100 points please help ! Write a paragraph, flowchart or 2- column proof for the following conjecture

Mathematics

1 answer:

lara [203]3 years ago

8 0

How I would write my paragraph:

If angle 1 is congruent to angle 4, angle 1 must also be congruent to angle 3 by the transitive property. This is because is angle 3 and angle 4 are vertical angles, and they must be congruent. If angle 1 is congruent to angle 3, then the two lines in the middle must also be parallel due to the converse of the corresponding angles theorem. Because the two lines in the middle are parallel, angle 3 must be congruent to angle 2 by the alternate interior angles theorem.

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Please show ur work

Fiesta28 [93]

B. 1/7 i just took the test and thats what i got hope it helps

3 0

3 years ago

Use four rectangles to estimate the area between the graph of the function f(x) = V3x + 5 and the x-axis on the interval[0, 4] u

yuradex [85]

Answer:

12.123

Step-by-step explanation:

You want the area under the curve f(x) = √(3x+5) on the interval [0, 4] estimated using the left sum and four subintervals.

<h3>Riemann sum</h3>

When the interval [0, 4] is divided into four equal parts, each has unit width. That means the area of the rectangle defined by the curve and the interval width will be equal to the value of the curve at the left end of the interval.

The area we want is the sum ...

f(0) +f(1) +f(2) +f(3)

As the attachment shows, that sum is ...

area ≈ 12.123 . . . square units

<em>Additional comment</em>

The table values in the attachment are rounded to 7 decimal places. Trailing zeros are not shown. Actual values used have 12 significant digits, as the total shows.

Such a sum is called a Riemann sum, named for a German mathematician. Four such sums are commonly used, and further refinements are possible. Those are the left sum (as here), the right sum, the midpoint sum, and a sum using a trapezoidal approximation of the rectangle area.

For left, right, and midpoint sums, n function values are required for n subintervals. When the trapezoidal approximation is used, n+1 function values are required.