She added 64 grams which is 34 grams less than Wat was needed
Answer:
![\sqrt[n]{a} =a^{\frac{1}{n}}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Ba%7D%20%20%3Da%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D)
Explanation:
Roots of real numbers can be represented by <em>radicals</em> or by<em> exponents. </em>
First, I present some examples to show how exponents and radicals are related, and then generalize.
![\sqrt[3]{8}=(8)^{\frac{1}{3}}=(2^3)^{\frac{1}{3}}=(2)^{\frac{3}{3}}=2^1=2](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B8%7D%3D%288%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%3D%282%5E3%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%3D%282%29%5E%7B%5Cfrac%7B3%7D%7B3%7D%7D%3D2%5E1%3D2)
When you write 5² = 25, then 5 is the square root of 25.
And in general, if n is a positive integer and 
, then 
is the nth root of x.
Also, if n even (and positive) and is positive, then 
is the positive nth root of
Thus,
We are going to prove it like this:
Lets use the formula sinA+sinB=2sin(A+B/2)cos(A-B/2)
Now we are going to take the left side of equation
sin10+sin40+sin50+sin20
Arranging
=(sin50+sin10)+(sin40+sin20)
Applying the above formula.
=2sin(50+10/2)cos(50-10/2)+2sin(40+20/…
=2sin(30)cos(20)+2sin(30)cos(10)
=2sin30{cos20+cos10}
Again using the formula
cosA+cosB= 2cos(A+B/2)cos(A-B/2)
=2sin30{2cos(20+10/2).cos(20-10/2)}
=2sin30{2cos(15).cos(5)}
=2(1/2){2cos15.cos5} as sin30=1/2
=2cos15.cos5
Taking right side of equation
sin70+ sin80
Using the formula
sinA+sinB
= 2sin(A+B/2)cos(A-B/2)
=2sin(70+80/2)cos(70-80/2)
=2sin75cos5
=2sin(90-15)cos5
=2cos15.cos5
<span>Hope this helps</span>
Answer: x = 7
Step-by-step explanation: All the angles of a parallelogram add to 360°
Any two of the consecutive angles add to 180°
Using that information, we can create an equation with the angle measurements given:
(7x + 33) + (11x + 21) = 180 . Combine like terms:
7x + 11x + 33 + 21 =180
18x + 54 = 180 . Subtract 54 from both sides
18x = 126 Divide both sides by 18
x = 7
