a) is conservative if it is the gradient field for some scalar function . This would require
Integrating both sides of the first equation with respect to yields
Differentiate with respect to :
Differentiate with respect to :
We want to be independent of and ; we can make them both disappear by picking .
b) This is the so-called triple product, which has the property
Computing the determinant is easy with a cofactor expansion along the first column:
c) Let
Compute the partial derivatives and evaluate them at :
Then the tangent plane to at (1, 1, 1) has equation
d) In polar coordinates, is the set
Then the integral evaluates to
e) By the chain rule,
Eliminating the parameter, we find
so that when .
Compute derivatives:
Then at the point (1, 1), the derivative we want is
divide total miles by time:
157.5 / 2.5 = 63 miles per hour
Step-by-step explanation:
1. 3x+5+4x-1
7x+4
2. 5x-3-2x+1
3x-2
3. -7x+4-5x-12
-12x-8
4. 4x-10-5x-2
-x-12
plz mark brainliest
Answer:
x=60° , y=30° , z= 75°
Step-by-step explanation:
note...an equilateral triangle has the same angles all equal to 60°. so based on this x is 60°
the angle next to y is on a straight line therefore
60 +y =90
y=90-60
y=30°
the triangle with the y and z angles is an isosceles triangle...so the base angles must be equal
z+z+30=180
2z+30=180
2z=180-30
2z=150
z=75°
Answer:
B. m
Step-by-step explanation:
Hey there!
A variable is an unknown quantity in an equation or problem.
For example, the problem 3x=15
We want to find out what times 3 will give us 15. x is our unknown quantity.
Hope this helps you! Feel free to comment any questions you may have for me!