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2 years ago

What is the sum of the first five terms of the geometric series 2 − 8 + 32 −

Mathematics

1 answer:

MrMuchimi2 years ago

5 0

Answer:

∑ (n = 1 to 5) (2·(-4)^(n - 1))

S5 = 2·((-4)^5 - 1)/((-4) - 1) = 410

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Find the area, correct to the nearest square

Lady bird [3.3K]

Answer:

1269 square meters

Step-by-step explanation:

The path and the plot of land form two concentric circles (they have the same center). The radius of the plot of land is 100m (half of the diameter) and the radius of the larger circle, formed by putting a 2m wide path around the plot of land, is 102m. Thus, the area of the path is $\pi *102^2$ minus $\pi *100^2$ which will be $10404\pi-10000\pi$ which is $404\pi$ . Estimate $\pi$ to 3.141 and calculate, getting 1268.964... which is 1269, rounded to the nearest square meter.

Hope this helps :)

7 0

2 years ago

Five students participated in an Easter egg hunt. Ally snatched up one

babunello [35]

Answer:

There were a total of 72 Easter eggs.

Step-by-step explanation:

Since five students participated in an Easter egg hunt, where Ally snatched up one quarter of all of the eggs, Brett only managed to get half of what Ally found, Lee snagged six more than Brett, Jen ended up with half of Lee's take, While Lisa snagged three times that, to determine how many eggs were there in total, the following calculation must be performed:

Ally: 0.25X

Brett: 0.125X

Read: 0.125X + 6

Jen: 0.0625X + 3

Smooth: 0.1875X + 9

X - 0.25X - 0.125X - 0.125X - 0.0625X - 0.1875X = 0.25

0.25X = 6 + 3 + 9

0.25X = 18

Ally: 18

Brett: 9

Jen: 7.5

Smooth: 22.5

18 + 9 + 15 + 7.5 + 22.5 = X

72 = X

Thus, there were a total of 72 Easter eggs.

4 0

3 years ago

Od 2 ( 2 7 1-3 1 3 1-2 6:1-6 b = d = IDONE

Lena [83]

Answer:

$a = \boxed{1},\: b=\boxed{0}\\\\c=\boxed{0},\: d=\boxed{1}$

Step-by-step explanation:

$\begin{bmatrix} 2 & 7\\\\1 & 3\end{bmatrix}\:\begin{bmatrix} -3 & 7\\\\1 & -2\end{bmatrix}=\begin{bmatrix} a & b\\\\c & d\end{bmatrix}$

Multiply both the matrices on left side, we find:

$\begin{bmatrix} 2(-3)+7(1) & 2(7)+7(-2)\\\\1(-3)+3(1) & 1(7)+3(-2)\end{bmatrix}=\begin{bmatrix} a & b\\\\c & d\end{bmatrix}$

$\rightarrow\begin{bmatrix} -6+7 & 14-14\\\\-3+3 & 7-6\end{bmatrix}=\begin{bmatrix} a & b\\\\c & d\end{bmatrix}$

$\rightarrow\begin{bmatrix} 1 & 0\\\\0 & 1\end{bmatrix}=\begin{bmatrix} a & b\\\\c & d\end{bmatrix}$

Comparing the corresponding elements of both the matrices on both sides, we find:

$a = \boxed{1},\: b=\boxed{0},\:c=\boxed{0},\: d=\boxed{1}$

7 0

2 years ago

Work out an estimate for 31 times 9.87 over 0.509

Ganezh [65]

Answer:

620

Step-by-step explanation:

9.87 is about 10 and 0.509 is about 0.5

(31 * 10) / 0.5 = about 620

5 0

3 years ago

estimate the answer by rounding first number to nearest tenth and second number to nearest hundred. 0.65 × 1754. have to type an

Levart [38]

Answer:

1260

Step-by-step explanation:

Round 0.65 to 0.7 and round 1754 to 1800. To get 1260, I recommend an easy way to do this. I would take 18 and multiply it by 7, giving us 126. Because it was supposed to be 0.7, not 7, we multiply by 10 because 7/10 is 0.7. This gives us 126 times 10 which equals 1260.

7 0

3 years ago