Answer:
Step-by-step explanation:
For example, to find the common (positive) multiples of 4 and 6, we might list: Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, … Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, … The numbers 12, 24, 36, and 48 appear on both of these lists, and more would appear if the lists were longer.
Answer:
it would be A 160
Step-by-step explanation:
4 square plus + 12 square = 16+144=160
Answer:
x = 5.13 yards to the nearest tenth
Step-by-step explanation:
The diagram is redrawn and labelled in the attached photo.
It is labelled as triangle ABC. Angle A is determined to be 25 degrees. This is because it is alternate to 25 degrees at the top.
To find x, we will apply trigonometric ratio
Tan # =opposite side / adjacent side
Where # = 25 degrees
Opposite side = x
Adjacent side = 11
Tan 25 = x/11
x = 11tan25
x = 11× 0.4663
x = 5.1293 yards
x = 5.13 yards to the nearest tenth.
You do the implcit differentation, then solve for y' and check where this is defined.
In your case: Differentiate implicitly: 2xy + x²y' - y² - x*2yy' = 0
Solve for y': y'(x²-2xy) +2xy - y² = 0
y' = (2xy-y²) / (x²-2xy)
Check where defined: y' is not defined if the denominator becomes zero, i.e.
x² - 2xy = 0 x(x - 2y) = 0
This has formal solutions x=0 and y=x/2. Now we check whether these values are possible for the initially given definition of y:
0^2*y - 0*y^2 =? 4 0 =? 4
This is impossible, hence the function is not defined for 0, and we can disregard this.
x^2*(x/2) - x(x/2)^2 =? 4 x^3/2 - x^3/4 = 4 x^3/4 = 4 x^3=16 x^3 = 16 x = cubicroot(16)
This is a possible value for y, so we have a point where y is defined, but not y'.
The solution to all of it is hence D - { cubicroot(16) }, where D is the domain of y (which nobody has asked for in this example :-).
(Actually, the check whether 0 is in D is superfluous: If you write as solution D - { 0, cubicroot(16) }, this is also correct - only it so happens that 0 is not in D, so the set difference cannot take it out of there ...).
If someone asks for that D, you have to solve the definition for y and find that domain - I don't know of any [general] way to find the domain without solving for the explicit function).
Answer:
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Step-by-step explanation:
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