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Ipatiy [6.2K]
3 years ago
14

Solve the following equation

Mathematics
1 answer:
atroni [7]3 years ago
7 0

First of all, you can simplify the right hand side, since 12/4=3.

Then, multiply both sides of the equation by 5:

\dfrac{x}{5}=3 \iff x=15

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Dmitry [639]
Ten x plus four divided by seven
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Find the minimum and maximum value of the function on the given interval by comparing values at the critical points and endpoint
Kitty [74]

Answer:

maximum: y = 1

minimum: y = 0.

Step-by-step explanation:

Here we have the function:

y = f(x) =  √(1 + x^2 - 2x)

we want to find the minimum and maximum in the segment [0, 1]

First, we evaluate in the endpoints, which are 0 and 1.

f(0)  =√(1 + 0^2 - 2*0) = 1

f(1) = √(1 + 1^2 - 2*1) = 0

Now let's look at the critical points (the zeros of the first derivate)

To derivate our function, we can use the chain rule:

f(x) = h(g(x))

then

f'(x) = h'(g(x))*g(x)

Here we can define:

h(x) = √x

g(x) = 1 + x^2 - 2x

Then:

f(x) = h(g(x))

f'(x)  =  1/2*( 1 + x^2 - 2x)*(2x - 2)

f'(x) = (1 + x^2 - 2x)*(x - 1)

f'(x) = x^3 - 3x^2 + x - 1

this function does not have any zero in the segment [0, 1] (you can look it in the image below)

Thus, the function does not have critical points in the segment.

Then the maximum and minimum are given by the endpoints.

The maximum is 1 (when x = 0)

the minimum is 0 (when x = 1)

7 0
3 years ago
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Sauron [17]
The answer is C) 2730
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Gnoma [55]

Answer:

y =  - 3 +  \frac{1}{2} xxer

Step-by-step explanation:

move variable to the right-hand side and change its sign

- 6y = 18 - 3x

divide both sides of the equation

y = 3 +  \frac{1}{2} x

8 0
2 years ago
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