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Jet001 [13]
2 years ago
6

1) The graph of a quadratic f(x) intersects the x-axis at -2 and 10. What is a possible

Mathematics
1 answer:
Rainbow [258]2 years ago
6 0

Answer:

The polynomial f(x) = x^2 - 8x - 20

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Find the dimensions of the rectangle with largest area that can be inscribed in an equilateral triangle with sides of 1 unit, if
prohojiy [21]
<span>Maximum area = sqrt(3)/8 Let's first express the width of the triangle as a function of it's height. If you draw an equilateral triangle, then a rectangle using one of the triangles edges as the base, you'll see that there's 4 regions created. They are the rectangle, a smaller equilateral triangle above the rectangle, and 2 right triangles with one leg being the height of the rectangle and the other 2 angles being 30 and 60 degrees. Let's call the short leg of that triangle b. And that makes the width of the rectangle equal to 1 minus twice b. So we have w = 1 - 2b b = h/sqrt(3) So w = 1 - 2*h/sqrt(3) The area of the rectangle is A = hw A = h(1 - 2*h/sqrt(3)) A = h*1 - h*2*h/sqrt(3) A = h - 2h^2/sqrt(3) We now have a quadratic equation where A = -2/sqrt(3), b = 1, and c=0. We can solve the problem by using a bit of calculus and calculating the first derivative, then solving for 0. But since this is a simple quadratic, we could also take advantage that a parabola is symmetrical and that the maximum value will be the midpoint between it's roots. So let's use the quadratic formula and solve it that way. The 2 roots are 0, and 1.5/sqrt(3). The midpoint is (0 + 1.5/sqrt(3))/2 = 1.5/sqrt(3) / 2 = 0.75/sqrt(3) So the desired height is 0.75/sqrt(3). Now let's calculate the width: w = 1 - 2*h/sqrt(3) w = 1 - 2* 0.75/sqrt(3) /sqrt(3) w = 1 - 2* 0.75/3 w = 1 - 1.5/3 w = 1 - 0.5 w = 0.5 The area is A = hw A = 0.75/sqrt(3) * 0.5 A = 0.375/sqrt(3) Now as I said earlier, we could use the first derivative. Let's do that as well and see what happens. A = h - 2h^2/sqrt(3) A' = 1h^0 - 4h/sqrt(3) A' = 1 - 4h/sqrt(3) Now solve for 0. A' = 1 - 4h/sqrt(3) 0 = 1 - 4h/sqrt(3) 4h/sqrt(3) = 1 4h = sqrt(3) h = sqrt(3)/4 w = 1 - 2*(sqrt(3)/4)/sqrt(3) w = 1 - 2/4 w = 1 -1/2 w = 1/2 A = wh A = 1/2 * sqrt(3)/4 A = sqrt(3)/8 And the other method got us 0.375/sqrt(3). Are they the same? Let's see. 0.375/sqrt(3) Multiply top and bottom by sqrt(3) 0.375*sqrt(3)/3 Multiply top and bottom by 8 3*sqrt(3)/24 Divide top and bottom by 3 sqrt(3)/8 Yep, they're the same. And since sqrt(3)/8 looks so much nicer than 0.375/sqrt(3), let's use that as the answer.</span>
7 0
3 years ago
Read 2 more answers
Tim just took a job working for a software company. His contract states he will receive an annual salary of $61,500 and be paid
PilotLPTM [1.2K]

Answer:

$3,722.875

Step-by-step explanation:

It was stated that the $61,500 would be payed to Tim annually, therefore before we can calculate the deductions we would first have to divide the annual pay by 12 (months in a year). You would then find that Tim receives $5,125 each month. The total value of the deductions would be 21.7% ( 6.2 + 1.5 + 3 + 11 = 21.7). 21.7% of 5,125 is 1,112.125 therefore, we would subtract this value and the value for the insurance from his monthly pay to find his net paycheck per month [5,125 - (1,112.125 + 290) = $3,722.875]

3 0
2 years ago
Marvin marked off the ground for a rectangular garden. The garden was to have an area represented by the polynomial expression 2
mafiozo [28]

Answer:  621

Step-by-step explanation: 28^2+ 13 − 176

length, width, and height.

8 0
2 years ago
Is it legal to travel down a road in reverse, as long as your following the direction of the traffic?
raketka [301]

technically yes but please do not.

4 0
2 years ago
Solve by completing the square. Round your answers to the nearest tenth and then locate the greater solution. <img src="https://
Andrews [41]

Step-by-step explanation:

Step 1: Write our Givens

{x}^{2}  + 10x - 7 = 0

Move the constant term ,(the term with no variable) to the right side.

Here we have a negative 7, so we add 7 to both sides

{x}^{2}  + 10x = 7

Next, we take the linear coeffeicent and divide it by 2 then square it.

( \frac{10}{2} ) {}^{2}  = 25

Then we add that to both sides

{x}^{2}  + 10x + 25 = 7 + 25

{ {x}^{2} } + 10x + 25 = 32

Next, we factor the left,

(x + 5)(x + 5) = 32

we got 5 because 5 add to 10 and multiply to 25 as well.

so we get

(x + 5) {}^{2}  = 32

This is called a perfect square trinomial.

Next, we take the square root of both sides

x + 5 = ± \sqrt{32}

± menas that we have a positive and negative solution.

Subtract 5 form both side so we get

x =  - 5± \sqrt{32}

The greater solution is when sqr root of 32 is positive so the answer to that is

\sqrt{32}  - 5 = 0.7

3 0
2 years ago
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