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1 year ago

Find the angle of this sector. on the image

Mathematics

2 answers:

babymother [125]1 year ago

7 0

$\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ s=15\\ r=8 \end{cases}\implies 15=\cfrac{\theta \pi (8)}{180}\implies 15=\cfrac{2\pi \theta }{45} \\\\\\ 675=2\pi \theta \implies \cfrac{657}{2\pi }=\theta \implies 104.56^o\approx \theta =a$

KatRina [158]1 year ago

5 0

Answer:

$\alpha =107.4^{o}$

Step-by-step explanation:

$15=\frac{\pi (8)\alpha }{180}$

$\alpha =\frac{(15)(180)}{8\pi } =\frac{2700}{25.13}=107.4$

Hope this helps

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A sprinkler sprays a section of 200 degrees with a radius of water reaching 5 meters.

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Answer: The area that it covers is 78.53 square meters

Step-by-step explanation:

Hi, to answer this question we have to apply the next formula:

Area of a circle (A): π r²

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So, replacing with the values given:

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2 years ago

When sarah was 6 months old, she was 21 inches tall and her head had a diameter of 4.5 inches. now, at 20 year sold, she is 6 ft

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Answer: Yes, she could be considered similar to herself at 6 months of age.

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2 years ago

(1 point) A fish tank initially contains 15 liters of pure water. Brine of constant, but unknown, concentration of salt is flowi

Drupady [299]

Answer:

a. $\dfrac{dx}{dt} = 6\frac{2}{3} \cdot c$

b. $x(t) = 6\frac{2}{3} \cdot c \cdot t$

c. $c = \dfrac{3}{8} \ g/L$

Step-by-step explanation:

a. The volume of water initially in the fish tank = 15 liters

The volume of brine added per minute = 5 liters per minute

The rate at which the mixture is drained = 5 liters per minute

The amount of salt in the fish tank after t minutes = x

Where the volume of water with x grams of salt = 15 liters

dx = (5·c - 5·c/3)×dt = 20/3·c = $6\frac{2}{3} \cdot c \cdot dt$

$\dfrac{dx}{dt} = 6\frac{2}{3} \cdot c$

b. The amount of salt, x after t minutes is given by the relation

$\dfrac{dx}{dt} = 6\frac{2}{3} \cdot c$

$dx = 6\frac{2}{3} \cdot c \cdot dt$

$x(t) = \int\limits \, dx = \int\limits \left ( 6\frac{2}{3} \cdot c \right) \cdot dt$

$x(t) = 6\frac{2}{3} \cdot c \cdot t$

c. Given that in 10 minutes, the amount of salt in the tank = 25 grams, and the volume is 15 liters, we have;

$x(10) = 25 \ grams(15 \ in \ liters) = 6\frac{2}{3} \times c \times 10$

$6\frac{2}{3} \times c =\dfrac{25 \ grams }{10}$

$c =\dfrac{25 \ g/L }{10 \times 6\frac{2}{3} } = \dfrac{25 \ g/L}{10 \times \dfrac{20}{3} } =\dfrac{3}{200} \times 25 \ g/L= \dfrac{75}{200} \ g/L = \dfrac{3}{8} \ g/L$

$c = \dfrac{3}{8} \ g/L$

4 0

2 years ago

Find the angle of this sector. on the image ​

Find the angle of this sector. on the image