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jok3333 [9.3K]
3 years ago
5

In this exercise, we show that the orthogonal distance d from the plane p with equation

Mathematics
1 answer:
kodGreya [7K]3 years ago
3 0
Use the cross product to find the orthogonal vector, solve the parametric equation to see at which (t) the point + orthogonal vector intersects the plane, the distance is (t) * norm of vector
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What is the sum? (1/x+2)+(1/x+3)+(1/X^2+5+6)
PolarNik [594]
For this case we have the following expression:
 (1 / x + 2) + (1 / x + 3) + (1 / X ^ 2 + 5 + 6)
 Rewriting we have:
 (1 / x + 2) + (1 / x + 3) + (1 / ((x + 2) * (x + 3)))
 By doing common factor we have:
 (1 / ((x + 2) * (x + 3))) * (x + 3 + x + 2 + 1)
 Rewriting:
 (1 / ((x + 2) * (x + 3))) * (2x + 6)
 The sum is:
 ((2x + 6) / ((x + 2) * (x + 3)))
 Answer:
 
((2x + 6) / ((x + 2) * (x + 3)))
7 0
3 years ago
If your barn is 100 feet by 50 feet, how many square feet do you have in your barn? Type in your answer.
zavuch27 [327]

Answer: 5,000 square feet

Step-by-step explanation:

50 feet multiplying by 100 feet equal to 5,000 sq ft.

7 0
2 years ago
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In a single growing season at the smith family orchard, the average yield per apple tree is 150 apples when the number of trees
Mariana [72]

Answer:

100 trees should be planted per acre to maximize the total yield (15000 apples per acre)

Step-by-step explanation:

<u>Functions </u>

Expressing some quantities in terms of other(s) comes in handy to understand the behavior of the situations often modeled by those functions.

Our problem tells us about the smith family orchard, where the average yield per apple tree is 150 apples when the number of trees per acre is 100 (or less). But the average yield per tree decreases when more than 100 trees are planted. The rate of decrease is 1 for each additional tree is planted

Let's call x the number of trees planted per acre in a single growing season. We have two conditions when modeling:  when x is less than 100, the average yield per apple tree (Ay) is (fixed) 150.

Ay(x)=150\ ,\ x\leqslant 100

When x is more than 100:

Ay(x)=150-x\ ,\ 100< x\leqslant 150

The upper limit is 150 because it would mean the Average yield is zero and no apples are to be harvested

Part 1

We are asked what happens if the number of trees per acre was doubled, but we don't know what the original number was. Let's make it x=60

If x=60, then we must use the first function, and

Ay(60)=150

The yield per acre will be 150*60=9000 apples

If we doubled x to 120, we would have to use the second function

Ay(120)=150-x=30

The yield per acre will be 30*120=3600 apples

Note that doubling the number of trees would make the production decrease

If we started with x=30, then  

Ay(30)=150, and we would have 150*30=4500 apples per acre

We already know that for x=60 (the double of 30), our production will be 9000 apples per acre

This shows us that in some cases, increasing the number of trees is beneficial and in other cases, it is not

Part 2

The total yield is computed as

Y(x)=x.Ay(x)

This function will be different depending on the value of x

Y(x)=150x\ ,\ x\leqslant 100

Y(x)=150x-x^2\ ,\ 100< x\leqslant 150

To find the maximum total yield we take the first derivative

Y'(x)=150\ ,\ x\leqslant 100

Y'(x)=150-2x\ ,\ 100< x\leqslant 150

The first expression has no variable, so the total yield must be evaluated in the endpoints

Y(0)=0

Y(100)=15000

Now, the second expression contains variable, it will be set to 0 to find the critical point

150-2x=0

x=75

x is outside of the boundaries, we cannot find the maximum in this interval

Answer: 100 trees should be planted per acre to maximize the total yield (15000 apples per acre)

7 0
3 years ago
A food processor packages orange juice in small jars. The weights of the filled jars are approximately normally distributed with
vovikov84 [41]

Answer:

6.68 %.

Step-by-step explanation:

The standardised z-score = ( 10.95 - 10.5) /  0.3

= 1.5.

Looking up the Normal Distribution tables ( area to the left) 1.5 corresponds to  0.93319 so for   a  weight above 10.95 the proportion is

1 - 0.93319 = 0.06681

= 6.68%.

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2 years ago
The chord XY is a diameter of of O. True or false?
steposvetlana [31]

Answer:

False

Step-by-step explanation:

XY is the diameter of the circle with the centre of this circle being O.

But O on it's own is just a coordinate, and not the circle.

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