Using compatible numbers 911-347

When I see the words "instantaneous rate of change", I have to assume that you're in some stage of pre-calculus in your math class.

The instantaneous rate of change of a function is just its first derivative.

We have the function

V(r) = 3 π r²

and we need its first derivative with respect to ' r '. That shouldn't be
too hard, because the ' 3 π ' is nothing but constants.

Watch me while I do it slowly for you:

-- The derivative of ' r² ' with respect to ' r ' is ' 2r '.

-- The derivative of V(r) with respect to ' r ' is (3 π) times the derivative of ' r² '.

-- The derivative of V(r) with respect to ' r ' is (3 π) times (2r) = 6 π r .

The value of the derivative when r=3 is (6 π 3) = 18π = about 56.5 feet³/foot .

3 0

3 years ago

Suppose that the neighboring cities of Tweed and Ledee are long-term rivals. Neal, who was born and raised in Tweed, is confiden

Makovka662 [10]

Complete Question

The option to the blank space are shown on the first uploaded image

Answer:

Neal's decision is to fail to reject the null hypothesis (p 0.066). There is no sufficient evidence to prove the claim that the average electricity consumption of all Ledee household is greater than , 854.28 kWh

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 854.11$

The sample size is $n = 65$

The sample mean is $\= x = 879.28 \ kWh$

The standard deviation is $\sigma = 133.29 \ kWh$

The level of significance is $\alpha = 0.05$

The null hypothesis is $H_o: \mu = 854.11$

The alternative hypothesis is $H_a : \mu > 854.11$

The t-statistics is $t = 1.522$

The p-value is $p-value = 0.066$

Now from the given data we can see that

$p-value < \alpha$

Generally when this is the case , we fail to reject the null hypothesis

So

Neal's decision is to fail to reject the null hypothesis (p 0.066). There is no sufficient evidence to prove the claim that the average electricity consumption of all Ledee household is greater than , 854.28 kWh

8 0

3 years ago

S1 W2 Hwk

Vaselesa [24]

Answer: (7) see below (8) see below (9) NO (20) see below

Step-by-step explanation:

Inverse is when you swap the x's and y's, so switch the coordinates for the inverse.

(7)

f⁻¹(x) = (5, -13), (-9, -9), (-2, -5), (-5, 1), (-4, 0), (6, 4), (10, 9), (32, 14)

This is a function because there are no duplicate x-values.

(8)

The endpoints and vertex on the given graph are (-7, 2), (-1, -2), & (1, 4)

The graph should swap the x and y-values of the coordinates above for the endpoints and vertex, which results in (2, -7), (-2, -1) & (4, 1)

To graph the inverse, draw a line from (2, -7) to (-2, -1) and another line from (-2, -1) to (4, 1).

(9) This is not a function because it fails the vertical line test. In other words, there are duplicate x-values. You can draw a vertical line through x = 0 (as an example) and it touches two points.

In order to make this a function, you would have to restrict the domain to: x > 2

(20)

f⁻¹(x) = (5, -3), (-9, -2), (-2, -1), (-5, 0), (-4, 1), (6, 2), (10, 3), (8, 4)

This is a function because there are no duplicate x-values.

4 0

3 years ago