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alexgriva [62]
2 years ago
15

The volume of a cube is 1.8 m3. Find the length of its edge to the nearest tenth of a

Mathematics
1 answer:
Firdavs [7]2 years ago
5 0

The length of an edge is the cubic root of the volume.

Cubic root 1.8 = 1.2 meters

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HELP ASAP
GaryK [48]

Answer:

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3 0
3 years ago
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
A frequency table for the 30 best lifetime baseball batting averages of all time is shown to the right. These data can be graphi
Mashcka [7]

Answer: B

Step-by-step explanation:

Histogram is a statistical graph with the use of bar. The bar are not seperated unlike bar chart.

0.320 to 0.329 and 0.360 to 0.369 are of the same frequency which is equal to one. 0.350 to 0.359 is of frequency 2 a little above frequency 1.

Option B and D are very close to each other in value representation. But the frequency of 0.350 to 0.359 in option D is 3. This renders option D invalid and make option B the correct answer.

5 0
3 years ago
Sara has 24 sweets
Tresset [83]
<h2>Hello!</h2>

The answer is:

The expression for the number of sweets that Sara and Tim have now, are:

Sara=(17-x)Sweets\\\\Tim=\frac{(24+x)Sweets}{2}

<h2>Why?</h2>

To write the expressions for the number of sweets that Sara and Tim have now, we need to follow the next steps:

Sara starts with 24 sweets and Tim starts with 24 sweets

Sara=24 Sweets\\Tim=24 Sweets

Then, Sara gives Tim x Sweets

Sara=(24-x)Sweets\\Tim=(24+x)Sweets

Then. Sara eats 7 of her Sweets

Sara=(24-x-7) Sweets\\Sara=(17-x )Sweets\\Tim=(24+x) Sweets

Then, Tim eats half of his sweets

Sara=(17-x)Sweets\\\\Tim=\frac{(24+x)Sweets}{2}

So, the expression for the number of sweets that Sara and Tim have now, are:

Sara=(17-x) Sweets\\\\Tim=\frac{(24+x)Sweets}{2}

Have a nice day!

8 0
3 years ago
Multiplier method increase £88 by 14%
Morgarella [4.7K]

Answer:

if you just want 14% of 88

14% of 88 = 12.32, 0.14 * 88

if you want 14% of 88 + 88

114% of 88 = 100.32, 1.14 * 88

Step-by-step explanation:

2% of x = 0.02 * x

20% of x = 0.2 * x

200% of x = 2 * x

6 0
3 years ago
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