Answer:
The total distance traveled by the particle is S = 30.
Step-by-step explanation:
Given that velocity,
v(t) = 2t + 1
To find the total distance travel, we integrate the velocity function, v(t), to obtain the distance function s(t), and evaluate the resulting distance at the interval given. That is at t = 0 to t = 5.
Integrating v(t) with respect to t, we have
s(t) = t² + t + C.
At t = 5
s(5) = 5² + 5 + C
= 25 + 5 + C
= 30 + C
At t = 0
S(0) = 0 + 0 + C
= C
The required distance is now
S(5) - S(0)
= 30 + C - C
= 30.
The formula for simple annual interest is:
I = Prt
where,
I = Interest accumulated = $910.90
P = Principal Amount = $62000
r = Interest rate = 9.4% = 0.094
t = time in years
Using the values in above equation, we get:
910.90 = 62000 x 0.094 x t
⇒ t = 910.90/(62000 x 0.094) = 0.156
This is the time in years. Since there are 365 days in a year, the time in days will be:
t = 0.156 x 365 = 57 (rounded to nearest day)
This means, Nate kept the borrowed money for 57 days
1. Divide wire b in parts x and b-x.
2. Bend the b-x piece to form a triangle with side (b-x)/3
There are many ways to find the area of the equilateral triangle. One is by the formula A=

A=

Another way is apply the formula A=1/2*base*altitude,
where the altitude can be found by applying the pythagorean theorem on the triangle with hypothenuse (b-x)/3 and side (b-x)/6
3. Let x be the circumference of the circle.

so

Area of circle =

4. Let f(x)=

be the function of the sum of the areas of the triangle and circle.
5. f(x) is a minimum means f'(x)=0
f'(x)=

=0



6. So one part is

and the other part is b-
Answer:
After simplifying we get (x,y) as (1,3).
Step-by-step explanation:
Given:
,

We need to use elimination method to solve the and simplify the equations.
Solution;
Let
⇒ equation 1
Also Let
⇒ equation 2
Now by solving the equation we get;
first we will Add equation 2 from equation 1 we get;

Now Dividing both side by 5 using division property of equality we get;

Now Substituting the vale of x in equation 1 we get;

subtracting both side by 1 using subtraction property of equality we get;

Now Dividing both side by 7 using division property of equality we get;

Hence we can say that, After simplifying we get (x,y) as (1,3).