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
Factor the following polynomial completely. x2n – y2n
Answer:
(x/y)^2n-2n
(x/y)⁰
=1
since any number raised to power of 0 is 1
1. Two students are asked to find the angle measures of AEFG, given that the triangle is isosceles. AEFG has an exterior angle at which has a measure of 110%. Their work is shown below.
Which answer is correct? Explain below.
Serin's Answer: The measure of Angle G is 70 degrees. Since the base angles are congruent, the measure of Angel F is also 70degrees.This leaves 40 degrees for Angle E.
Lam's Answer: The measure of angle G is 70degrees. Since an isosceles triangle has two congruent angles, the measure of Angle E and Angle F must be 55degrees
O Both are correct.
ONeither is correct.
Answer:
∆EFG has an exterior angle at G which has a measure of 110°. Which answer is incorrect ... Since external angle is 110 degrees, the internal is 70 degrees
Step-by-step explanation:
no problem we all get stuck
The angles can be ∠ G = 70°, ∠ F = 70° and ∠E = 40° or ∠ G = 70°, ∠ F = ∠ E = 55° hence both are correct so, option C is correct.
What is triangle?
Three straight lines coming together create a triangle. There are three sides and three corners on every triangle (angles). A triangle's vertex is the intersection of two of its sides. Any one of a triangle's three sides can serve as its base, however typically the bottom side is used.
Given:
The triangle is isosceles, and AEFG has an exterior angle at which has a measure of 110°,
Calculate the interior angles of the triangle as shown below,
∠ G = 180 - 110 (exterior angle)
∠ G = 70°
Since the remaining angles can be ∠ F = 70° and ∠E = 180 - 70 + 70 = 40°
or ∠ F = ∠ E = 55°
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0.35 is best known as what number
What is the slope of the graph of the given line?
Answer:
slop = 2/3
Step-by-step explanation:
slope = rise/run
Start at the lower left point (-2, -1).
We need to go to the upper right point (4, 3) by going only vertically (rise) and horizontally (run).
First we go up 4. The rise is 4.
Then we go right 6. The run is 6.
slope = m = rise/run = 4/6 = 2/3
slope = 2/3
What is an equation of the line that passes through the point (-7, -6) and is
parallel to the line 2 - y = 7?
Answer:
[tex]y = -6[/tex]
Step-by-step explanation:
Because is a line is of the form
[tex]y = mx + b[/tex]
and its parallel to the line
[tex]2 - y &= 7\\- y &= 5\\y = -5[/tex]
So that's meaning that the slope [tex]m[/tex] is equal to 0 then the equation now is of the form
[tex]y = b[/tex]
Then if pass for the point -6 and [tex]b[/tex] is the point of cut with the [tex]y[/tex] axis then our equation of the line is equal to
[tex]y = -6[/tex]
1/6 to 4/7 what is the ratio? Pls hurry!
Answer:
7:24
Step-by-step explanation:
Find the common denominator for both fractions: 42
1/6 x 7/7 = 7/42
4/7 x 6/6 = 24/42
7:24
what are the coordinates of the point 2/3 of the way from A to B? A (-5,-5). B(7,8)
A rectangle of dimensions 60 units x 40 units is drawn on grid paper with vertices in
the nodes of the grid. A cell of the grid is 1 unit * 1 unit. A diagonal of the rectangle is
drawn. How many cells have been cut into two (not necessarily equal) parts?
The number of cells which have been cut into two parts is approximately ; 72 units
According to the question;
The rectangle has dimensions 60 units x 40 units.Provided a cell of the grid is 1 unit * 1 unit.
When a diagonal of the rectangle is drawn;
The number of cells which have been cut into 2 pieces is the length of the diagonal of the rectangle.
Diagonal, D² = 60² + 40²D² = 3600 + 1600D² = 5,200D = √5200D = 72.11 unitsRead more;
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Answer: 80
see attached
Step-by-step explanation:
If you do a 3x2 units, and draw a diagonal line, you'll see 4 units are cut. because it's 60x40, then means BOTH lengthwise & widthwise you'll repeat 20 times, so 20*4 units = 80 units.
Mr smith’s Pizza parlor
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Convert 4.5 to a mixed number help for brainlist with explanation!
Answer:
4 1/2
Step-by-step explanation:
the 4 means that the whole number will be 4. .5 means that there is one half of 1, so 1/2 will be the decimal
we can also write the decimal as an improper fraction.
45/10
then, reduce the fraction by 5
9/2
2 can go into 9 four times, so that is our whole number. 2 times 4 is 8, so there is 1 left in the numerator.
4 1/2
9. Gregory's nine chickens laid an average of six eggs each per week. Gregory sold those eggs for $300 per dozen. How much money did he collect in two weeks if he sold all his eggs??
Step-by-step explanation:
Average in one week 6eggs
2 weeks 12 eggs
1 dozen =12 eggs
1 dozen =300 dollars
2*300=600 ans
Answer:
$2,700
Step-by-step explanation:
The first thing we should do is to find the number of eggs in two weeks.
6 eggs each for 9 chickens which means:
6 * 9 = 54
54 eggs per week.
In two weeks,
54 * 2 = 108
108 eggs for two weeks
Now a dozen is equivalent to 12 eggs. So if you divide 108 to 12:
108 ÷ 12 = 9
So it is 9 dozens. Then he's selling those eggs for $300 per dozen.
300 * 9 = $2,700
That's it.
File uploaded. Please help I don't understand this.
Answer:
Ms. Brown needs 0.18 more cents to afford the pounds of granola and cranberry mix.
Step-by-step explanation:
Ms. Brown = $10 limit
Purchases 1.75 lbs of granola and 2.9 lbs of cranberry mix
Cranberry per lb = $3.25
Granola per lb = $2.19
1.75 x 2.19 = 3.8325 (Cost of granola)
2.9 x 2.19 = 6.351 (Cost of cranberry)
3.8325 + 6.351 = 10.1835 (Total cost of both cranberry and granola)
10.1835 rounded to nearest cent = 10.18
10 < 10.18
Ms. Brown doesn't have enough money to buy the pounds of granola and cranberry mix.
8 I am 8 yeard old, my father is24 years older than iam ,how old was my father 5 years ago?
Step-by-step explanation:
He was 19 years old when you were 5
(Pythagorean theorem) do the following lengths form a right triangle? Show steps
Answer:
8^2+6^2=10^10?
64+36=100
Yes
Hope This Helps!!!
Answer:
Yes,
Step-by-step explanation:
8^2 +6^2=100
[tex]\sqrt 100\\[/tex]= 10
If the vertical length is 10, what is the horizontal length?
Answer:
5
Step-by-step explanation:
it is half of ten which is 5
Hope this helps
Answer:
top one is correct I think
Una compañía de frutas entrega sus frutas en dos tipos de caja: grande y pequeña. Una entrega de 3 cajas grandes y 5 cajas pequeñas tiene un peso total de 112 kilogramos. Una entrega de 6 cajas grandes y 2 cajas pequeñas tiene un peso total de 118 kilogramos. ¿Cuánto pesa cada tipo de caja?
Usando un sistema de ecuaciones, se encuentra que:
Cada caja grande pesa 15.25 kg.Cada caja pequeña pesa 13.25 kg.Para el sistema, considera-se que:
x es el peso de una caja grande.y is el peso de una caja pequeña.Una entrega de 3 cajas grandes y 5 cajas pequeñas tiene un peso total de 112 kilogramos, o ea:
[tex]3x + 5y = 112[/tex]
Una entrega de 6 cajas grandes y 2 cajas pequeñas tiene un peso total de 118 kilogramos, o sea:
[tex]6x + 2y = 118[/tex]
Simplificando por 2 :
[tex]3x + y = 59 \rightarrow y = 59 - 3x[/tex]
Reemplazando en la primera ecuación:
[tex]3x + 5y = 112[/tex]
[tex]3x + 5(59 - 3x) = 112[/tex]
[tex]3x + 295 - 15x = 112[/tex]
[tex]12x = 183[/tex]
[tex]x = \frac{183}{12}[/tex]
[tex]x = 15.25[/tex]
[tex]y = 59 - 3x = 59 - 3(15.25) = 13.25[/tex]
Cada caja grande pesa 15.25 kg.Cada caja pequeña pesa 13.25 kg.Un problema similar es dado en https://brainly.com/question/24646137
what is the difference of 23xand 9 x
Answer:
14x
Step-by-step explanation:
.....................
PLEASE HELP.
Use the drawing tool(s) to form the correct answer on the provided graph. The graph of f(x) = x is shown on the coordinate plane. Function g is a transformation of f as shown below. g(x) = f(-2/3x)
WILL GIVE 100 POINTS.
Step-by-step explanation:
Given function:
f(x) = xThe transformation of f(x) is g(x):
g(x) = f(-2/3x) = -2/3xThe graph of g(x) is attached below
HELPPPPP!!!!!!!!!!!!!!!!!!
Answer:
I think b im not too sure
Step-by-step explanation:
Answer:
C 8
Step-by-step explanation:
3 apples/2 oranges = 12 apples/x
3/2 = 12/x
3x = 24
x = 8 oranges
What is the equation for this? please help!!
Answer:
the equation is y=x^2+8
One member of the solution set of 3x + 2 > x + 8 is
(A) 1
(B) 3
(C) 5
(D) -4
Anyone know the answer to this ?
3x + 2 > x + 8
3x - x > 8 -2
2x > 6
x > 3
ok done. Thank to me :>
The water park is a popular field trip destination this year the senior class at High School A and a senior class at High School B both planned trips there. The senior class at High School A rented and filled 10 vans and six buses with 220 students. High School B rented and filled 11 vans and 12 buses with 350 students. Every van had the same number of students in it as did the buses. Find the number of students in each vans and each bus.
Please answer it respectfully, I need it right now. Hope somebody will answer it correctly.
10x+6y=220 divided by 11x+12y=350
Answer:
da gaba
Step-by-step explanation:
ngano nag pina
bdsbs
An unopened cereal box contains 15/28 cubic foot of cereal. If the box is full, and the length and height of the box are 5/7 foot and 1 1/2 feet, respectively, what is the width of the box?
Answer: the answer is 1/2
Step-by-step explanation:
7. Write an equation for the line in slope- intercept form
Answer:
y equals -2x - 3
Step-by-step explanation:
hope it helps
(would appreciate mark brainliest)
I need help with this :')
Answer:
Rate of change is 15/2
Step-by-step explanation:
Rate of change is the same as slope of a line.
( y1 - y2 ) / ( x1 - x2 )
( 30 - 15 ) / ( 4 - 2 )
15 / 2
Hopefully this helps!
Brainliest please?
The Shanghai Maglev Train takes 8 minutes to travel a distance of 30.5 kilometres.
Work out the average speed of the train.
Answer:
228.75 km/h
Step-by-step explanation:
average speed = total distance / total time
The Average speed is 228.75 Km/h.
What is speed- Distance Formula?Speed = Distance/TimeDistance = Speed X Time, and Time = Distance / Speed,Given:
Distance= 30.5 Km
Time= 8 min
= 8/60 hr= 2/15 hour
Now, Average speed= Distance / time
= 30.5 x 15/2
= 228.75 Km/ h
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Sam is 4 years younger than Linda. The sum of their ages is 28. Find both Sam and Linda’s age and show your work.
Answer:
Sam = 6 years
Linda = 22 years
Step-by-step explanation:
this is best solved by using an algebraic equation
let Sam's age be x
let Linda's age be 4x
now that we defines our variables let's make an algebraic equation
the sum of their ages is 28 so
4x + x = 28
combine like terms
5x = 28
find for x
x = 28÷ 5 = 5.6 (don't approximate yet let's take the raw age)
Sam is 5.6 years
Linda is 4 years older so we multiply Sam's age by 4
4 × 5.6 = 22.4
Linda is 22.4 years
now let's round our answers to the nearest whole
5.6 ~ 6 years
22.4 ~ 22 years
let's double check and add our answers now
22 + 6 = 28
the answer is correct
The base of a triangle is 13 cm rounded to the nearest integer.
The perpendicular height of the triangle is 4.7 cm rounded to 1 dp.
Write the error interval for the area, a, of the triangle in the form m ≤ a < n.
Answer:
30.55 <_ a < 30.55
Step-by-step explanation:
a = 1/2 × b × h
a = 1/2 × 13 × 4.7
a = 30.55 cm^2
30.55 <_ a < 30.55
What expression is equivalent to 42+18
I think the answer is 20+40...
is 5/8 greater than 61%? thanks i have late stuff that i need done
Answer:
5/8 is 62.5% which makes it greater
Step-by-step explanation:
Convert the fraction to a decimal and then just multiply it with 100
5/8 is 0.625
0.625×100 is 62.5
just add a %
then you get 62.5%