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Norma-Jean [14]
3 years ago
13

Sam is measuring the velocity of a car at different times. After two hours, the velocity of the car was 50km/h. After six hours,

the velocity of the car is 54km/h.
Part A: Write an equation in two variables in standard form that can be used to describe the velocity of the car at different times. Show your work and define the variables used. (5points)

Part B: How can you graph the obtained in Part A for the first seven hours? (5points)
Mathematics
1 answer:
netineya [11]3 years ago
3 0
You are given the time and speed so from there you can get the points (2,50) and (6,54) once you got that you can see how the slope is 1 and 
b=48
x-y=-48 (standard form)
 
part B= 
1    49
2    50
3    51
4    52
5    53
6    54
7    55
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Use calculus to find the area of the triangle with the vertices (0, 5), (2, -2), and (5, 1).
guajiro [1.7K]

The area of the triangle with the vertices (0, 5), (2, -2), and (5, 1) by using the calculus is  21 square unit.

We need to find the equation among all possible pairs and then integrate the equations from one co-ordinate to another co-ordinate

Equation of line passing through (0,5) and (2,-2) is

y-5 = [(-2-5)/(2-0)](x-0)

=>y-5 = (-7) /2x

=>y= (-7/2x)+5 -------(eq1)

Equation of line passing through (0,5) and (5,1) is

y-5 = [(1-5) / (5-0)](x-0)

=>y-5 = (-4/5)x

=>y = (-4/5)x+5-------(eq2)

Equation of line passing from (2,-2) and (5,1) is

y-(-2) = [[1 - (-2)] / (5-2)] / (x-2)

=>y+2=(3/3)(x-2)

=>y=x-4--------(eq3)

Now, we use definite integration to find the area between the different equation of line.

So, area enclosed between the equations is given by the

area =\int\limits^5_2[(-4/5)x+5 - (-7/2)x + 5)dx  + \int\limits^5_1[(-4/5)x+5 -(x-4)]dx

=>area=\int\limits^5_2(7/2-4/5)x dx + \int\limits^5_1((-9/5)x+9)dx

Using properties of integration,\int\limits x\, dx=x^{2}/2

=>area=\int\limits^5_2(27/10)x dx + \int\limits^5_1(-9/5)x+9)dx

=>area=([27/10)×[5² - 2²])/2 + [ (-9/5)×(5²-1²) ]/2 +9×(5-1)

=>area=(27/20)×(25-4) + (-9/5)×24+9×4

=>area = (27×21)/20 + (-216)/5+ 36

=>area=(567/20) - (216/5) + 36

=>area= [(567-261×4)+(36×20)]/20

=>area=[(567-864)+720]/20

=>area=423/20

=>area=21 square unit.

Hence, area of triangle is 21 square unit.

To know more about area of triangle, visit here:

brainly.com/question/19305981

#SPJ4

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Someone helppppp plsss j suck at math. ( pls answer only if your sure ur right)
Degger [83]

Answer:

Step-by-step explanation:

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Evaluate the expression x + 8/27. Evaluate the expression for x=8/9
diamong [38]

Answer:

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Step-by-step explanation:

Evaluate for x=

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8 /9  + 8 /27

=32/27

(Decimal: 1.185185)

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