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san4es73 [151]
2 years ago
8

!!HURRY!!

Mathematics
2 answers:
horrorfan [7]2 years ago
7 0
The answer would be 14
DENIUS [597]2 years ago
7 0
The answer to this question is 14!!!
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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

4 0
1 year ago
How do you evaluate fuctions?
Evgen [1.6K]

Step-by-step explanation: To evaluate functions substitute the given number or expression function's variable.

6 0
2 years ago
Least to greatest -20 7/20,7/28,20,20.75
horsena [70]

Answer:

-20 7/20, 7/28, 20, 20.75  

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
NEED HELP FAST PLEASE<br> Evaluate the limit.<br><br> a.4<br> c.1<br> b.2<br> d.limit does not exist
BlackZzzverrR [31]
We have the following limit:
 (8n2 + 5n + 2) / (3 + 2n)
 Evaluating for n = inf we have:
 (8 (inf) 2 + 5 (inf) + 2) / (3 + 2 (inf))
 (inf) / (inf)
 We observe that we have an indetermination, which we must resolve.
 Applying L'hopital we have:
 (8n2 + 5n + 2) '/ (3 + 2n)'
 (16n + 5) / (2)
 Evaluating again for n = inf:
 (16 (inf) + 5) / (2) = inf
 Therefore, the limit tends to infinity.
 Answer:
 
d.limit does not exist
7 0
3 years ago
Complete the equation so that it has infinitely many solutions <br>1/2(4-z)​
I am Lyosha [343]

Answer:

4 - z

 —---

   2  

Step-by-step explanation:

3 0
2 years ago
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