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Korolek [52]
3 years ago
6

The domain of the function is

Mathematics
1 answer:
lyudmila [28]3 years ago
8 0

Answer:

Unknown

Step-by-step explanation:

We need to know the function first, like a graph or chart or something.

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find two positive real numbers such that they sum to 108 and the product of the first times the square of the second is a maximu
topjm [15]

The two positive numbers are 36 and 72 which gives a sum equal to 108 and the product of 36 and the square of 72 is a maximum.

Any integer greater than zero is considered a positive number. A positive number can either be written as a number or with the "+" symbol in front of it.

Let us consider the two positive real numbers as x and y. Then, their sum is written as,

x+y=108

Then, y=108-x

And the product is written as,

P=xy²

Substitute value of y in the above equation, we get,

\begin{aligned}P&=x(108-x)^2\\&=x(11664-216x+x^2)\\&=11664x-216x^2+x^3\\&=x^3-216x^2+11664x\end{aligned}

Now, differentiate P with respect to x, and we get,

\begin{aligned}\frac{dP}{dx}&=3x^2-432x+11664\\&=x^2-144x+3888\end{aligned}

Solving the above equation to zero, we get,

\begin{aligned}x^2-144x+3888&=0\\x^2-36x-108x+3888&=0\\x(x-36)-108(x-36)&=0\\(x-108)(x-36)&=0\\x&=\text{108 or 36}\end{aligned}

Substitute values of x in y=108-x, to get values of y.

If we substitute x=108, we get the y value as zero which doesn't give the required solution.

But, if we substitute x=36, we get,

\begin{aligned}y&=108-36\\y&=72\end{aligned}

Thus, the two positive numbers are 36 and 72.

To know more about positive numbers:

brainly.com/question/1635103

#SPJ4

4 0
1 year ago
A triangle has sides with lengths of 11 miles, 15 miles, and 17 miles. Is it a right triangle?​
dybincka [34]

Answer:

Below.

Step-by-step explanation:

If its a right triangle it will obey the Pythagoras theorem.

17^2 = 289

11^2 + 15^2 = 121 + 225  = 346

- so NOT a right triangle.

3 0
3 years ago
A construction zone on Interstate 15 has a speed limit of 40 mph. The speeds of vehicles passing through this construction zone
monitta

Answer:

a. The percentage of vehicles who pass through this construction zone who are exceeding the posted speed limit =90.82%

b. Percentage of vehicles travel through this construction zone with speeds between 50 mph and 55 mph= 2.28%

Step-by-step explanation:

We have to find

a) P(X>40)= 1- P(x=40)

Using the z statistic

Here

x= 40 mph

u= 44mph

σ= 3 mph

z=(40-44)/3=-1.33

From the  z-table   -1.67 = 0.9082

a) P(X>40)=

Probability exceeding the speed limit = 0.9082 = 90.82%

b) P(50<X<55)

Now

z1 = (50-44)/3 = 2

z2 = (55-44)/3= 3.67

Area for z>3.59 is almost equal to 1

From the z- table we get

P(55 < X < 60) = P((50-44)/3 < z < (55-44)/3)

     = P(2 < z < 3.67)

     = P(z<3.67) - P(z<2)

     = 1 - 0.9772

     = 0.0228

or 2.28%

3 0
3 years ago
A bin contains 10 cards labeled A to J and 20 cards labeled 1 to 20. The cards are shuffled and one card is chosen at random. Wh
Fudgin [204]
So you ave a 3 out of 10 chance to get a letter in eh word DIG then you have a 1 in 2 chance of drawing an odd number add those together.

13 out of 30 chance

Simplify if necessary, hope this helps
7 0
3 years ago
Evaluate the expression when a=10,b=9, and c=4.<br> 3a+2b−6c =
pav-90 [236]

Answer:24

Step-by-step explanation:

Multiply 3 times ten, 2 times 9, and 6 times 4 and solve you get 24

6 0
3 years ago
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