A fence is to be built to enclose a rectangular area of 1800 square feet. The fence along three sides is to be made of material
1 answer:
Answer:
length = 60 foot, width = 30 foot
Step-by-step explanation:
Area of rectangular part, A = 1800 ft²
Cost of fencing three sides is $ 6 per foot and cost of one side fencing is $18 per foot.
Let the length of the rectangle is l and the width of the rectangle is W.
Area = Length x width
A = L x W
1800 = L x W ...... (1)
Total cost of fencing, C = 6 x ( L + W + L) + 18 x W
C = 6 (2L + W) + 18 W
C = 12 L + 24 W
Substitute the value of W from equation (1), in equation (2)
Differentiate both sides with respect to L:
Put it equal to zero for maxima and minima
L = 60 foot
and W = 30 foot
So, the costing is minimum for length = 60 foot and the width = 30 foot.
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Answer:
(a)There are 500 integers from 1 through 1,000 are multiples of 2.
There are 111 integers from 1 through 1,000 are multiples of 9.
(b)0.611
Step-by-step explanation:
Given the set of Integers from 1 through 1000
The least multiple of 2 is 2 and the highest multiple of 2 in the interval is 1000.
To determine the number of terms, we use the formula for the nth term of an Arithmetic Progression, since 2,4,6,... is an Arithmetic Progression,
where first term, a =2, common difference, d =2
Nth term of an A.P,
- There are 500 integers from 1 through 1,000 are multiples of 2.
Similarly,
Given the set of Integers from 1 through 1000
The least multiple of 9 is 9 and the highest multiple of 9 in the interval is 999.
To determine the number of terms, we use the formula for the nth term of an Arithmetic Progression, since 9,18,27,... is an Arithmetic Progression,
where first term, a =9, common difference, d =9
Nth term of an A.P,
- There are 111 integers from 1 through 1,000 are multiples of 9.
(b)Probability that an integer selected at random is a multiple of 2 or a multiple of 9.
There are a total of 1000 numbers between from 1 through 1,000
n(S)=1000
n(Multiples of 2)=500
n(Multiples of 9)=111
Therefore:
Like all problems that involve images within the question, we should definitely try to draw this out. In the picture above, I have done this.
Now, we can see that this is just a simple proportion problem. For every 2.5 cm of height of the flower, we are 2 cm from the opening, or aperture. For every 20 cm of height, how far are we? We can set up the problem like this:
20 ............2.5
-------- = ---------
...x ............. 2
where x is the unknown distance to the aperture from the flower. Now, we just need to get x by itself. A typical way of solving something like this is by doing "butterfly multiplication" which is really just a shortcut haha. Anyway, I can rewrite that equation ^ as:
20×2 = 2.5 × x
Then, to solve for x, we would divide both sides by 2.5. (If you don't know why that is, please let me know and I'll elaborate).
We would then have:
20×2
------- = x
2.5
Which then simplifies to:
x = 16
Try using the same logic for your second question, and if you get stuck, I'd be happy to help! please let me know if any of this doesn't make sense. :)
Now, we can see that this is just a simple proportion problem. For every 2.5 cm of height of the flower, we are 2 cm from the opening, or aperture. For every 20 cm of height, how far are we? We can set up the problem like this:
20 ............2.5
-------- = ---------
...x ............. 2
where x is the unknown distance to the aperture from the flower. Now, we just need to get x by itself. A typical way of solving something like this is by doing "butterfly multiplication" which is really just a shortcut haha. Anyway, I can rewrite that equation ^ as:
20×2 = 2.5 × x
Then, to solve for x, we would divide both sides by 2.5. (If you don't know why that is, please let me know and I'll elaborate).
We would then have:
20×2
------- = x
2.5
Which then simplifies to:
x = 16
Try using the same logic for your second question, and if you get stuck, I'd be happy to help! please let me know if any of this doesn't make sense. :)