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Andrews [41]
3 years ago
13

From 10:00 am to noon, the rise in temperature is 4 degrees C, and from 3:00 pm to 5:00 pm, the fall in temperature is 6 degrees

C. What is the average rate of: a) The rise in temperature per hour? b) The fall in temperature per hour?
Mathematics
1 answer:
lyudmila [28]3 years ago
3 0

Answer:

(a) 2 degree celsius per hour

(b) 3 degree celsius per hour.

Step-by-step explanation:

From the question,

(a) Avearge rate of rise in temperature per hour(T') = Rise in temperature(T)/Time required for the rise(t).

T' = T/t.................... Euqation 1

Rise in temperature (T) = 4 degree celsius, t = 10.00 am to noon = 2 hours.

Substitute into equation 1

T' = 4/2

T' = 2 degree celsius per hour.

(b) Also,

Average rate of fall in temperature per hour (T') = Fall in temperature (T)/Time(t)

T' = T/t

Given: T = 6 degree celsius, t = 3:00 pm to 5:00 pm = 2 hours

T' = 6/2

T' = 3 degree celsius per hour

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Answer:

m(∠C) = 18°

Step-by-step explanation:

From the picture attached,

m(arc BD) = 20°

m(arc DE) = 104°

Measure of the angle between secant and the tangent drawn from a point outside the circle is half the difference of the measures of intercepted arcs.

m(∠C) = \frac{1}{2}[\text{arc(EA)}-\text{arc(BD)}]

Since, AB is a diameter,

m(arc BD) + m(arc DE) + m(arc EA) = 180°

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Therefore, m(∠C) = \frac{1}{2}(56^{\circ}-20^{\circ})

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Answers:

  1. Discrete
  2. Continuous
  3. Discrete
  4. Continuous

==============================================

Explanations:

  1. This is discrete because we can't have half a basketball, or any non-whole decimal value to represent the number of basketballs. We can only consider positive whole numbers {1,2,3,4,...}. A discrete set like this has gaps between items. In other words, the midpoint of 2 and 3 (the value 2.5) isn't a valid number of basketballs.
  2. This is continuous because time values are continuous. We can take any two different markers in time, and find a midpoint between them. For example, the midpoint of 5 minutes and 17 minutes is 11 minutes since (5+17)/2 = 22/2 = 11. Continuous sets like this do not have any gaps between items. We can consider this to be densely packed.
  3. This is the same as problem 1, so we have another discrete function. You either score a bullseye or you don't. We can't score half a bullseye. The only possible values are {1,2,3,4,...}
  4. This is similar to problem 2. This function is continuous. Pick any two different positive real numbers to represent the amount of gallons of water. You will always be able to find a midpoint between those values (eg: we can have half a gallon) and such a measurement makes sense.

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