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.
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.
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Answer: discrete
Step-by-step explanation:
The graph would be discrete, because you can only order a whole number of pizzas. This means you cannot have 0.4 of a pizza or 3/5 of a pizza. Therefore, p can only be whole numbers, so you cannot draw a line through the points, since prices for non-whole pizzas are not possible.
The graph representing the cost of delivered pizzas depending on the number ordered is discrete because you can only order a whole number of pizzas, therefore the graph will show distinct points for each whole number of pizzas.
The graph representing the cost C, in dollars, for delivered pizza depending on the number p of pizzas ordered would be discrete. This is because you can only order a whole number of pizzas, not a fraction of a pizza. In this case, the number of pizzas p is a discrete variable, as is the cost C. A continuous graph has points that are connected, showing all possible values, while a discrete graph consists of isolated points representing specific values. In our pizza scenario, the graph would indicate specific costs for 1 pizza, 2 pizzas, 3 pizzas, and so on. Hence, the graph will be a series of distinct points, making it a discrete graph.
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Find the longest side of a parallelogram.
Perimeter of parallelogram = 2 ( a + b )
We know that,
Perimeter of parallelogram = 2 ( a + b )
★ Substituting the values in the above formula,we get:
⇒ 66 = 2 ( 3x + 1 + 2x - 3 )
⇒ 66 = 2 ( 5x - 2 )
⇒ 66/2 = 5x - 2
⇒ 33 = 5x - 2
⇒ 5x - 2 = 33
⇒ 5x = 33 + 2
⇒ 5x = 35
⇒ x = 35/5
⇒ x = 7 ft
Now,
One side,a = 3x + 1
★ Putting the value of x
⇒ 3 × 7 + 1
⇒ 21 + 1
⇒ 22 ft
Other side,b = 2x - 3
★ Putting the value of x
⇒ 2 × 7 - 3
⇒ 14 - 3
⇒ 11 ft
Hence,thelongestSideofgivenparallelogramis22ft(3x+1).
AB = AD
AB = AC
AB= AC times AE/AD
AB= AE times AD/AB
Answer:
AB= AC times AE/AD
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional
so
In this problem
AB/AC=AE/AD
solve for AB
AB=(AC)(AE)/AD
Answer:
AB= AC times AE/AD
Step-by-step explanation:
AB is on the segment AC, therefore it is proportional to AC.
In order to fulfill the requirement that triangle ABE is a smaller scaled replica of triangle ACD, a scale factor must be applied to the sides of the original figure; in this case, the factor is AE/AD.