Step-by-step explanation:
A left Riemann sum approximates a definite integral as:
Given ∫₂⁸ cos(x²) dx:
a = 2, b = 8, and f(x) = cos(x²)
Therefore, Δx = 6/n and x = 2 + (6/n) (k − 1).
Plugging into the sum:
∑₁ⁿ cos((2 + (6/n) (k − 1))²) (6/n)
Therefore, the answer is C. Notice that answer D would be a right Riemann sum rather than a left (uses k instead of k−1).
Answer:
25
Step-by-step explanation:
Since each of the six possible outcomes is equally likely, you can expect to get each of the outcomes 150/6 = 25 times.
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explanation in the attached picture
The x-y coordinates for the given equation are: (-2,11),(-1,7),(0,3), (1,-1) and (2,-5).
<h3>Linear Function</h3>
A linear function can be represented by a line. The standard form for this equation is: ax+b , for example, y=2x+7. Where:
- a= the slope;
- b=the constant term that represents the y-intercept.
The given equation is 16x + 4y = 12. For solving this question, you should replace the given values of x for finding the values of y.
Thus,
- For x= -2, the value of y will be:
16*(-2)+4y=12
-32+4y=12
4y=12+32
4y=44
y=11
- For x= -1, the value of y will be:
16*(-1)+4y=12
- -16+4y=12
- 4y=12+16
- 4y=28
- y=7
- For x= 0, the value of y will be:
16*(0)+4y=12
- For x= 1, the value of y will be:
16*(1)+4y=12
- 16+4y=12
- 4y=12-16
- 4y=-4
- y= -1
- For x= 2, the value of y will be:
16*(2)+4y=12
- 32+4y=12
- 4y=12-32
- 4y=-20
- y= -5
Read more about the linear equation here:
brainly.com/question/1884491
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Answer:
the constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other. Once you know the constant of proportionality you can find an equation representing the directly proportional relationship between x and y, namely y=kx, with your specific k.
Step-by-step explanation:
