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grin007 [14]
3 years ago
8

1. (04.01) Which of the sets of ordered pairs represents a function? (4 points)

Mathematics
1 answer:
leonid [27]3 years ago
6 0

Answer:only b

Step-by-step explanation:

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Find where the slope of the curve is defined:<br> x^2y-xy^2=4
Natali [406]
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). 
3 0
4 years ago
4/7 + 1/8 = what does this equal
Fudgin [204]

Answer:

39/56

Step-by-step explanation:

When you add fractions, both of the base numbers (denominators) have to be the same number in order to add the top numbers (numerators).

The easiest way to do this is to multiply each denominator by the other number. For example, 8 * 7 and 7 * 8. So you will have 56 and 56. You also need to multiple the numerator by that number. So, 1 * 7 and 4 * 8. So you will have 7 and 32. This will show as 7/56 + 32/56. Finally, add the numerators - > 39/56

3 0
3 years ago
Read 2 more answers
Mrs. habib has 46.25 feet of ribbon for a border around a bulletin board for her classroom.The board is 3.75 feet tall and 8.3 f
Kisachek [45]
46.25 - (2(3.75) + 2(8.3)) = 22.15 feet leftover. 
4 0
3 years ago
Why can't 1.07 be a strong positive correlation?
sineoko [7]
It cannot because it is almost a perfect correlation, and its not a high enough correlation.
4 0
3 years ago
The equation of a parabola is given in factored form.
ValentinkaMS [17]

Answer:

The parabola's axis of symmetry is x = -6

Step-by-step explanation:

Parabola general equation:

y = a*(x - r1)*(x - r2)

Equation given:

y = (-1/4)*(x + 2)*(x + 10)

a = -1/4

r1 = -2

r2 = -10

To check if the parabola passes through the point (2, 10) it is necessary to replace x = 2 and check the y-value, as follows:

y = (-1/4)*(2+ 2)*(2 + 10) = -12

Then, point (2, 10) is not included in the parabola.

If a > 0 then the parabola opens upward; if a < 0 then the parabola opens downward. Then, the parabola opens downward

Axis of symmetry:

h = (r1 + r2)/2

h = (-2 + -10)/2 = -6

Then, The parabola's axis of symmetry is x = -6

To find Parabola's vertex, replace with the axis of symmetry:

y = (-1/4)*(-6 + 2)*(-6 + 10) = 4

Therefore, the parabola has a vertex at (-6, 4)

7 0
4 years ago
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