Lucas has a bag that contains 11

A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 29 ft/s. Its height

Ilia_Sergeevich [38]

Answer:

$\overline{v}_{@\Delta t=0.01s}=-15.22ft/s, \overline{v}_{@\Delta t=0.005s}=-15.11ft/s, \overline{v}_{@\Delta t=0.002s}=-15.044ft/s, \overline{v}_{@\Delta t=0.001s}=-15.022ft/s$

Step-by-step explanation:

Now, in order to solve this problem, we need to use the average velocity formula:

$\overline{v}=\frac{y_{f}-y_{0}}{t_{f}-t_{0}}$

From this point on, you have two possibilities, either you find each individual $y_{f}, y_{0}, t_{f}, t_{0}$ and input them into the formula, or you find a formula you can use to directly input the change of times. I'll take the second approach.

We know that:

$t_{f}-t_{0}=\Delta t$

and we also know that:

$t_{f}=t_{0}+\Delta t$

in order to find the final position, we can substitute this final time into the function, so we get:

$y_{f}=29(t_{0}+\Delta t)-22(t_{0}+\Delta t)^{2}$

so we can rewrite our formula as:

$\overline{v}=\frac{29(t_{0}+\Delta t)-22(t_{0}+\Delta t)^{2}-y_{0}}{\Delta t}$

$y_{0}$ will always be the same, so we can start by calculating that, we take the provided function ans evaluate it for t=1s, so we get:

$y_{0}=29t-22t^{2}$

$y_{0}=29(1)-22(1)^{2}$

$y_{0}=7ft$

we can substitute it into our average velocity equation:

$\overline{v}=\frac{29(t_{0}+\Delta t)-22(t_{0}+\Delta t)^{2}-7}{\Delta t}$

and we also know that the initil time will always be 1, so we can substitute it as well.

$\overline{v}=\frac{29(1+\Delta t)-22(1+\Delta t)^{2}-7}{\Delta t}$

so we can now simplify our formula by expanding the numerator:

$\overline{v}=\frac{29+29\Delta t-22(1+2\Delta t+\Delta t^{2})-7}{\Delta t}$

$\overline{v}=\frac{29+29\Delta t-22-44\Delta t-22\Delta t^{2}-7}{\Delta t}$

we can now simplify this to:

$\overline{v}=\frac{-15\Delta t-22\Delta t^{2}}{\Delta t}$

Now we can factor Δt to get:

$\overline{v}=\frac{\Delta t(-15-22\Delta t)}{\Delta t}$

and simplify

$\overline{v}=-15-22\Delta t$

Which is the equation that will represent the average speed of the ball. So now we can substitute each period into our equation so we get:

$\overline{v}_{@\Delta t=0.01s}=-15-22(0.01)=-15.22ft/s$

$\overline{v}_{@\Delta t=0.005s}=-15-22(0.005)=-15.11ft/s$

$\overline{v}_{@\Delta t=0.002s}=-15-22(0.002)=-15.044ft/s$

$\overline{v}_{@\Delta t=0.001s}=-15-22(0.001)=-15.022ft/s$

5 0

3 years ago

The perimeter of a rectangular swimming pool at the park is 60 meters. The length of the pool is 4 meters more than the width. W

ra1l [238]

P = 60 meters
l = 4 meters

60 / 4 = 20 <-- Because retangles have 4 sides.
If l=4 then subtract 4 from 20
So w=16

8 0

4 years ago

a pet store sells only dogs and cats. The ratio of dogs to cats at the pet store was 6:5. If there are 154 pets at the pet store

Y_Kistochka [10]

Step-by-step explanation:

assume the number of dogs and cats to be 6x and 5x

dogs + cats = 11x

we are given that 11x= 154

hence x=11

dogs = 6x = 6×11 = 66

5 0

4 years ago

Read 2 more answers

A right triangle has one side that measures 4in. The angle opposite that side measures 80 degrees. What is the length of the hyp

Crazy boy [7]

Hello from MrBillDoesMath!

Answer:

4/sin(80)

which is approximately 4.06

Discussion:

From the triangle, not drawn too accurately (see attachment)

sin(80) = side opposite /hypotenuse =>

sin (80) = 4/c => multiply both sides by "c"

c sin(80) = 4/c * c =>

c sin(80) = 4 => divide both sides by sin(80)

c = 4/sin(80)

and 4/sin(80) is approximately 4.06

Thank you,

MrB

6 0

3 years ago

Write 79% as a fraction or mixed number in simplest form.

icang [17]

Answer: 39 25/50

Step-by-step explanation:

0.78 ( 78% ) = 39/50

0.79 ( 79% ) = 39/50 + 1/2

25 is half of 50

39 25/50

7 0

3 years ago

Read 2 more answers