Answer:
4.5 sq. units.
Step-by-step explanation:
The given curve is ![y = (3x)^{\frac{1}{2} }](https://tex.z-dn.net/?f=y%20%3D%20%283x%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%20%7D)
⇒
...... (1)
This curve passes through (0,0) point.
Now, the straight line is y = 3x - 6 ....... (2)
Now, solving (1) and (2) we get,
![y^{2} - y - 6 = 0](https://tex.z-dn.net/?f=y%5E%7B2%7D%20-%20y%20-%206%20%3D%200)
⇒ (y - 3)(y + 2) = 0
⇒ y = 3 or y = -2
We will consider y = 3.
Now, y = 3x - 6 has zero at x = 2.
Therefor, the required are = ![\int\limits^3_0 {(3x)^{\frac{1}{2} } } \, dx - \int\limits^3_2 {(3x - 6)} \, dx](https://tex.z-dn.net/?f=%5Cint%5Climits%5E3_0%20%7B%283x%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%20%7D%20%7D%20%5C%2C%20dx%20-%20%5Cint%5Climits%5E3_2%20%7B%283x%20-%206%29%7D%20%5C%2C%20dx)
= ![\sqrt{3} [{\frac{x^{\frac{3}{2} } }{\frac{3}{2} } }]^{3} _{0} - [\frac{3x^{2} }{2} - 6x ]^{3} _{2}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D%20%5B%7B%5Cfrac%7Bx%5E%7B%5Cfrac%7B3%7D%7B2%7D%20%7D%20%7D%7B%5Cfrac%7B3%7D%7B2%7D%20%7D%20%7D%5D%5E%7B3%7D%20_%7B0%7D%20-%20%5B%5Cfrac%7B3x%5E%7B2%7D%20%7D%7B2%7D%20-%206x%20%5D%5E%7B3%7D%20_%7B2%7D)
= ![[\frac{\sqrt{3}\times 2 \times 3^{\frac{3}{2} } }{3}] - [13.5 - 18 - 6 + 12]](https://tex.z-dn.net/?f=%5B%5Cfrac%7B%5Csqrt%7B3%7D%5Ctimes%202%20%5Ctimes%203%5E%7B%5Cfrac%7B3%7D%7B2%7D%20%7D%20%20%7D%7B3%7D%5D%20-%20%5B13.5%20-%2018%20-%206%20%2B%2012%5D)
= 6 - 1.5
= 4.5 sq. units. (Answer)
<u>Answer:</u>
The probability of getting two good coils when two coils are randomly selected if the first selection is replaced before the second is made is 0.7744
<u>Solution:</u>
Total number of coils = number of good coils + defective coils = 88 + 12 = 100
p(getting two good coils for two selection) = p( getting 2 good coils for first selection )
p(getting 2 good coils for second selection)
p(first selection) = p(second selection) = ![\frac{\text { number of good coils }}{\text { total number of coils }}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctext%20%7B%20number%20of%20good%20coils%20%7D%7D%7B%5Ctext%20%7B%20total%20number%20of%20coils%20%7D%7D)
Hence, p(getting 2 good coil for two selection) = ![\frac{88}{100} \times \frac{88}{100} =\bold{0.7744}](https://tex.z-dn.net/?f=%5Cfrac%7B88%7D%7B100%7D%20%5Ctimes%20%5Cfrac%7B88%7D%7B100%7D%20%3D%5Cbold%7B0.7744%7D)
Answer:
20/24
Step-by-step explanation:
let the variable be x and x-4
5/6 = x-4/x
cross multiply
5x = 6x - 24
24= x
thus, x is 24 and x-4 is 20
<u>20/24</u>
4x^5 + 3x + 1...the ^5 makes it a fifth degree....and the leading coefficient is 4
Answer: C
Step-by-step explanation:
A= 1/2(a+b)xh
A=1/2(7+10)x5
A=8.5x5
A=42.5