Answer:

Step-by-step explanation:
The slope-intercept form of an equation of a line:

m - slope
b - y-intercept → (0, b)
The formula of a slope:

We have two points (8, -4) and (0, 2) → b = 2.
Calculate the slope:

Therefore the equation of a line t in the slope-intercept form is:

25=2,500, 278= 27800%, 2.9=290, 3.0=300, 0.67= 67
We are given one angle is 3 times less than other.
Let us assume one angle measure is x degrees and another is 4x.
Because x is 3x less than 4x. ( We can check 4x-x= 3x)
Sum of complementary angles is 90 degrees.
So, we can setup an equation
First angle measure + first angle = 90 degrees.
x+4x = 90.
Adding x and 4x, we get 5x.
So, 5x = 90.
Dividing both sides by 5, we get
5x/5 = 90.
x= 18.
So, one angle is of 18 degrees.
Another angle = 4x = 4 times 18 = 72 degrees.
So, required angles are of 18 degree and 72 degree.
Answer:
$1.80
Step-by-step explanation:
Let the cost of a hot dog = x
The cost of a hot dog roll = y
Eight hot dogs and seven hot dog rolls cost $\$13.60$.
8x + 7x = $13.60..... Equation 1
Seven hot dogs and eight hot dog rolls cost $\$13.40$.
7x + 8x = $13.40...... Equation 2
Combining both Equation
8x + 7x = $13.60..... Equation 1
7x + 8x = $13.40...... Equation 2
Eliminating x
Multiply 1 by 7
Multiply 2 by 8
56x + 49y = 95.2..... Equation 3
56x + 64y = 107.2 ..... Equation 4
Subtracting 4 from 3
-15y = -12
y = -12/-15
y = 0.8
Cost of one hot dog roll = $0.8
Solving for x
8x + 7x = $13.60
8x + 7(0.8) = 13.60
8x + 5.6 = 13.60
8x = 13.60 - 5.60
8x = 8.0
x = 8.0/8
x = 1.
Cost of one hot dog = $1.0
The cost in dollars of a hot dog and a hot dog roll cost combined is
x + y
= $1 + $0.8
= $1.80
For
to be conservative, we need to have



Integrate the first PDE with respect to
:

Differentiate with respect to
:

Now differentiate
with respect to
:

So we have

so
is indeed conservative.