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iren [92.7K]
3 years ago
9

HELP MEEEEEEE PLEASE

Mathematics
1 answer:
tresset_1 [31]3 years ago
7 0
The answer will be d
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Using 4 equal-width intervals, show that the trapezoidal rule is the average of the upper and lower sum estimates for the integr
prisoha [69]

Split up the interval [0, 2] into 4 subintervals, so that

[0,2]=\left[0,\dfrac12\right]\cup\left[\dfrac12,1\right]\cup\left[1,\dfrac32\right]\cup\left[\dfrac32,2\right]

Each subinterval has width \dfrac{2-0}4=\dfrac12. The area of the trapezoid constructed on each subinterval is \dfrac{f(x_i)+f(x_{i+1})}4, i.e. the average of the values of x^2 at both endpoints of the subinterval times 1/2 over each subinterval [x_i,x_{i+1}].

So,

\displaystyle\int_0^2x^2\,\mathrm dx\approx\dfrac{0^2+\left(\frac12\right)^2}4+\dfrac{\left(\frac12\right)^2+1^2}4+\dfrac{1^2+\left(\frac32\right)^2}4+\dfrac{\left(\frac32\right)^2+2^2}4

=\displaystyle\sum_{i=1}^4\frac{\left(\frac{i-1}2\right)^2+\left(\frac i2\right)^2}4=\frac{11}4

4 0
3 years ago
How does the rate of change of f(x)=3x+5 compare to the rate of change of g(x)=2x+5 ?
elena55 [62]
Do you know how to do it on your calculator?
6 0
3 years ago
Marcos sees a cake advertised as $15 or 2 for $25. What is the difference of the unit rate?
Mekhanik [1.2K]

Answer:

A. 2.50

Step-by-step explanation:

25 ÷ 2 = 12.5

15 - 12.5 = 2.50

6 0
3 years ago
The slope of a line parallel to the graph of 4x-5y=12
Leya [2.2K]
Parallel lines have the same slope.

4x-5y=12 \\ -5y=-4x+12 \\ y= \frac{4}{5}x- \frac{12}{5}   \\  \\ slope:\frac{4}{5}
6 0
3 years ago
What attribute must be present for a quadrilateral to also be a trapezoid?
konstantin123 [22]

Answer:

At least two of the opposite sides must be parallel.

Step-by-step explanation:

In the picture below, the segment AB must be parallel to the segment DC so that the figure can be called a trapezoid.

3 0
3 years ago
Read 2 more answers
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