X+y=11

x is longer than y
x>y
x is 4 less than 4 times y
x=-4+4y

sub back
x+y=11
-4+4y+y=11
-4+5y=11
add 4 to both sides
5y=15
divide both sides by 5
y=3

sub back
x=-4+4y
x=-4+4(3)
x=-4+12
x=8

the pieces are 8ft and 3ft

4 0

3 years ago

For each of the following vector fields F, decide whether it is conservative or not by computing curl F. Type in a potential fun

Burka [1]

Answer:

1,2 and 4 are conservatives

3 is not conservative

Step-by-step explanation:

We calculate the Curl F

Remember that:

Curl F = < $\frac{dFz}{dy} - \frac{dFy}{dz}, \frac{dFz}{dx} - \frac{dFx}{dz}, \frac{dFy}{dx} - \frac{dFx}{dy}$ >

1. Curl F = <0,0,5-5> = <0,0,0>

The potential function f so that ∇f=F

f(x,y,z) = $-3x^{2} +5xy + 5y^{2}$

Then F is conservative

2. Curl F = < 0, 0 ,0>

The potential function f so that ∇f=F

f(x,y,z) = $-3/2x^{2} -y^{2}+z$

Then F is conservative

3. Curl F = <0 ,0, 10+3xsin(y) - (-cos(y))>

= <0 ,0 , 10 +3xsin(y) + cos(y)<

How the field's divergence is not zero the vector field is not conservative

4. Curl F = <0, 0, 0>

The potential function f so that ∇f=F

f(x,y,z) = $x^{3}+(5/3)y^{3}+(5/3)z^{3}$

Then F is conservative

5 0

3 years ago

The value of John's baseball card collection decreases exponentially over time, and the value of his silver collection increases

RoseWind [281]

Answer: The value of John's silver collection changes at a faster rate than the value of John's baseball card collection.

V = 500(1.05)2t + 600(0.95)t

Step-by-step explanation:

4 0

3 years ago