Answer:
Rectangular area as a function of x : A(x) = 200*x + 2*x²
A(max) = 5000 m²
Dimensions:
x = 50 m
l = 100 m
Step-by-step explanation:
"x" is the length of the perpendicular side to the wall of the rectangular area to be fenced, and we call "l" the other side (parallel to the wall of the barn) then:
A(r) = x* l and the perimeter of the rectangular shape is
P = 2*x + 2*l but we won´t use any fencing material along the wll of the barn therefore
P = 2*x + l ⇒ 200 = 2*x + l ⇒ l = 200 - 2*x (1)
And the rectangular area as a function of x is:
A(x) = x * ( 200 - 2*x) ⇒ A(x) = 200*x + 2*x²
Taking derivatives on both sides of the equation we get:
A´(x) = 200 - 4*x ⇒ A´= 0
Then 200 - 4*x = 0 ⇒ 4*x = 200 ⇒ x = 50 m
We find the l value, plugging the value of x in equation (1)
l = 200 - 2*x ⇒ l = 200 - 2*50 ⇒ l = 100 m
A(max) = 100*50
A(max) = 5000 m²
Area of a triangle is 1/2b×h
a=1/2b×h
64=1/2 8×h
64= 4 × h
64÷4=16
Answer: the height is 16 inches
Answer: You would divide the rectangle into half, to form two congruent triangles. When you multiply the area of 1 of the triangles, it gives you the area of both triangles, and so the area of the triangle as a whole
X + (x − 2) + (x − 4) = ? ; In which
<span>
x + x </span>− 2 + x − 4 ;
Combine the "like terms" ;
x + x + x = 3x ;
− 2 − 4 = −6 ;
So we have: "3x − 6" as the sum. ;
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The sum of three consecutive odd integers, in which "x" is the greatest integer; is: "3x − 6" .
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Note: The three consecutive odd integers, from least to greatest, are:
"(x − 4)" , "(x − 2)" , and "x" .
The sum is: "(3x − 6)<span>" .
</span>_____________________________________________
Note: "(3x − 6)" factors into: " 3(x −2)" .
Note that: " (x − 2) " is the second integer.
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So the sum total, which is: "(3x − 6)" ; is 3 (three) times the value of the second integer; that is, "3 (x − 2)" .
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Answer:
\int\limits^{\pi/2} _0 (1+4cos^{2} (2x)dx
Step-by-step explanation:
Arc length is calculated by dividing the arcs in to small segments ds
By pythagoren theorem
then integrate ds to get arc length.
We are given a function as
y = sin 2x in the interval [0, pi/2]
To find arc length in the interval
Arc length 
Hence arc length would be
B) 
