El desplazamiento (en metros) de una partícula que se mueve
en línea recta esta dado por s = 12 – 8t + 18, donde t se
mide en segundos.
a) Encuentre la velocidad promedio en cada intervalo de
tiempo:
i) [3, 4] ii) [3.5, 4]
iii) [4, 5] iv) [4, 4.5]
b) Halle la velocidad instantánea cuando t = 4.
c) Dibuje la grafica de s como función de t y trace las rectas
secantes cuyas pendientes son las velocidades promedio
en el inciso a) y la recta tangente cuya pendiente es la
velocidad instantánea en el inciso b).

Answer:

c

Step-by-step explanation:

hize la misma pregunta que vos

The average velocities for the given time intervals are,

(i) -8 m/s,

(ii) -12 m/s,

(iii) 4 m/s, and

(iv) 4 m/s. The instantaneous velocity at t = 4 is -8 m/s. The attached graph of s as a function of t is a straight line with slope -8, showing the secant and tangent lines.

a) To find the average velocity in each time interval,

calculate the change in displacement (Δs) divided by the change in time (Δt) within each interval.

s = 12 - 8t + 18

i) [3, 4]:

Δs = s(4) - s(3) = (12 - 8(4) + 18) - (12 - 8(3) + 18) = -8

Δt = 4 - 3 = 1

Average velocity = Δs / Δt = -8 / 1 = -8 m/s

ii) [3.5, 4]:

Δs = s(4) - s(3.5) = (12 - 8(4) + 18) - (12 - 8(3.5) + 18) = -6

Δt = 4 - 3.5 = 0.5

Average velocity = Δs / Δt = -6 / 0.5 = -12 m/s

iii) [4, 5]:

Δs = s(5) - s(4) = (12 - 8(5) + 18) - (12 - 8(4) + 18) = 4

Δt = 5 - 4 = 1

Average velocity = Δs / Δt = 4 / 1 = 4 m/s

iv) [4, 4.5]:

Δs = s(4.5) - s(4) = (12 - 8(4.5) + 18) - (12 - 8(4) + 18) = 2

Δt = 4.5 - 4 = 0.5

Average velocity = Δs / Δt = 2 / 0.5 = 4 m/s

b) To find the instantaneous velocity when t = 4, we'll find the derivative of s with respect to t and then substitute t = 4.

s = 12 - 8t + 18

ds/dt = -8

Instantaneous velocity at t = 4 is equal to the derivative at t = 4:

Instantaneous velocity at t = 4: ds/dt (t=4) = -8 m/s

c) To sketch the graph of s as a function of t and draw the secant lines (average velocities) and the tangent line (instantaneous velocity):

Attached graph.

The graph of s as a function of t is a straight line with a slope of -8 and a y-intercept of 30. At t = 4, the instantaneous velocity is -8 m/s.

Secant lines:

Draw a straight line connecting the points (3, 10) and (4, 2) for the interval [3, 4].

Draw a straight line connecting the points (3.5, 4) and (4, 2) for the interval [3.5, 4].

Draw a straight line connecting the points (4, 2) and (5, 6) for the interval [4, 5].

Draw a straight line connecting the points (4, 2) and (4.5, 4) for the interval [4, 4.5].

Tangent line:

At t = 4, draw a straight line with a slope of -8 and passing through the point (4, 2).

The attached graph will show the secant lines with different slopes as the average velocities in each interval and the tangent line with a slope of -8 as the instantaneous velocity at t = 4.

learn more about average velocity here

brainly.com/question/32663715

#SPJ2

The above question is incomplete , the complete question is:

The displacement (in meters) of a moving particle

in a straight line is given by s = 12 – 8t + 18, where t is

measured in seconds.

a) Find the average velocity in each time interval:

i) [3, 4] ii) [3.5, 4]

iii) [4, 5] iv) [4, 4.5]

b) Find the instantaneous velocity when t = 4.

c) Plot s as a function of t and draw the secant lines whose slopes are the average velocity in part (a) and the tangent line whose slope is the

instantaneous velocity in part (b).

Steven paid $60 for 3 cardio dance workout classes. He’s trying to set up an equation to help him find the cost of each class. What should Steven put in the blank of the following equation? c=$___÷3?

4 divided 1/5 hep me plz

Sarah is solving for X by the process of completing the square for the following problem..

2x^2+16x-12=0

She got to this point below - type the number that goes in the (?) spot

(x+?)^2=22

5. x=a+b+4 and anyz; bo when y=2; x=18 and when y=1; x=-3. Find tu
90​

Classify each triangle by its angles and its sides.


PLSSS ANSWER!

What is the area of the trapezoid shown below?

A circular pool has a diameter of 25 feet. A 2 foot-wide sidewalk borders the entire pool. What is the approximate circumference of the outside edge of the sidewalk
A. 91 feet
B. 85 feet
C. 50 Feet
D. 27 feet
I’ll mark brainalist + points for answer / explanation

The ratio of cups of sugar to cups of water

What is 0.11 / 22.77

slove for q: q/10 = 4

WILL GIVE BRAINLIST PLS HELP Find x. Round your answer to the nearest tenth.

In a town, 65% of people had high speed internet in their homes. If the population of the town is 80,000, how many
people do not have access to high speed internet in their homes?
Show work

Could someone please solve?

What is the 3rd quartile in the following data set? You may want to draw a box & whisker plot
to find the 3rd quartile. *
(5 Points)
{5, 16, 12, 3, 20, 15, 8)
16
12
15
5

what is the value of angle x?​

Maximize −4x + 5y + 70 subject to the constraints:

2x + y ≤ 8
x + 3y ≥ 5
x + y ≤ 6
x ≥ 0,
y ≥ 0

a. Fix any constraints, as needed, and then convert the linear programming problem into a system of linear equations.
b. Give a fully labeled initial tableau, and circle the pivot element.

Find the area of the shaded polygons

Which intervals are most appropriate for a histogram
displaying the mileage ratings?
The list shows the mileage rating (in mpg) for some 2019
vehicles with all-wheel or four-wheel drive.
11, 13, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 17, 18,
18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21,
21, 21, 21, 22, 22, 22, 22, 22, 23, 23, 23, 23, 23, 24, 24,
24, 24, 24, 24, 25, 25, 25, 26, 26, 26, 27, 27, 27, 28, 29,
30, 31, 32, 33, 34
O 0-15, 15-30, 30-45
O 0–20, 20-40, 40-60
O 10-15, 15-20, 20-25, 25-30, 30-35
O 0-5,5–10, 10-15, 15-20, 25-25, 25-30

Yes or No: Is this triangle a Right Triangle with side measures 21, 28, 35?

In the finals of a singing contest at Greenvale Middle School, 300 students vote on which
contestant they liked best. The circle graph shows the results of the vote. How many
more votes did Gamba get than Ahmed?

PLEASE NO LINKS I REALLY NEED HELP ​

If 78% of the total is 156 marks, find the total marks in the test
200
206
176
210

Which expression is equivalent to 6x^2+16x-6

The number of calories in fruit smoothies varies from brand to brand. The population distribution of calories is strongly skewed to the right. The central limit theorem says that:___________
a. the average calorie count of a large number of fruit smoothie brands has a sampling distribution that is exactly Normal.
b. the average calorie count of a large number of fruit smoothie brands has a sampling distribution that is close to Normal.
c. as the number of brands of fruit smoothies increases, their average calorie count gets ever closer to the mean μ for all fruit smoothies of this type.
d. the average amount of calories of a large number of fruit smoothie brands has a sampling distribution with the same shape (strongly skewed) as the population distribution.
e. the average calorie count of a large number of fruit smoothie brands has a sampling distribution with a similar shape but not as extreme (skewed, but not as strongly) as the population distribution.

X/23 = 21/34 round to hundredths place

2/3 - 3/7

explain, please...

Write this equation in standard form y=3x+10

Diego has run 4/5 of a race distance. He has run 7 2/3 ​

how do you write this number out in words 506,341,209.54​

How many groups of 1/4 are in 3. Draw a tape diagram