What is the equation of the line that passes through the point (-4,-8)(−4,−8) and has a slope of 4
1 answer:
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Answer:
Step-by-step explanation:
The area of a pie-slice shape can be found with the equation where n is the angle of the shape and r is the radius of the circle. In this case, n=60 and r=6. Therefore, the total area of the pie-slice is
Next, the triangle that makes up the unshaded part of the segment is an equilateral triangle because the angle is 60. The area of an equilateral triangle is where r is the length of one of its side (in this case, r=6). Plugging that in, we get an area of
Finally, the area of the shaded is the area of the pie-slice minus the area of the triangle:
Answer:
Dimensions: 125 m x 250 m
Area: 31,250 m²
Step-by-step explanation:
Given information:
- Total amount of fencing = 500m
- Only 3 sides of the land need to be fenced
First, let us assume that the land is <u>rectangular</u> in shape.
Let = length of the side opposite the river
Let = length of the other 2 sides of the land
Therefore, we can create two equations from the given information:
<u>Area of land</u>:
<u>Perimeter of fence</u>:
Rearrange the equation for the perimeter of the fence to make y the subject:
Substitute this into the equation for Area:
To find the value of x that will make the area a <em>maximum</em>, <u>differentiate</u> A with respect to x:
Set it to zero and solve for x:
Substitute the found value of x into the original equation for the perimeter and solve for y:
Therefore, the dimensions that will give Christine the maximum area are:
125 m x 250 m (where 250 m is the side opposite the river)
The maximum area is: