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Leno4ka [110]
3 years ago
15

1. A = 1/2bh

Mathematics
1 answer:
OleMash [197]3 years ago
8 0
1 and 2 i can't answer without proper data.
3. x+2x+2x+6 = 86
5x+6 = 86
-6 -6
5x = 80
x = 16
Side one: x is 16
Side two: 2x is 2(16) = 32
Side three: 2x+6 is 38
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A peach orchard owner wants to maximize the amount of peaches produced by her orchard.
qaws [65]

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.

\displaystyle Y(x)=\left\{\begin{array}{lcl}900&\text{for}&x\le 30\\900-40(x-30)&\text{for}&x>30\end{array}\right.

__

b) The yield per acre is the product of the number of trees and the yield per tree:

  T(x) = x·Y(x)

\displaystyle T(x)=\left \{\begin{array}{lcl}900x&\text{for}&x\le 30\\2100x-40x^2& \text{for}&x>30\end{array}\right.

__

c) The derivative is ...

\displaystyle\frac{dT}{dx}=\left \{\begin{array}{lcl}900&\text{for}&x\le 30\\2100-80x& \text{for}&x>30\end{array}\right.

_____

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.

6 0
3 years ago
The length of a rectangular piece of land is 9 cm more than 3 times its width. The perimeter is 418 cm. Find its dimensions.
SashulF [63]

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.

3 0
3 years ago
Consider the surface f (x comma y comma z )f(x,y,z)equals=negative 2 x squared plus 2 y squared minus 3 z squared plus 3 equals
trapecia [35]

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

f(x,y,z)=-2x^2+2y^2-3z^2+3

The gradient of this function is the vector

(\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z})=(-4x,4y,-6z)

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

(-2-x,2-y,1-z)\cdot(8,8,6)=0\Rightarrow -16-8x+16-8y+6-6z=0\Rightarrow 4x+4y+3z=-3

and the equation of the desired plane is

4x+4y+3z = -3

3 0
3 years ago
A teacher wants to know whether the boys in the entire school prefer watching television or playing outdoor games after school.
sweet-ann [11.9K]
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!
7 0
3 years ago
Carlos completed x3 squats as part of his football workout. if x=5, how many squats did he complete?
omeli [17]

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/

5 0
3 years ago
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