Answer:
Step-by-step explanation:
n + 2 = 3(1/3n + 6)
n + 2 = n + 18
NO NUMBERS....because this equation has no solution
Answer:
x = 35
y = 7
Step-by-step explanation:
See how the image looks like two overlapping triangles. It is given that the triangles are congruent. Its easier to see whats what if you draw the triangles separately. I also flipped over the triangle on the right so they match. Record the given angle measures. Since A is 45° then D is also 45°. DBC is 30°, so we can find the missing angle in triangle DBC. Angles in a triangle add up to 180° so
C + 45 + 30 = 180
C + 75 = 180
C = 105°
This is angle DCB.
Now all the angles are marked. We can set up equations to find x and y. see image.
Answer:
x = 8,49 ft
y = 4,24 ft
Step-by-step explanation:
Let x be the longer side of rectangle and y the shorter
Area of rectangle = 36 ft² 36 = x* y ⇒ y =36/x
Perimeter of rectangle:
P = 2x + 2y for convinience we will write it as P = ( 2x + y ) + y
C(x,y) = 1 * ( 2x + y ) + 3* y
The cost equation as function of x is:
C(x) = 2x + 36/x + 108/x
C(x) = 2x + 144/x
Taking derivatives on both sides of the equation
C´(x) = 2 - 144/x²
C´(x) = 0 2 - 144/x² = 0 ⇒ 2x² -144 = 0 ⇒ x² = 72
x = 8,49 ft y = 36/8.49 y = 4,24 ft
How can we be sure that value will give us a minimun
We get second derivative
C´(x) = 2 - 144/x² ⇒C´´(x) = 2x (144)/ x⁴
so C´´(x) > 0
condition for a minimum
Answer:
Part A: 60
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60.
12, 24, 36, 48, 60.
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Part B: 9
81 / 72 = 9
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Part C: 9 (8 + 9)
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GCF of 72 and 81 is 9...
Divide 72 by 9 and get 8.
Divide 81 by 9 and get 9.
To check multiply 9 with 8, and multiply 9 by 9.
