Please simplify each expression for 18, 20, and 21

Tri-Star Industries employs electrical, plumbing, and air conditioning technicians. Their home office is made up of three square

Molodets [167]

Answer:

6084 $\text{ft}^2$ .

Step-by-step explanation:

Please find the attachment.

We have been given that the home-office of Tri-star industries is made up of three square buildings, one for each department, with a triangular atrium in the middle. The area of the Plumbing building is 5,184 $\text{ft}^2$ and the area of the A/C building is 900 $\text{ft}^2$ .

We know that area of square is square of its side length. Since all building are squares, so to find the area of electrical building, we will use Pythagoras theorem.

$a^2+b^2=c^2$

We can see from our attachment that side length of electrical building is hypotenuse (c) of the right triangle.

Upon substituting our given information in Pythagoras theorem, we will get:

$5184+900=c^2$

$6084=c^2$

Therefore, the area of electrical building is 6084 square feet.

3 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

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