For each of the following pairs of functions ff and gg, determine if the level curves of the functions cross at right angles, and find their gradients at the indicated point. a) f(x, y)=5x+5y,

g(x, y)=5x−5y.

Do the level curves of f and g cross at right angles? gradfientf(6,5) = ? gradient(6,5) = ?

b) f(x, y)=x^2−y,

g(x, y)=2y+ln(|x|)

Do the level curves of f and g cross at right angles? gradfientf(6,5) = ? gradient(6,5) = ?

answer

the correct answer is

explanation

the given function is

the excluded values are obtained by solving:

we factor to obtain:

the excluded values are

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2

the workers who do no drive has no reasonable reason to buy gasoline due to they don't have anything to use it for

yes the total will be same because in both of them the expression.is rearranged but their sign remains the same hence it hss just been shuffled