Answer: Midpoint = (11.5, 14.5)
Concept:
Here, we need to know the idea of the midpoint formula.
Solve:
<u>Given information</u>
(x₁. y₁) = (2, 3)
(x₂, y₂) = (11, 16)
<u>Given expression</u>
<u>Substitute values into the expression</u>
<u>Simplify the numerator by addition</u>
<u>Simplify by division</u>
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The given curve is --- y = x^5 + x^3 - 2x
<span>First derivative to this curve is y' = 5 x^4 + 3 x^2 - 2 </span>
<span>=> Slope (m) = 5 x^4 + 3 x^2 - 2 </span>
<span>For the minimum value of m we calculate dm/dx and put it = 0 </span>
<span>=> d( 5 x^4 + 3 x^2 - 2 ) / dx = 0 </span>
<span>=> 20 x^2 + 6 x = 0 </span>
<span>=> x ( 20 x + 6 ) = 0 </span>
<span>Turning values of x are 0 and - 6 / 20 = ( - 3 / 10 ) </span>
<span>At x = 0 , m = - 2 </span>
<span>and at x = - 3/10 </span>
<span>m = 5 x^4 + 3 x^2 - 2 </span>
<span>=> m = 5 ( - 3 / 10 )^4 + 3 ( - 3 / 10 )^2 - 2 = - 1.68 </span>
<span>Hence at turning points, the slope is minimum at x = 0 and is equal to = - 2 </span>
<span>MINIMUM VALUE OF THE SLOPE = - 2</span>
4m.
You can get this answer by setting the legs equal to x and x+4 and the hypotenuse as 2x-4. Then use the Pythagorean Theorem and the quadratic equation to solve.
Let p be the probability of success, p = 0.4.
Pr[2 success] = nC2 * p^2 * (1-p)^3 = 0.346
Pr[3 success] = nC3 * p^3 * (1-p)^2 = 0.230
Pr[4 success] = nC4 * p^4 * (1-p)^1 = 0.077
So, the probability of getting 2, 3, or 4 success, would be 0.356 + 0.230 + 0.077 = 0.663, alternatively, 66.3%.
Answer:
x ≈ 11.23
Step-by-step explanation:
Given
tan24° = 
( multiply both sides by x )
x × tan24° = 5 ( divide both sides by tan24° )
x = 
≈ 11.23 ( to 2 dec. places )
