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3 years ago

What is the sum of the geometric series 20 + 21 + 22 + 23 + 23 + 24 + … + 29?

Mathematics

2 answers:

Oxana [17]3 years ago

8 0

Answer:

1023

Step-by-step explanation:

2^0+2^1+2^2+2^3+2^4+2^5+2^6+2^7+2^8+2^9

1+2+8+16+32+64+128+256+512=1023

ikadub [295]3 years ago

3 0

ok so i have recently discovered An easy way to find the sum is to simply add all the numbers together since there aren't that many of them.

so try to work it out ,ur smart,ur on brainly

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Find the inverse of this matrix. 1 -1 -1 -1 2 3 1 1 4

zheka24 [161]

Let's use Gaussian elimination. Consider the augmented matrix,

$\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\-1 & 2 & 3 & 0 & 1 & 0\\1 & 1 & 4 & 0 & 0 & 1\end{array}\right]$

• Add row 1 to row 2, and add -1 (row 1) to row 3:

$\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 2 & 1 & 1 & 0\\0 & 2 & 5 & -1 & 0 & 1\end{array}\right]$

• Add -2 (row 2) to row 3:

$\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 2 & 1 & 1 & 0\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right]$

• Add -2 (row 3) to row 2:

$\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 0 & 7 & 5 & -2\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right]$

• Add row 2 and row 3 to row 1:

$\left[\begin{array}{ccc|ccc}1 & 0 & 0 & 5 & 3 & -1\\0 & 1 & 0 & 7 & 5 & -2\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right]$

So the inverse is

$\begin{bmatrix}1&-1&-1\\-1&2&3\\1&1&4\end{bmatrix}^{-1} = \boxed{\begin{bmatrix}5&3&-1\\7&5&-2\\-3&-2&1\end{bmatrix}}$

3 0

3 years ago

Part A: The sun produces 3.9 ⋅ 10^33 ergs of radiant energy per second. How many ergs of radiant energy does the sun produce in

expeople1 [14]

(3.9 * 10^33)(1.55 * 10^7)
3.9 * 1.55 = 6.045
10^33 * 10^7 = 10^40
6.045 * 10^40 <=== ur answer for the 1st one

1.6 * 10^-3 = 1.6 * 1 / 10^3 = 1.6/1000 = 0.0016 <== its probably this one...the 1.6 * 10^-3

5 0

3 years ago

A metalworker has a metal alloy that is 15% copper and another alloy that is 60% copper. How many kilograms of each alloy shou

coldgirl [10]

18 kg of 15% copper and 72 kg of 60% copper should be combined by the metalworker to create 90 kg of 51% copper alloy.

Step-by-step explanation:

Let x = kg of 15% copper alloy

Let y = kg of 60% copper alloy

Since we need to create 90 kg of alloy we know:

x + y = 90

51% of 90 kg = 45.9 kg of copper

So we're interested in creating 45.9 kg of copper

We need some amount of 15% copper and some amount of 60% copper to create 45.9 kg of copper:

0.15x + 0.60y = 45.9

but

x + y = 90

x= 90 - y

substituting that value in for x

0.15(90 - y) + 0.60y = 45.9

13.5 - 0.15y + 0.60y = 45.9

0.45y = 32.4

y = 72

Substituting this y value to solve for x gives:

x + y = 90

x= 90-72

x=18

Therefore, in order to create 90kg of 51% alloy, we'd need 18 kg of 15% copper and 72 kg of 60% copper.

6 0

3 years ago

PLS HELP ME

Wittaler [7]

It takes them 5 hours to drive 325 miles!

Since they travel 65 miles per hour, you multiply 65 x 5 and you get 325! Hope I helped :)

8 0

3 years ago

One batch of walnut muffins uses

Sholpan [36]

Answer:

4 cups

Step-by-step explanation:

8 0

3 years ago