Answer:
∫
= 
Step-by-step explanation:
To find:
∫
Solution:
Method of substitution:
Let 
Differentiate both sides with respect to 
[use 
]
So,
∫ = ∫ 
= 
where 
is a variable.
(Use ∫
)
Put 
∫ = 
Use 
So,
∫ = 
where 
Without using substitution:
∫ = ∫
= 
So, same answer is obtained in both the cases.
1) Answer: 21
As y varies directly with x, this means that the ratio y/x is always a constant.
In other words, the equation can be written as y = kx, where k is a constant term.
Thus,
y = 21
2) Answer: C
Exactly the same process as above.
Here's another method:
25 = k(140)
k = 25/140 = 5/28
Thus, when y = 36, 36 = kx
36 = 5/28(x)
36 * 28/5 = x; x = 201.6
3) 9 = k(12)
9/12 = k and k = 3/4
4) On the graph, it hits y = 1 at x = 4.
Thus, we can rewrite the equation as:
y = (1/4)x, where the constant term is 1/4
5) y = kx
The distance represents the x-ordinates, and the time represents the y-ordinates.
9.5/475 = 0.02
4 = 0.02(x), in hours.
x = 200 miles.
-6-7(c+10)
-6-7c-70
-76-7c
B
If each inch is 40 miles then 7(40) = 280 and add the 1/4 which is 10 so the answer is 290
Interest = PRT/100
Compound interest = P(1 + (R/100))^T
Where P = Principle ( amount )
R = Rate
T = Time
Since the time is only 1 year, the answer will be the same for both interest and compound interest formulae.
∴ 4000(2)(1)/100 =$80 (This is the interest value)
Note if question ask you what is the total amount after x years, be sure to add the interest with the principle.
