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Zanzabum
3 years ago
10

In your lab, a substance's temperature has been observed to follow the function T(x) = (x − 1)3 + 5. The turning point of the gr

aph is where the substance changes from a liquid to a gas. Using complete sentences in your written answer, explain to your fellow scientists how to find the turning point of this function. Hint: The turning point of the graph is similar to the vertex of a quadratic function. (10 points)
Mathematics
1 answer:
Iteru [2.4K]3 years ago
4 0
If it is a calculus question then you can find the derivative dT/dx, set it to zero and solve for x.  If this is a pre-calculus question, then you can answer is it as follows: 

The function T = x^3 has a turning point at x = 0. We can determine this simply by looking at the graph T = x^3. Therefore, (0,0) is the turning point for the graph T = x^3. The function T(x) = (x - 4)^3 + 6 will be the graph T = x^3 shifted to the right by 4 units and shifted up by 6 units. Therefore, the turning point will also shift from (0,0) to 4 units to the right and 6 units up. The turning point will be (4,6) for the function T(x) = (x - 4)^3 + 6.

You're welcome :)


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The height of a trapezoid is 26 yards and the bases are 14 and 30 yards. What is the area (in square yards)?
faust18 [17]

Answer: 572 yards

Step-by-step explanation:

The equation to find the area of a (base1 + base2) x height/2

The two bases are 14 and 30. Add them up to get 44.

Then, times that by the height. You get 1,144.

Lastly, divide 1,144 by 2. You get 572.

I hope this helped!

5 0
2 years ago
SO basically uhh I suck at math
postnew [5]
Ok so you plug them in. -5 squared is 25 minus 27
6 0
3 years ago
Read 2 more answers
Suppose the diameter of a circle is 6 units What is its circumference?
Kipish [7]

Answer:

18.84 estimated, 6π exactly

Step-by-step explanation:

Hi!

<u>The formula for finding the circumference of a circle is 2πr:</u>

In that case, all we need to do <em>first </em>is to divide the diameter by 2, so we can substitute that into the equation.

6 ÷ 2 = 3

So we have 2π × 3 to solve.

2π × 3 = 6π

We can estimate the circumference by multiplying by 3.14.

6 × 3.14 = 18.84

(actually multiplying by π gives 18.849... which is pretty close!)

Thus, the circumference is \boxed{6\pi{\text{\:or\:18.84\:roughly}}}.

Hope this helps!

6 0
2 years ago
What is 1+9-6+5-9+3-6-7+2-5=…….
Scorpion4ik [409]

Answer:

The anwser to your question would be negative 23 (-23)

3 0
2 years ago
One person wants to get a 95% z-confidence interval with a margin of error of at most 15 based on a population standard deviatio
Bess [88]

Answer:

n=(\frac{1.96(60)}{15})^2 =61.46 \approx 62  

So the answer for this case would be n=62 rounded up to the nearest integer  

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

\bar X represent the sample mean for the sample  

\mu population mean

\sigma=60 represent the population standard deviation  

n represent the sample size (variable of interest)  

Confidence =95% or 0.95

The margin of error is given by this formula:  

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}} (1)  

And on this case we have that ME =15, and we are interested in order to find the value of n, if we solve n from equation (1) we got:  

n=(\frac{z_{\alpha/2} \sigma}{ME})^2 (2)  

The critical value for 95% of confidence interval is provided, z_{\alpha/2}=1.96, replacing into formula (2) we got:  

n=(\frac{1.96(60)}{15})^2 =61.46 \approx 62  

So the answer for this case would be n=62 rounded up to the nearest integer  

6 0
3 years ago
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