Answer:
Yes, the relationship between x and y is a non-linear function.
Step-by-step explanation:
Given the table
Edge Length, x Surface Area, y
1 6
2 24
3 54
4 96
- The table values clearly represent a function, because each input value has one and only one output value. i.e. there is no repetition of x values.
- Also from the table values and the graph, it is clear that the function is not a linear function, because the graph is not a straight line. Also, In a cubic function, the highest power over the x variable(s) is 3. So, it is not a linear function.
Hence, we conclude that Yes, the relationship between x and y is a non-linear function.
Therefore, the 'last option' is correct.
Answer:
(2, 11/2)
Step-by-step explanation:
This is a vertical parabola; we know that because x is squared here, while y is not. The standard equation of a vertical parabola with vertex (h,k) is
4p(y-k) = (x-h)^2, where p is the distance between the vertex and the focus. Comparing
4p(y-k) = (x-h)^2 to
10(y-3) = (x-2)^2, we see that 4p = 10. Therefore, p = 10/4 = 5/2, which is the vertical distance between the focus and the vertex.
Since the coordinates of the vertex are easily read from the given equation
(x-2)^2=10(y-3): (h,k) = (2, 3)
all we need to do is to add p (5/2) to the y-coordinate (3);
The focus is at (2, 3 + 5/2), or (2, 11/2).
Answer: D
Step-by-step explanation:
All would add up to 241 instead of 2.41 because you are not using decimals for the constants (Example: 25q not .25q)
<u>Answer:</u>
If PQ=RS then PQ and RS have the same length. Hence option D is correct
<u>Solution:</u>
Given that, pq = rs
And, we have to find which of the given options are true.
<u><em>a) pq and rs form a straight angle
</em></u>
We can’t decide the angle in between pq and rs just by the statement pq = rs.
So this statement is false.
<u><em>b) pq and rs form a zero angle.
</em></u>
We can’t decide the angle in between pq and rs just by the statement pq = rs.
So this statement is false.
<u><em>c) pq and rs are same segment.
</em></u>
If two things equal then there is no condition that both represents a single item.
So this statement is false.
<u><em>d) pq and rs have the same length
</em></u>
As given that pq = rs, we can say that they will have the same length
Hence, option d is true.
As usual, draw a diagram. You can easily see that if you are x away from the wall,
<span>the angle of elevation of the bottom of the screen (A) is </span>
<span>cotA = x/3 </span>
<span>A = arccot(x/3) </span>
<span>angle B to the top is </span>
<span>cotB = x/10 </span>
<span>B = arccot(x/10) </span>
<span>So, since θ = B-A </span>
<span>dθ/dt = dB/dt - dA/dt </span>
<span>= -3/(x^2+9) + 10/(x^2+100) </span>
<span>= 7(x^2-30)/((x^2+9)(x^2+100)) </span>
<span>so, at x=30 </span>
<span>dθ/dt = 203/30300</span>
