Standard form is x + y = number.
y = -2/5 x
y + 2/5 x = 0
2/5 x + y = 0
In standard form, the coefficient of x or y cannot be a fraction.
Therefore we have to multiply the whole equation by 5.
2x + 5y = 0
<span>12.3
Volume function: v(x) = ((18-x)(x-1)^2)/(4pi)
Since the perimeter of the piece of sheet metal is 36, the height of the tube created will be 36/2 - x = 18-x.
The volume of the tube will be the area of the cross section multiplied by the height. The area of the cross section will be pi r^2 and r will be (x-1)/(2pi). So the volume of the tube is
v(x) = (18-x)pi((x-1)/(2pi))^2
v(x) = (18-x)pi((x-1)^2/(4pi^2))
v(x) = ((18-x)(x-1)^2)/(4pi)
The maximum volume will happen when the value of the first derivative is zero. So calculate the first derivative:
v'(x) = (x-1)(3x - 37) / (4pi)
Convert to quadratic equation.
(3x^2 - 40x + 37)/(4pi) = 0
3/(4pi)x^2 - (10/pi)x + 37/(4pi) = 0
Now calculate the roots using the quadratic formula with a = 3/(4pi), b = -10/pi, and c = 37/(4pi)
The roots occur at x = 1 and x = 12 1/3. There are the points where the slope of the volume equation is zero. The root of 1 happens just as the volume of the tube is 0. So the root of 12 1/3 is the value you want where the volume of the tube is maximized. So the answer to the nearest tenth is 12.3</span>
Answer:
4.
Step-by-step explanation:
inverse proportion:
12/3=x/9.
3x3=9 therefore 12/3 which is 4.
The missing coordinate is 4.
Hope this helps plz hit the crown :D
Answer:
-7
Step-by-step explanation:
Answer:
The probability of getting a pair of red socks is 0.322
Step-by-step explanation:
According to the given data we have that A drawer contains 11 identical red socks and 8 identical black socks, hence, the total number of socks is 19, therefore, in order to calculate the probability of getting a pair of red socks we would have to use the following formula:
probability of getting a pair of red socks=11C2/19C2
probability of getting a pair of red socks=55/171
probability of getting a pair of red socks=0.322
The probability of getting a pair of red socks is 0.322
