Compare the sets of numbers given and place them in the correct column or incorrect column.

A sequence is defined recursively using the equation . If f(1)=100, what is f(6)?

Dennis_Churaev [7]

Step-by-step explanation:

A sequence is defined recursively using the equation f(n + 1) = f(n) – 8. If f(1) = 100, what is f(6) ?

Since, A sequence is defined recursively using the equation f(n + 1) = f(n) – 8. If f(1) = 100,we have to find the value of f(6).

Consider

f(n+1) = f(n)-8

Let n =1, we get

f(1+1) = f(2) = f(1) - 8 = 100-8 = 92

Let n =2, we get

f(2+1) = f(3) = f(2) - 8 = 92-8 = 84

Let n =3, we get

f(3+1) = f(4) = f(3)-8 = 84 - 8 = 76

Let n =4, we get

f(4+1) = f(5) = f(4)-8 = 76 - 8 = 68

Let n =5, we get

f(5+1) = f(6) = f(5) - 8 = 68-8 = 60

Therefore, the value of f(6) is 60.

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3 years ago

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A master painter can paint 110 square yards of surface area with a roller in 1 hour, while his apprentice can paint 85 square fe

7nadin3 [17]

The apprentice needs 6.25 hours to complete the job using the brush

<h3><u>Solution:</u></h3>

Given, A master painter can paint 110 square yards of surface area with a roller in 1 hour

$\text { Then, his rate of painting }=110 \text { yard }^{2}$

We know that 1 yard = 3 feet

$=110 \times(1 \text { yard })^{2}=110 \times(3 \text { feet })^{2}=110 \times 9 \text { feet }^{2}=990 \text { square feet. }$

While his apprentice can paint 85 square feet of surface area per hour with a brush

Together they are painting a building with a surface area of 5100 square feet.

After painting for $4\frac{1}{4}$ hours , the master painter lets the apprentice Finish the job.

Now, they worked for $4\frac{1}{4}$ hours

Then, area painted = area painted by master + area painted by apprentice

$\text { Area painted }=990 \text { square feet per hour } \times 4 \frac{1}{4} \text { hours }+85 \text { square feet per hour } \times 4 \frac{1}{4} \text { hours }$

$\text { Area painted }=990 \times \frac{4 \times 4+1}{4}+85 \times \frac{4 \times 4+1}{4}$

$\begin{array}{l}{\text { Area painted }=990 \times \frac{17}{4}+85 \times \frac{17}{4}=(990+85) \times \frac{17}{4}} \\\\ {\text { Area painted }=1075 \times \frac{17}{4}=4568.75 \text { square feet. }}\end{array}$