Which of the following does not have a sum of -4?-8 + 4
-6 + 2
(-4) + 8
2 + (-6)

Answers

Answer 1

Answer: (-4) + 8 = 4
(-----------------)

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Is the number ��12/4 rational

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Yes because

12/4 is 3

if the perimeter of a circular sector is fixed at 100 ft, what values of r and s give the sector the greatest area? ...?

Answers

The sector arc length is just a fraction of the circumference:
Laʀc = (2πR) • (θ ⁄ 2π) = R • θ ... where θ = central angle (of sector)

Ps = R + R + (R • θ) ... perimeter of sector = Ps

Ps = R • (2 + θ) ... Ps = 100 ft

100 = R • (2 + θ)

θ = (100 ⁄ R) – 2

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...

Similarly, the sector area is just a fraction of the circle area:

As = (πR²) • (θ ⁄ 2π) ... area of sector = As

As = R² • θ ⁄ 2 ... substitute for θ

As = R² • [(100 ⁄ R) – 2 ] ⁄ 2

As = 50R – R² ... differentiate

As' = 50 – 2R ... set to zero

0 = 50 – 2R

R = 25 ft ... optimum radius

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...

As = 50R – R² ... evaluate at: R = 25 ft

As = 50(25) – (25)²

As = 625 ft² ... maximum area

Note ... at any other R_value, the sector area is less.

" θ " can be determined using: θ = (100 ⁄ R) – 2

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Final answer:

For a circular sector with a fixed perimeter of 100 ft, the values of radius (r) and arc length (s) that will maximize the sector's area are r=25 and s=50.

Explanation:

The perimeter of a circular sector is composed by the length of the arc (s) plus twice the radius (r). If this sum is fixed at 100 ft, then the length of the arc s is equal to 100 - 2r. The area A of a circular sector can be defined as A = 0.5 * r * s.

Substituting the expression for s into the area formula obtains A = 0.5 * r * (100-2r). Simplifying results in A = 50r - r^2 which is a downward opening parabola.

The maximum value of a parabola occurs at the vertex. For a parabola in the form y=ax^2 + bx + c, the x-coordinate of the vertex is -b/(2a). In this case, a=-1 and b=50, hence r=-50/2*(-1) = 25. Substituting r=25 back into the formula for s obtains s = 100-2*25 = 50. Therefore, the values for r and s that will give the circular sector the greatest area are r=25 and s=50.

Learn more about Perimeters and Areas here:

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Help plsss I’m a little confused
We started this today :/

Answers

We can’t see the question

I can’t see the question later

Round to the nears ten 9.42?

Answers

Answer:

Step-by-step explanation:

In order to round to the nearest ten you must think: what is the nearest multiple of 10. For example, to round 68 to the nearest 10, the nearest whole number is 70, so the answer would be 70. However if you were to round 63 to the nearest 10, to would be 50 since that is the nearest multiple of 10

Answer:9

Step-by-step explanation:

Since the next number is below five you don’t round up it just stays the same

Two men decide to drive to a distant town, taking the same route. The first leaves 2 hours ahead of the second and drives at 60 km per hour, while the second man drives at 90 km per hour. How many hours will it take the second man to catch up with the first man?

Answers

Answer:

$t = 6\,h$

Step-by-step explanation:

Given that both men moves at constant speed on the same trail, the motion equations that describes each motion are, respectively:

Man 1

$x = 60 \cdot t$

Man 2

$x = 90 \cdot (t-2)$

Where x is measure in kilometers and t in hours, respectively.

The time taken for both men to meet each other is:

$60\cdot t = 90\cdot (t-2)$

$30\cdot t = 180$

$t = 6\,h$

Answer: 4 hours

Step-by-step explanation:

2 x 60 =120

90-60=30

120/30= 4

What is the slope of the line that passes through the pair of points (2,6)(7,0)

Answers

Hi!

To find the slope, we use this equation.
$(y2 - y1)/(x2 - x1)$
Insert the values
$(0 - 6)/(7-2)$
Solve
$- (6)/(5)$

The answer is $- (6)/(5)$

Hope this helps! :)
-Peredhel