Answer:
5
Step-by-step explanation:
Hope this helps :)
<u>Given</u>:
Given that two lines are intersecting at the point.
The angles (3x - 8)° and (2x + 12)° are the angles formed by the intersection of the two lines.
We need to determine the equation to solve for x and the value of x.
<u>Equation:</u>
The two angles (3x - 8)° and (2x + 12)° are vertically opposite. Hence, the vertically opposite angles are always equal.
Hence, we have;

Hence, the equation is 
<u>Value of x:</u>
The value of x can be determined by solving the equation 
Thus, we have;

Subtracting both sides of the equation by 2x, we get;

Adding both sides of the equation by 8, we get;

Thus, the value of x is 20.
Hence, the equation and the value of x are 
Thus, Option D is the correct answer.
Multiplying both sides by
gives

so that substituting
and hence
gives the linear ODE,

Now multiply both sides by
to get

so that the left side condenses into the derivative of a product.
![\dfrac{\mathrm d}{\mathrm dx}[x^3v]=3x^2](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Bx%5E3v%5D%3D3x%5E2)
Integrate both sides, then solve for
, then for
:




![\boxed{y=\sqrt[3]{1+\dfrac C{x^3}}}](https://tex.z-dn.net/?f=%5Cboxed%7By%3D%5Csqrt%5B3%5D%7B1%2B%5Cdfrac%20C%7Bx%5E3%7D%7D%7D)
Answer:
15.2 mph
Step-by-step explanation:
2.4÷(x+4)=1.4÷(x-4)
1.4(x+4)=2.4(x-4)
1.4x+5.6=2.4x-9.6
-x=-15.2
x=15.2
Hope this helps!
Answer:
a) the probability that the minimum of the three is between 75 and 90 is 0.00072
b) the probability that the second smallest of the three is between 75 and 90 is 0.396
Step-by-step explanation:
Given that;
fx(x) = { 1/5 ; 50 < x < 100
0, otherwise}
Fx(x) = { x-50 / 50 ; 50 < x < 100
1 ; x > 100
a)
n = 3
F(1) (x) = nf(x) ( 1-F(x)^n-1
= 3 × 1/50 ( 1 - ((x-50)/50)²
= 3/50 (( 100 - x)/50)²
=3/50³ ( 100 - x)²
Therefore P ( 75 < (x) < 90) = ⁹⁰∫₇₅ 3/50³ ( 100 - x)² dx
= 3/50³ [ -2 (100 - x ]₇₅⁹⁰
= (3 ( -20 + 50)) / 50₃
= 9 / 12500 = 0.00072
b)
f(k) (x) = nf(x) ( ⁿ⁻¹_k₋ ₁) ( F(x) )^k-1 ; ( 1 - F(x) )^n-k
Now for n = 3, k = 2
f(2) (x) = 3f(x) × 2 × (x-50 / 50) ( 1 - (x-50 / 50))
= 6 × 1/50 × ( x-50 / 50) ( 100-x / 50)
= 6/50³ ( 150x - x² - 5000 )
therefore
P( 75 < x2 < 90 ) = 6/50³ ⁹⁰∫₇₅ ( 150x - x² - 5000 ) dx
= 99 / 250 = 0.396