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VladimirAG [237]
3 years ago
7

A man s five times as old as his son.in three years time,the product of their ages will be 380.

Mathematics
1 answer:
Mademuasel [1]3 years ago
6 0

Answer:

son age: X

man_age= 5X

in 3 years: we have:  (man_age+3)(X+3)=380

we can replace the man age by 5X and we get :

(5X+3)(X+3)=380

it is a quadratic equation with 2 solutions. One negative and 7

The solution is thus 7, since age can not be negative.

The son is thus 7 and the dad 5 times more 35

Step-by-step explanation:

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there are 3 times as many adults as children at a book fair what is the ratio of people at the book fair​
kakasveta [241]

Answer:

1:3

Step-by-step explanation:

There are 3 adults per 1 child at the book fair. I think this is right but im not 100% sure :)

3 0
3 years ago
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
What is 10 pie × 3 9 cow to the power of 10 10ths
spayn [35]
The answer to this question is 21
7 0
3 years ago
If transports can carry only 5 tauntauns each, how many transports are needed to carry all 38 tauntauns at once?
finlep [7]

AnsweR

8

Step-by-step explanation

5 0
3 years ago
Read 2 more answers
Karens batting average is 0.444.she was at bat 45 times. how many hits did she get
alexgriva [62]

Answer:

A batting average is simply the ratio of hits/at-bats.  So, if Karen were up to bat 1,000 times and she got a hit 444 times, that makes her batting average 444/1,000 = .444.

The good news is you can multiply this ratio by number of at bats to get the number of hits.

So, 45 hits x .444 = your answer.

Hope that helps.

4 0
3 years ago
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