Logarithms 8^(x-9) = 19^(3x+2)
1 answer:
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Answer:
The number of tomatoes must be less than 40.
Step-by-step explanation:
Stephanie and Bryson both grow tomatoes to sell at farmers' markets. Stephanie grew a total of 70 pounds of tomatoes to sell. She plans to sell the tomatoes for $3.50 per pound. The equation below represents the profit in dollars, f(x), she will earn by selling x pounds of the tomatoes.
f(x) = 3.50x -110
Bryson plans to sell his tomatoes at a different farmers' market. He grew a total of 90 pounds of tomatoes.
The table below shows the profit, in dollars, he will earn by selling different numbers of pounds of
tomatoes.
Bryson's Tomato Sales
-97.50 -55.00 -12.50 30,00
Profit (dollars)
Pounds of
Tomatoes Sold
10
20
30
40
Solution:
For Stephanie, let x represent the number tomatoes sold and f(x) represent the profit in dollars. The profit is given by:
f(x) = 3.5x - 110
For Bryson, let x represent the number tomatoes sold and y represent the profit in dollars. From the table, the profit can be represented by the points (10, -97.5) and (40, 30). The profit can be gotten using the formula:
Stephanie profit > Bryson profit
3.5x - 110 > 4.25x - 140
3.5x - 4.25x > -140 + 110
-0.75x > -30
x < 40
Answer:
see explanation
Step-by-step explanation:
(3)
Given cosΘ = -
Then by Pythagoras' theorem the third side is 3 ( 3,4, 5 triangle )
Since Θ in second quadrant then sinΘ > 0
sinΘ =
Using the trigonometric identity
sin2Θ = 2sinΘcosΘ, then
sin2Θ = 2 × × -
= -
(4)
Using the trigonometric identity
cos(x - y) = cosxcosy + sinxsiny
note cos15° = cos(45 - 30)°
cos(45 - 30) = cos45cos30 + sin45sin30
= ( ×
) + (
×
)
=