Answer:
x = 2 cm
y = 2 cm
A(max) = 4 cm²
Step-by-step explanation: See Annex
The right isosceles triangle has two 45° angles and the right angle.
tan 45° = 1 = x / 4 - y or x = 4 - y y = 4 - x
A(r) = x* y
Area of the rectangle as a function of x
A(x) = x * ( 4 - x ) A(x) = 4*x - x²
Tacking derivatives on both sides of the equation:
A´(x) = 4 - 2*x A´(x) = 0 4 - 2*x = 0
2*x = 4
x = 2 cm
And y = 4 - 2 = 2 cm
The rectangle of maximum area result to be a square of side 2 cm
A(max) = 2*2 = 4 cm²
To find out if A(x) has a maximum in the point x = 2
We get the second derivative
A´´(x) = -2 A´´(x) < 0 then A(x) has a maximum at x = 2
Answer:
6 different primes.
3, 7, 13, 29, 31 , 89.
Step-by-step explanation:
Try dividing by primes starting with 3:
3 ) 65529009
3 ) 21843003
7) 7281001
13) 1040143
29) 80011
31 ( 2759
89. 89 is a prime number.
Answer:
180 cm²
Step-by-step explanation:
From inspection of the diagram, the surface area is made up of the area of 4 congruent triangles and the area of one square.
Area of a square = x² (where x is the length of one side)
⇒ area of the square = 6² = 36 cm²
Area of a triangle = 1/2 x base x height
⇒ area of one triangle = 1/2 x 6 x 12 = 36 cm²
Total surface area = 4 x area of one triangle + area of the square
= 4 x 36 + 36
= 144 + 36
= 180 cm²
Answer:
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Step-by-step explanation:
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