Which equation describes the relationship between the values in the table?

A rectangular floor is 21 ft long and 12ft wide. Reuben wants to carpet the floor with carpet tiles sold by the square yard. Use

zmey [24]

1 yard = 3 feet:

21 feet / 3 ft = 7 yards

12 feet / 3 feet = 4 yards

7 x 4 = 28 square yards

he will need 28 tiles

6 0

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

Plzzzzzzzz helppppp meeeeeeee

andriy [413]

The rectangle has an area of 18x8 = 144 sq in. The circle has an area of (pi)r^2 or (pi)3^2 =28.27sq in. Subtract 144 - 28.27 = 115.73

3 0

3 years ago

Find the measure of DB (a curvy line is on top of DB btw)

klasskru [66]

Answer:

Arc DB = 146

x = 5

Step-by-step explanation:

Remark

The relationship between the large arc, the small arc and the intersecting angle is

1/2 (large arc - small arc) = intersecting angle.

Givens

Large arc = 25x + 21

Small arc = 96

5x

Solution

1/2*(25x + 21 - 96) = 5x*2 Multiply both sides by 2

25x + 21 - 96 = 10 x Combine

25x - 75 = 10x Subtract 25x from both sides

-75 = 10x - 25x

-15x = -75

x = 5

DB = 25x + 21

DB = 25*5 + 21

DB = 125 + 21

DB = 146

Tell me if this is not in the choices.

5 0

3 years ago

Amani purchased a prepaid phone card for $15. Long distance calls cost 19 cents a minute using this card. Amani used her card on

Iteru [2.4K]

Subtract the balance from the original amount:

15 - 12.34 = 2.66

Now divide the amount spent by price per minute:

2.66 / 0.19 = 14

The call lasted 14 minutes.

7 0

3 years ago