Answer: 18x^2 + 48x - 50
Step-by-step explanation: In order to determine the area of the rectangle not covered by the turtle pond, we shall calculate the area of the square pond and subtract it from the area of the rectangle.
The area of the square is given as
Area = L x B, where A and B are of equal measurement (sides of a square)
Area = 8 x 8
Area = 64 ft^2
Next we calculate the area of the rectangle which is given as
Area = L x B, where L = 6X + 2 and W = 3X + 7
Area = (6X + 2) (3X +7)
Area = 18X^2 + 42X + 6X + 14
Area = 18X^2 + 48X + 14
We can now subtract the area of the square from the area of the rectangle
That is Area of the shaded region
= 18X^2 48X + 14 - 64
= 18X^2 + 48X - 50
Therefore, the area of the shaded region = 18X^2 + 48X - 50
Answer: 490 grams of the first alloy should be used.
30 grams of the second alloy should be used.
Step-by-step explanation:
Let x represent the weight of the first alloy in grams that should be used.
Let y represent the weight of the second alloy in grams that should be used.
A chemist has two alloys, one of which is 15% gold and 20% lead. This means that the amount of gold and lead in the first alloy is
0.15x and 0.2x
The second alloy contains 30% gold and 50% lead. This means that the amount of gold and lead in the second alloy is
0.3y and 0.5y
If the alloy to be made contains 82.5 g of gold, it means that
0.15x + 0.3y = 82.5 - - - - - - - - - - - -1
The second alloy would also contain 113 g of lead. This means that
0.2x + 0.5y = 113 - - - - - - - - - - - - -2
Multiplying equation 1 by 0.2 and equation 2 by 0.15, it becomes
0.03x + 0.06y = 16.5
0.03x + 0.075y = 16.95
Subtracting, it becomes
- 0.015y = - 0.45
y = - 0.45/- 0.015
y = 30
Substituting y = 30 into equation 1, it becomes
0.15x + 0.3 × 30 = 82.5
0.15x + 9 = 82.5
0.15x = 82.5 - 9 = 73.5
x = 73.5/0.15
x = 490
The cofunction of cos is sin(90-x)
90 degrees is equal to PI/2
The cofunction becomes sin(PI/2 - 2PI/9)
Rewrite both fractions to have a common denominator:
PI/2 = 9PI/18
2PI/9 = 4PI/18
Now you have sin(9PI/18 - 4PI/18)
Simplify:
Sin(5PI/18)
2/7 as a fraction rounds to 0.3
0.3 * 3 = 0.9
3 x 2/7 is less than 3
Answer:
55 = 550
Step-by-step explanation:
