Answer:
a) Y(x) = {900, x≤30; 900-40(x-30), x>30}
b) T(x) = {900x, x≤30; 2100x-40x², x>30}
c) dT/dx = {900, x≤30; 2100-80x, x>30}
Step-by-step explanation:
a) The problem statement gives the function for x ≤ 30, and gives an example of evaluating the function for x = 35. So, replacing 35 in the example with x gives the function definition for x > 30.
__
b) The yield per acre is the product of the number of trees and the yield per tree:
T(x) = x·Y(x)
__
c) The derivative is ...
_____
The attached graph shows the yield per acre (purple, overlaid by red for x<30), the total yield (black), and the derivative of the total yield (red). You will note the discontinuity in the derivative at x=30, where adding one more tree per acre suddenly makes the rate of change of yield be negative.
Let w represent the width of the rectangle in cm. Then its length in cm is (3w+9). The perimeter is the sum of two lengths and two widths, so is ...
... 418 = 2(w + (3w+9))
... 209 = 4w +9 . . . . . . divide by 2, collect terms
... 200 = 4w . . . . . . . . subtract 9
... 50 = w . . . . . . . . . . divide by 4
... length = 3w+9 = 3·50 +9 = 159
The dimensions of this piece of land are 159 cm by 50 cm.
Answer:
a) (8,8,-6)
b) 4x+4y+3z = -3
Step-by-step explanation:
a)
The surface is given by the equation
f(x,y,z) = 0 where
The gradient of this function is the vector
If we evaluate it in the point P = (-2,2,1) we obtain the point
(8,8,-6)
b)
The vectors with their tails at P are of the form
(-2,2,1)-(x,y,z) = (-2-x, 2-y, 1-z)
as they must be orthogonal to the gradient, they must be orthogonal to the vector (8,8,6) so their inner product is 0
and the equation of the desired plane is
4x+4y+3z = -3
Hello!
You want a choice where everyone has an equal chance to answer
The answer is D) All students in each grade because A is biased because students won't be able to answer, B is biased because it is limited to only to football team and C doesn't give girls the chance to answer
The answer is D) All students in each grade
Hope this helps!
3x
We need to substitute x with 5 because the question is asking how many squats Carlos has completed if he completed 5.
3 x 5 = 15
Therefore, Carlos completed 15 squats as part of his football workout.
By the way, this question is very simple and basic. I recommend reviewing Algebra for your benefit/
