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lina2011 [118]
3 years ago
14

Help -------------------------

Mathematics
1 answer:
34kurt3 years ago
8 0

Answer:

(A) -3 ≤ x ≤ 1

Step-by-step explanation:

The given function is presented as follows;

h(x) = x² - 1

From the given function, the coefficient of the quadratic term is positive, and therefore, the function is U shaped and has a minimum value, with the slope on the interval to the left of <em>h</em> having a negative rate of change;

The minimum value of h(x) is found as follows;

At the minimum of h(x), h'(x) = d(h(x)/dx = d(x² - 1)/dx = 2·x = 0

∴ x = 0/2 = 0 at the minimum

Therefore, the function is symmetrical about the point where x = 0

The average rate of change over an interval is given by the change in 'y' and x-values over the end-point in the interval, which is the slope of a straight line drawn between the points

The average rate of change will be negative where the y-value of the left boundary of the interval is higher than the y-value of the right boundary of the interval, such that the line formed by joining the endpoints of the interval slope downwards from left to right

The distance from the x-value of left boundary of the interval that would have a negative slope from x = 0 will be more than the distance of the x-value of the right boundary of the interval

Therefore, the interval over which <em>h</em> has a negative rate of change is -3 ≤ x ≤ 1

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Answer:

(b) P(\textrm{Event of getting a 3 in the spinner)}  =  \frac{11}{61}

Step-by-step explanation:

Let E: Event of getting a 3 in the spinner.

So, the number of favorable outcomes  =  11

Total number of outcomes = Number of times the outcomes is {1,2,3,4,5,6}

= {13 +10 +11+16+11}  = { 61}

So, the total number of outcomes = 61

\textrm{Probability of Event E}  = \frac{\textrm{Number of favorable events}}{\textrm{Total number of outcomes}}

So, here P(\textrm{Event of getting a 3 in the spinner)}  =  \frac{11}{61}

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3 years ago
a car can travel 1 km in 1 minute and 12 seconds. How many km will the car travel in 1 hour at the given rate?
vampirchik [111]
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------------- =  ------------
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3 years ago
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Step-by-step explanation:

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