Find the area of the sector

A rancher plans to make 4 identical and adjacent rectangular pens against a barn (see figure below), each with an area of 100 m^

Tasya [4]

Answer:

10 by 10 meters

Step-by-step explanation:

In calculus terms, you can use the formula for the perimeter which is 2l + 2w, and the area l × w.

Then since the area is 100

l × w = 100. So w = 100/l

Then substitute this into the perimeter formula.

w = 100/l → 2l + 2(w) = 2l + 2(100/l) = 2l + 200/l.

Then take the derivative d/dx [take the derivative of a quantity with respect to x], by using a simpler method known as the power rule:

d/dx[x^n] = nx^n-1

so p = 2l + 200/l becomes p' = 2 - 200/l^2

Since the derivative of a constant is 0, to solve for l, set p' to 0

0 = 2 - 200/l^2 → -200/l^2 = -2 → 200/l^2 = 2 → 2l^2 = 200 → l^2 = 100 → l = √100, l = 10.

Now that we know the length is 10, We can substitute the length in the original equation to find the width.

l = 10 → w = 100/l → w = 100/10, w = 10.

Therefore the perimeter of each rectangular pen is 40, with a length of 10 and width of 10.

If you want to do this algebraicly, there are more steps involved

7 0

3 years ago

The morning temperature in northern Canada was −28.9∘ F. The temperature rose 33.2°F during the day before reaching its high tem

My name is Ann [436]

The high temperature for the day was 4.3°F

6 0

3 years ago

What two positive real numbers whose product is 50 have the smallest possible sum?

Llana [10]

X * y = 50
y = 50 / x
S = x + y = x + 50 / x
S` = 1 - 50 / x²
1 - 50 / x² = 0
50 / x² = 1
x² = 50
x = √ 50 = 5 √2
y = 50 / 5√2 = 5 √2
Answer:
Those numbers are: x = 5√2 and y = 5√2.

7 0

3 years ago

Po is an oncologist with seven patients in their care. the probability that a patient will survive five years after being diagno

alekssr [168]

Answer:

0.0923 = 9.23% probability that four of the patients are still alive after five years.

Step-by-step explanation:

For each patient, there are only two possible outcomes. Either they are still alive after five years, or they are not. The probability of a patient being alive is independent of any other patient, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Po is an oncologist with seven patients in their care.

This means that $n = 7$

The probability that a patient will survive five years after being diagnosed with stage three breast cancer is 0.82.

This means that $p = 0.82$

What is the probability that four of the patients are still alive after five years?

This is P(X = 4). So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 4) = C_{7,4}.(0.82)^{4}.(0.18)^{3} = 0.0923$

0.0923 = 9.23% probability that four of the patients are still alive after five years.

5 0

3 years ago

10. A movie theater advertises that a family of two adults, one student, and one child between the ages of 3

BlackZzzverrR [31]

Answer:

Students ticket = $4

Child ticket = $1

Adult ticket = $5

Step-by-step explanation:

Let the price of the student ticket be $x and the price of a child ticket be $y. An adult ticket costs as much as the combined cost of a student ticket and a child ticket, so the price of one adult ticket is $(x+y).

1. A movie theater advertises that a family of two adults, one student, and one child between the ages of 3 and 8 can attend a movie for $15. Then

$2(x+y)+x+y=15$

2. If you purchase 1 adult ticket, 4 student tickets, and 2 child tickets for $23, then

$(x+y)+4x+2y=23$

Now, solve the system of two equations:

$\left\{\begin{array}{l}2(x+y)+x+y=15\\ \\(x+y)+4x+2y=23\end{array}\right.\Rightarrow \left\{\begin{array}{l}3(x+y)=15\\ \\5x+3y=23\end{array}\right.\\ \\\left\{\begin{array}{l}x+y=5\\ \\5x+3y=23\end{array}\right.\\ \\\left\{\begin{array}{l}y=5-x\\ \\5x+3(5-x)=23\end{array}\right.$

Solve the last equation

$5x+15-3x=23\\ \\2x=23-15\\ \\2x=8\\ \\x=4\\ \\y=5-x=5-4=1$

Students ticket = $4

Child ticket = $1

Adult ticket = $5

8 0

3 years ago

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