The roots of the polynomial <span><span>x^3 </span>− 2<span>x^2 </span>− 4x + 2</span> are:
<span><span>x1 </span>= 0.42801</span>
<span><span>x2 </span>= −1.51414</span>
<span><span>x3 </span>= 3.08613</span>
x1 and x2 are in the desired interval [-2, 2]
f'(x) = 3x^2 - 4x - 4
so we have:
3x^2 - 4x - 4 = 0
<span>x = ( 4 +- </span><span>√(16 + 48) </span>)/6
x_1 = -4/6 = -0.66
x_ 2 = 2
According to Rolle's theorem, we have one point in between:
x1 = 0.42801 and x2 = −1.51414
where f'(x) = 0, and that is <span>x_1 = -0.66</span>
so we see that Rolle's theorem holds in our function.
Answer:
The area of sector AOB is 75.36 unit²
Step-by-step explanation:
Consider the provided information.
Circle O with minor arc AB=60 degrees and OA =12.
We need to find the area of sector.
Area of the sector: 
Substitute 
and r =12 in above formula.
Hence, the area of sector AOB is 75.36 unit²
The complete proof for the given parallelogram is given in the image attached below.
<h3>What is a Parallelogram?</h3>
A parallelogram is a quadrilateral whose opposite sides are parallel and also congruent to each other.
The complete proof would be as shown below:
1. ABCD is a parallelogram [given]
2. AB║CD [Definition of parallelogram]
3. ∠1 ≅ ∠2, ∠3 ≅ ∠4 [alternate interior angles theorem]
4. AB ≅ CD [Definition of parallelogram]
5. ΔABE ≅ ΔCDE [ASA]
6. AE ≅ CE, BE ≅ DE [CPCTC]
7. AC and BD bisects each other at E [definition of segment bisector]
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Answer:
F = 3x +(2.7×10^7)/x
Step-by-step explanation:
The formulas for area and perimeter of a rectangle can be used to find the desired function.
<h3>Area</h3>
The area of the rectangle will be the product of its dimensions:
A = LW
Using the given values, we have ...
13.5×10^6 = xy
Solving for y gives ...
y = (13.5×10^6)/x
<h3>Perimeter</h3>
The perimeter of the rectangle is the sum of the side lengths:
P = 2(L+W) = 2(x+y)
<h3>Fence length</h3>
The total amount of fence required is the perimeter plus one more section that is x feet long.
F = 2(x +y) +x = 3x +2y
Substituting for y, we have a function of x:
F = 3x +(2.7×10^7)/x
__
<em>Additional comment</em>
The length of fence required is minimized for x=3000. The overall size of that fenced area is x=3000 ft by y=4500 ft. Each half is 3000 ft by 2250 ft. Half of the total 18000 ft of fence is used for each of the perpendicular directions: 3x=2y=9000 ft.
The solution of the equation (√x-8) + 2 = 7 is x = 13.
According to the given question.
We have an equation
Since, we solve the above equation for x .
Therefore,
⇒ (√x - 8) = 7 - 2
⇒ (√x - 8) = 5
Squarring both the sides.
⇒ x - 8 = 5
⇒ x = 5 + 8
⇒ x = 13
Hence, the solution of the equation (√x-8) + 2 = 7 is x = 13.
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