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3 years ago

A circle with area 36π has a sector with a central angle of 11/6π radians. What is the area of the sector?

Mathematics

1 answer:

bazaltina [42]3 years ago

4 0

Answer:

33pi or 103.62 squre units

Step-by-step explanation:

$central \: angle \: ( \theta) \\ = \frac{11}{6} {\pi}^{c} = \frac{11}{6} \times 180 \degree = 330 \degree \\ \\ area \: of \: sector \\ = \frac{ \theta}{360 \degree} \times area \: of \: circle \\ \\ = \frac{ 330 \degree}{360 \degree} \times 36 \: \pi \\ \\ = \frac{ 330 }{10 } \pi \\ \\ = \red{ \bold{33\pi}} \: {units}^{2} \\ = 33 \times 3.14 \\ = 103.62 \: {units}^{2} \\$

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One angle of a triangle measures 60°. The other two angles are in a ratio of 7:17. What are the measures of those two angles?

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Answer:

35° and 85°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Since one angle = 60° then the sum of the other 2 angles = 120°

Sum the parts of the ratio 7 + 17 = 24 parts, hence

$\frac{120}{24}$ = 5° ← value of 1 pat of the ratio, hence

7 parts = 7 × 5° = 35°

17 parts = 17 × 5° = 85°

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Step-by-step explanation:

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3 years ago

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3 years ago

What is the correct order of operations for simplifying the expression (x+3)^2-(x^2+9)/2x^2?

kramer

Answer:

The given expression is simplified as $\frac{(x+3)^2-(x^2 +9)} {2x^2} = \frac{3}{x}$

Step-by-step explanation:

Here, the given expression is:

$\frac{(x+3)^2-(x^2 +9)} {2x^2}$

Now, with ALGEBRAIC IDENTITIES:

$(a+b)^2 = a^2 + b^2 + 2ab$

Now, similarly: $(x+3)^2 = x^2 + (3)^2 + 2x(3) = (x^2 + 9 + 6x)$

Now, substituting the values in the given expression, we get:

$\frac{(x+3)^2-(x^2 +9)} {2x^2} \implies \frac{(x^2 + 9 + 6x)-(x^2 +9)} {2x^2}\\= \frac{(x^2 + 9 + 6x-x^2 -9)} {2x^2} \\= \frac{ 6x} {2x^2} = \frac{3}{x}$

Hence, the given expression $\frac{(x+3)^2-(x^2 +9)} {2x^2} = \frac{3}{x}$

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3 years ago