Help solving this math

Mathematics

1 answer:

9966 [12]3 years ago

6 0

Answer:

24 cm²
6400 -1600π ≈ 1373.45 square units

Step-by-step explanation:

1. You can look at this several ways.

It can be considered to be a stack of 1+2+3 = 6 squares that are 2 cm on a side, so have a total area of 6 × (2 cm)² = 24 cm².

You can lop off one of the squares sticking out and put it into the empty corner to form a 6 cm by 4 cm rectangle with an area of (6 cm)(4 cm) = 24 cm².

You can consider it to be a 6 cm square with 3 squares cut out of it that are 2 cm on a side: (6 cm)² -3(2 cm)² = (36 -12) cm² = 24 cm².

2. The shaded area is the difference in areas of a square 80 units on a side and a circle of 40 units radius. If we let d represent the side dimension of the square, then the area formulas are ...

Square area = d²

Circle area = π(d/2)²

So the difference area is ...

shaded area = d² -(π/4)d² = d²(1 -π/4)

For d=80, the shaded area is ...

shaded area = 80²(1 -π/4) = 6400 -1600π ≈ 1373.45 square units

You might be interested in

What is the sum of the first 70 consecutive odd numbers? Explain.

expeople1 [14]

The sum of the first n odd numbers is n squared! So, the short answer is that the sum of the first 70 odd numbers is 70 squared, i.e. 4900.

Allow me to prove the result: odd numbers come in the form 2n-1, because 2n is always even, and the number immediately before an even number is always odd.

So, if we sum the first N odd numbers, we have

$\displaystyle \sum_{i=1}^N 2i-1 = 2\sum_{i=1}^N i - \sum_{i=1}^N 1$

The first sum is the sum of all integers from 1 to N, which is N(N+1)/2. We want twice this sum, so we have

$\displaystyle 2\sum_{i=1}^N i = 2\cdot\dfrac{N(N+1)}{2}=N(N+1)$

The second sum is simply the sum of N ones:

$\underbrace{1+1+1\ldots+1}_{N\text{ times}}=N$

So, the final result is

$\displaystyle \sum_{i=1}^N 2i-1 = 2\sum_{i=1}^N i - \sum_{i=1}^N 1 = N(N+1)-N = N^2+N-N = N^2$

which ends the proof.

5 0

2 years ago

2. Explain how the order of operations determines how you simplify a numeric expression. Be sure to explain the rules for additi

IgorLugansk [536]

P-paratheses (do any math that has parentheses around the numbers) y=(2x5)+25
E-exponents (do the exponents next) y=(2x5)+5^2
M-multiplying. (Basically everything is self explanatory from here to then cuz im lazy to list examples)
Just basically if you don't use PEMDAS, you'll get the wrong answer

4 0

3 years ago

Diana invested $3000 in a savings account for 3 years. She earned $450 in interest over that time period. What interest rate did

In-s [12.5K]

$\bf \qquad \textit{Simple Interest Earned}\\\\
I = Prt\qquad 
\begin{cases}
I=\textit{interest earned}\to &\$450\\
P=\textit{original amount deposited}\to& \$3000\\
r=rate\to r\%\to \frac{r}{100}\\
t=years\to &3
\end{cases}
\\\\\\
450=3000\cdot r\cdot 3\implies \cfrac{450}{3\cdot 3000}=r\implies \cfrac{1}{20}=r
\\\\\\
r\%\implies \cfrac{1}{20}\cdot 100\implies r=\stackrel{\%}{5}$