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2 years ago

Find the surface area of the composite solid. Round your answer to the nearest hundredth.

Mathematics

1 answer:

iogann1982 [59]2 years ago

6 0

The surface area of the composite solid is 579.84 square feet

<h3>How to determine the surface area of the solid?</h3>

The composite solid that completes the question is added as an attachment

From the attached figure, we have the following figures:

Rectangular prism
Cylinder

The surface area of a rectangular prism is

A = 2(lw + lh + wh)

Using the dimensions of the prism, we have:

A = 2(6 * 11 + 6 * 8 + 8 * 11)

This gives

A = 404

The surface area of a cylinder is

A = 2πr^2 + 2πrh

Using the dimensions of the cylinder, we have:

A = 2 * 3.14 * 4^2 + 2 * 3.14 * 4 * 5

Evaluate

A = 226.08

The area of the circle between both shapes is

A = πr^2

This gives

A = 3.14 * 4^2

A = 50.24

The surface area of the composite solid is then calculated as:

Surface area = Area of rectangular prism + Area of cylinder - Area of circle

This gives

Surface area = 404 + 226.08 - 50.24

Evaluate

Surface area = 579.84

Hence, the surface area of the composite solid is 579.84 square feet

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Gino and Milla each open a savings account with an initial deposit of $6,300. Gino's account pays 2% simple interest annually. M

Keith_Richards [23]

Answer:

Milla's account would earn $63 more that Gino's account after 1 year.

Step-by-step explanation:

Both Gino and Milla made an initial deposit of $6300.

Principal = $6300

Gino's rate = 2% = 0.02

Milla's rate = 3% = 0.03

number of years = 1

Interest = Principal x Rate x Time

So that,

for Gino;

Interest = 6300 x 0.02 x 1

= 126

The interest on Gino's savings after a year is $126.

for Milla;

Interest = 6300 x 0.03 x 1

= 189

The interest on Milla's savings after a year is $189.

Milla's interest - Gino's interest = 189 - 126

= 63

Milla's account would earn $63 more that Gino's account after 1 year.

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3 years ago

What is 3.42 as a fraction and what is it simplified

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3.42 = 3 42/100

divide the numerator and denominator by 2

3 21/50

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3 years ago

Read 2 more answers

P and Q are sunsets of the universal set U={n:1<n<10} and n is an integer. P consists of even numbers less than 7 and Q co

Sauron [17]

Part A

<h3>Answer: P' u Q' = {3,4,5,6,7,8,9}</h3>

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

Work Shown:

The universal set here is U = {2,3,4,5,6,7,8,9} so we're listing all the integers between 2 and 9. We don't include 1 or 10 since n is larger than 1, and smaller than 10.

P = even numbers less than 7, subset of U

P = {2,4,6,8}

P ' = {3,5,7,9}

Note how the set P' is the set of everything in U that is not in set P. It's the opposite of set P. We call this the complement of set P.

Q = prime numbers less than 10, subset of U

Q = {2,3,5,7}

Q ' = {4,6,8,9}

Applying the union set operation on the sets P' and Q' leads to

P' u Q' = {3,5,7,9, 4,6,8,9}

All I did was combine the two sets of numbers under one umbrella. From here we toss out the duplicate entry of 9. This next step is optional, but sorting the values is standard convention.

Doing all this leads to

P' u Q' = {3,4,5,6,7,8,9}

This set represents all the values that are in set P' or in set Q' or both.

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

Part B

<h3>Answer: P' n Q' = {9}</h3>

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

Work Shown:

Now we're looking at the intersection of sets P' and Q'

List out those sets

P ' = {3,5,7,9}

Q ' = {4,6,8,9}

We see that only the value 9 is in common

Therefore,

P' n Q' = {9}

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

Part C

Answer:

(P' n Q')' = {2,3,4,5,6,7,8}

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

Work Shown:

You start with the result from part B. Then you erase that item (9) from the universal set. Everything in this answer set is not found in the set {9}

Put another way: we're finding the complement or opposite of P' n Q'

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

Part D

<h3>Answer: (P u Q)' = {9}</h3>

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

Work Shown:

P = {2,4,6,8}

Q = {2,3,5,7}

P u Q = {2,3,4,5,6,7,8}

Everything in set P u Q is either found in P, Q, or both. Any duplicates are tossed out.

Take the opposite of this to get

(P u Q)' = {9}

It is not a coincidence we get the same result as part B. It turns out that the two equations are true for any two sets P and Q

(P u Q)' = P' n Q'
(P n Q)' = P' u Q'

For more information, check out De Morgan's Laws. Use of a Venn Diagram may help visualize what is going on, so you can organize the values.

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Answer:

The answer is C

Step-by-step explanation:

(5/6)(5/8) = 25/48

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3 years ago