This would be a percent increase, so the formula would be:
New amount - Original amount / Original amount
Replace the numbers:
440 - 154 / 440
Simplify.
286 / 440
The chance would be 0.65, or 65%.
Answer:
By translating the function cos(x) 90 degrees to the right.
Step-by-step explanation:
The sine function is just the cosine function translated 90 degrees to the right. You can see the visualization below. They overlap.
If you're wondering why the diagram shows a shift in
That's just the equivalent to 90 degrees in radians.
Let X = the 29% alloy and Y = the 60% alloy.
They want a total of 80kg, so you have X +Y = 80
Rewrite that to get X = 80-Y
You also want 0.20X + 0.60Y = 0.52(80)
Replace X with 80-y:
0.20(80-y) + 0.60y = 0.52(80)
Simplify:
16 - 0.20y + 0.60y = 41.6
Combine like terms:
16 +0.40y = 41.6
Subtract 16 from each side:
0.40y = 25.6
Divide both sides by 0.40
y = 25.6 / 0.40
y = 64
Now you have Y replace y with 80 in X = 80-Y
X = 80 - 64
X = 16
They need 64 Kg of the 60% alloy and 16 Kg of the 20% alloy.
Given the radius, circumference can be solved by the equation, C = 2πr. The circumference of the circle above is C = 2π(8 in) = 16<span>π in. To solve for the length of the segment joining the arc is the circumference times the ratio of central angle and 360 degrees.
Length of the segment = (16</span>π in)(60/360) = 8/3 <span>π in
Thus, the length of the segment is approximately 8.36 in. </span>
We can use the FOIL method to simplify.
= (3x – 1)(2x + 9)
= (3x * 2x) + (3x * 9) + (-1 * 2x) + (-1 * 9)
= 6x + 27x + (-2x) + (-9)
= 33x - 11
Hope This Helped! Good Luck!