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sergiy2304 [10]
1 year ago
5

Follow the steps to find the area of the shaded region. 14 46 14

Mathematics
1 answer:
konstantin123 [22]1 year ago
6 0

The area of the shaded region is 8.1838. The area of the shaded region is calculated by subtracting the area of the triangle from the area of the sector of the circle.

<h3>How to calculate the area of the sector?</h3>

The area of the sector of a circle with a radius 'r' and an angle of sector 'θ' is

A = (θ/360) πr² sq. units

<h3>How to calculate the area of a triangle with an angle?</h3>

The area of the triangle with measures of two sides and an angle between them is

A = 1/2 × a × b × sinC sq. units

Where a and b are the lengths of sides and ∠C is the angle between those sides.

<h3>Calculation:</h3>

It is given that,

The area of the sector shown in the diagram is 78.6794 cm² and the area of the triangle is 70.4956 cm².

Then to calculate the area of the shaded region, subtract the area of the sector and the area of the triangle. I.e.,

Area of the shaded region = Area of the sector - Area of the triangle

⇒ 78.6794 - 70.4956

⇒ 8.1838 cm²

Therefore, the required area of the shaded region is 8.1838 sq. cm.

Learn more about the area of a sector here:

brainly.com/question/22972014

#SPJ1

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salantis [7]

Answer:

\displaystyle  \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \frac{1}{2}

General Formulas and Concepts:

<u>Calculus</u>

Limits

Limit Rule [Variable Direct Substitution]:                                                                     \displaystyle \lim_{x \to c} x = c

L'Hopital's Rule

Differentiation

  • Derivatives
  • Derivative Notation

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]:                                                                                    \displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)

Step-by-step explanation:

We are given the limit:

\displaystyle  \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)}

When we directly plug in <em>x</em> = 0, we see that we would have an indeterminate form:

\displaystyle  \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \frac{0}{0}

This tells us we need to use L'Hoptial's Rule. Let's differentiate the limit:

\displaystyle  \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \displaystyle  \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)}

Plugging in <em>x</em> = 0 again, we would get:

\displaystyle \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)} = \frac{0}{0}

Since we reached another indeterminate form, let's apply L'Hoptial's Rule again:

\displaystyle \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)} = \lim_{x \to 0} \frac{\frac{-[cos^2(2x) + 1]}{[cos(2x)]^{\frac{2}{3}}} + \frac{cos^2(3x) + 2}{[cos(3x)]^{\frac{5}{3}}}}{2cos(x^2) - 4x^2sin(x^2)}

Substitute in <em>x</em> = 0 once more:

\displaystyle \lim_{x \to 0} \frac{\frac{-[cos^2(2x) + 1]}{[cos(2x)]^{\frac{2}{3}}} + \frac{cos^2(3x) + 2}{[cos(3x)]^{\frac{5}{3}}}}{2cos(x^2) - 4x^2sin(x^2)} = \frac{1}{2}

And we have our final answer.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

6 0
3 years ago
Mr.chan made 252 cookies for the annual fifth grade class bake sale . they sold 3/4 of them and 3/9 of the remaining cookies wer
Eva8 [605]
So, personally I would take 252 and divide it by 4. this will give you 63 which is 1/4 of the cookies. Then add that 63 three times to get a total of 189 cookies which would be your 3/4 sold. so since there is only 63 cookies left then you would go into your final problem. 3/9 is equal to 1/3, so all you would do is divide 63 by 3 and get a total of 21 cookies given to the pta.
5 0
3 years ago
Integrate the following: ∫<img src="https://tex.z-dn.net/?f=5x%5E4dx" id="TexFormula1" title="5x^4dx" alt="5x^4dx" align="absmid
Fiesta28 [93]

Answer:

A. x^5+C

Step-by-step explanation:

This is a great question! The first thing we want to do here is to take the constant out of the expression, in this case 5. Doing so we would receive the following expression -

5\cdot \int \:x^4dx

We can then apply the power rule " \int x^adx=\frac{x^{a+1}}{a+1} ", where a = exponent ( in this case 4 ),

5\cdot \frac{x^{4+1}}{4+1}

From now onward just simplify the expression as one would normally, and afterward add a constant ( C ) to the solution -

5\cdot \frac{x^{4+1}}{4+1}\\ - Add the exponents,

5\cdot \frac{x^{5}}{5} - 5 & 5 cancel each other out,

x^5 - And now adding the constant we see that our solution is option a!

3 0
3 years ago
Read 2 more answers
Look at this triangle work out length AB
Paha777 [63]

Answer:

2√137

Step-by-step explanation:

To find AB, we can use the Pythagorean Theorem (a² + b² = c²). In this case, a = 22, b = 8 and we're solving for c, therefore:

22² + 8² = c²

484 + 64 = c²

548 = c²

c = ± √548 = ± 2√137

c = -2√137 is an extraneous solution because the length of a side of a triangle cannot be negative, therefore, the answer is 2√137.

3 0
2 years ago
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Which ones are linear &amp; which are exponential ?
AveGali [126]

Answer:

11 - exponential, 12-linear, 13 exponential, 14 exponential

Step-by-step explanation:

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2 years ago
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