Given: 3y cos x = x² + y²
Define
Then by implicit differentiation, obtain
3y' cos(x) - 3y sin(x) = 2x + 2y y'
y' [3 cos(x) - 2y] = 2x + 3y sinx)
Answer:
To add these amounts together, we must first find their least common multiple in order to get common denominators (b/c when you add fractions, the denominators must be the same).
We'll start by listing some of their multiples.
To do this, count by whatever the denominator is:
4 1/2 (denominator is 2): 2 4 6 8 10 12 14
2 1/4 (denominator is 4): 4 8 12 16
6 1/3 (denominator is 3): 3 6 9 12 15
Look and see which is the first multiple that all three denominators have. Circle them if it helps you. In this case, it's 12.
So now we have to multiply the denominators by whatever number it takes to reach 12, and multiply by the same number to the numerator:
4 1/2 (times 6 to both top and bottom) =
4 6/12
2 1/4 (times 3) = 2 3/12
6 1/3 (times 4) = 6 4/12
Add all these fractions together, and you get 12 13/12, which is equal to 13 1/12.
Thus, Peter makes a total of 13 1/2 cups.
Hope this made sense! tell me if anything is confusing/incorrect :))
Answer:
x + 8
Step-by-step explanation:
-4(x - 2) + 5x = 0
-4x + 8 + 5x = 0
<em><u>x + 8 = 0</u></em>
Given recursive formula is
f(n) = 22 * f(n - 1)
Where first term : f(1) = 10
And we need to find the first five terms of this sequence. So , let's find the second term by plug in n = 2 in the above formula. Therefore,
f (2) = 2.2 * f ( 2 -1)
= 2.2 * f(1)
= 2.2 * 10
= 22
So second term is 22.
Similarly plug in 3 for n to get the third term. Hence,
f(3) = 2.2 * f(3 -1) = 2.2 * f(2) = 2.2 * 22= 48.4
f(4) = 2.2 *f( 4 -1) = 2.2 * f(3) = 2.2* 48.4 = 106.48
f(5) = 2.2* f(5-1)= 2.2 * f(4) = 2.2 * 106.48 = 234.256
So, the first five terms are 10, 22, 48.4, 106.48 and 234.256.
Hope this helps you!
