Hi! May I please have some help?

Mathematics

2 answers:

yaroslaw [1]3 years ago

8 0

answer

explanation

21+18×2-12+1 (21-12+1=9)

9+18×2(9+18=27)

27×2(27×2=54)

54(answer)

max2010maxim [7]3 years ago

6 0

Steps:
18 x 2
What is that?
You can also think of it as 9 x 4 if that is easier
Then whatever you got for that, add 21 then subtract 12 and add 1

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Please help me with this!

ZanzabumX [31]

9514 1404 393

Answer:

2 1/2 feet

Step-by-step explanation:

The Pythagorean theorem is not useful in this problem.

If you reflect the triangle over the vertical line, you find that line to be the altitude of an equilateral triangle. That is, all of the vertex angles are 60°.

The base of that equilateral triangle is necessarily twice the length of the base of the triangle shown. All sides of the equilateral triangle are the same length, so all are 5 ft. The base of the triangle shown is half that.

The base (short leg) of the triangle shown is 2 1/2 feet.

_____

Since angles are given, this can be solved using trigonometry. The short leg will be (5 ft)·cos(60°) = (5 ft)(0.5) = 2.5 ft. (The cosine of 60° is one of the few exact rational values of trig functions of exact angles measured in degrees.)

5 0

3 years ago

4. Using the geometric sum formulas, evaluate each of the following sums and express your answer in Cartesian form.

nikitadnepr [17]

Answer:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=1$

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=0$

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})=\frac{1}{2}$

Step-by-step explanation:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=\frac{1}{2}(\sum_{n=0}^9 (e^{\frac{i\pi n}{2}}+ e^{\frac{i\pi n}{2}}))$

$=\frac{1}{2}(\frac{1-e^{\frac{10i\pi}{2}}}{1-e^{\frac{i\pi}{2}}}+\frac{1-e^{-\frac{10i\pi}{2}}}{1-e^{-\frac{i\pi}{2}}})$

$=\frac{1}{2}(\frac{1+1}{1-i}+\frac{1+1}{1+i})=1$

2nd

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=\frac{1-e^{\frac{i2\pi N}{N}}}{1-e^{\frac{i2\pi}{N}}}$

$=\frac{1-1}{1-e^{\frac{i2\pi}{N}}}=0$

3th

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})==\frac{1}{2}(\sum_{n=0}^\infty ((\frac{e^{\frac{i\pi n}{2}}}{2})^n+ (\frac{e^{-\frac{i\pi n}{2}}}{2})^n))$