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2 years ago

I do not understand this problem

Mathematics

1 answer:

Vesnalui [34]2 years ago

4 0

Answer:

16c² + 32cd + 16d²

Step-by-step explanation:

A polynomial is an expression consisting of variables and coefficients. For example, $4x^3+3x^2+6x-4$ is an example of a cubic polynomial.

Area of a square = side length x side length

Therefore, given the side length of this square is 4c + 4d, then the area can be expressed as:

area = (4c + 4d) x (4c x 4d) = (4c + 4d)²

If we expand the brackets we get:

area = 16c² + 32cd + 16d²

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The median would decrease because the temperature given is lower than the median

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3 years ago

Which expression has a value of 31?

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Answer:

d. Is the answer from this question

Step-by-step explanation:

3(5+7)-5

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3 years ago

Which of these demonstrates the identity property of multiplication

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Step-by-step explanation:

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3 years ago

Sin(x)^4+ cos(x)^4=1/2

posledela

I'll assume that what was meant was $\sin ^4 x + \cos ^4 x = \dfrac{1}{2}$ .

The exponent in the funny place is just an abbreviation: $\sin ^4 x = (\sin x)^4$ .

I hope that's what you meant. Let me know if I'm wrong.

Let's start from the old saw

$\cos^2 x + \sin ^2x = 1$

Squaring both sides,

$(\cos^2 x + \sin ^2x)^2 = 1^2$

$\cos^4 x + 2 \cos ^2 x \sin ^2x +\sin ^4x = 1$

$\cos^4 x + \sin ^4x = 1 - 2 \cos ^2 x \sin ^2x$

So now the original question

$\sin ^4 x + \cos ^4 x = \dfrac{1}{2}$

becomes
$1 - 2 \cos ^2 x \sin ^2x = \dfrac{1}{2}$

$4 \cos ^2 x \sin ^2x = 1$

Now we use the sine double angle formula

$\sin 2x = 2 \sin x \cos x$

We square it to see

$\sin^2 2x = 4\sin^2 x \cos^2 x = 1$

Taking the square root,

$\sin 2x = \pm 1$

Not sure how you want it; we'll do it in degrees.

When we know the sine of an angle, there's usually two angles on the unit circle that have that sine. They're supplementary angles which add to $180^\circ$ . But when the sine is 1 or -1 like it is here, we're looking at $90^\circ$ and $-90^\circ$ , which are essentially their own supplements, slightly less messy.

That means we have two equations:

$\sin 2x = 1 = \sin 90^\circ$

$2x = 90^\circ + 360^\circ k \quad$ integer $k$

$x = 45^\circ + 180^\circ k$

or

$\sin 2x = -1 = \sin -90^\circ$

$2x = -90^\circ+ 360^\circ k$

$x = - 45^\circ + 180^\circ k$

We can combine those for a final answer,

$x = \pm 45^\circ + 180^\circ k \quad$ integer $k$

Check. Let's just check one, how about

$x=-45^\circ + 180^\circ = 135^\circ$

$\sin(135)= 1/\sqrt{2}$

$\sin ^4(135)=(1/\sqrt{2})^4 = 1/4$

$\cos ^4(135)=(-1/\sqrt{2})^4 = 1/4$

$\sin ^4(135^\circ) +\cos ^4(135^\circ) = 1/2 \quad\checkmark$

6 0

3 years ago

Miller's Bank is offering a new certificate of deposit (CD) with daily compounding and an annual interest rate of 4.65% for a te

ladessa [460]

Answer:

$20,086.35

Step-by-step explanation:

To calculate the maturity value by compound interest, we will use the formula

$A=P(1+\frac{r}{n})^{nt}$