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Can you solve all quadratic equations?
NO!!!! On a graph a quadratic equation becomes a parabolic curve. If this curve intersects the x-axis in two places. then there are two different answers. If the curve just touches the x-axix on one place then there are two answers which both have the same valuer. If the curve does NOT touch the x-axis the there are NO solutions.
Where do you find the solutions to a quadratic equation on a graph?
The solutions to a quadratic equation on a graph are the two points that cross the x-axis. NB A graphed quadratic equ'n produces a parabolic curve. If the curve crosses the x-axis in two different points it has two solution. If the quadratic curve just touches the x-axis , there is only ONE solution. It the quadratic curve does NOT touch the x-axis , then there are NO solutions. NNB In a quadratic equation, if the 'x^(2)' value is positive, then it produces a 'bowl' shaped curve. Conversely, if the 'x^(2)' value is negative, then it produces a 'umbrella' shaped curve.
How do you find the area between a given curve and x-axis?
Take the definite integral (and your bounds should be the two places where the curve crosses the x-axis).
Why not every line has both an x- and a y- intercept?
Some lines does not touch the x-axis or y-axis. For example, when the equation of line is y=1, the line never touches the y-axis [coordinates on the line would be (_,1)]. Equations such as y=1/x will not touch both axis.
Which of these is a closed curve that is longer along one axis?
ellipse
Do the Asymptotic means that the normal curve gets closer and closer to the X-axis but never actually touches it?
yes, an asymptote is a curve that gets closer but never touches the x axis.
Can marginal rate of substitution may increase or decrease in absolute value as one moves southeast along an indifference curve depending upon whether the substitution or income effect is dominant?
Indifference curves are downward sloping (negative slope) - therefore they are flatter towards the south east. the marginal rate of substitution is defined as the amount of good y (along the y axis) that is necessary to substitute for 1 good x (along the x axis) so that the effective bundle (or utility) remains the same. In effect the MRS is the slope of the indifference curve at a particular point. Therefore, MRS decreases as you move southeast along an indifference curve.
Can you solve all quadratic equations?
NO!!!! On a graph a quadratic equation becomes a parabolic curve. If this curve intersects the x-axis in two places. then there are two different answers. If the curve just touches the x-axix on one place then there are two answers which both have the same valuer. If the curve does NOT touch the x-axis the there are NO solutions.
Describe the characteristics of indifference curve?
Properties/Characteristics of Indifference Curve:Definition, Explanation and Diagram:An indifference curve shows combination of goods between which a person is indifferent. The main attributes or properties or characteristics of indifference curves are as follows:(1) Indifference Curves are Negatively Sloped:The indifference curves must slope down from left to right. This means that an indifference curve is negatively sloped. It slopes downward because as the consumer increases the consumption of X commodity, he has to give up certain units of Y commodity in order to maintain the same level of satisfaction.In fig. 3.4 the two combinations of commodity cooking oil and commodity wheat is shown by the points a and b on the same indifference curve. The consumer is indifferent towards points a and b as they represent equal level of satisfaction.At point (a) on the indifference curve, the consumer is satisfied with OE units of ghee and OD units of wheat. He is equally satisfied with OF units of ghee and OK units of wheat shown by point b on the indifference curve. It is only on the negatively sloped curve that different points representing different combinations of goods X and Y give the same level of satisfaction to make the consumer indifferent.(2) Higher Indifference Curve Represents Higher Level:A higher indifference curve that lies above and to the right of another indifference curve represents a higher level of satisfaction and combination on a lower indifference curve yields a lower satisfaction.In other words, we can say that the combination of goods which lies on a higher indifference curve will be preferred by a consumer to the combination which lies on a lower indifference curve.In this diagram (3.5) there are three indifference curves, IC1, IC2 and IC3 which represents different levels of satisfaction. The indifference curve IC3 shows greater amount of satisfaction and it contains more of both goods than IC2 and IC1 (IC3 > IC2 > IC1).(3) Indifference Curve are Convex to the Origin:This is an important property of indifference curves. They are convex to the origin (bowed inward). This is equivalent to saying that as the consumer substitutes commodity X for commodity Y, the marginal rate of substitution diminishes of X for Y along an indifference curve.In this figure (3.6) as the consumer moves from A to B to C to D, the willingness to substitute good X for good Y diminishes. This means that as the amount of good X is increased by equal amounts, that of good Y diminishes by smaller amounts. The marginal rate of substitution of X for Y is the quantity of Y good that the consumer is willing to give up to gain a marginal unit of good X. The slope of IC is negative. It is convex to the origin.(4) Indifference Curve Cannot Intersect Each Other:Given the definition of indifference curve and the assumptions behind it, the indifference curves cannot intersect each other. It is because at the point of tangency, the higher curve will give as much as of the two commodities as is given by the lower indifference curve. This is absurd and impossible.In fig 3.7, two indifference curves are showing cutting each other at point B. The combinations represented by points B and F given equal satisfaction to the consumer because both lie on the same indifference curve IC2. Similarly the combinations shows by points B and E on indifference curve IC1 give equal satisfaction top the consumer.If combination F is equal to combination B in terms of satisfaction and combination E is equal to combination B in satisfaction. It follows that the combination F will be equivalent to E in terms of satisfaction. This conclusion looks quite funny because combination F on IC2 contains more of good Y (wheat) than combination which gives more satisfaction to the consumer. We, therefore, conclude that indifference curves cannot cut each other.(5) Indifference Curves do not Touch the Horizontal or Vertical Axis:One of the basic assumptions of indifference curves is that the consumer purchases combinations of different commodities. He is not supposed to purchase only one commodity. In that case indifference curve will touch one axis. This violates the basic assumption of indifference curves.In fig. 3.8, it is shown that the in difference IC touches Y axis at point C and X axis at point E. At point C, the consumer purchase only OC commodity of rice and no commodity of wheat, similarly at point E, he buys OE quantity of wheat and no amount of rice. Such indifference curves are against our basic assumption. Our basic assumption is that the consumer buys two goods in combination.
Where do you find the solutions to a quadratic equation on a graph?
The solutions to a quadratic equation on a graph are the two points that cross the x-axis. NB A graphed quadratic equ'n produces a parabolic curve. If the curve crosses the x-axis in two different points it has two solution. If the quadratic curve just touches the x-axis , there is only ONE solution. It the quadratic curve does NOT touch the x-axis , then there are NO solutions. NNB In a quadratic equation, if the 'x^(2)' value is positive, then it produces a 'bowl' shaped curve. Conversely, if the 'x^(2)' value is negative, then it produces a 'umbrella' shaped curve.
What does tangent to the y axis mean?
Normally a straight line is a tangent to a curved line but, presumably, that relationship can be reversed. So a tangent to the y axis would be a curve that just touches the y axis but does not cross it - at least, not at the point of tangency.
Why two tail of normal distribution do not touch the horizontal axis?
The domain of the Normal distribution is the whole of the real line. As a result the horizontal axis is asymptotic to the Normal distribution curve. The curve gets closer and closer to the axis but never, ever reaches it.
What are characteristics of indifference curve?
1.it is convex to the origin 2.they can not intersect each other 3.they dnt need to be parallel to each other 4. they can't touch the axis 5.they are negativley sloped
Distinguish between demand curve and engel curve?
The difference is the Y- axis. In the case of the Demand curve the Y - axis is the retail price of the good. On the Engel's curve the Y -axis is the amount of income over a set period of time.
What is the y-intercept of x equals 8?
The graph of [ x=8 ] is a vertical line through the point 8 on the x-axis. It never touches the y-axis, and has no y-intercept.
What is typically displayed on the x-axis of a solubility curve?
The x-axis of a solubility curve typically displays temperature in degrees Celsius.
How do you find the area between a given curve and x-axis?
Take the definite integral (and your bounds should be the two places where the curve crosses the x-axis).
