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avanturin [10]
3 years ago
8

Find the total surface area of the following pyramids: A regular triangular pyramid has base edges of length 30 and height 10.

Mathematics
1 answer:
lawyer [7]3 years ago
3 0

Answer:

1130 units²

Step-by-step explanation:

SA = sum of area of 4 triangles.

All sides equal means it's an equlateral triangle, which has all angles 60)

1 in the base:

A1 = ½(30)(30)sin(60) = 225sqrt(3)

3 slant triangles:

base = 30

Height to be obtained using pythagoras theorem:

Perpendcular distance of the edge from the mid of the base = ½(distance of one vertex from the midpoint of the opposite edge)

Let the distance of a vertex form the midpoint of the edge opposite to it 'd'

30² = 15² + d²

d² = 675

d = 15sqrt(3)

d/2 = 15sqrt(3)/2

height² = 10² + [15sqrt(3)/2]²

height² = 268.75

height = sqrt(268.75) = 16.4

Area of 1 slant triangle:

A2 = ½(30)(16.4) = 246

SA = A1 + 3 A2

= 225sqrt(3) + 3(246)

= 1127.7 units²

= 1130 units² (3sf)

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How many different 11-letter arrangements can be made using the letters in the word Firecracker?
zhenek [66]

Answer:

Total number of arrangements = 1,663,200

Step-by-step explanation:

Given:

11 - letter

FIRECRACKER

F = 1

I = 1

R = 3

E = 2

C = 2

A =1

K = 1

Find:

Total number of arrangements = ?

Computation:

Note: Repeated letter will be avoid.

Number\ of\  arrangements = \frac{!11}{!3 \times !2 \times !2}\\\\Number\ of\  arrangements = \frac{!11}{!3 \times !2 \times !2} \\\\Number\ of\  arrangements = \frac{11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3}{3 \times 2 \times 2 } \\\\Number\ of\  arrangements = 1,663,200

Total number of arrangements = 1,663,200

6 0
3 years ago
the sum of three numbers is 63. The first number is twice the second number, and the third number is three times the first numbe
HACTEHA [7]

Answer:

Step-by-step explanation:

2x+x+3(2x)=63

3x+6x=63

9x=63

9x/9=63/9

X=7

2x=14

3(2x)=42

3 0
3 years ago
The perimeter of a square is represented by 20n-8. Write an expression that will represent each side of the square.
Over [174]

Answer:

n=3

Step-by-step explanation:

20+20+20 length +width+ height

20×3

5 0
2 years ago
Read 2 more answers
Two lines are parallel to each other if they have the same slope. True or false?
wariber [46]

Answer:

true

Step-by-step explanation:

8 0
3 years ago
Select the correct answer.
Brums [2.3K]

Answer:

5 4/9

Step-by-step explanation:

Convert a mixed number 2 19

to a improper fraction: 2 1/9 = 2 19 = 2 · 9 + 19 = 18 + 19 = 199

To find new numerator:

a) Multiply the whole number 2 by the denominator 9. Whole number 2 equally 2 * 99 = 189

b) Add the answer from previous step 18 to the numerator 1. New numerator is 18 + 1 = 19

c) Write a previous answer (new numerator 19) over the denominator 9.

Two and one ninth is nineteen ninths

Add: 19

9+ (-29) = 19 + (-2)9= 179

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(9, 9) = 9. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 9 = 81. In the next intermediate step the fraction result cannot be further simplified by canceling.

In words - nineteen ninths plus minus two ninths = seventeen ninths.

Conversion a mixed number 3 59

to a improper fraction: 3 5/9 = 3 59= 3 · 9 + 59= 27 + 51 = 329

To find new numerator:

a) Multiply the whole number 3 by the denominator 9. Whole number 3 equally 3 * 99 = 279

b) Add the answer from previous step 27 to the numerator 5. New numerator is 27 + 5 = 32

c) Write a previous answer (new numerator 32) over the denominator 9.

Three and five ninths is thirty-two ninths

Add: the result of step No. 2 + 32

9= 179+ 329 = 17 + 329 = 499

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(9, 9) = 9. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 9 = 81. In the next intermediate step the fraction result cannot be further simplified by canceling.

In words - seventeen ninths plus thirty-two ninths = forty-nine ninths.

7 0
2 years ago
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