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ser-zykov [4K]
3 years ago
15

Muke is sick with the flu but he still cors to school on monday. He areives at 8am and by 9am (hour 1) muke has already infected

two of his friends
Mathematics
1 answer:
Volgvan3 years ago
6 0

Answer:

\begin{array}{ccccccccc}{Hours} & {0} & {1} & {2} & {3} & {4}& {5} & {6} & {7} \ \\ {Persons} & {1} & {2} & {4} & {8} & {16}& {32} & {64} & {128} \ \end{array}

Step-by-step explanation:

Given

See attachment for complete question

Solving (a): Complete the table

Let

x = hours

y = persons

From the table question, we have:

(x_1,y_1) = (0,1)

(x_2,y_2) = (1,2)

(x_3,y_3) = (2,4)

The pattern follows that, an increment in x by doubles the value of 1.

So, the other values are:

(x_4,y_4) = (3,8)

(x_5,y_5) = (4,16)

(x_6,y_6) = (5,32)

(x_7,y_7) = (6,64)

(x_8,y_8) = (7,128)

So, the complete table is:

\begin{array}{ccccccccc}{Hours} & {0} & {1} & {2} & {3} & {4}& {5} & {6} & {7} \ \\ {Persons} & {1} & {2} & {4} & {8} & {16}& {32} & {64} & {128} \ \end{array}

Solving (b): The graph

The table follows an exponential function:

y = ab^x

We have: (x_1,y_1) = (0,1)

This gives:

y = ab^x

1 = ab^0

b^0 \to 1

So:

1 = a*1

1 = a

a =1

Also: (x_5,y_5) = (4,16)

This gives:

y = ab^x

16 = 1 * b^4

16 = b^4

16 \to 2^4

So:

2^4 = b^4

Cancel the exponents (4)

2 =b

b = 2

So, the function y = ab^x is:

y = 2^x

<em>See attachment 2 for graph</em>

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Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 3 at x = −3 and a local minimum value of 0 at
Amiraneli [1.4K]

Answer:

The cubic function is f(x) = (27/32)·x  - 3/32·x³ - -9/32·x² - 9/32

Step-by-step explanation:

The given function is f(x) = a·x³ + b·x² + c·x + d

By differentiation, we have;

3·a·x² + 2·b·x + c = 0

3·a·(-3)² + 2·b·(-3) + c = 0

3·a·9 - 6·b + c = 0

27·a - 6·b + c = 0

3·a·(1)² + 2·b·(1) + c = 0

3·a + 2·b + c = 0

a·(-3)³ + b·(-3)² + c·(-3) + d = -3

-27·a + 9·b - 3·c + d = -3...(1)

a + b + c + d = 0...(2)

Subtracting equation (1) from equation (2) gives;

28·a - 8·b + 4·c = 3

Therefore, we have;

27·a - 6·b + c = 0

3·a + 2·b + c = 0

28·a - 8·b + 4·c = 0

Solving the system of equations using an Wolfram Alpha gives;

a = -3/32, b = -9/32, c = 27/32 from which we have;

a + b + c + d = 0 3 × (-3/32) + 2 × (-9/32) + (27/32) + d = 0

d = 0 - (0 3 × (-3/32) + 2 × (-9/32) + (27/32)) = -9/32

The cubic function is therefore f(x) = (-3/32)·x³ + (-9/32)·x² + (27/32)·x + (-9/32).

4 0
3 years ago
HELP PLEASE!!!! What is the formula to this......dry beans, cereal, popcorn, rice, or other small grain (about 4 cups)  heavywe
topjm [15]

Answer:

9101

Step-by-step explanation:

do the math

3 0
3 years ago
When I add two to my number and then multiply it by five, I get thirty. What is my number?
rjkz [21]
30/5= 6
6 - 2 = 4
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6 0
3 years ago
Read 2 more answers
Find the perimeter use pi
balandron [24]
Since d x pi = circumference
I use 3.14 as pie

I did 9 x pi = 28.26 I DID NOT divide this by two because there are three half circles and 28.26 counts as two of them

Since there is another half circle I divide 28.26 by 2

28.26 + 14.13 = 42.39

Now plus the bottom length

42.39 + 9 = 51.39


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8 0
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A car rental charge is $100 plus $5.00 per mile traveled. Create an equation for the situation above.
Elis [28]
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X = 100$ + 5a$
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