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lisabon 2012 [21]
3 years ago
15

What is the best estimate for the volume of the pyramid?

Mathematics
1 answer:
laila [671]3 years ago
6 0

<span>Volume of the pyramid = (1/3) * base area * height
Base area = 230</span>² = 52,900 m²
<span>Volume of the pyramid = (1/3) * 52,900 * 138 = 2,433,400 m</span>³
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Evaluate each finite series for the specified number of terms. 1+2+4+...;n=5
zaharov [31]

Answer:

31

Step-by-step explanation:

The series are given as geometric series because these terms have common ratio and not common difference.

Our common ratio is 2 because:

1*2 = 2

2*2 = 4

The summation formula for geometric series (r ≠ 1) is:

\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}} or \displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}

You may use either one of these formulas but I’ll use the first formula.

We are also given that n = 5, meaning we are adding up 5 terms in the series, substitute n = 5 in along with r = 2 and first term = 1.

\displaystyle \large{S_5=\frac{1(2^5-1)}{2-1}}\\\displaystyle \large{S_5=\frac{2^5-1}{1}}\\\displaystyle \large{S_5=2^5-1}\\\displaystyle \large{S_5=32-1}\\\displaystyle \large{S_5=31}

Therefore, the solution is 31.

__________________________________________________________

Summary

If the sequence has common ratio then the sequence or series is classified as geometric sequence/series.

Common Ratio can be found by either multiplying terms with common ratio to get the exact next sequence which can be expressed as \displaystyle \large{a_{n-1} \cdot r = a_n} meaning “previous term times ratio = next term” or you can also get the next term to divide with previous term which can be expressed as:

\displaystyle \large{r=\frac{a_{n+1}}{a_n}}

Once knowing which sequence or series is it, apply an appropriate formula for the series. For geometric series, apply the following three formulas:

\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}\\\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}

Above should be applied for series that have common ratio not equal to 1.

\displaystyle \large{S_n=a_1 \cdot n}

Above should be applied for series that have common ratio exactly equal to 1.

__________________________________________________________

Topics

Sequence & Series — Geometric Series

__________________________________________________________

Others

Let me know if you have any doubts about my answer, explanation or this question through comment!

__________________________________________________________

7 0
2 years ago
Roy and Sam start solving the equation as follows.
denpristay [2]

Answer:

The correct option is D.

Step-by-step explanation:

The given equation is

-3x+4=5x-6

According to the addition property of equality a=b and a+c=b+c are equivalent equations.

Use addition property of equality, add 3x on both the sides.

-3x+4+3x=5x-6+3x

4=8x-6

Therefore Sam's work is incorrect because he make calculation mistake.

According to the subtraction property of equality a=b and a-c=b-c are equivalent equations.

Use subtraction property of equality, subtract 5x from both the sides.

-3x+4-5x=5x-6-5x

-8x+4=-6

Therefore Roy's work is correct because he used subtraction property.

Option D is correct.

7 0
2 years ago
Factor the polynomial: 6x^2 + x - 35
umka21 [38]

Answer:

= (2x+5)x(3x-7)

Step-by-step explanation:

3 0
2 years ago
Which sample is biased?
djyliett [7]

Answer:

D

Step-by-step explanation:

sorry if im wrong, but first two say random and third one says its and online survey, so everyone takes it, but the fourth one just say "two employees" those could be anyone, from only fat people to people that dislike coffee.

4 0
2 years ago
Read 2 more answers
The vertex parabola is (-2,-3) when the x value is -1 the y-value is -5 what is the coefficient of the squared expression in the
zhannawk [14.2K]
The equation can be written in vertex form as
  y = a(x +2)² - 3
Substituting the given values, we can find the coefficient "a".
  -5 = a(-1+2)² -3
  -2 = a . . . . . . . . . add 3 and simplify

The coefficient of the squared term is -2.

4 0
3 years ago
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