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Korolek [52]
3 years ago
12

PLEASE HELP 10 Points!!!!

Mathematics
1 answer:
lidiya [134]3 years ago
3 0
Soccer ball = a = 5
basketball = b = 9
volleyball = c = 7

a + b + c = 21
2a + c = 17
2b + c = 25
2a + b + c = 26

Seeing that....
a + b + c = 21
2a + b + c = 26
We can deduce that a = 5

2a + c = 17
2(5) + c = 17
10 + c = 17
Subtract 10 from both sides
c = 7

2a + b + c = 26
2(5) + b + 7 = 26
10 + b + 7 = 26
17 + b = 26
Subtract 17 from both sides
b = 9

Hope this helped!
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It takes 4 hours and 15 minutes to fly from Orlando, Florida, to Boston, Massachusetts. The distance between the two cities is 1
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Answer:

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Step-by-step explanation:

Given: It takes 4 hours and 15 minutes to fly from Orlando, Florida, to Boston, Massachusetts. The distance between the two cities is 1114 miles

To Find: the average speend of the plane in miles per hour, If every mile is approximately 1.6 kilometers, the speed of the airplane in kilometers per hour

Solution:

Distance between Orlando,Florida and Boston, Massachusetts=1114 \text{miles}

Time taken to cover the distance =4\text{hours} and 15\text{minutes}

We know that,

\text{Average Speed}=\frac{\text{Total Distance}}{\text{Total time}}

                                          =\frac{1114}{\frac{17}{4}}

                                          =\frac{1114\times4}{17}

                                          =262.12 \text{mph}

It is given that,

1\text{mile}=1.6\text{kilometer}

therefore,

1\text{mph}=1.6\text{kph}

Speed Of plane in Kilometers per hours =\text{speed in mph}\times1.6

                                                                   419.4\text{kph}

Speed of in miles per hour  is 262.12 \text{mph} and Speed in kilometer per hour  419.4\text{kph}

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see below

Step-by-step explanation:

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Vertical angles are equal

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Answer:

b. Engine oil E will cause a significant improvement is gas mileage.

Step-by-step explanation:

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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

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