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liq [111]
2 years ago
10

If f(1) = 10 and f(n) = f(n-1) + 2 the find the value of f (6)

Mathematics
1 answer:
belka [17]2 years ago
6 0

Answer:

20

Step-by-step explanation:

to find f(6) we are going to use the equation provided- f(n) = f(n-1) +2.

n will now = 6, so it will look like f(6) = f(6-1)+2

f (6) = f (5) + 2

 **side note: f (2) = f (1) +2 = 12; f (3) = f (2) + 2 = 14; and so on

so, f (6) = 18 + 2, which would be equal to 20

i hope this helps :)

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Using differential calculus, maximize the volume of a box made of cardboard (top is open) as shown in Figure A. 15, subject to t
lana [24]

The maximum volume of the box is 40√(10/27) cu in.

Here we see that volume is to be maximized

The surface area of the box is 40 sq in

Since the top lid is open, the surface area will be

lb + 2lh + 2bh = 40

Now, the length is equal to the breadth.

Let them be x in

Hence,

x² + 2xh + 2xh = 40

or, 4xh = 40 - x²

or, h = 10/x - x/4

Let f(x) = volume of the box

= lbh

Hence,

f(x) = x²(10/x - x/4)

= 10x - x³/4

differentiating with respect to x and equating it to 0 gives us

f'(x) = 10 - 3x²/4 = 0

or, 3x²/4 = 10

or, x² = 40/3

Hence x will be equal to 2√(10/3)

Now to check whether this value of x will give us the max volume, we will find

f"(2√(10/3))

f"(x) = -3x/2

hence,

f"(2√(10/3)) = -3√(10/3)

Since the above value is negative, volume is maximum for x = 2√(10/3)

Hence volume

= 10 X 2√(10/3)  -  [2√(10/3)]³/4

= 2√(10/3) [10 - 10/3]

= 2√(10/3) X 20/3

= 40√(10/27) cu in

To learn more about Maximization visit

brainly.com/question/14682292

#SPJ4

Complete Question

(Image Attached)

3 0
1 year ago
Pls just type it in no files pls and thank you
Nana76 [90]

Answer:

31

Step-by-step explanation:

First type of clay required 3 cups of flour per batch

She made 5 batches

5 * 3 = 15

So she used 15 cups of flour for the first type of clay

Second kind of clay required 4 cups of flour per batches

She made 4 batches

4 * 4 = 16

So she used 16 cups of flour for the second type of clay

we now add the total number of cups of flour used for each type of clay

16 + 15 = 31

She used a total of 31 cups of flour

5 0
3 years ago
-6.3x+14 and 1.5x-6<br> answer in simplified form
koban [17]

Answer:

The simplified form of -6.3x+14 and 1.5x-6 is -4.8x+8

Step-by-step explanation:

We have to simplify the following

-6.3x+14 and 1.5x-6

it can be written as:

=(-6.3x+14) + (1.5x-6)

Adding the like terms

=(-6.3x+1.5x)+(14-6)

= (-4.8x)+(8)

= -4.8x+8

So, the simplified form of -6.3x+14 and 1.5x-6 is -4.8x+8

3 0
3 years ago
According to the 1993 World Almanac, the number of calories a person walking at 3 mph burns per minute depends on the persons we
zaharov [31]
150 pounds is your answer
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3 years ago
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Oduvanchick [21]

Answer:

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4. 97

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7. 195

5 0
3 years ago
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