Answer:
Step-by-step explanation:
Maximum rate of change of a function f(x,y) is expressed as the gradient of such function at the given point. Gradient of a function is expressed as;
∇f(x,y) =
Given f(x,y)=ln(x²+y²) at the point (-2, 2)
<em>Hence the maximum rate of range of the function at the point (-2,2) is </em><em></em>
To get the direction, we willl use the formula;
From the vector gotten, x = -1/2 and y = 1/2
<em>Since tan theta is negative in the second quadrant, the direction in which it occurs will be 180-45 = 135°</em>
<span>A swimming pool had 2.5 million liters of water in it. Some water evaporated, and then the pool only had 2 million liters of water in it. The water that evaporate would be: 2.5 </span>million liters - 2 million liters = 0.5 million liters <span>
The percent of water evaporated would be:
percent of water evaporated: </span>evaporated water/ original swimming pool volume * 100%
0.5 million liters / 2.5 million liters * 100%=
1/5 *100%= 20%
Answer:
z = -3
Step-by-step explanation:
Simplifying
3z + -3 = 2z + -6
Reorder the terms:
-3 + 3z = 2z + -6
Reorder the terms:
-3 + 3z = -6 + 2z
Solving
-3 + 3z = -6 + 2z
Solving for variable 'z'.
Move all terms containing z to the left, all other terms to the right.
Add '-2z' to each side of the equation.
-3 + 3z + -2z = -6 + 2z + -2z
Combine like terms: 3z + -2z = 1z
-3 + 1z = -6 + 2z + -2z
Combine like terms: 2z + -2z = 0
-3 + 1z = -6 + 0
-3 + 1z = -6
Add '3' to each side of the equation.
-3 + 3 + 1z = -6 + 3
Combine like terms: -3 + 3 = 0
0 + 1z = -6 + 3
1z = -6 + 3
Combine like terms: -6 + 3 = -3
1z = -3
Divide each side by '1'.
z = -3
Simplifying
z = -3
-10y^2
Explanation: when combining like terms everything cancels out except for -10y^2
Answer:
If they work together, they take 48 minutes to line the football field.
Step-by-step explanation:
Given: Reggie can line a football field in 120 minutes. Rosalinda can line a football field in 80 minutes.
To find : If they work together, how many minutes does it take them to line a football field?
Solution :
If they work together,
Let the number of minutes(x) they take to line the foot ball field.
According to question,
Cross multiply,
Therefore, If they work together, they take 48 minutes to line the football field.