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Wewaii [24]
3 years ago
11

Please show your work. Thanks

Mathematics
1 answer:
Vika [28.1K]3 years ago
8 0

Answer:

Step-by-step explanation:

7√3-4√6+√48-√54

=7√3-4√6-√(16×3)-√(9×6)

=7√3-4√6-4√3-3√6

=3√3-7√6

You might be interested in
HELP ME PLEASEEEEE PLEASEEEEE
viktelen [127]

Answer:

5.46π cm³

Step-by-step explanation:

Volume of sphere= 4/3πr³

= 4/3×π×(1.6)³ cm³

=5.46π cm³

hope this helped you!

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
There’s also D <br><br> D: 4m on top and 4m on the side
Wewaii [24]

B hope this helped have a nice day! =D

Oh yes 4x5 is another answer so yep god I forgot that sorry!

4 0
3 years ago
Read 2 more answers
The tigers won 12 games last year.this year the tigers won 20 games. What is the percent increase in the number of games the tig
sergejj [24]
Its is 60% because 12/20 is 60%

4 0
4 years ago
A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 449 gram setting. It is
stealth61 [152]

Answer:

We accetp  H₀

Step-by-step explanation:

Information:

Normal distribution  

Population mean      =   μ₀  = 449

Population standard deviation  σ   unknown

Sample size   n  =  23        n < 30    we use t-student test

so   n  =  23    degree of fredom   df = n  - 1  df  = 23- 1   df = 22

Sample mean    μ =  448

Sample standard deviation   s  =  20

Significance level  α  =  0,05  

1.-Hypothesis Test

Null hypothesis                               H₀     μ₀  =  449

Alternative hypothesis                    Hₐ     μ₀  ≠  449

Problem statement ask for determine decision rule for rejecting the null hypothesis. For rejecting the null hypothesis we have to  get an statistic parameter wich implies  that μ is bigger or smaller than μ₀

2.-Significance level   α  =  0,05  ;  as we have a two tail test

α/2    =  0,025

Then from t - student table for  df =  22   and 0,025 (two tail-test)

t(c)  =  ±  2.074

3.- Compute  t(s)

t(s)   =  (  μ  -  μ₀ )  /  s /√n

plugging in values

t(s)   =  (448  -  449) /  20 /√23    ⇒   t(s)   =  -  1*√23 /20

t(s)   =  - 0.2398

4.-Compare t(c)   and  t(s)

t(s)  <  t(c)         - 0.2398  <  - 2.074

Therefore  t(s)  in inside acceptance region.  We accept  H₀

7 0
4 years ago
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