<u><em>Answer:</em></u>
AC = 10sin(40°)
<u><em>Explanation:</em></u>
The diagram representing the question is shown in the attached image
Since the given triangle is a right-angled triangle, we can apply the special trig functions
<u>These functions are as follows:</u>
sin(θ) = opposite / hypotenuse
cos(θ) = adjacent / hypotenuse
tan(θ) = opposite / adjacent
<u>Now, in the given diagram:</u>
θ = 40°
AC is the side opposite to θ
AB = 10 in is the hypotenuse
<u>Based on these givens</u>, we will use the sin(θ) function
<u>Therefore:</u>
There’s no picture under your question
Let the length be x and the width be w
The perimeter will be:
2x+3w=1500
thus
3w=(1500-2x)
w=(1500-2x)/3
w=500-2/3x
The area will be:
A=x*w
A=x(500-2/3x)
A=500x-(2/3)x²
The above is a quadratic equation; thus finding the axis of symmetry we will evaluate for the value of x that will give us maximum area.
Axis of symmetry:
x=-b/(2a)
from our equation:
a=(-2/3) and b=500
thus
x=-500/[2(-2/3)]
x=375
the length will be 375 m
The width will be 250 m
If you multiply 38*(-36) you would get -1368. And to convert that into a fraction it could be -1368/1, -13680/10, etc.
The area of the shaded region is 40π/3 square cm if the radius of the small circle r is 3 cm and the radius of the large circle R is 7 cm.
<h3>What is a circle?</h3>
It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have a circle in which the shaded region is shown.
The radius of the small circle r = 3 cm
The radius of the large circle R = 3+4 = 7 cm
The area of the shaded region:
= area of the large circle sector - an area of the small circle sector
= (120/360)[π7²] - (120/360)[π3²]
= 49π/3 - 3π
= 40π/3 square cm or
= 13.34π square cm
Thus, the area of the shaded region is 40π/3 square cm if the radius of the small circle r is 3 cm and the radius of the large circle R is 7 cm.
Learn more about circle here:
brainly.com/question/11833983
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