When is cos (x) = 0? <em>at 90° (aka π/2)</em>
Answer: 
Answer:
see explanation
Step-by-step explanation:
Assuming you are factoring the expression
Given
4y² + 26y + 30 ← factor out 2 from each term
= 2(2y² + 13y + 15) ← factor the quadratic
Consider the factors of the product of the coefficient of the y² term and the constant term which sum to give the coefficient of the y- term.
product = 2 × 15 = 30 and sum = 13
the factors are 10 and 3
Use these factors to split the y- term
2y² + 10y + 3y + 15 ( factor the first/second and third/fourth terms )
= 2y(y + 5) + 3(y + 5) ← factor out (y + 5) from each term
= (y + 5)(2y + 3)
Thus
4y² + 26y + 30
= 2(y + 5)(2y + 3)
Given:
Cost to build a bookshelf = $20
Cost to build a table = $45
Amount available to spend = $600
Let x = number of bookshelves built.
Let y = number of tables built.
The total number of bookshelves and tables = 18.
Therefore
x + y = 18.
That is,
y = 18 - x (1)
The total amount available to build x bookshelves and y tables = $600. Therefore
20x + 45y = 600
That is (dividing through by 5),
4x + 9y = 120 (2)
Substitute (1) into (2).
4x + 9(18 - x) = 120
4x + 162 - 9x = 120
-5x = -42
x = 8.4
From (1),obtain
y = 18 - 8.4 = 9.6
Because we cannot have fractional bookshelves and tables, we shall test values of x=8, 9 and y=9,10 for profit
Note: The profit is $60 per bookshelf and $100 per table.
If x = 8, then y = 18-8 = 10.
The profit = 8*60 + 10*100 = $1480
If x = 9, then y = 18-9 = 9.
The profit = 9*60 + 9*100 = $1440
The choice of 8 bookshelves and 10 tables is more profitable.
Answer: 8 bookshelves and 10 tables.
The given point (t, P) is (0, 1000), and the slope is given as ∆P/∆t = 30. Using the point-slope form of the equation for a line, the equation can be written as
... P = 30t + 1000
