-step explanation:

5/6  costs 80

Multiply both parts by 6/5:

5/6 * 6/5 ( = 1 ) costs 80 * 6/5

= 16 * 6

= $96.

Answer:

y=7

Step-by-step explanation:

Answer:

10

explanation

The y doesn't change so all you have to do is just count the distance from -7 to 3 easy :)

a. The data modelling the situation is an exponential function.

b. The definition of the exponential function is given as follows: y = 2(2)^x.

c. The average rate of change between station 2 and station 4 is of 4.

In this problem, we can see that when x is increased by one, y is multiplied by two, hence the function is exponential with a rate of change per day given as follows:

b = 2.

When x = 1, y = 4, hence the intercept a, which is the value of y when x = 0, is obtained as follows:

a = 4/2

a = 2.

Per each station, the average rate of change is of 2, hence for two stations, between station 2 and station 4, the average rate of change is given as follows:

2² = 4.

More can be learned about exponential functions at https://brainly.com/question/25537936

#SPJ1

Answer:

3 seconds: 14 seconds

Step-by-step explanation:

90:7

let's turn everything into seconds

90:420

take the zero out

9:42

divide by 3

3:14

this is the simplest form

Answer:

simplest form is 3/14

Step-by-step explanation:

First we have to convert 7 into min

60× 7= 420

90/430 = 9/42

÷ 3= 3/14

Answer:

option c is the correct ans...

Step-by-step explanation:

Plz mark it as brainliest...

Answer: C.

When you multiply exponential factors with the same base, you add the exponents. 3 + 8 = 11

Step-by-step explanation:

Answer:

x > 2

Step-by-step explanation:

5x +7 > 17

5x > 10

x > 2

Answer:

the solution of the Awnser is (x | x>2)

Step-by-step explanation:

Let's solve your inequality step-by-step.

5x+7>17

Step 1: Subtract 7 from both sides.

5x+7−7>17−7

5x>10

Step 2: Divide both sides by 5.

5x5>105

x>2

Answer:

9

Step-by-step explanation:

set triangles as x and squares as y

x+3y=4x+y, now plug in 6 for each triangle

6+3y=4(6)+y, solve for the weight of the squares

3y-y=24-6

2y=18

y=9, each sqaure weighs 9 units