## 20 Reputation

10 years, 189 days

## Infinite series and Pi Approximation....

The value of Pi can be approximated by the infinite series 4-(4/3)+(4/5)-(4/7)+(4/9)-(4/11)+... . Write a procedure that takes as an input the integer n and uses a for-loop to return the decimal point approximation of using the nth partial sum of the infinite series. Determine the minimum value of n that gives the true value of to 5 decimal places.

the 99 bottles of beer on the wall for loop is alot easier than this one. can some one walk me through it? i only have a general idea how to implement it.

## introduction into loops....

im having issues with a problem on my homework. we are supposed to find all primes between 1000 through 1015. using the for loop, for in loop and while loop.

the while loop seemed the easiest.

i:=1000;
1000
while i<=1015 do
i, "Is it a prime?", isprime(i);
i:=i+1;
end;

the for loop and the for in loop have gotten me abit comfused ive tried several times with each and nothing.

## Optimization hw 02 help...

question 2 of my homework is actually abit more simple imo. i think i performed all the operations correctly but however my 3dplot shows just a flat plane. i dont think thats right. if someone could take a look at my code in reference to this question. it would be great.

Suppose that a baseball is hit from 5 feet off of the ground with an initial velocity of 40 feet per second at an angle of above the horizontal. Let the horizontal and vertical components of the position, velocity, and acceleration be denoted respectively by and . Assume that the only acceleration is due to gravity (i.e, ).

a) If , plot the parametric equations over the time period that the ball is in the air.

b) Clear in maple by typing theta:='theta'; Now, suppose that we write in Cartesian form by solving for t: t:=solve(rx=x,t); Typing in ry should now yield a function that involves only x and . Make a 3-dimensional plot of for ,

ax:=0;ay:=-32;
0
-32
vx:=int(ax,t)+C1;
C1
vy:=int(ax,t)+C2;
C2
v0:=40;
40
theta:=Pi/3;
1
- Pi
3
C1:=solve(subs(t=0,vx)=v0*cos(theta),C1);
20
C2:=solve(subs(t=0,vy)=v0*sin(theta),C2);
(1/2)
20 3
vx; vy;
20
(1/2)
20 3
rx:=int(vx,t)+C3;
20 t
ry:=int(vy,t)+C4;
(1/2)
20 3 t + 5
C3:=solve(subs(t=0,rx)=0,C3);
0
C4:=solve(subs(t=0,ry)=5,C4);
5

ry;
(1/2)
20 3 t + 5
plot([rx, ry, t = 0 .. infinity]);

## Optimization Homework Help...

Maple 16

I want to begin by saying hello! im new to the forums i hope some one can give me a push in the right direction with some of my maple homework. im sort of stuck on a few of these questions and would be greatfull for some help.

Let .

a) Let g be the tangent line to f when x = c. Use Maple to find g as a function of c.

b) Use Maple to plot f and g(3) using view = [0..5, -25..100].

c) Define a function called plot_tan that plots both f and g(c) where f is blue and g(c) is red. Also use the same view as in part (b). Note that plot_tan is also a function of c.

d) Using your function plot_tan, the following all in one graph using the display command:

plot_tan(1), plot_tan(1.5), plot_tan(2), plot_tan(2.5), plot_tan(3), plot_tan(3.5), plot_tan(4), plot_tan(4.5), plot_tan(5).

e) Try using the option insequence = true in the display command. What does this option do? (You will need to click on the graph and play around with some buttons).

now it seems to me i have to use the point slope formula to get to a fuction g of c. thanks in advance! i hope you can help

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