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3 years ago

Find the area of the shaded segment of the circle. Please help

Mathematics

1 answer:

natka813 [3]3 years ago

5 0

Answer:

1.4 m²

Step-by-step explanation:

The area of a sector with central angle θ (in radians) is given by the formula

A = (1/2)r²θ

The area of the triangle with central angle θ is given by the formula

A = (1/2)r²sin(θ)

The area of the shaded segment is the difference of these:

A = (1/2)r²(θ -sin(θ))

Your segment has a central angle of 60° = π/3 radians, so its area is ...

A = (1/2)(4 m)²(π/3 -sin(π/3)) = (8 m²)(π/3 -(√3)/2)

A ≈ 1.4 m²

The area of the shaded segment is about 1.4 m².

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(1.1.8 in the book) Let P be the proposition ’I bought a lottery ticket this weekend’ and Q be the proposition ’I won the millio

Karolina [17]

Answer:

~ is for negation

^ is for "and"

v is for "or"

=> for "if then"

<=> for "if and only if"

Step-by-step explanation:

(a) ~P (negation of P)

I didn't buy a lottery ticket this weekend.

(b) P v Q (P is in disjunction Q)

I have either bought a lottery ticket this weekend or won the million dollar jackpot.

I won the million dollar jackpot because I bought a lottery ticket this weekend.

(d) P ^ Q (P is in conjunction with Q)

I bought a lottery ticket this weekend, and I won the million dollar jackpot.

(e) P <=> Q (P and Q are dependent on each other)

If only I had bought a lottery ticket this weekend, I would have won the million dollar jackpot.

(f) ~P => ~Q (negation of Q is a consequence of negation of P)

I didn't win the million dollar jackpot because I didn't buy a lottery ticket this weekend.

(g) ~P ^ ~Q (negation of P is in conjunction with negation of Q)

I neither bought a lottery ticket this weekend nor won the million dollar jackpot.

(h) ~P v (P ^ Q)

This is logically equivalent to (~P v P) ^ (~P v Q) (negation of P is in disjunction with P, and also with disjunction with Q), and can be best expressed as:

It didn't matter that I bought a jackpot ticket or not, I won the million dollar jackpot.

8 0

3 years ago

If an investment of $3000 grows to $4432.37 in eight years with interest compounded annually , what is the interest rate?

melamori03 [73]

$\bf \qquad \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad 
\begin{cases}
A=\textit{accumulated amount}\to &\$4432.37\\
P=\textit{original amount deposited}\to &\$3000\\
r=rate\to r\%\to \frac{r}{100}\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{annually, thus once}
\end{array}\to &1\\
t=years\to &8
\end{cases}$

$\bf 4432.37=3000\left(1+\frac{r}{1}\right)^{1\cdot 8}\implies \cfrac{4432.37}{3000}=(1+r)^8
\\\\\\
\sqrt[8]{\cfrac{4432.37}{3000}}=1+r\implies \sqrt[8]{\cfrac{4432.37}{3000}}-1=r
\\\\\\
0.0500001086\approx r\qquad\qquad\cfrac{r\%}{100}\approx 0.0500001086
\\\\\\
r\%\approx 100\cdot 0.0500001086\implies r=\stackrel{\%}{5}$

6 0

3 years ago

Jules ran 2/3 miles. Miles ran 5/8 more than Jules. How many miles did Miles run?

kifflom [539]

2/3 is equivalent to 16/24
and 5/8 is equivalent to 15/24 miles
15/24+16/24= 31/24

31/24 simplifies to 1 6/24
Which simplifies down to 1 1/6

Miles ran 1 and 1/6 miles

3 0

3 years ago

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Consider the functions:

jolli1 [7]

The x and y axis so that’s why it’s true

5 0

3 years ago

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NEED HELP ASAP!! (25 POINTS)

sergij07 [2.7K]

Answer: