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3 years ago

3√2 times 8√8 rational or no

Mathematics

1 answer:

Dmitriy789 [7]3 years ago

4 0

Answer:

Yes.

Step-by-step explanation:

3√2 times 8√8 can be simplified into 24√16.

Since 16 is a perfect square, you can simplify this into: 24*4 = 96.

So the product will be 96.

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John ran the 100-m dash with a time of 9.81 sec. if this pace could be maintained for an entire 26-mi marathon, what would his t

Dmitry_Shevchenko [17]

Answer:

4104.79 Seconds or about 1.14 Hours

Step-by-step explanation:

26mi = 41842.9m

100/9.81 = 41842.9/x

41842.9 x 9.81 = 100x

410478.849 = 100x

x = 4104.78849

7 0

3 years ago

Solve the equation for all real values of x.<br> cosxtanx - 2 cos x=-1

IceJOKER [234]

Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

<u>Step-by-step explanation:</u>

Here we have , $cosxtanx - 2 cos^2 x=-1$ . Let's solve :

⇒ $cosxtanx - 2 cos^2 x=-1$

⇒ $cosx(\frac{sinx}{cosx}) - 2 cos^2 x=-1$

⇒ $sinx = 2 cos^2 x-1$

⇒ $sinx = 2 (1-sin^2x)-1$

⇒ $sinx = 1-2sin^2x$

⇒ $2sin^2x+sinx-1=0$

By quadratic formula :

⇒ $sinx = \frac{-b \pm \sqrt{b^2-4ac} }{2a}$

⇒ $sinx = \frac{-1 \pm \sqrt{1^2-4(2)(-1)} }{2(2)}$

⇒ $sinx = \frac{-1 \pm3}{4}$

⇒ $sinx = \frac{1}{2} , sinx =-1$

⇒ $sinx = sin\frac{\pi}{6} , sinx = sin\frac{3\pi}{2}$

⇒ $x=\frac{\pi}{6} , x=\frac{3\pi}{2}$

But at $x=\frac{3\pi}{2}$ we have equation undefined as $cos\frac{3\pi}{2}=0$ . Hence only solution is :

⇒ $x=\frac{\pi}{6}$

Since , $sin(\pi -x)=sinx$

⇒ $x=\pi -\frac{\pi}{6} = \frac{5\pi}{6}$

Now , General Solution is given by :

⇒ $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$

Therefore , Solution to equation $cosxtanx - 2 cos^2 x=-1$ for all real values of x is $x=2k\pi + \frac{\pi}{6} , x=2k\pi + \frac{5\pi}{6}$ .

3 0

3 years ago

The graph of which function(s) will contain the point (3, 6)?

alekssr [168]

The first and third one

5 0

3 years ago

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Express 30 as a product of its prime factors

Olegator [25]

Answer:

5 * 3 * 2

Step-by-step explanation:

15 * 2

5 * 3 * 2

3 0

2 years ago

Read 2 more answers

Jane brought x shirts for $20 each and y skirts for $25 each she spent $210 in all. which equation represents this situation 2

miv72 [106K]

Answer:

Part A

20x + 25y = 210 --> D.

Part B

If jane purchased exactly 4 shirts she must have purchased Exactly ___ skirts. (round to the nearest tenth)

20*4 + 25y = 210 --> y = 5.2

is it possible for jane to purchase exactly 4 shirts? ____(yes or no)

no, because she can't buy 5.2 skirts.

5 0

3 years ago

Read 2 more answers