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Blababa [14]
3 years ago
10

Which angle of rotation is determined by the matrix below?{1/2 -sqrt3/2 sqrt3/2 1/2] 30° 60° 120° 300°

Mathematics
1 answer:
strojnjashka [21]3 years ago
3 0

Answer:

  60°

Step-by-step explanation:

You have the rotation matrix ...

  \left[\begin{array}{cc}\cos{\theta}&-\sin{\theta}\\\sin{\theta}&\cos{\theta}\end{array}\right]=\left[\begin{array}{cc}\dfrac{1}{2}&-\dfrac{\sqrt{3}}{2}\\\dfrac{\sqrt{3}}{2}&\dfrac{1}{2}\end{array}\right]

This tells you the angle of rotation is ...

  \tan{\theta}=\dfrac{\sin{\theta}}{\cos{\theta}}=\dfrac{\left(\dfrac{\sqrt{3}}{2}\right)}{\left(\dfrac{1}{2}\right)}=\sqrt{3}\\\\\theta=\arctan{\sqrt{3}}=60^{\circ}

The angle of rotation is 60°.

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A certain number divided by 4 equals 6. Find the number.<br> Let n = the number.
Elena L [17]
N=24
You can find the answer by doing inverse operations.
Multiply 6 and 4 and you will get 24.
To double check, you can do 24 divided by 4 and you will get 6. Hope this helped
6 0
3 years ago
Read 2 more answers
Zoe has 1500 beads. She wants to make 6 friendship bracelets. She needs 215 beads for each bracelet. How many beads will Zoe hav
drek231 [11]
First you would need to find out how many beads are needed for the bracelets.

215 beads per bracelet x 6 bracelets = 1290 beads

This tells us that to make all 6 bracelets, it will use up 1290 beads, now subtract that from your total number of beads.

1500-1290= 210

So Zoe will have 210 beads left over. Since this is a word problem, it is best to answer it in the same format:

Zoe will use 1290 beads to make 6 friendship bracelets. After all of the bracelets are made, she will have 210 beads left over.

hope this helps!
3 0
3 years ago
Evaluate the function f(-2) - h(4) given the following functions: f(x) = 4x​ 2​+ 9 h(x) = 3x - 14
Goryan [66]

Answer:

-86

Step-by-step explanation:

simplify each equation as much as possible

f(x)= 4x(2+9) add

4x(11) multiply

f(x)=44x

substitute given numbers into each equation

44(-2)=-88                3(4)-14= 12-14=-2

combine equations

-88-(-2)= -86   add since you are subtracting a negative number

4 0
3 years ago
If a car can travel 250 miles on 10 gallons of fuel, how many gallons are required to travel 1,325 miles?
Varvara68 [4.7K]
1325                      250
-------          =        -------      
    x                           10

1325(10) = 250x

13250/250 = 250x/250

x = 53 

53 gallons are required to travel 1325 miles

hope this helps

8 0
4 years ago
What is 144/36 simplified?
NARA [144]
144/36 in lowest terms is 4.


To show my work, here.


1. Find the GCF of 144 and 36 so now we divide (144/36 = 4 and 36/36 is 1)

2. Now we have 4/1 so we simplify again so divide 4/1 and its 4
7 0
4 years ago
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