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Alona [7]
2 years ago
5

Find the extreme values of the function and where they occur. f(x)=x-4sqrt(x)

Mathematics
1 answer:
Tema [17]2 years ago
3 0
The extreme values of the function f(x) = x - 4sqrt(x) occur at the values of x for which f'(x) = 0

f'(x) = 1 - 2/sqrt(x) = 0
sqrt(x) - 2 = 0
sqrt(x) = 2
x = 4
To check for minimum or maximum,
f''(x) = 1/(sqrt(x))^3 = 1/(sqrt(4))^3 = 1/(2^3) = 1/8 => the point is a minimum.

Therefore, the minimum value = f(4) = 4 - 4sqrt(4) = 4 - 4(2) = 4 - 8 = -4 and occurs at x = 4.
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The following stem-and-leaf plot represents the scores earned by Mr. Roberts's class on their most recent science test.
Alinara [238K]
First we need to count the total number scores. This can be done from the stem and leaf plot. The total number of scores are 19. The total number of values is odd, so the median position will be:

\frac{19+1}{2}=10th

Thus the 10th score is the median score for the class of Mr. Robert. The 10th score from the stem and leaf plot is 81.

Thus 81 is the median score of Mr. Robert's Class. 
5 0
3 years ago
Read 2 more answers
Sally had 7 stars and eric had 186 stars .he gave 27 to sally how many does he have left?
Ilya [14]
To solve this you can use subtraction
186-27=159 (for the amount Eric gave away)
So Eric has 159 stars left!
Hope this helped!!
3 0
2 years ago
Read 2 more answers
How do I find the vertex and the standard form? Plz explain
xenn [34]

Answer:

Vertex form

y = -4(x + 3)^2 + 10

Standard form;

y = -4x^2-24x - 26

Step-by-step explanation:

Mathematically, we have the vertex form as

y = a(x-h)^2 + k

(h,k) represents the vertex

We have h as -3 and k as 10

y = a(x+3)^2 + 10

To get a, we substitute any of the points

Let us use (-1,-6)

-6 = a(-1+3)^2 + 10

-6-10 = 4a

4a = -16

a = -16/4

a = -4

So we have the equation as;

y = -4(x+3)^2 + 10

For the standard form;

We expand the vertex form;

y = -4(x + 3)(x + 3) + 10

y = -4(x^2 + 6x + 9) + 10

y = -4x^2 - 24x -36 + 10

y = -4x^2 -24x -26

7 0
2 years ago
A circular garden is enlarged so that the new diameter is twice the old diameter. What is the ratio of the original area to the
Amanda [17]

Answer:

  • Explained briefly below.

Step-by-step explanation:

<u>For old circular garden:</u>

take the radius as r.

then use the formula to find area of circle: πr² ......this is old garden area.

<u>For new enlarged garden:</u>

the radius is twice the old radius so, radius = 2 * r = 2r ......enlarged radius

now find area for this new garden:  π(2r)² → 4πr²

In common fractions: (old garden)/(new garden)

                                : ( πr² ) / ( 4πr² )

                                 :    1/4

7 0
2 years ago
Read 2 more answers
On a particular airline, bags checked in must weigh less than 50 pounds. Betty packed 32 pounds of clothes and five gifts that w
andreev551 [17]

Answer:

5x + 32 < 50

Step-by-step explanation:

On a particular airline, bags checked in must weigh less than 50 pounds. Betty packed 32 pounds of clothes and five gifts that weigh the same amount.

If each gift weighs w pounds, then the weight of five gifts will be 5w pounds and an additional 32 pounds of clothes will make it total (32 + 5w) pounds.  

Now, this total weight has to be less than 50 pounds.

Therefore, the inequality equation that can be used to find the possible weight of each gift, w is  

5x + 32 < 50 (Answer)

3 0
3 years ago
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