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3 years ago

lvava is calculating the area of a circle with a radius of 3/4 which of the following gives the BEST estimation of the area?

Mathematics

1 answer:

STALIN [3.7K]3 years ago

8 0

Answer:

28.274

Step-by-step explanation:

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Which is the most reasonable estimate for the height of a two-story house 15 centimeters, 15 meters,or 15 kilometers?

LUCKY_DIMON [66]

15 meters should be about right. hope this helped

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2 years ago

Find the amount and the compound interest on 62500 for1*1/2 years at 8% compounded half-yearly

Anettt [7]

principal (p)=62500,Time (T)=1.5 years,Rate (R)=8% Ammount=p (1+R÷100) =62500 × 1.1664 =72900 again, compound interest = p(1+R÷100)-1=62500×0.1664 = 10400

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2 years ago

Find e^cos(2+3i) as a complex number expressed in Cartesian form.

ozzi

Answer:

The complex number $e^{\cos(2+31)} = \exp(\cos(2+3i))$ has Cartesian form

$\exp\left(\cosh 3\cos 2\right)\cos(\sinh 3\sin 2)-i\exp\left(\cosh 3\cos 2\right)\sin(\sinh 3\sin 2)$ .

Step-by-step explanation:

First, we need to recall the definition of $\cos z$ when $z$ is a complex number:

$\cos z = \cos(x+iy) = \frac{e^{iz}+e^{-iz}}{2}$ .

Then,

$\cos(2+3i) = \frac{e^{i(2+31)} + e^{-i(2+31)}}{2} = \frac{e^{2i-3}+e^{-2i+3}}{2}$ . (I)

Now, recall the definition of the complex exponential:

$e^{z}=e^{x+iy} = e^x(\cos y +i\sin y)$ .

So,

$e^{2i-3} = e^{-3}(\cos 2+i\sin 2)$

$e^{-2i+3} = e^{3}(\cos 2-i\sin 2)$ (we use that $\sin(-y)=-\sin y)$ .

Thus,

$e^{2i-3}+e^{-2i+3} = e^{-3}\cos 2+ie^{-3}\sin 2 + e^{3}\cos 2-ie^{3}\sin 2)$

Now we group conveniently in the above expression:

$e^{2i-3}+e^{-2i+3} = (e^{-3}+e^{3})\cos 2 + i(e^{-3}-e^{3})\sin 2$ .

Now, substituting this equality in (I) we get

$\cos(2+3i) = \frac{e^{-3}+e^{3}}{2}\cos 2 -i\frac{e^{3}-e^{-3}}{2}\sin 2 = \cosh 3\cos 2-i\sinh 3\sin 2$ .

Thus,

$\exp\left(\cos(2+3i)\right) = \exp\left(\cosh 3\cos 2-i\sinh 3\sin 2\right)$

$\exp\left(\cos(2+3i)\right) = \exp\left(\cosh 3\cos 2\right)\left[ \cos(\sinh 3\sin 2)-i\sin(\sinh 3\sin 2)\right]$ .

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2 years ago

Martin is covering his bathroom floor with square tiles. When he gets to the end of a row of tiles, he needs to cut the length o

kati45 [8]

All squares are equal sides.Let X be the side of a square. $\\$ Area of square,A = x^2

Here a tile is a square of side length 'x'. The following polynomial represents,

(x - 4) represents "the width of the new tile" (because 4 inches cut from the tile)

4x represents "the area removed from the tile" (since one side of removed tile is 'x' and other is 4 inches.)

x2 represents "area of original tile" of side equal to 'x'

x represents "the length of the new tile" (since length of new tile is not reduced. Length =x and breadth is x-4

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3 years ago

Elian's credit card had a balance of $132.20 on April 1. On April 5, he charged $74.50. On April 18, he made a payment of $52. O

FinnZ [79.3K]

Answer:

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1 year ago