Answer:
Step-by-step explanation:
To find the rate of change of temperature with respect to distance at the point (3, 1) in the x-direction and the y-direction we need to find the Directional Derivative of T(x,y). The definition of the directional derivative is given by:
Where i and j are the rectangular components of a unit vector. In this case, the problem don't give us additional information, so let's asume:
So, we need to find the partial derivative with respect to x and y:
In order to do the things easier let's make the next substitution:
and express T(x,y) as:
The partial derivative with respect to x is:
Using the chain rule:
Hence:
Symplying the expression and replacing the value of u:
The partial derivative with respect to y is:
Using the chain rule:
Hence:
Symplying the expression and replacing the value of u:
Therefore:
Evaluating the point (3,1)
Step-by-step explanation:
For square
A=bh
A=30(20)
A=60in²
For triangle
A=½bh
A=½(40)(30)
A=½(120)
A=60in²
Add
60+60=120in²
The angle θ that the field e⃗ makes with the surface of the slab, which is perpendicular to the x direction is <span>θ = -1.57 <span>rad
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Answer:
We need 5 bags of Vigoro Ultra Turf and 4 bags of Parkers Premium fertilizer.
Step-by-step explanation:
Let's first list the percentage compositions of each fertilizer type:
<u>Vigoro Ultra Turf:</u>
Nitrogen (N) = 29 kg
Phosphoric Acid (P2O5) = 3 kg
Potash (K2O) = 4 kg
<u>Parkers Premium</u>
Nitrogen (N) = 18 kg
Phosphoric Acid (P2O5) = 25 kg
Potash (K2O) = 6 kg
We can set up simultaneous equations to find out the amount of 100 kg bags of each fertilizer needed:
x = Vigoro Ultra turf (one bag)
y = Parkers Premium (one bag)
29x + 18y = 217 -Equation 1
3x + 25y = 115 -Equation 2
4x + 6y = 44 -Equation 3
Solving for x and y, we get:
x = 5
y = 4
This means we need 5 bags of Vigoro Ultra Turf and 4 bags of Parkers Premium fertilizer.
Answer:
1/2 (1 half)
Step-by-step explanation:
The number of different sandwiches is calculated multiplying all of the possibilities for each material used:
rye or white bread: 2 options
ham or turkey: 2 options
cheese or no cheese: 2 options
So the number of different sandwiches that can be made is 2*2*2 = 8.
From these 8 different sandwiches, 4 have cheese and 4 have no cheese, as the staff made a equal number of each type of sandwich.
So, if from 8 different type of sandwiches, 4 have cheese, the chances of Mary getting a sandwich with cheese is 4/8 = 1/2 (1 half).
