1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
soldi70 [24.7K]
3 years ago
7

Work out the length x. 4.5 cm 11 cm

Mathematics
1 answer:
Effectus [21]3 years ago
5 0

Answer:

12.3

Step-by-step explanation:

A^2 + B^2 = C^2

11^2 + 4.5^2 = C^2

132 + 20.25 = C^2

152.25 = C^2

Square root of 152.25 = 12.3

You might be interested in
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
Kayla drives 15 miles in 20 minutes. If she drove one hour in total at the same rat how far did she go? Before you try that prob
alisha [4.7K]

Answer:

Kayla drove 45miles

5 0
3 years ago
Read 2 more answers
What type of triangle is triangle ABC?<br> Give reason for your answer.
Liono4ka [1.6K]
The triangle has two equal sides and two equal angles :)
3 0
2 years ago
When Denine gets home, she wants to make a model of the pyramid she saw on a tour. The base of the pyramid is about 230 meters w
sammy [17]

Answer:

it would be about 63.44..

Step-by-step explanation:

you can do 230/87=24/x where x is the new height, when you cross multiply and divide, x should be about 63

5 0
3 years ago
Read 2 more answers
Help please <br>3/11 × 4/9 =​
dedylja [7]

Answer:

4/33

Step-by-step explanation:

Multiply 3x4 across which equals 12

Multiply 11x9 across which equals 99

Simplify to equal 4/33

Hope this helps!! :)

7 0
3 years ago
Read 2 more answers
Other questions:
  • Triangle PQR is transformed to similar triangle P’Q’R’:
    8·1 answer
  • Please help me find the value of x and show and explain work
    9·2 answers
  • Antwon makes hot chocolate by mixing 2 cups of milk with 5 tablespoons of cocoa.
    13·2 answers
  • A store offers packing and mailing services to customers. The cost of shipping a box is a combination of a flat
    5·1 answer
  • Which list shows all the positive factors of 24​
    9·1 answer
  • -12 - 5x^2 + 2x^4 =0
    10·1 answer
  • fivestar farm purchased 2400 apple trees. If 80 trees can be planted on each acre of land, how many acres will be needed to plan
    12·1 answer
  • A debt payment of $5,500 is due in 27 months. If money is
    10·1 answer
  • Please answer, I desperately need your help! There's a great reward in store if you prove yourself to be of assistance!
    7·1 answer
  • You are at a grocery store and the cost of your groceries is $32.75. You need to add the sales tax, which is 6%. You have one $2
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!