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DiKsa [7]
3 years ago
7

Use f(x) = 1/2x and f -1(x) = 2x to solve the problems.

Mathematics
1 answer:
DENIUS [597]3 years ago
4 0

f(2) = \frac{1}{2}  \times 2 = 1\\f^{-1}(1) = 2 \times 1 = 2\\f^{-1}(f(2)) = f^{-1}(1) = 2

Note: f^{-1}(f(x)) = x because f -1 and f cancel each other out.

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Use the method of lagrange multipliers to find
Yanka [14]

Answer:

a) The function is: f(x, y) = x + y.

The constraint is: x*y = 196.

Remember that we must write the constraint as:

g(x, y) = x*y - 196 = 0

Then we have:

L(x, y, λ) = f(x, y) +  λ*g(x, y)

L(x, y,  λ) = x + y +  λ*(x*y - 196)

Now, let's compute the partial derivations, those must be zero.

dL/dx =  λ*y + 1

dL/dy =  λ*x + 1

dL/dλ = (x*y - 196)

Those must be equal to zero, then we have a system of equations:

λ*y + 1 = 0

λ*x + 1 = 0

(x*y - 196) = 0

Let's solve this, in the first equation we can isolate  λ to get:

λ = -1/y

Now we can replace this in the second equation and get;

-x/y + 1 = 0

Now let's isolate x.

x = y

Now we can replace this in the last equation, and we will get:

(x*x - 196) = 0

x^2 = 196

x = √196 = 14

then the minimum will be:

x + y = x + x = 14 + 14 = 28.

b) Now we have:

f(x) = x*y

g(x) = x + y - 196

Let's do the same as before:

L(x, y, λ) = f(x, y) +  λ*g(x, y)

L(x, y, λ) = x*y +  λ*(x + y - 196)

Now let's do the derivations:

dL/dx = y + λ

dL/dy = x + λ

dL/dλ = x + y - 196

Now we have the system of equations:

y + λ = 0

x + λ = 0

x + y - 196 = 0

To solve it, we can isolate lambda in the first equation to get:

λ = -y

Now we can replace this in the second equation:

x - y = 0

Now we can isolate x:

x = y

now we can replace that in the last equation

y + y - 196 = 0

2*y - 196 = 0

2*y = 196

y = 196/2 = 98

The maximum will be:

x*y = y*y = 98*98 = 9,604

6 0
3 years ago
In a survey of 400 randomly selected​ people, it was determined that 22 play soccer. What is the probability that a randomly sel
insens350 [35]

Answer:

5.5% probability that a randomly selected person plays​ soccer

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Desired outcomes:

People surveyed who play soccer, so D = 22

Total outcomes:

Total people surveyed, so P = 400

What is the probability that a randomly selected person plays​ soccer?

P = \frac{D}{T} = \frac{22}{400} = 0.055

5.5% probability that a randomly selected person plays​ soccer

6 0
3 years ago
What is the length of the hypotenuse of the triangle?
sergey [27]
If you use the pothaorian theorym (A squared + B squared= C squared) youll be able to figure out the right answer is 65.
8 0
3 years ago
Read 2 more answers
What is the value of cos A?
BlackZzzverrR [31]

Step-by-step explanation:

  • h²=p²+b²
  • h²=24²+7²
  • h²=576+49
  • h=√625
  • h=25

tanA=p/h

  • 24/25

its yr ans

hope it helps.

<h2>stay safe healthy and happy....</h2>
3 0
2 years ago
Select three expressions equivalent to -3/4
Daniel [21]

Answer:

0.75 as a decimal for -3/4

I hope this helps

5 0
3 years ago
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