Answer:
Distance of ladder top from ground = 9.2 meter (Approx.)
Step-by-step explanation:
Given:
Angle of elevation between ground and ladder = 43°
Length of ladder = 13.5 meter
Find:
Distance of ladder top from ground
Computation:
Length of ladder = Hypotenuse
Distance of ladder top from ground = Perpendicular
Sinθ = Perpendicular / Hypotenuse
Sin 43 = Distance of ladder top from ground / Length of ladder
0.6819 = Distance of ladder top from ground / 13.5
Distance of ladder top from ground = 9.20565
Distance of ladder top from ground = 9.2 meter (Approx.)
The number of ways to deal 5 cards to 5 players from a 52-card deck in a game of poker is (52!)/[(27!)*(5!)^5].
- Permutations and combinations define nCr as ways of selecting 'r' number of items from 'n' items.
- nCr = (n!)/[r!(n-r)!]
- here we want to deal 5 playing cards to each player.once we deal 5 playing cards to any participant,
- the playing cards left inside the deck are reduced through five.
- We deal a total of 25 playing cards, i.e., 5 playing cards to 5 gamers.
- The number of ways to deal five playing cards to the primary participant is 52C5.The number of approaches to deal 5 playing cards to the second one participant is 47C5.
- The wide variety of ways to deal 5 cards to the 0.33 player is 42C5.
- The variety of methods to deal 5 cards to the fourth participant is 37C5.
- The quantity of ways to deal 5 playing cards to the 5th player is 32C5.
- the full quantity of methods is the general multiplication.
- The total number of solutions = 52C5 * 47C5 * 42C5 * 37C5 * 32C5
- When we simplify, we get (52!)/[(27!)*(5!)^5].
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Answer:
7 - 2x
Step-by-step explanation:
We start with
-2x + 7
And we can separate the terms
(-2x) (+7)
and move them around
(+7) (-2x)
7 - 2x is an equivalent expression.
Answer:
<em>27 feet for the south wall and 18 feet for the east/west walls</em>
Maximum area= 
Step-by-step explanation:
<u>Optimization</u>
This is a simple case where an objective function must be minimized or maximized, given some restrictions coming in the form of equations.
The first derivative method will be used to find the values of the parameters that control the objective function and the maximum value of that function.
The office space for Billy-Sean will have the form of a rectangle of dimensions x and y, being x the number of feet for the south wall and y the number of feet for the west wall. The total cost of the space is
C=8x+12y
The budget to build the office space is $432, thus
Solving for y
The area of the office space is
Replacing the value found above
Operating
This is the objective function and must be maximized. Taking its first derivative and equating to 0:
Operating
Solving
Calculating y
Compute the second derivative to ensure it's a maximum
Since it's negative for x positive, the values found are a maximum for the area of the office space, which area is
