For the given points to lie on the parabola,
a = -3 and k = 10.
An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the directrix and focus, respectively. It's also crucial to remember that the fixed point is not located on the fixed line. A parabola is a locus of any point that is equally distant from a given point (focus) and a certain line (directrix).
According to the question,
Equation of parabola : y = a
+ k
Points A(1,7) and B(4,-2)
For the points to lie on the parabola,
7 = a
+k
7 = a + k
Similarly,
-2 = a
+ k
-2 = 4a + k
On solving the two equations simultaneously, we get,
a = -3
k = 10
Learn more about parabolas here:
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11 for the first one and 12 for the second one
Answer:
At 0 hours, there are 100 grams of the substance remaining.
Step-by-step explanation:
Hey there!
This linear equation is written in standard form, a form in which it's quite easy to find intercepts for one main reason. This reason revolves around zeros. When you see an x intercept, there's always a zero for the y, and when there's a y you see a zero for the x. Therefore, we can do this to get the intercepts.
For x:
2x-5(0) =10
2x = 10
x = (5,0)
For y:
2(0) -5y = 10
-5y=10
y= (0,-2)
Now, to find the slope, we can easily convert it to slope intercept form:
y = mx+b
Where m is the slope and b is he y intercept.
2x-5y=10
-5y=-2x+10
y = 2/5x-2
(notice how we divided both sides by -5)
Therefore, our slope is 2/5. Hope this helps!
