Helppp needed ASAP!!!!

Helppp Needed ASAP!!!!

Answers

Answer 1

Answer:

The two missing sides are : 79.54m and 58.62m

Step-by-step explanation:

first we look for the missing angle in the triangle

sum of angle in a triangle = 180°let make the missing angle be A 180 = A + 25 + 35180 = A + 60A = 180 - 60A = 120°

so now we use sine rules:

a/(sin A) = b/(sin B) = c/(sin C)

Let us make:

The side facing 35° be called bThe side facing 25° be called cThe side facing 120° be called a

so :

120/(sin 120°) = b/(sin 35°)120/(0.866) = b/0.574138.57 = b/0.574b = 138.57 x 0.57479.54m

so the side facing 35° = 79.54m

b/(sin B) = c/(sin C)79.54/(sin 35) = c/(sin 25)79.54/ (0.574) = c/(0.423)138.57 = c/(0.423)c = 138.57 x 0.423c = 58.62m

To find the area of this triangle


Related Questions

Practice Exercise 3.1 Fill in the blanks: (i) The factors of 12 are (ii) The least non-zero multiples of any number is (iii) ......... is a factor of every number. ing with Numbers​

Answers

Answer:

i.)1,2,3,4,6,12

ii).the number itself

iii.)1

Which choice is equivalent to the expression below? √-12

A. 12i
B. -12i
C. -2√3
D. 2i √3
E. -2√3i

PLEASE DON’T GUESS

Answers

Answer:

D.  2i√3

Step-by-step explanation:

You have the expression √-12.  You can divide the number in the radical sign into the numbers that make up the expression.  After you do this, you will be able to take numbers out of the radical sign

√(-12)

√(-1 × 4 × 3)

√-1 = i

√4 = 2

√3 = √3

2i√3

The answer is D.

joe went to to the store and spent a total of $37 .84. if paid with a $50 then how much change did he get back?

Answers

Answer:

$ 12.16

Step-by-step explanation:

Spent = $ 37.84

Paid = $ 50

Change = $50 - $37.84

Change = $ 12.16

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

~AH1807Peace!

Answer:

$12.16

Step-by-step explanation:

You must subtract his total from his payment. $50-$37.84=$12.16

It’s question 14 I need help with please it’s due soon

Answers

if you are trying to work out -3/4 - (-1/4 - 1/2) then the answer is 0

What is the rise over run for the slope -11/9

Answers

Answer:  11 down and 9 right

Step-by-step explanation:

Slope IS rise over run where the top number of the fraction (numerator) determines the vertical distance --> positive is up, negative is down

and the bottom number of the fraction (denominator) determines the horizontal distance --> positive is right, negative is left.

Given slope = -11/9

the numerator is -11 so the "rise" is  DOWN 11 units

the denominator is 9 so the "run" is RIGHT 9 units

Write an expression to represent the given statement. Use n for the variable. Three times the absolute value of the sum of a number and 6

Answers

Answer:

3 · |x+6|

Step-by-step explanation:

Write out what you see. "Three times" is 3 · something; "the absolute value of the sum of a number and 6" is |number + 6|. We'll use x for our number. Put it all together and you get 3 · |x+6|

The expression of the statement, Three times the absolute value of the sum of a number and 6 is  [tex]\[3\left| n+6 \right|\][/tex] .

Representation of statement:Let n be the number.The sum of the numbers n and 6 is n+6.The absolute value of the sum of the numbers n and 6 is  [tex]\[\left| n+6 \right|\][/tex].Hence, three times the absolute value of the sum of a number and 6 is [tex]\[3\left| n+6 \right|\][/tex].

 

Learn more about the representation of an expression:

https://brainly.com/question/10905086?referrer=searchResults

#SPJ2

Solve 13x + 14 = 12x -5 (make sure to type the number only)

Answers

Answer:

x = -19

Step-by-step explanation:

13x + 14 = 12x - 5

subtract 12x from both sides

x + 14 = -5

subtract 14 from both sides

x = -19

Answer:

x= -19

Step-by-step explanation:

13x+14=12x−5

Subtract 12x from both sides.

13x+14−12x=−5

Combine 13x and −12x to get x.

x+14=−5

Subtract 14 from both sides.

x=−5−14

Subtract 14 from −5 to get −19

x=−19

15P! NEED TODAY! WILL MARK BRAINLIEST! HELP! 15P! NEED TODAY! WILL MARK BRAINLIEST! HELP! You need to solve a system of equations. You decide to use the elimination method. Which of these is not allowed? Equation 1: 2x - 3y = 12 Equation 2: -2x + y = 8 A. Add the left side of equation 2 to the left side of equation 1. B. Multiply equation 2 by 3. Then substract the result from equation 1. C. Add equation 2 to equation 1.

Answers

Answer:

(A)

Step-by-step explanation:

That rule isn't used in the elimination methods for systems of equations, but, rather, it is used in substitution methods. The other rules are used in elimination.

Please tell me if I got it wrong.  I really hope it is correct.

A. Add the left side of equation 2 to the left side of equation 1.

B. Multiply equation 2 by 3. Then subtract the result from equation 1.

C. Add equation 2 to equation 1.

Mr. Howe ate 1/3 of a pizza and then Mr. Kurt ate 1/8 of the same pizza. How
much of the pizza has been eaten? *

Answers

12/24

Step One: We need to convert 1/3 and 1/8 so both have the same denominator, so we need to find the a number that is able to be multiply by 3 and 8 for the process.

Step Two: 1/3 x 8= 8/24 and 1/8x3= 3/24

Step Three: Add our new fractions: 3/24+8/24= 12/24

Step Four: Subtract 12 by 24: 24-12= 12; our answer is 12/24 or half the pizza was eaten

I hope I've help!

At the "cloth for you" shop, you can buy a top for £10.00 and a Bermuda trouser for £12.00. Due to a sensational sell, there is a 20% discount on all tops. If you buy one top and two Bermuda trousers, how much money do you spend in total?

Answers

Answer:

£32 in total for the top and two trousers

Step-by-step explanation:

The price for a top In the "cloth for you" shop= £10

The price for a bermuda trouser In the "cloth for you" shop= £12

There is a 20% discount on tops

The price If I bought one top and would trouser will be

(10-(0.2*10)) for the top

2(12) for the trouser

Total= (10-(0.2*10))+ 2(12)

Total = 10-2+24

Total = £32

So I spent £32 in total for the top and two trousers

I need help with this please

Answers

You know x, so just plug it in for the answers. Like AB = x + 7, so since x is 3, then AB is 3 + 7 = 10
BD is 2x + 3x -1 = 6 + 9 - 1 = 14
CE is 3x - 1+ 2x + 3 = 9-1+6+3= 17

find the surface area of the prism HURRY HURRY

Answers

Answer:

should be 192

Step-by-step explanation:

What is the simplified form of x minus 5 over x squared minus 3x minus 10⋅ x plus 2 over x squared plus x minus 12 ? (6 points) Select one: a. 1 over the quantity x minus 3 times the quantity x plus 4 b. 1 over the quantity x minus 3 times the quantity x plus 2 c. 1 over the quantity x plus 4 times the quantity x minus 5 d. 1 over the quantity x plus 2 times the quantity x minus 5

Answers

Answer:

  [tex]\ \text{a. }\quad\dfrac{1}{(x-3)(x+4)}[/tex]

Step-by-step explanation:

Maybe you want the product ...

  [tex]\dfrac{x-5}{x^2-3x-10}\cdot\dfrac{x+2}{x^2+x-12}=\dfrac{x-5}{(x-5)(x+2)}\cdot\dfrac{x+2}{(x-3)(x+4)}\\\\=\boxed{\dfrac{1}{(x-3)(x+4)}}[/tex]

__

Numerator factors of (x-5) and (x+2) cancel those in the denominator.

Can someone help me?

Answers

Answer:

7w

Step-by-step explanation:

∫∫D(x2 + y2 + 2020)dxdy D: x2 +y2 +2ax ≤ 0 (a > 0)

Answers

Answer:

good morning

Step-by-step explanation:

hope u have a nice day

According to a Pew Research Center study, in May 2011, 40% of all American adults had a smart phone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is higher among community college students. She selects 341 community college students at random and finds that 147 of them have a smart phone. Then in testing the hypotheses:

H0: p = 0.4 versus

Ha: p > 0.4,

what is the test statistic?

z =________________. (Please round your answer to two decimal places.)

B.)

According to a Pew Research Center study, in May 2011, 33% of all American adults had a smart phone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is higher among community college students. She selects 349 community college students at random and finds that 138 of them have a smart phone. In testing the hypotheses:

H0: p = 0.33 versus

Ha: p > 0.33,

she calculates the test statistic as z = 2.5990.

Then the p‑value =________________ .

(Please round your answer to four decimal places.)

Answers

Answer:

z = 1.17

P - value = 0.0047

Step-by-step explanation:

A.

From the given information;

H0: p = 0.4 versus

Ha: p > 0.4,

Let's calculate the population proportion for the point estimate;

the population proportion [tex]\hat p[/tex] = 147/341

the population proportion  [tex]\hat p[/tex] = 0.431085

However; the test statistics can therefore be determined by using the formula:

[tex]z = \dfrac{\hat p - p_o}{\sqrt{\dfrac{p_o(1-p_o)}{n}}}[/tex]

[tex]z = \dfrac{0.431085 - 0.40}{\sqrt{\dfrac{0.40(1-0.40)}{341}}}[/tex]

[tex]z = \dfrac{0.031085}{\sqrt{\dfrac{0.40(0.60)}{341}}}[/tex]

[tex]z = \dfrac{0.031085}{\sqrt{\dfrac{0.24}{341}}}[/tex]

[tex]z = \dfrac{0.031085}{\sqrt{7.03812317 \times 10^{-4}}}[/tex]

[tex]z = \dfrac{0.031085}{0.0265294613}[/tex]

z = 1.1717

z = 1.17             to two decimal places

B.)

The null and the alternative hypothesis is given as:

H0: p = 0.33 versus

Ha: p > 0.33,

The z = 2.5990.

The objective here is to determine the p-value from the z test statistics.

P - value = P(Z > 2.5990)

P- value = 1 -  P(Z < 2.5990)

P - value = 1 - 0.9953

P - value = 0.0047

I need help with this question

Answers

Answer:

a. 2

b. x^2 + 10x + 26

c. x^2 + 2x + 2

Step-by-step explanation:

For each part, replace x with the value you are given and simplify.

f(x) = x^2 - 2x + 2

a.

f(2) = 2^2 - 2(2) + 2 = 2

b.

f(x + 6) = (x + 6)^2 - 2(x + 6) + 2

= x^2 + 12x + 36 - 2x - 12 + 2

= x^2 + 10x + 26

c.

f(-x) = (-x)^2 - 2(-x) + 2

= x^2 + 2x + 2

A. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 4; C: at least one of the numbers is 1; and D: the numbers do not add to 10. Express the given event in symbols.
The red die shows 1 and the numbers add to 4.
How many elements does it contain?
B. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 3; B: the numbers add to 2; C: at least one of the numbers is 1; and D: the numbers do not add to 10. Express the given event in symbols. HINT [See Example 5.]
The numbers do not add to 2.
How many elements does it contain?
C. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 2; C: at least one of the numbers is 3; and D: the numbers do not add to 11. Express the given event in symbols. HINT [See Example 5.]
Either the numbers add to 11 or the red die shows a 1.
How many elements does it contain?
D. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 4; B: the numbers add to 5; C: at least one of the numbers is 1; and D: the numbers do not add to 9. Express the given event in symbols. HINT [See Example 5.]
Either the numbers add to 5, or they add to 9, or at least one of them is 1.
How many elements does it contain?

Answers

Answer:

1. elements it contains =  (1,3)

2.  elements it contains = 35

3.  elements it contains = 8

4.  elements it contains = 17

Step-by-step explanation:

A. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 4; C: at least one of the numbers is 1; and D: the numbers do not add to 10. Express the given event in symbols.

The red die shows 1 and the numbers add to 4.

How many elements does it contain?

B. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 3; B: the numbers add to 2; C: at least one of the numbers is 1; and D: the numbers do not add to 10. Express the given event in symbols. HINT [See Example 5.]

The numbers do not add to 2.

How many elements does it contain?

C. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 2; C: at least one of the numbers is 3; and D: the numbers do not add to 11. Express the given event in symbols. HINT [See Example 5.]

Either the numbers add to 11 or the red die shows a 1.

How many elements does it contain?

D. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 4; B: the numbers add to 5; C: at least one of the numbers is 1; and D: the numbers do not add to 9. Express the given event in symbols. HINT [See Example 5.]

Either the numbers add to 5, or they add to 9, or at least one of them is 1.

How many elements does it contain?

NB. Attached is the solution to the problems stated above

Four items are purchased at prices of $5.30, $1.29, $.53, and $.68. Sales tax applies at 5% of the total purchase price. What is the total charge?

Answers

Answer:

$8.19

Step-by-step explanation:

1. Add the cost of the items together

5.3 + 1.29 + 0.53 + 0.68 = 7.8

2. Solve for 5% of the cost of the items

5% = 0.05

7.8 · 0.05 = 0.39

3. Add the sales tax to the price of the items

7.8 + 0.39 = 8.19

Answer:  $8.19

Explanation:

Add up the prices

5.30 + 1.29 + 0.53 + 0.68 = 7.80

This is the total amount before tax is added. To find the amount after tax, we multiply by 1.05 to get

1.05*7.80 = 8.19

Or a longer way is to find 5% of 7.80 getting 0.05*7.80 = 0.39 in the amount of tax owed, which is added on top of the previous total we got earlier. So we have 7.80 + 0.39 = 8.19

The use of the multiplier 1.05 is handy when you need to apply multiple percentage increases (it also works if you have multiple discounts as well).

what is a prime number

Answers

A number that can be divided exactly only by itself and 1.

For Eg:- 7, 10, 13.

Answer:

A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic:

A car dealership is advertising a car for $16,299.99. If the sales tax rate is 6.5 percent, what
is the total tax paid for the car?
A. S993 34
B. $1.000.00
CS1.059 50
DS1.359.19

Answers

Answer:

C.

Step-by-step explanation:

16,299.99*0.065=1059.50

3/4=x/20,find the value of 'x'​

Answers

Answer:

[tex]\boxed{x=15}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4} =\frac{x}{20}[/tex]

[tex]\sf Cross \ multiply.[/tex]

[tex]4 \cdot x = 20 \cdot 3[/tex]

[tex]4x=60[/tex]

[tex]\sf Divide \ both \ sides \ by \ 4.[/tex]

[tex]\frac{4x}{4} =\frac{60}{4}[/tex]

[tex]x=15[/tex]

For a data set with Mean -20, SD-3 find the Z scores for each of the following raw scores: 23, 17, 15, 22, 30. 23: 17: 15: 22: 30:
A. 23
B. 17
C. 15
D. 22
E. 30
4. Look at your result from the previous question in regards to raw score of 15

Answers

Answer:

A. 1

B. -1

C. -1.67

D. 0.67

E. 3.33

Step-by-step explanation:

Mathematically;

z-score = (x-mean)/SD

From the question, mean = 20 , SD = 3 while x represents the individual values

A. 23

Z = (23-20)/3 = 3/3 = 1

B. 17

z = (17-20)/3 = -3/3 = -1

C. 15

z = (15-20)/3 = -5/3 = -1.67

D. 22

z = (22-20)/3 = 2/3 = 0.67

E. 30

z = (30-20)/3 = 10/3 = 3.33

What is the value of 2 in 9,274

Answers

Answer:

200

Step-by-step explanation:

4 is in the ones place so 4 just 4

7 is in the tens place so it is 70

2 is the hundreds place so 200

9 is in the thousands place so 9.000

Prove that if n is an integer, these four statements are equivalent: (i) n is even, (ii) n 1 is odd, (iii) 3n 1 is odd, (iv) 3n is even.

Answers

Answer:

Step-by-step explanation:

Hello,

If n is even, it means that we can find k integer such that n = 2 * k.

Then n+1=2*k+1 is odd.

3n+1=6k+1=2*(3k)+1 where 3k is an integer so 3n+1 is odd.

3n = 2*(3k) is even.

Besides, if n+1 is odd we can find an integer p so that n+1=2p+1 so n = 2p is even.

3n+1 is odd means that we can find an integer q such that 3n+1=2q+1 so 3n=2q as 3 is not dividable by 2, it means that n is a multiple of 2, then n is even.

3n is even means that we can write 3n = 2z where z is an integer and again it means that n is a multiple of 2 and then n is even.

Thank you.

What is 17,210,000,000 written in scientific notation?

Answers

Answer and Step-by-step explanation:

The answer is 1722.1 x [tex]10^8[/tex]

#teamtrees #PAW (Plant And Water)

Answer:

1.72x10^10

Step-by-step explanation:

POSITIVE EXPONENT: means a number is huge

NEGATIVE EXPONENT: indicates a number is teeny-tiny

The double number line shows that Toni can type 180 words in
2 minutes.



Based on the ratio shown in the double number line, how many words can Toni type in 3 minutes?

Answers

Answer:

120 words

Step-by-step explanation:

as a ratio it's

2:180

In real life the longer you do something the more words you type

so since you can't get to 3 from 2 easily you go to 1 instead.

2:180

1:360

3:120

Gina, Sam, and Robby all rented movies from the same video store. They each rented some dramas, comedies, and documentaries. Gina rented 11 movies total. Sam rented twice as many dramas, three times as many comedies, and twice as many documentaries as Gina. He rented 27 movies total. If Robby rented 19 movies total with the same number of dramas, twice as many comedies, and twice as many documentaries as Gina, how many movies of each type did Gina rent?

Answers

Hi there! :)

Answer:

Gina rented 3 dramas, 5 comedies, and 3 documentaries.

Step-by-step explanation:

To solve, we will need to set up a system of equations:

Let x = # of dramas, y = # of comedies, and z = # of documentaries:

Write equations to represent each person:

Gina:

x + y + z = 11

Sam:

2x + 3y + 2z = 27

Robby:

x + 2y + 2z = 19

Write the system:

x + y + z = 11

2x + 3y + 2z = 27

x + 2y + 2z = 19

Begin by subtracting the third equation from the second:

2x + 3y + 2z = 27

x + 2y + 2z = 19

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

x + y = 8

If x + y = 8, plug this into the first equation:

(8) + z = 11

z = 11 - 8

z = 3

We found the # of documentaries Gina rented, now we must solve for the other variables:

Subtract the top equation from the third. Substitute in the value of z we solved for:

x + 2y + 2(3) = 19

x + y + (3) = 11

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

y + 3 = 8

y = 5

Substitute in the values for y and z to solve for x:

x + 5 + 3 = 11

x + 8 = 11

x = 11 - 8

x = 3.

Therefore, Gina rented 3 dramas, 5 comedies, and 3 documentaries.

Answer:

B- x + y + z = 11

2x + 3y + 2z = 27

x + 2y + 2z = 19

Step-by-step explanation:

I took the quiz

which of the following greatest
6+(-2)
6-(-2)
6×(-2)
6+(-2)​

Answers

Out of
4
8
-12
4

8, or 6-(-2) is greatest

Use spherical coordinates. Evaluate e x2 + y2 + z2 dV, E where E is enclosed by the sphere x2 + y2 + z2 = 25 in the first octant.

Answers

Answer:

[tex]\displaystyle \iiint_E {e^{\sqrt{x^2 + y^2 + z^2}}} \, dV = \frac{\pi (17e^5 - 2)}{2}[/tex]

General Formulas and Concepts:
Calculus

Integration

Integrals

Integration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:
[tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Integration Method [Integration by Parts]:
[tex]\displaystyle \int {u} \, dv = uv - \int {v} \, du[/tex]

[IBP] LIPET: Logs, Inverses, Polynomials, Exponentials, Trig

Multivariable Calculus

Triple Integrals

Cylindrical Coordinate Conversions:

[tex]\displaystyle x = r \cos \theta[/tex][tex]\displaystyle y = r \sin \theta[/tex][tex]\displaystyle z = z[/tex][tex]\displaystyle r^2 = x^2 + y^2[/tex][tex]\displaystyle \tan \theta = \frac{y}{x}[/tex]

Spherical Coordinate Conversions:

[tex]\displaystyle r = \rho \sin \phi[/tex][tex]\displaystyle x = \rho \sin \phi \cos \theta[/tex][tex]\displaystyle z = \rho \cos \phi[/tex][tex]\displaystyle y = \rho \sin \phi \sin \theta[/tex][tex]\displaystyle \rho = \sqrt{x^2 + y^2 + z^2}[/tex]

Integral Conversion [Spherical Coordinates]:
[tex]\displaystyle \iiint_T {f( \rho, \phi, \theta )} \, dV = \iiint_T {\rho^2 \sin \phi} \, d\rho \, d\phi \, d\theta[/tex]

Step-by-step explanation:

*Note:

Recall that φ is bounded by 0 ≤ φ ≤ 0.5π from the z-axis to the x-axis.

I will not show/explain any intermediate calculus steps as there isn't enough space.

Step 1: Define

Identify given.

[tex]\displaystyle \iiint_E {e^{\sqrt{x^2 + y^2 + z^2}}} \, dV[/tex]

[tex]\displaystyle \text{Region E:} \ x^2 + y^2 + z^2 = 25 \ \text{bounded by first octant}[/tex]

Step 2: Integrate Pt. 1

Find ρ bounds.

[Sphere] Substitute in Spherical Coordinate Conversions:
[tex]\displaystyle \rho^2 = 25[/tex]Solve:
[tex]\displaystyle \rho = 5[/tex]Define limits:
[tex]\displaystyle 0 \leq \rho \leq 5[/tex]

Find θ bounds.

[Sphere] Substitute in z = 0:
[tex]\displaystyle x^2 + y^2 = 25[/tex][Circle] Graph [See 2nd Attachment][Graph] Identify limits [Unit Circle]:
[tex]\displaystyle 0 \leq \theta \leq \frac{\pi}{2}[/tex]

Find φ bounds.

[Circle] Substitute in Cylindrical Coordinate Conversions:
[tex]\displaystyle r^2 = 25[/tex]Solve:
[tex]\displaystyle r = 5[/tex]Substitute in Spherical Coordinate Conversions:
[tex]\displaystyle \rho \sin \phi = 5[/tex]Solve:
[tex]\displaystyle \phi = \frac{\pi}{2}[/tex]Define limits:
[tex]\displaystyle 0 \leq \phi \leq \frac{\pi}{2}[/tex]

Step 3: Integrate Pt. 2

[Integrals] Convert [Integral Conversion - Spherical Coordinates]:
[tex]\displaystyle \iiint_E {e^{\sqrt{x^2 + y^2 + z^2}}} \, dV = \iiint_E {e^{\sqrt{x^2 + y^2 + z^2}} \rho^2 \sin \phi} \, d\rho \, d\phi \, d\theta[/tex][dρ Integrand] Rewrite [Spherical Coordinate Conversions]:
[tex]\displaystyle \iiint_E {e^{\sqrt{x^2 + y^2 + z^2}}} \, dV = \iiint_E {e^{\rho} \rho^2 \sin \phi} \, d\rho \, d\phi \, d\theta[/tex][Integrals] Substitute in region E:
[tex]\displaystyle \iiint_E {e^{\sqrt{x^2 + y^2 + z^2}}} \, dV = \int\limits^{\frac{\pi}{2}}_0 \int\limits^{\frac{\pi}{2}}_0 \int\limits^5_0 {e^{\rho} \rho^2 \sin \phi} \, d\rho \, d\phi \, d\theta[/tex]

We evaluate this spherical integral by using the integration rules, properties, and methods listed above:

[tex]\displaystyle \begin{aligned} \iiint_E {e^{\sqrt{x^2 + y^2 + z^2}}} \, dV & = \int\limits^{\frac{\pi}{2}}_0 \int\limits^{\frac{\pi}{2}}_0 \int\limits^5_0 {e^{\rho} \rho^2 \sin \phi} \, d\rho \, d\phi \, d\theta \\ & = \int\limits^{\frac{\pi}{2}}_0 \int\limits^{\frac{\pi}{2}}_0 {\bigg[ (\rho^2 - 2 \rho + 2) e^{\rho} \sin \phi \bigg] \bigg| \limits^{\rho = 5}_{\rho = 0}} \, d\phi \, d\theta\end{aligned}[/tex]

[tex]\displaystyle \begin{aligned}\iiint_E {e^{\sqrt{x^2 + y^2 + z^2}}} \, dV & = \int\limits^{\frac{\pi}{2}}_0 \int\limits^{\frac{\pi}{2}}_0 {(17e^5 - 2) \sin \phi} \, d\phi \, d\theta \\& = \int\limits^{\frac{\pi}{2}}_0 {\bigg[ -(17e^5 - 2) \cos \phi \bigg] \bigg| \limits^{\phi = \frac{\pi}{2}}_{\phi = 0}} \, d\theta \\& = \int\limits^{\frac{\pi}{2}}_0 {17e^5 - 2} \, d\theta \\& = (17e^5 - 2) \theta \bigg| \limits^{\theta = \frac{\pi}{2}}_{\theta = 0} \\& = \frac{\pi (17e^5 - 2)}{2}\end{aligned}[/tex]

∴ the given integral equals [tex]\displaystyle \bold{\frac{\pi (17e^5 - 2)}{2}}[/tex].

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Learn more about spherical coordinates: https://brainly.com/question/16415822

Learn more about multivariable calculus: https://brainly.com/question/4746216

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Topic: Multivariable Calculus

Unit: Triple Integrals Applications

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