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VLD [36.1K]
3 years ago
10

Simplify. (2 x 108) + (4 * 103) Give the answer in scientific notation

Mathematics
1 answer:
lions [1.4K]3 years ago
6 0

Answer:

628

Step-by-step explanation:

216+412 = 628

First you get rid of the brackets by solving what's in them. Then you just add up the numbers and BOOM. The equation is solved. :-)

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One side of a square is 8 centimeters long what is the area
Leni [432]
A= b(h)
a= 8(8)
a= 64cm^2
5 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
What is 1/10 + 50/100?
erastovalidia [21]

Answer:

\large\boxed{\dfrac{3}{5}=0.6}

Step-by-step explanation:

\bold{METHOD\ 1:}\\\\\dfrac{1}{10}+\dfrac{50}{100}=\dfrac{1}{10}+\dfrac{50\!\!\!\!\diagup}{100\!\!\!\!\diagup}=\dfrac{1}{10}+\dfrac{5}{10}=\dfrac{1+5}{10}=\dfrac{6}{10}=\dfrac{6:2}{10:2}=\dfrac{3}{5}\\\\\bold{METHOD\ 2:}\\\\\text{Convert the fractions to decimal:}\\\\\dfrac{1}{10}=0.1\\\\\dfrac{50}{100}=0.50=0.5\\\\\dfrac{1}{10}+\dfrac{50}{100}=0.1+0.5=0.6

4 0
4 years ago
Pls i need HeLp<br><br>13 + 7 to the 2nd power ÷7<br>______________________<br>9 - 20 ÷ 4 +16​
FromTheMoon [43]

Answer:

1

Step-by-step explanation:

By using Order of Operations, or Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction, or (PEMDAS) for short.

4 0
3 years ago
You download a video game to your computer. You have a 60 minute free trial of the game. It takes 5 minutes to set up the game a
den301095 [7]

Answer:

You can play 7 full levels for free.

Step-by-step explanation:

60-5= 55 minutes left to play

55/7=7.857

So.... 7 full levels for free

4 0
3 years ago
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