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2 years ago

Finding area of shaded sectors.

Mathematics

1 answer:

tekilochka [14]2 years ago

5 0

Answer:

69.81 sq. m. (rounded to 2 decimal places)

Step-by-step explanation:

The sector of a circle is "part" or "portion" of a circle. The formula for the area of a sector is:

$A=\frac{\theta}{360}*\pi r^2$

Where

$\theta$ is the central angle

r is the radius

Given the figure, the arc is given as 80 degrees, but not the central angle of the shaded sector. But from geometry we know that the central angle and the intercepted arc have the same measure. So we can say:

$\theta = 80$

Also, the radius of the circle shown is 10 meters, so

r = 10

Now, we substitute in formula and find our answer:

$A=\frac{\theta}{360}*\pi r^2\\A=\frac{80}{360}*\pi (10)^2\\A=\frac{2}{9}*100\pi\\A=\frac{200\pi}{9}\\A=69.81$

Thus,

The area of the shaded sector is 69.81 sq. meters.

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2x+5x=100 x intercept

Papessa [141]

This is an equation involving x alone, so the most you can do is solve it:

$2x+5x=100x \iff 7x=100x \iff 0=93x \iff x=0$

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3 years ago

The residual value in a car lease agreement is what the leasing company believes the car will be worth at the end of your lease.

jok3333 [9.3K]

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Step-by-step explanation:

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3 years ago

Mohamed and Li Jing were asked to find an explicit formula for the sequence -5, -25, -125, -625,....

Nuetrik [128]

Answer:

Li Jing's formula i.e. $\boxed{g_n=-5\cdot \:5^{n-1}}$ is right.

Step-by-step explanation:

Considering the sequence

$-5,\:-25,\:-125,\:-625,...$

A geometric sequence has a constant ratio r and is defined by

$g_n=g_0\cdot r^{n-1}$

$\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{g_{n+1}}{g_n}$

$\frac{-25}{-5}=5,\:\quad \frac{-125}{-25}=5,\:\quad \frac{-625}{-125}=5$

$\mathrm{The\:ratio\:of\:all\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}$

$r=5$

So, the sequence is geometric.

$\mathrm{The\:first\:element\:of\:the\:sequence\:is}$

$g_1=-5$

$r=5$

$g_n=g_1\cdot r^{n-1}$

$\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}\:$

$g_n=-5\cdot \:5^{n-1}$

Therefore, Li Jing's formula i.e. $\boxed{g_n=-5\cdot \:5^{n-1}}$ is right.

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3 years ago

A game decreased in price by 1 5 . After the reduction it was priced at £48. What was the original price of the game?

vovikov84 [41]

Answer:

£63

Step-by-step explanation:

when we subtract 15 from 48 ,we get 63 which is the answer.

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2 years ago

Marine biologists have determined that when a shark detectsthe presence of blood in the water, it will swim in the directionin w

siniylev [52]

Solution :

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$C(x,y) = e^{-(x^2+2y^2)/10^4}$

are actually the curves

$e^{-(x^2+2y^2)/10^4}=k$

where k is a positive constant.

The equation is equivalent to

$x^2+2y^2=K$

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We sketch the level curves for K =1,2,3 and 4.

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Then we know the shark's path is perpendicular to the level curves it intersects.

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$\triangledown C= \frac{\partial C}{\partial x}i+\frac{\partial C}{\partial y}j$

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