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Ichiro throws a baseball with an initial speed of 145 feet per second at an angle of 20° to the horizontal.  The ball leaves Ichiro's hand at a height of 5 feet.

I am going to let gravity be 32 feet/sec^2

I am going to put this on a grid where the hand is at at the point (0,0)

So the ball will het the ground where y=-5

time is in seconds

Acceleration is in feet/sec^2

Velocity is in feet/sec

Displacement is in feet

(a)  Find parametric equations that model the position of the ball as a function of time.

Initial condition:

\(\ddot x=0\\ \dot x =145cos20\\ x=0\\~\\ \ddot y = -32\;feet/sec^2\\ \dot y = 145sin20\\ y =0 \\~\\ \)

\(Continuing\; equations:\\ \ddot x=0\\ \dot x =145cos20\\ x=(145cos20)t\\~\\ \ddot y = -32\\ \dot y = -32t+(145sin20)\\ y =-16t^2+(145sin20)t\\~\\ \mbox{So the parametric model of the position of the ball is}\\ x=(145cos20)t \qquad and \qquad y =-16t^2+(145sin20)t\)

Because the induction proof is FORMAL and i don't know why but formal proofs make you do that sorta crud. I'm actually doing those as we speak. Wish me luck :c

n is the variable in the question.

An example of a mathematical induction question is

For n > 1,  2 + 22 + 23 + 24 + ... + 2n = 2n+1 – 2

k is a specific integer.   That means    k is a constant.

So you

1) Show it is true for  n=1

2)  Then you assume it is true  for a specific integer and you let that integer be k        n=k

Using this assumption you prove it will be true fo the next integer  where n=k+1

3) Then you know that one integer that k could have been was 1 (that means it is true for n=1) and you have proven that if it is true for one ingeter it must be true for the next so it will be true for n=2, n=3 etc.

So although it is a bit confusing, n and k are not exactly the same thing.   n is a varable and k is a constant.

The expression cannot be simplified  :)

Hi Adonai,

Welcome to the web2.0calc forum.

If the question is too simple, or it can be answered obviously on any calculator, is is best totally ignore the question. This is also true if the post is offensive for any reason. 

If the question is unclear it is best to say so. If you want to guess what was meant you can answer afterwards:)

Let the cost of Hotel per night=n
Let the cost of car rental per day=r
3n + 4r =675
4n + 5r =875

Solve the following system:
{3 n+4 r = 675 |     (equation 1)
4 n+5 r = 875 |     (equation 2)
Swap equation 1 with equation 2:
{4 n+5 r = 875 |     (equation 1)
3 n+4 r = 675 |     (equation 2)
Subtract 3/4 × (equation 1) from equation 2:
{4 n+5 r = 875 |     (equation 1)
0 n+r/4 = 75/4 |     (equation 2)
Multiply equation 2 by 4:
{4 n+5 r = 875 |     (equation 1)
0 n+r = 75 |     (equation 2)
Subtract 5 × (equation 2) from equation 1:
{4 n+0 r = 500 |     (equation 1)
0 n+r = 75 |     (equation 2)
Divide equation 1 by 4:
{n+0 r = 125 |     (equation 1)
0 n+r = 75 |     (equation 2)
Collect results:
Answer: |  n = $125               and                 r=$75
 

This graph shows the exponential rise in balance on an initial investment of $1,500 over 25 years at 5% APR. After 10 years about how much interest has the

How much compound interest will an account of $12,000 bear after 6 years at 3.2% APR, compounded annually

Your question is incomplete. However, the total interest earned on $1,500 @ 5% APR after 10 years will be=$2,443.34 - $1,500 =$943.34

The interest on $12,000 @ 3.2% APR after 6 years will be:

$14,496.38 - $12,000 =$2,496.38

2, 2sqrt19, 10sqrt 19, and the last can't be simplified. 

I think you mean 10.8666667124646806=sqrt163

You would need a z-score of approximately 0.842 to separate the top 20% from the bottom 89%.

0.842  =  (z - 85)/5     --->     z > 89

So what are you solving for? If x is a variable and it doesn't equal anything specific the answers are limitless.

X is a variable with some value 

What does x equal?

Ok so so we have 3/8 divide by -2. We know that dividing by a number is the same as multiplying by the reciprocal. Therefore we can rewrite it as 3/8*-1/2, which is much easier to see is -3/16. 

See this very good video:https://www.youtube.com/watch?v=UXHUih_YVEE  

-1/16

can any one help

Hello Guest!

Calculate the force due to gravitational attraction between the Earth and the spacecraft in N.

The Earth's radius is 6370 km.

The orbital radius is r = 6370 km + 270 km = 6640 km away.

The mass of the spacecraft is 2400 kg.

The gravitational acceleration g = 9.81 m/s²

The acceleration of gravity is in 270 km altitude a = 9,02875 m / s²

F = m v² / r

F = m a

m v² / r = m a

v² = r a

F = m * r * a / r

F = 2400 kg * 9.02875 m / s²

F = 21669 (kgm/s²)*(Ns²/kgm)

F = 21669 N

v = √(rg) = √(6 640 000 m * 9.02875 m/s²)

v = 7742.797 m / s

The satellite is drawn with 21669 N center of the earth.
The centrifugal force is equal, namely 21669 N.

It flies at a speed of 7742.797 m/s around the earth.

Greetings asinus :- )

 !

Use Newton's famous gravitational formula: F=G.M.m/r^2

F=[6.67E-11 x 5.97E24 x 2400] /[6,371,000+270,000]^2

F=21,669.28 newtons-gravitational force on the spacecraft at 270 km above Earth's surface.

5 + 2/3X = 2X

5 = 2X - 2/3 X

5 = 4/3 X

multiple both sides by 3/4

x = 15/4 = 3 3/4

at least I don't THINK I'm a robot!

Let's suppose that it could be....then

5√9 = 5*3  = 15.........and this must mean that.....

15 = √45       square both sides

225  = 45     and this clearly isn't true

use the slope-intercept formula

it is m=y2-y1

            x2-x1

For example (6,5) and (11,10)

take the second y-value and subtract it from the first y-value and do the same with the x-values

y-values: 10-5=5

x-values: 11-6=5                                                        5

Then make it a fraction from the top and the bottom 5 which equals 1

Distance =

√ [ ( 10 - 4)^2 + ( 13 - 5)^2 ]    = √ [ 6^2 + 8^2 ]  = √ [36 + 64]  = √100  = 10 units