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).
Answers
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.
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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).
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Step-by-step explanation:
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Step-by-step explanation:
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What is Expression?An expression is combination of variables, numbers and operators.
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Answer:
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What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
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We have,
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x + y = 35/4
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Answers
Answer:
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Step-by-step explanation:
You would have to pay to repair it.
Answer:
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Can someone help me plzzzz with this math question!!!!!! “Buy one, get one free” special at T-Mobile for an iPhone 12. The cost is $1150. Calculate what you are actually paying for each item since you are getting two for one price. What is the sale price of each phone?
Answers
Answer:
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Step-by-step explanation
1150/2 = 575
Answer:
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Step-by-step explanation:
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Answer:
student randomly selected from a list of all students at the school
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820
660
1
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Answer:
∠1 = 148°
Step-by-step explanation:
the triangle interior angles = 180°
the unknown interior angle = 180° - 82° - 66° = 32°
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A clothing business finds there is a linear relationship between the number of shirts, n (in thousands) it can sell and the price, P, it can charge per shirt. In particular, historical data shows that 3 thousand shirts can be sold at a price of $69 each, and that 7 thousand shirts can be sold at a price of $61 each. Find the equation of the form P(n)
Answers
Answer:
The equation of the form P(n) is:
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Step-by-step explanation:
From the information provided, you have two points: (3000, 69) and (7000, 61). With this, you can find the slope using the following formula:
m=(p1-p2)/(n1-n2)
m=slope
p1=69
p2=61
n1=3000
n2=7000
m=(69-61)/(3000-7000)
m=8/-4000
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Now that you have the slope, you can find the the equation of the form P(n):
P(n)=-0.002(n-3000)+69
P(n)=-0.002n+6+69
P(n)=-0.002n+75
According to this, the answer is that the equation of the form P(n) is:
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work out the circumference of this circle
give your answer in terms of pi
Answers
Answer:
37.68
Step-by-step explanation:
Well, the first thing first is to know the outline of the question. So I made sure I knew the diameter. In this case we didn't, so I multipilied 6 by 2 and got 12. Then I multipyed 12 by 3.14 to get 37.68
an oil company bores a hole 80m deep estimate the cost of boring if the cost is £30 for drilling the first meter with an increase in cost of £2 per meter for each succeeding meter
Answers
Answer: £188
Step-by-step explanation:
Given
The depth of the hole is 80 m
For the first meter, it is £30
After that, it is £2 per meter
after a meter, it is 79 m more
The total cost is C
[tex]\Rightarrow C=30+2\times 79\\\Rightarrow C=30+158=188[/tex]
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Step-by-step explanation:
if I had to guess it's probably true
In ΔVWX, w = 770 inches, x = 520 inches and ∠V=81°. Find the area of ΔVWX, to the nearest square inch.
Answers
Answer: 197735
Step-by-step explanation: deltamath
Answer:
197735
Step-by-step explanation:
see attached image
