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3 years ago

Will give brainliest to best awnser

Mathematics

1 answer:

Snowcat [4.5K]3 years ago

3 0

Answer:

Step-by-step explanation:

We will use the Phythagorean Theorem, which states a^2+b^2=c^2

So the length of diagonal SQ would be:

16^2+8^2=SQ^2

256+64=SQ^2

SQ^2=320

SQ=√320

The length of diagonal OM is:

8^2+8^2=OM^2

64+64=OM^2

OM^2=128

OM=√128

So, now Ada believes that the length of diagonal SQ is two times the length of diagonal OM.

Lets check it out.

√320=17.88854382

2*√128=22.627416998

So, √320≠2√128

So, Ada is wrong. The length of diagonal SQ is NOT two times the length of diagonal OM.

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Suppose m = 2 + 6i, and | m + n | = 3√10, where n is a complex number.

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Answer: a) √50

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Step-by-step explanation:

first, the modulus of a complex number z = a + bi is

IzI = √(a^2 + b^2)

The fact that n is complex does not mean that n doesn't has a real part, so we must write our numbers as:

m = 2 + 6i

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for example, a = 1 and b = 7

1^2 + 7^2 = 1 + 49 = 50

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n = 1 + 7i

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3 years ago

Suppose $1000 is invested at a rate of 13% per year compounded monthly. (Round your answers to the nearest cent.)

masya89 [10]

Answer:

a. $1010.83

b.$1066.77

c. $1138.00

d.$13,269.22

Step-by-step explanation:

Given the annual rate as 13%(compounded monthly) and the principal amount as $1000.

a. #first we calculate the effective annual rate;

$i_m=(1+i/m)^m-1\\\\i_{12}=(1+0.13/12)^{12}-1=0.1380$

The compounded amount after 1 month is therefore:

$P_1=P(1+I_m)^n, n=1/12, i_m=0.1380, P=1000\\\\P_1=1000(1+0.1380)^{1/12}\\\\P_1=1010.83$

Hence, the principle after one month is $1010.83

b. The principal after 6 months:

-From a above we have the effective annual rate as 0.1380 and our time is 6 months:

$P_{6m}=P(1+i_m)^n, \ n=6m, P=1000, i_m=0.1380\\\\P_{6m}=1000(1+0.1380)^{6/12}\\\\=1066.77$

Hence, the principal after 6 months is $1066.77

c.The principal after 1 year:

-From a above we have the effective annual rate as 0.1380 and our time is 12 months:

$P_{1y}=P(1+I_m)^n, n=1/12, i_m=0.1380, P=1000\\\\P_{1y}=1000(1+0.1380)^{12}\\\\P_{1y}=1138$

Hence, the principal after 1 year is $1138.00

d. The principal after 20years:

-From a above we have the effective annual rate as 0.1380 and our time is 20yrs:

$P_{20y}=P(1+I_m)^n, n=1/12, i_m=0.1380, P=1000\\\\P_{20y}=1000(1+0.1380)^{12}\\\\P_{20y}=13269.22$

Hence, the principal after 20 years is $13,269.22

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3 years ago