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Ivenika [448]
2 years ago
15

The area of a sector in a circle is given by the formula: A=12r2θ , where r is the radius and θ is the central angle measured in

radians. Find the rate of change of A with respect to θ if r remains constant. What is the rate when r=2?
Mathematics
1 answer:
sergeinik [125]2 years ago
3 0

Answer:

Step-by-step explanation:

A=\frac{1}{2} r^{2} \theta\\\frac{dA}{d\theta} =r \\\\when r=2\\rate of change at r=2 is  2

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James has saved $24.60. Dillon saved 2/3 of
stepan [7]

James saved 24.60 dollars, and we know Dillon saved 2/3 of the amount James saved.

Dillon's amount: 2/3 * 24.60 = 16.40

So we have two amounts:

James = 24.60 dollars

Dillon = 16.40

Mara = 16.40 * 2 = 32.80 dollars.

The question is asking for the total, so we add them together:

24.60 + 16.40 + 32.80 = 73.8 dollars.

4 0
2 years ago
Read 2 more answers
A baby otter was born 3/4 of a month early. At birth it's weight was 7/8 kilograms which is 9/10 kilogram less than the average
Assoli18 [71]

Answer:

The average weight of new born otter was, 1\frac{31}{40}

Step-by-step explanation:

Let average weight of new born otter be x.

As per the given statement: At birth it's weight was 7/8 kilograms which is 9/10 kilogram less than the average weight of a new born otter in the aquarium

"\frac{9}{10} kg less than average weight of a new born otter" means x-\frac{9}{10}

As per the given information, we have;

\frac{7}{8} = x -\frac{9}{10}

Add  \frac{9}{10} both sides, we have;

\frac{7}{8} + \frac{9}{10} = x

Take LCM of 8 and 10 is, 40

⇒\frac{35+36}{40}=x

Simplify:

x = \frac{71}{40} = 1\frac{31}{40}

Therefore, the average weight of new born otter was, 1\frac{31}{40}




6 0
2 years ago
Read 2 more answers
Mrs. Stevens wants to have $18,000 in the bank in 3 years. If she deposits $9500 today at 4% compounded quarterly for 3 years, h
serg [7]
\bf \qquad \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\qquad 
\begin{cases}
A=\textit{current amount}\\
P=\textit{original amount deposited}\to &\$9500\\
r=rate\to 4\%\to \frac{4}{100}\to &0.04\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{quarterly, 4 quarters a year}
\end{array}\to &4\\

t=years\to &3
\end{cases}

so.. if she deposits a principal of 9,500 today, compounding quarterly for 3 years, she'll have A amount

how much additional amount?  well, 18,000 - A
7 0
2 years ago
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Solve for x in the equation ? 2x^2 +3 x-7 =x^2 +5x +39
otez555 [7]

Answer:

1 ± √47

Step-by-step explanation:

Combine like terms in 2x^2 +3 x-7 =x^2 +5x +39:

2x^2 - x^2 = x^2 (first term);

3x - 5x = -2x (second term);

-7 - 39 = -46 (third term)

Then we have, all on the left side, x^2 - 2x - 46, which is a quadratic equation.  Here the coefficients are a = 1, b = -2 and c = -46.

Then the discriminant, b^2 - 4ac, is:

(-2)^2 - 4(1)(-46) = 4 + 184.

The roots are:

     -(-2) ±√188         2 ± √4√47

    ------------------- = -------------------

              2                         2

                             = 1 ± √47 (last of the answer choices)

=

x = ------------------

3 0
2 years ago
Morgan, Dakota and Taylor showed their work solving the equation 7x + 5x +1= 73. Identify the student with the invalid first ste
Pavel [41]

Answer:

Morgan, Dakota and Taylor showed their work solving the equation 7x + 5x +1= 73. Identify the student with the invalid first step and justify your reasoning. Morgan 7x + 5x + 1 = 73 12x + 1 = 73 Dakota 7x + 5x + 1 = 73 7x + 6x = 73 Taylor 7x + 5x + 1 = 73 7x + 5x = 72​

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
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