Hello, this is my brother's homework. I'm a little bit confused since I studied this lesson a long time ago..Can someone help me? I am not sure about my answer..​

If v(t) and h(t) denote the ball's velocity and height at time t, respectively, then we have h(0) = 1.2 m and v(0) = 58 m/s.

The ball is in free fall after being tossed, so its acceleration is constant at any time t :

[tex]a(t) = -9.8 \dfrac{\rm m}{\mathrm s^2}[/tex]

By the fundamental theorem of calculus, the velocity function is given by

[tex]\displaystyle v(t) = v(0) + \int_0^t a(u) \, du[/tex]

Compute the integral:

[tex]\displaystyle v(t) = 58 \frac{\rm m}{\rm s} - \left(9.8 \frac{\rm m}{\mathrm s^2}\right) \int_0^t du[/tex]

[tex]\displaystyle v(t) = 58 \frac{\rm m}{\rm s} - \left(9.8 \frac{\rm m}{\mathrm s^2}\right) (t - 0)[/tex]

[tex]\displaystyle \boxed{v(t) = 58 \frac{\rm m}{\rm s} - \left(9.8 \frac{\rm m}{\mathrm s^2}\right) t}[/tex]

Similarly, the height function is given by

[tex]\displaystyle h(t) = h(0) + \int_0^t v(u) \, du[/tex]

[tex]\displaystyle h(t) = 1.2 \, \mathrm m + \int_0^t \left(58 \frac{\rm m}{\rm s} - \left(9.8 \frac{\rm m}{\mathrm s^2}\right) t\right) \, du[/tex]

[tex]\displaystyle h(t) = 1.2 \, \mathrm m + \left(58 \frac{\rm m}{\rm s}\right) (t - 0) - \frac12 \left(9.8 \frac{\rm m}{\mathrm s^2}\right) (t^2 - 0^2)[/tex]

[tex]\displaystyle \boxed{h(t) = 1.2 \, \mathrm m + \left(58 \frac{\rm m}{\rm s}\right) t - \frac12 \left(9.8 \frac{\rm m}{\mathrm s^2}\right) t^2}[/tex]

Answer:

V(t) = 58-9.8t

h(t)=1.2+58t-4.9[tex]t^{2}[/tex]

Step-by-step explanation:

Using the standard formula

a=V f-Vi/t --rearrange

at=V f-Vi

V f=V i + a t

therefore

V(t)=58-9.8t

same with height

H= Hi+Vit+1/2at^2

therefore

h(t)=1.2+58t-4.9t^2

Answer:

r≈93

Step-by-step explanation:

V=4/3πr³

3,367,575=4/3(3.14)r³

3,367,575=314/75r³

multiply both sides by 75/314

804357 27/314=r³

∛804357 27/314=∛r³

r≈93

Answer:

161 Remainder 4

Step-by-step explanation:

trust me on this

Answer:

_

161.2 BUT if with remainder it is 161 with a remainder of 4

Step-by-step explanation:

By the way the 2 is a repeating number so make sure to add that line at the top.

Answer:

Step-by-step explanation:

The equation of this line is:

y = -5/2 x + 2.

Answer:

look at the picture i have sent

Answer:

c. 60 mins

Step-by-step explanation:

12 * 5 = 60

15 * 4 = 60

Answer:

-3/7

Step-by-step explanation:

Hi,

First of all, we know that the slope is not undefine because both the x-coordinates are not the same.

To find the slope, do change in y/change in x. Here, it would be ((2/7)-(5/7))/(2-1) or (-3/7)/1. Hence, the slope is -3/7.

Answer:

left 2 units, up 3 units

Step-by-step explanation:

(x-2, y+3)

-2 means 2 to the left

+3 means 3 up

So it would be left 2 units, up 3 units.

Answer:

Step-by-step explanation:

Rule:

If  x+b   right in b units

if  x-b    left   in b untits

if  y+b    up   in  b units

if  y-b  down in  b  units

You don 't have to use this rule if you know that on the Ox axis the line goes horizontally (the abscissa axis); And on the Oy axis vertically (the ordinate axis)

Then :

x-2    left in 2 units

y+3   up  in  3 units

Answer:

5:3=8

3/8 x 120

3/1 x 15

3 x 15=45

Step-by-step explanation:

hope this helps

sorry

Answer:

0.55%

Step-by-step explanation:

230÷100=2.30%

175÷100=1.75%

2.30-1.75=0.55%

I think ‍♂️

Answer:

17

Step-by-step explanation:

20 divided by 5 + 19 - 6

20 divided by 5 = 4

4 + 19 = 23

23 - 6 = 17

Answer:

The pantograph is spring-loaded and pushes a contact shoe up against the underside of the contact wire to draw the current needed to run the train.    As the train moves, the contact shoe slides along the wire and can set up standing waves in the wires which break the contact and degrade current collection.

Step-by-step explanation:

Here

Show sum of interior angles is 180°

[tex]\\ \sf\longmapsto <NBA+<NAB=180[/tex]

[tex]\\ \sf\longmapsto <NAB+103=180[/tex]

[tex]\\ \sf\longmapsto <NAB=180-103[/tex]

[tex]\\ \sf\longmapsto <NAB=77°[/tex]

Vertical angles are supplementary

We need m<NAB

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

The equivalent expression is ~

[tex] \boxed{27 {x}^{2} }[/tex]

[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]

Let's solve ~

Answer:

-7

Step-by-step explanation:

there are 16 increments in total, and half are labeled

so the answer is -7 because if the increments are 1 and it is left of zero, so do 7*-1 because it is to the left

Answer:

-7

Step-by-step explanation:

Answer:

you're wrong

Step-by-step explanation:

should have been "Why are all the answers on this website saying my work is wrong?"

Answer:

2

Step-by-step explanation:

Plug in 3 for the a's and -2 for the b's:

[tex]-2^{2} -(-2 + 3(3)) + 3 = ?[/tex]

Then simplify:

[tex]4 - (-2 + 9) + 3 = ?[/tex]

remember to add 1 as a placeholder if the sign before the parenthesis is a minus:

[tex]4 + 4 - 9 + 3 = ?[/tex]

Solve:

[tex]4 +4 -9+3=2[/tex]

Answer:

The 7 in 137 represents ten times the 7 in 137 (the second option)

Step-by-step explanation:

The seven in 137 equals 7

The seven in 174 equals 70

7 times 10 = 70

I hope this helped!

Step-by-step explanation:

sorry for my ugly handwriting, hope it helps

Answer:

4

Step-by-step explanation:

[tex]\frac{10}{25}[/tex] × 10

[tex]\frac{100}{25}[/tex]

4

Answer:

3  ( x  +  29 )

Step-by-step explanation:

The best I can do is factor them, hope it helps!

Answer:

see below

Step-by-step explanation:

just reduce to 3 digits before the decimal place and count how many are behind the decimal for what power the 10 is, not including numbers that were already behind the decimal

a. 107.92*10^2

b. 376.932*10^0

c. 998.461*10^3

Answer:

When rounding significant figures the standard rules of rounding numbers apply, except that non-significant digits to the left of the decimal are replaced with zeros.

Step-by-step explanation:

(a) 10792 ≈ 10800

(b) 376.932 ≈ 377

(c) 998461 ≈ 998000

A restricted lifestyle is not an advantage of renting.

Option D is the correct answer.

Renting a property has several advantages, such as ease of mobility, fewer responsibilities, and lower initial costs.

We have,

Ease of mobility is an advantage because it is easier for renters to move to a new location since they are not tied down to a specific property.

Fewer responsibilities are another advantage because the landlord is usually responsible for maintaining the property, making repairs, and paying for utilities.

This means that renters do not have to worry about these tasks or expenses.

Lower initial costs are also an advantage because renters do not have to pay for a down payment or closing costs, which can be a significant expense when purchasing a property.

A restricted lifestyle is not an advantage of renting.

This is because renters may be limited in terms of decorating, making changes to the property, or having pets.

Renters may also have to abide by certain rules set by the landlord or property management company.

This can limit their freedom and personalization of the space.

Thus,

A restricted lifestyle is not an advantage of renting.

Learn more about renting here:

https://brainly.com/question/26268428

#SPJ5

I believe it is 9681/10.

Answer:

the answer is 9681/10

Step-by-step explanation:

9681/10