Answer: c
Step-by-step explanation:
Answer:
6(x+5)
Step-by-step explanation:
Answer:
∫ C ( y + e√x) dx + ( 2x + cosy² ) dy = 1/3
Step-by-step explanation: See Annex
Green Theorem establishes:
∫C ( Mdx + Ndy ) = ∫∫R ( δN/dx - δM/dy ) dA
Then
∫ C ( y + e√x) dx + ( 2x + cosy² ) dy
Here
M = 2x + cosy² δM/dy = 1
N = y + e√x δN/dx = 2
δN/dx - δM/dy = 2 - 1 = 1
∫∫(R) dxdy ∫∫ dxdy
Now integration limits ( see Annex)
dy is from x = y² then y = √x to y = x² and for dx
dx is from 0 to 1 then
∫ dy = y | √x ; x² ∫dy = x² - √x
And
∫₀¹ ( x² - √x ) dx = x³/3 - 2/3 √x |₀¹ = 1/3 - 0
∫ C ( y + e√x) dx + ( 2x + cosy² ) dy = 1/3
Answer: b.14
Step-by-step explanation:
We have two shelves, the top shelf
and the bottom shelf
.
Now, firstly we are told the top shelf has 10 more than 1/3 the number of books on the bottom shelf. This can be expressed as:
(1)
Then, we are told there are 12 books on the bottom shelf:
(2)
Substituting (2) in (1):
(3)
(4)
(5) This is the number of books on the top shelf
Hence, the correct option is b.
The best thing to do is to rewrite the fractions as decimals
-2/3 is approx. equal to -0.6666667
So a little past half way (to the left) between -1 and 0
1 1/5 is 1.5 so that is right between 1 and 2
Hope this helps :)