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oee [108]
3 years ago
10

I need help on this question please

Mathematics
1 answer:
Fynjy0 [20]3 years ago
5 0

Answer: NEITHER

Step-by-step explanation:

From the equation of lines given above, to know if relationships exist between the two lines, we must  first determine that  from their gradients or slopes.

From first equation

2x - y = 5,

      y = 2x - 5

Therefore, m₁ = 2

From the second equation

3x - y = 5

       y = 3x - 5

Therefore m₂ = 3

Recall, For the two lines to be parallel, m₁ = m₂ , and for the two line to be perpendicular, m₁m₂ = -1

since none fulfilled the conditions stated above, the answer then is

NEITHER

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Estimate the integral ∫6,0 x^2dx by the midpoint estimate, n = 6
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Splitting up the interval [0, 6] into 6 subintervals means we have

[0,1]\cup[1,2]\cup[2,3]\cup\cdots\cup[5,6]

and the respective midpoints are \dfrac12,\dfrac32,\dfrac52,\ldots,\dfrac{11}2. We can write these sequentially as {x_i}^*=\dfrac{2i+1}2 where 0\le i\le5.

So the integral is approximately

\displaystyle\int_0^6x^2\,\mathrm dx\approx\sum_{i=0}^5({x_i}^*)^2\Delta x_i=\frac{6-0}6\sum_{i=0}^5({x_i}^*)^2=\sum_{i=0}^5\left(\frac{2i+1}2\right)^2

Recall that

\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6
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so our sum becomes

\displaystyle\sum_{i=0}^5\left(\frac{2i+1}2\right)^2=\sum_{i=0}^5\left(i^2+i+\frac14\right)
=\displaystyle\frac{5(6)(11)}6+\frac{5(6)}2+\frac54=\frac{143}2

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2 years ago
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Step-by-step explanation:

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3 years ago
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Answer:

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Step-by-step explanation:

The spinner is split into 4 equal parts labeled 1, 2, 3, 4

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The total possible outcome is 4, because the spinner could land on 1, or 2, or 3, or 4.

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Answer:

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Step-by-step explanation:

(2^3)^5

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Answer: \frac{1}{3^6}=3^{-6}

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