Write a trinomial with 3x as the GCF of its terms.

Use finite approximation to estimate the area under the graph of f(x) = 5^2 and above the graph of f(x) = 0 from X(o) = 0 to x(n

In-s [12.5K]

Finite approximation method of estimating the area under the curve of the

given function makes use of rectangular approximation of the area.

The correct responses are;

i) The estimated area using a lower sum with two rectangles of equal width is 1,715 square units.

ii) The estimated area using a lower sum with four rectangles of equal width is 3,001.25 square units.

iii) The estimated area using an upper sum with two rectangles of equal width is 8,575 square units.

iv) The estimated area using a upper sum with four rectangles of equal width is 6,431.25 square units.

Reasons:

The given function is f(x) = 5·x²

The given domain is x₀ to x₁₄

i) Estimate using lower sum with two rectangles of equal width;

$Let \ \Delta x = \dfrac{14}{2} = 7 \ we \ get;$

f(0) = 0

f(7) = 5 × 7² = 245

A = 0 × 7 + 245 × 7 = 1,715

The estimated area using a lower sum with two rectangles of equal width

is 1,715 square units.

ii) Estimate using lower sum with four rectangles of equal width;

$Let \ \Delta x = \dfrac{14}{4} = 3.5 \ we \ get;$

f(0) = 0

f(3.5) = 5 × 3.5² = 61.25

f(7) = 5 × 7² = 245

f(10.5) = 5 × 10.5² = 551.25

A = 0 × 3.5 + 61.25 × 3.5 + 245 × 3.5 + 551.25 × 3.5 = 3,001.25

The estimated area using a lower sum with four rectangles of equal width is 3,001.25 square units.

iii) Estimate using an upper sum with two rectangles of equal width;

$Let \ \Delta x = \dfrac{14}{2} = 7 \ we \ get;$

f(7) = 5 × 7² = 245

f(14) = 5 × 14² = 980

A = 245 × 7 + 980 × 7 = 8575

The estimated area using an upper sum with two rectangles of equal width

is 8,575 square units.

iv) Estimate using an upper sum with four rectangles of equal width;

$Let \ \Delta x = \dfrac{14}{4} = 3.5 \ we \ get;$

f(3.5) = 5 × 3.5² = 61.25

f(7) = 5 × 7² = 245

f(10.5) = 5 × 10.5² = 551.25

f(14) = 5 × 14² = 980

A = 61.25 × 3.5 + 245 × 3.5 + 551.25 × 3.5 + 980 × 3.5 = 6,431.25

The estimated area using a upper sum with four rectangles of equal width

is 6,431.25 square units.

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4 0

3 years ago

This isn't something specific I need to know for school, I'm just curious. I know the most commonly used variables are x, y, and

andre [41]

Answer:

Any letter you want

Step-by-step explanation:

The letters used for variables don't matter. What matters is what the variables represent: their numerical value. Variables are just to help identify what needs solving. Other common variables are a, b, and c which are found frequently in trigonometry. To answer your question, there are no "next letters." You can use any letter you'd like as a variable because it holds the same numerical value. Basically, the whole alphabet is at your disposal.

4 0

4 years ago

Karen drove her car 15 miles and used 2 gallons of gas she wants to know how many gallons she will use if she has to drive 75 mi

Airida [17]

Answer:

10 gallons of gas

Step-by-step explanation:

Create a proportion, where x is the number of gallons she will use if she drives 75 miles:

$\frac{15}{2}$ = $\frac{75}{x}$