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3 years ago

Calculate A the answer should be clear

Mathematics

2 answers:

Daniel [21]3 years ago

8 0

Step-by-step explanation:

The given figure is a trapezoid with area 20 sq cm and perpendicular height 4 cm.

$aera \: of \: trapezoid \: \\ = \frac{1}{2} (sum \: of \: lengths \: of \: \parallel \: sides) \\\times height \\ \\ \therefore \: 20 =\frac{1}{2} (6 + a) \times 4\\ \\ \therefore \: 20 =(6 + a) \times 2\\ \\ \therefore \: 20 =12 + 2a \\ \\ \therefore \: 20 - 12 = 2a \\ \\ \therefore \: 8 = 2a \\ \\ \therefore \: a = \frac{8}{2} \\ \\ \: \: \: \: \: \: \huge \orange{ \boxed{\therefore \: a = 4}}$

riadik2000 [5.3K]3 years ago

3 0

1/2(6+a)4
6x4=24
24/2=12
20-12=8
8/2=4
1/2(6+4)4
40/2 =20cm^2
A=4cm

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Identify whether the series sigma notation infinity i=1 15(4)^i-1 is a convergent or divergent geometric series and find the sum

const2013 [10]

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(d) This is a divergent geometric series. The sum cannot be found.

Step-by-step explanation: The given infinite geometric series is

$S=\sum_{i=1}^{\infty}15(4)^{i-1}.$

We are to identify whether the given geometric series is convergent or divergent. If convergent, we are to find the sum of the series.

We have the D' Alembert's ratio test, states as follows:

Let, $\sum_{i=1}^{\infty}a_i$ is an infinite series, with complex coefficients $a_i$ and we consider the following limit:

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For the given series, we have

$a_i=15(4)^{i-1},\\\\a_{i+1}=15(4)^i.$

So, the limit is given by

$L\\\\\\=\lim_{i\rightarrow \infty}\dfrac{a_{i+1}}{a_i}\\\\\\=\lim_{i\rightarrow \infty}\dfrac{15(4)^i}{15(4)^{i-1}}\\\\\\=\lim_{i\rightarrow \infty}\dfrac{15(4)^i}{15(4)^{i}4^{-1}}\\\\\\=\dfrac{1}{4^{-1}}\\\\=4>1.$

Therefore, L >1, and so the given series is divergent and hence we cannot find the sum.

Thuds, (d) is the correct option.

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The way I did it was, I looked at the chart. The highest it goes is 30 and 210. So for your answer, you have to multiply. 7x30 gives you 210 and there y=7x

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Elodia [21]

The answer is option 2.

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Calculate A the answer should be clear​

Calculate A the answer should be clear