Answer:
-4f-5
Step-by-step explanation:
M
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Answer:
N = L/P
8/3 pieces
Step-by-step explanation:
Length of the board = 5/6 ft
A carpenter wants to cut a board that is five sixth ft long into pieces that are five sixteenths ft long.
Length of each piece = 5/16 ft
Number of pieces that can be cut from the board = Total length of board / length of each piece
Let
N = Number of pieces that can be cut from the board
L = Total length of board
P = length of each piece
N = L / P
= 5/6 ÷ 5/16
= 5 / 6 × 16 / 5
= 80 / 30
= 8/3
The number of pieces that can be cut from the board is 8/3
The value maximizes angle APB.
In this question we need to determine the <em>maximum possible</em> angle APB, which can be determined by definition of dot product, that is to say:
(1)
Where:
- , - Magnitudes of and .
- - Internal angle, in sexagesimal degrees.
The magnitudes of each are respectively defined by line segment length formula: , ,
(2)
(3)
By (1), (2) and (3) we have the following expression:
(4)
From geometry we know that sum of internal angles in triangles equals 180°, which means that angle APB must meet this condition:
In addition, we know that <em>cosine</em> function is a bounded function between -1 and 1, where , ,
A quick approach consists in graphing (4) against x. Outcome is described in the second image attached. By direct inspection, we see that maximizes angle APB.
We kindly invite to check this question on optimization: brainly.com/question/4302495
Answer:
I need the expressions
Step-by-step explanation:
(I don't have the experresions but I think it might be helpful to simplify)
- f - 5 ( 2 f - 3)
−f−10f+15
−f−(10f−15)
(−f−10f)+15
<u>−11f+15
</u>
<u />
<u>Hope this helped</u>
S - the number of the t-shirts;
h - the number of hats:
The system of equations:
s + h = 23
10 s + 12 h = 246
--------------------------
s = 23 - h
10 * ( 23 - h ) + 12 h = 246
230 - 10 h + 12 h = 246
2 h = 246 - 230
2 h = 16
h = 16 : 2
h = 8
s = 23 - 8
s = 15
Answer: The basketball team sold 15 t-shirts and 8 hats.