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Kipish [7]
3 years ago
10

ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing. Show your work or give an explaination.

Mathematics
1 answer:
siniylev [52]3 years ago
3 0

Answer:

C

Step-by-step explanation:

When you multiply the x^2 portion of a parabola by a certain coefficient, the parabola will be stretched by that amount. Also, when you add a certain amount to the parabola, it will be shifted up by that amount. Therefore, the correct answer is C. Hope this helps!

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Does there exist a di↵erentiable function g : [0, 1] R such that g'(x) = f(x) for all x 2 [0, 1]? Justify your answer
agasfer [191]

Answer:

No; Because g'(0) ≠ g'(1), i.e. 0≠2, then this function is not differentiable for g:[0,1]→R

Step-by-step explanation:

Assuming:  the function is f(x)=x^{2} in [0,1]

And rewriting it for the sake of clarity:

Does there exist a differentiable function g : [0, 1] →R such that g'(x) = f(x) for all g(x)=x² ∈ [0, 1]? Justify your answer

1) A function is considered to be differentiable if, and only if  both derivatives (right and left ones) do exist and have the same value. In this case, for the Domain [0,1]:

g'(0)=g'(1)

2) Examining it, the Domain for this set is smaller than the Real Set, since it is [0,1]

The limit to the left

g(x)=x^{2}\\g'(x)=2x\\ g'(0)=2(0) \Rightarrow g'(0)=0

g(x)=x^{2}\\g'(x)=2x\\ g'(1)=2(1) \Rightarrow g'(1)=2

g'(x)=f(x) then g'(0)=f(0) and g'(1)=f(1)

3) Since g'(0) ≠ g'(1), i.e. 0≠2, then this function is not differentiable for g:[0,1]→R

Because this is the same as to calculate the limit from the left and right side, of g(x).

f'(c)=\lim_{x\rightarrow c}\left [\frac{f(b)-f(a)}{b-a} \right ]\\\\g'(0)=\lim_{x\rightarrow 0}\left [\frac{g(b)-g(a)}{b-a} \right ]\\\\g'(1)=\lim_{x\rightarrow 1}\left [\frac{g(b)-g(a)}{b-a} \right ]

This is what the Bilateral Theorem says:

\lim_{x\rightarrow c^{-}}f(x)=L\Leftrightarrow \lim_{x\rightarrow c^{+}}f(x)=L\:and\:\lim_{x\rightarrow c^{-}}f(x)=L

4 0
3 years ago
Segment addition, how do u solve it? Step by step.
weeeeeb [17]

Answer:

x=7  DO=25  OG=35

Step-by-step explanation:

4x-3+2x+21=60            4(7)-3                  2(7)+21

4x+2x   -3+21                 28-3=25             14+21=35

6x+18=60                     DO=25                  OG=35

60-18=42

6x=42

42/6=7

x=7

5 0
3 years ago
What is a unit rate?
Ksivusya [100]

Answer:

<em>A unit rate is something over a unit of something else. </em>

<u>Such as:</u>  (50 miles) / hour

If you have (150 miles) / 3 hours

This is not a unit rate, therefore you have to divide the top and bottom by 3 to get the unit rate

(150/3 miles) / (3/3 hours)

(50 miles) / hour

Hope this helps :)

5 0
3 years ago
The Beta Club is sponsoring a lollipop sale. If their goal is to raise at least $228, how many lollipops must they sell at $1.50
allsm [11]

Answer:

I believe they would have to sell 152 lollipops

Step-by-step explanation:

4 0
3 years ago
If you were to roll the dice one time what is the probability it will land on 4
vovangra [49]

Answer: 1/6

Step-by-step explanation: To find the probability of rolling a 4, let's use our ratio for the probability of an event which is shown below.

Number of favorable outcomes/total number of outcomes

Since only one side of a number cube has a 4 on it, the number of favorable outcomes for rolling a 4 is 1 and since there are six sides to a number cube and it's equally likely that the cube will land on any of these sides, the total number of outcomes is 6.

So the probability of rolling a 4 is 1/6 which is equivalent

to 0.167 or 16.7%.

That means it is't likely that you would roll a 4 for instance but it's just as likely as rolling any other number.

3 0
3 years ago
Read 2 more answers
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