Simplify 4^1 and explain which rule you used.

A rule that the sequence could follow is that the number so for example 1/8 will have to be multiplied by 1/2 so your answer would be 1/16.

Step-by-step explanation:

A rule that the sequence could follow is that the number so for example 1/8 will have to be multiplied by 1/2 so your answer would be 1/16.

Step-by-step explanation:

See explaination and attachment for theprogram code and output.

Explanation:

matlab program:

x1(1)=0;

y1(1)=0;

x2(1)=0;

y2(1)=0;

x3(1)=0;

y3(1)=0;

for i=1:10

x1(i+1)=0.5*x1(i);

y1(i+1)=0.5*y1(i);

x2(i+1)=0.5*x2(i)+0.25;

y2(i+1)=0.5*y2(i)+(sqrt(3)/4);

x3(i+1)=0.5*x3(i)+0.5;

y3(i+1)=0.5*y3(i);

end

figure

hold on

plot(x1,y1,'*')

plot(x2,y2,'*')

plot(x3,y3,'*')

hold off

Please kindly check attachment for output of 10, 100 and 1000 respectively.

1. d. d = 66t

The maximum speed of the wildebeest is v=66 ft/s. Speed is defined as the ratio between the distance covered (d) and the time taken (t):

Re-arranging the formula, we get

And substituting v=66 ft/s, we find

2. c. y = 5 - n

In fact, we can check that this rule satisfies all the numbers of the sequence:

n=3 --> y = 5 - 3 = 2

n=4 --> y = 5 - 4 = 1

n=5 --> y = 5 - 5 = 0

n=6 --> y = 5 - 6 = -1

3. d. $5.50, $11.00, $16.50; E = 5.50h

In fact, if we use the rule E=5.50 h, we see that the table is completed as follows:

h=1 --> E=(5.50)(1 h)=5.50$

h=2 --> E=(5.50)(2 h)=11.00 $

h=3 --> E=(5.50)(3 h)=16.50$

h=4 --> E=(5.50)(4 h)=22.00$

h=5 --> E=(5.50)(5 h)=27.50$

4. c. if d ≥ 5 then C = 4.70d, if d < 5 then C = 4.70d - 1; $17.80, $32.90

If the number of days is more than 5, the cost is 4.70$ per day, therefore c=4.70d (where d is the number of days); if the number of days is less than 5, one dollar is returned, so the cost will be C=4.70d-1. By applying this rule, we can calculate the rental cost after d=4 days and d=7 days:

- d=4 --> c=4.70*4-1=17.80$

- d=7 --> c=4.70*7=32.90$

5. b. y = 3x + 3

In fact, we can check this is the correct rule by substituting the numbers:

x=0 --> y=3*0+3=3

x=1 --> y=3*1+3=6

x=2 --> y=3*2+3=9

x=3 --> y=3*3+3=12

x=4 --> y=3*4+3=15

7. x -2 -1 0 1 2

y (-16 ) (-6 ) (4 ) (14 ) (24 )

The rule we have to apply is:

-10x + y = 4

Re-arranging it, we can solve for y:

y = 10x + 4

So, let's substitute the different values of x:

x=-2 --> 10*(-2)+4=-20+4= -16

x=-1 --> 10*(-1)+4=-10+4= -6

x=0 --> 10*0+4= 4

x=1 --> 10*1+4=10+4= 14

x=2 --> 10*2 +4 =20+4 = 24

8. y = -5x - 1

In fact, if substitute the different values of x given by the problem, we find:

x = -2 --> y = -5*(-2) -1= 10 -1 = 9

x = -1 --> y = -5*(-1) -1 = 5 -1 = 4

x = 0 --> y = -5*0 -1 = -1

x = 1 --> y = -5*1 - 1 = -6

x = 2 --> y = -5*2 -1 = -11

See explaination and attachment for theprogram code and output.

Explanation:

matlab program:

x1(1)=0;

y1(1)=0;

x2(1)=0;

y2(1)=0;

x3(1)=0;

y3(1)=0;

for i=1:10

x1(i+1)=0.5*x1(i);

y1(i+1)=0.5*y1(i);

x2(i+1)=0.5*x2(i)+0.25;

y2(i+1)=0.5*y2(i)+(sqrt(3)/4);

x3(i+1)=0.5*x3(i)+0.5;

y3(i+1)=0.5*y3(i);

end

figure

hold on

plot(x1,y1,'*')

plot(x2,y2,'*')

plot(x3,y3,'*')

hold off

Please kindly check attachment for output of 10, 100 and 1000 respectively.

1. d. d = 66t

The maximum speed of the wildebeest is v=66 ft/s. Speed is defined as the ratio between the distance covered (d) and the time taken (t):

Re-arranging the formula, we get

And substituting v=66 ft/s, we find

2. c. y = 5 - n

In fact, we can check that this rule satisfies all the numbers of the sequence:

n=3 --> y = 5 - 3 = 2

n=4 --> y = 5 - 4 = 1

n=5 --> y = 5 - 5 = 0

n=6 --> y = 5 - 6 = -1

3. d. $5.50, $11.00, $16.50; E = 5.50h

In fact, if we use the rule E=5.50 h, we see that the table is completed as follows:

h=1 --> E=(5.50)(1 h)=5.50$

h=2 --> E=(5.50)(2 h)=11.00 $

h=3 --> E=(5.50)(3 h)=16.50$

h=4 --> E=(5.50)(4 h)=22.00$

h=5 --> E=(5.50)(5 h)=27.50$

4. c. if d ≥ 5 then C = 4.70d, if d < 5 then C = 4.70d - 1; $17.80, $32.90

If the number of days is more than 5, the cost is 4.70$ per day, therefore c=4.70d (where d is the number of days); if the number of days is less than 5, one dollar is returned, so the cost will be C=4.70d-1. By applying this rule, we can calculate the rental cost after d=4 days and d=7 days:

- d=4 --> c=4.70*4-1=17.80$

- d=7 --> c=4.70*7=32.90$

5. b. y = 3x + 3

In fact, we can check this is the correct rule by substituting the numbers:

x=0 --> y=3*0+3=3

x=1 --> y=3*1+3=6

x=2 --> y=3*2+3=9

x=3 --> y=3*3+3=12

x=4 --> y=3*4+3=15

7. x -2 -1 0 1 2

y (-16 ) (-6 ) (4 ) (14 ) (24 )

The rule we have to apply is:

-10x + y = 4

Re-arranging it, we can solve for y:

y = 10x + 4

So, let's substitute the different values of x:

x=-2 --> 10*(-2)+4=-20+4= -16

x=-1 --> 10*(-1)+4=-10+4= -6

x=0 --> 10*0+4= 4

x=1 --> 10*1+4=10+4= 14

x=2 --> 10*2 +4 =20+4 = 24

8. y = -5x - 1

In fact, if substitute the different values of x given by the problem, we find:

x = -2 --> y = -5*(-2) -1= 10 -1 = 9

x = -1 --> y = -5*(-1) -1 = 5 -1 = 4

x = 0 --> y = -5*0 -1 = -1

x = 1 --> y = -5*1 - 1 = -6

x = 2 --> y = -5*2 -1 = -11