Answer:
0.5 Inches per hour
Step-by-step explanation:
Most normal people won't know exactly what unit rate is, or how to calculate it. So I'm here to help!
This is a fraction equal to
6 inches ÷ 12 hours
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 12
6 inches ÷ 12
12 hours ÷ 12
=
0.5 inches
1 hour
=
0.5 inches
hour
= 0.5 inches per hour
Glad I was able to help!
The minimum distance is the perpendicular distance. So establish the distance from the origin to the line using the distance formula.
The distance here is: <span><span>d2</span>=(x−0<span>)^2</span>+(y−0<span>)^2
</span> =<span>x^2</span>+<span>y^2
</span></span>
To minimize this function d^2 subject to the constraint, <span>2x+y−10=0
</span>If we substitute, the y-values the distance function can take will be related to the x-values by the line:<span>y=10−2x
</span>You can substitute this in for y in the distance function and take the derivative:
<span>d=sqrt [<span><span><span>x2</span>+(10−2x<span>)^2]
</span></span></span></span>
d′=1/2 (5x2−40x+100)^(−1/2) (10x−40)<span>
</span>Setting the derivative to zero to find optimal x,
<span><span>d′</span>=0→10x−40=0→x=4
</span>
This will be the x-value on the line such that the distance between the origin and line will be EITHER a maximum or minimum (technically, it should be checked afterward).
For x = 4, the corresponding y-value is found from the equation of the line (since we need the corresponding y-value on the line for this x-value).
Then y = 10 - 2(4) = 2.
So the point, P, is (4,2).
Answer:
Check below, please
Step-by-step explanation:
Step-by-step explanation:
1.For which values of x is f '(x) zero? (Enter your answers as a comma-separated list.)
When the derivative of a function is equal to zero, then it occurs when we have either a local minimum or a local maximum point. So for our x-coordinates we can say
2. For which values of x is f '(x) positive?
Whenever we have
then function is increasing. Since if we could start tracing tangent lines over that graph, those tangent lines would point up.
3. For which values of x is f '(x) negative?
On the other hand, every time the function is decreasing its derivative would be negative. The opposite case of the previous explanation. So
4.What do these values mean?
5.(b) For which values of x is f ''(x) zero?
In its inflection points, i.e. when the concavity of the curve changes. Since the function was not provided. There's no way to be precise, but roughly
at x=-4 and x=4
Answer:
70%
Step-by-step explanation:
Percentage is out of 100
35/50 change denominator
multiply both numerator and denominator by 2
70/100= 70%
Answer:
35/4 minutes per mile
Step-by-step explanation:
rate = time/distance, therefore the answer is 35/4
