Mathematics, 10.10.2019 15:30 liyah1361

Consider the area shown below. the height of the triangle is 8 and the length of its base is 3. we have used the notation dh for δh.

write a riemann sum for the area, using the strip shown and the variable h: riemann sum =σ now write the integral that gives this area: area =∫ba

Consider the area shown below. the height of the triangle is 8 and the length of its base is 3. we h

Answers: 1

Show answers

Answers

Answer from: nicolescaggs

The Riemann sum for the area of the triangle is $A = B\cdot \Sigma \left(1-\frac{h}{H} \right) \,\Delta h$ .

The integral that gives the area is $A = B\left[ \int\limits^H_0\, dh -\frac{1}{H} \int\limits^H_0 {h} \, dh\right]$ , where a = 0 and b = H

The exact area of the region is 12 square units.

The Riemann sum of the triangle is described by the following formula:

$A = \Sigma\, b(h) \Delta h$ (1)

Where:

- Base of the rectangle. $\Delta h$ - Height of the rectangle.

- Area of the rectangle.

Now we derive an expression for the base of the rectangle in terms of the base and height of the triangle:

$\frac{b(h)}{B} = \frac{H-h}{H}$

$\frac{b(h)}{B} = 1 -\frac{h}{H}$ (2)

Where:

- Base of the triangle.

- Height of the triangle.

- Position of the rectangle within the triangle.

By (2) in (1), we obtain a Riemann sum for the area of the triangle:

$A = B\cdot \Sigma \left(1-\frac{h}{H} \right) \,\Delta h$ (3)

The Riemann sum for the area of the triangle is $A = B\cdot \Sigma \left(1-\frac{h}{H} \right) \,\Delta h$ .

The integral that gives the area of the triangle is based on (3):

$A = B\left[ \int\limits^H_0\, dh -\frac{1}{H} \int\limits^H_0 {h} \, dh\right]$

The integral that gives the area is $A = B\left[ \int\limits^H_0\, dh -\frac{1}{H} \int\limits^H_0 {h} \, dh\right]$ , where a = 0 and b = H .

Now we obtain the exact expression by integration:

$A = B\cdot \left[(H-0)-\frac{1}{2\cdot H}\cdot (H^{2}-0^{2}) \right]$

$A = \frac{1}{2}\cdot B\cdot H$

If we know that B = 3 , H = 8 , a = 0 and b = H , then the exact area of the region is:

$A = \frac{1}{2}\cdot (3)\cdot (8)$

A = 12

The exact area of the region is 12 square units.

We kindly invite to check this question on area calculations by integrals: link

Answer from: Jasten

$\text{Riemann sum }=\sum \frac{3}{8}(8-h)Dh$

$\text{Area =}\int_{a}^{b} \frac{3}{8}(8-h)Dh$

Step-by-step explanation:

Since we have been given height of triangle as 8 and length of its base as 3. We can use similar triangles to express the base of the smaller triangle in terms of h.

The height of the smaller triangle will be (8-h)

Let x be the base of the smaller triangle. Therefore, using similar triangles, we can set the ratios of corresponding sides of the two triangles equal to each other as shown below:

$\frac{8-h}{x} =\frac{8}{3} \\x=\frac{3}{8}(8-h)$

Now, we can express the area of the small rectangular strip of length x and thickness Dh as shown below:

$DA=x*Dh\\DA=\frac{3}{8}(8-h)Dh$

Therefore, the required Riemann sum can be expressed as:

$\text{Riemann sum }=\sum \frac{3}{8}(8-h)Dh$

The required areas can be expressed as:

$\text{Area =}\int_{a}^{b} \frac{3}{8}(8-h)Dh$

Rest of your answers are correct. :)

Answer from: Quest

341

step-by-step explanation:

all you have to do is 9x31 (which equals 279) and then 20x31 (which equals 620). then you have to subtract. 620-279=341.

Answer from: Quest

5x+40

5(x + 8)

7x - 49

7(x - 7)

18x + 9

9(2x + 1)

15x - 10

5(3x - 2)

step-by-step explanation:

for number one all you have to do is factor 5 out of 5x + 40

for number 2 factor 7 out of 7x - 49

for number three factor 9 out of 18x + 9

for number four factor 5 out of 15x - 10

Another question on Mathematics

Mathematics, 21.06.2019 17:00

What expression is equivalent to (2x-1)(x-3)?

Answers: 1

Answer

Mathematics, 21.06.2019 17:10

Determine whether the points (–3,–6) and (2,–8) are in the solution set of the system of inequalities below. x ? –3 y < 5? 3x + 2 a. the point (–3,–6) is not in the solution set, and the point (2,–8) is in the solution set. b. neither of the points is in the solution set. c. the point (–3,–6) is in the solution set, and the point (2,–8) is not in the solution set. d. both points are in the solution set.

Answers: 3

Answer

Mathematics, 22.06.2019 00:00

When rolling 26 sided number cube what are the chances some of the role will be seven

Answers: 1

Answer

Mathematics, 22.06.2019 03:30

If using the method of completing the square to solve the quadratic equation x 2 + 16 x + 24 = 0 x 2 +16x+24=0, which number would have to be added to "complete the square"?

Answers: 1

Answer

You know the right answer?

Consider the area shown below. the height of the triangle is 8 and the length of its base is 3. we h...

Questions