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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 :)


You might be interested in
B
VARVARA [1.3K]

Answer:

Hypothenus = 22

Step-by-step explanation:

From the question given above, we were told that the triangles are congruent (i.e same size). Thus,

AC = EF

BC = DE

To obtain the length of each Hypothenus, we shall determine the value of y and x. This can be obtained as follow:

For y:

AC = y + 3

EF = 2y + 1

AC = EF

y + 3 = 2y + 1

Collect like terms

3 – 1 = 2y – y

2 = y

y = 2

For x:

BC = 5x + 7

DE = 6x + 2y

y = 2

DE = 6x + 2(2)

DE = 6x + 4

BC = DE

5x + 7 = 6x + 4

Collect like terms

7 – 4 = 6x – 5x

3 = x

x = 3

Finally, we shall determine the length of each Hypothenus. This can be obtained as follow:

Hypothenus = BC

Hypothenus = 5x + 7

x = 3

Hypothenus = 5x + 7

Hypothenus = 5(3) + 7

Hypothenus = 15 + 7

Hypothenus = 22

OR

Hypothenus = DE

DE = 6x + 2y

y = 2

x = 3

Hypothenus = 6(3) + 2(2)

Hypothenus = 18 + 4

Hypothenus = 22

5 0
3 years ago
Pi is an irrational number. could pi = 22/7? why or why not?
Marina CMI [18]
No, it can't.

Irrational numbers are numbers that cannot be expressed as fractions.

So therefore, Pi cannot equal 22/7.
4 0
3 years ago
Read 2 more answers
I asked before and didn’t get an answer I really don’t understand this thanks.
dmitriy555 [2]
The answer is D, because that is what you should get when you multiply it out.

4x^2 times x^2 = 4x^4 because...

1) multiply the 4 and the one in front of the x on the second term = 4 then

2) multiply x^2 times x^2 to get x^4, not x^3, so you can immediately eliminate A and B to save time.

Now let's deal with the second part..."may or may not be" part

A polynomial is an expression with more than two algebraic terms

terms are like...
2x + 3y ---there's two terms there, eventhough the 2 and x are multiplied, it doesn't count (same with the 3 and y)
since it only have two terms, not more than two terms, it is called a binomial, not polynomial. I think that's what they mean by that

one term with a variable (y,x,and so on) is called a monomial

one term with no var is called a constant

there's many more but hope this gave you some help
3 0
3 years ago
Read 2 more answers
Please help I don’t know how to do this! It’s circle theorem geometry
slega [8]

Answer:

AC = 10

Step-by-step explanation:

Two tangents drawn to a circle from the same exterior point are congruent.

AC = AB

Since AB = 10, then

AC = 10

3 0
3 years ago
So, the square root of 72 lies between the numbers which The number 72 lies between the perfect squares means the square root of
Contact [7]

Answer: 64 and 81

Step-by-step explanation: I used my brain. :)

8 0
3 years ago
Read 2 more answers
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