X is twenty
2x+6x+20=180
8x=160
X=20
The <em>instantaneous</em> rate of change of <em>g</em> with respect to <em>x</em> at <em>x = π/3</em> is <em>1/2</em>.
<h3>How to determine the instantaneous rate of change of a given function</h3>
The <em>instantaneous</em> rate of change at a given value of
can be found by concept of derivative, which is described below:

Where
is the <em>difference</em> rate.
In this question we must find an expression for the <em>instantaneous</em> rate of change of
if
and evaluate the resulting expression for
. Then, we have the following procedure below:




Now we evaluate
for
:

The <em>instantaneous</em> rate of change of <em>g</em> with respect to <em>x</em> at <em>x = π/3</em> is <em>1/2</em>. 
To learn more on rates of change, we kindly invite to check this verified question: brainly.com/question/11606037
Answer:
V ≈ 226.72 cm³
Step-by-step explanation:
Use the formula for volume of a cone using slant height and radius.
V = 1/3 π r² √ l² - r²
Then, plug in dimensions and solve.
V = 1/3 π (10)² √ 10² - 5²
V ≈ 226.72 cm³
Hope I could help!!! Good luck!!!
Answer:
Does this sample provide convincing evidence that the machine is working properly?
Yes.
Step-by-step explanation:
<u>Normal distribution test:</u>

Where,







Once the significance level was not given, It is usually taken an assumption of a 5% significance level.
Taking the significance level of 5%, which means a confidence level of 95%, we have a z-value of 
Therefore, we <u>fail to reject the null</u>. It means that the hypothesis test is not statistically significant: the average length is not different from 1.5!