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3 years ago

Which equation represents the general from circle w

Mathematics

1 answer:

aev [14]3 years ago

8 0

$d. \: {x}^{2} + {y}^{2} - 4x - 6y - 3 = 0 \\ \\ x = 2 + \infty \sqrt{(y - 7)(y + 1)} 2 - \infty \sqrt{(y - 7)(y + 1)}$

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3 years ago

Lowering powers write in terms of first power of cosine. Cos^6

yaroslaw [1]

The main identity you need is the double angle one for cosine:

$\cos^2x=\dfrac{1+\cos2x}2$

We get

$\cos^6x=(\cos^2x)^3=\left(\dfrac{1+\cos2x}2\right)^3=\dfrac{(1+\cos2x)^3}8$

Expand the numerator to apply the identity again:

$\cos^6x=\dfrac{1+3\cos2x+3\cos^22x+\cos^32x}8$

$\cos^6x=\dfrac{1+3\cos2x+3\left(\frac{1+\cos2(2x)}2\right)+\cos2x\left(\frac{1+\cos2(2x)}2\right)}8$

$\cos^6x=\dfrac{1+3\cos2x+\frac32+\frac32\cos4x+\frac12\cos2x(1+\cos4x)}8$

$\cos^6x=\dfrac5{16}+\dfrac7{16}\cos2x+\dfrac3{16}\cos4x+\dfrac1{16}\cos2x\cos4x$

Finally, make use of the product identity for cosine:

$\cos2x\cos4x=\dfrac{\cos6x+\cos2x}2$

so that ultimately,

$\cos^6x=\dfrac5{16}+\dfrac7{16}\cos2x+\dfrac3{16}\cos4x+\dfrac1{32}\cos2x+\dfrac1{32}\cos6x$

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4 years ago

HELP ASAP TEST IS OMOST OVER!!!!!!!!!!

svet-max [94.6K]

Answer: C)46 ft

Step-by-step explanation:

We know that the circumference of a circle can be calculated with this formula:

$C=2\pi r$

Where "r" is the radius of the circle.

Since John is putting a fence around his garden that is shaped like a half circle and a rectangle, then we can find how much fencing he needs by making this addition:

$Fencing=\frac{2\pi r}{2}+2l+w$

Where "l" is the lenght of the rectangle and "w" is the width of the rectangle.

Since we know that the radius of the circle is half its diameter, we can find "r". This is:

$r=\frac{7ft}{2}=3.5ft$

Then, substituting values (and using $\pi=\frac{22}{7}$ ), we get:

$Fencing=\frac{2(\frac{22}{7})(3.5ft)}{2}+2(14ft)+7ft=46ft$

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3 years ago

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