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irina1246 [14]
3 years ago
5

What does understand and plan and solve and check mean

Mathematics
2 answers:
kvasek [131]3 years ago
7 0
Check is to look over
solve is to figure out
plan is to arrange information
understand is to follow what you are supposed to do
Pachacha [2.7K]3 years ago
4 0
Check means to look over, solve means to figure out,plan means to arrange or gather information and understand means to follow what you are supposed to do
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Evaluate the definite integral using the graph of f(x)<br> (Image included)
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a) The first integral corresponds to the area under y = f(x) on the interval [0, 3], which is a right triangle with base 3 and height 5, hence the integral is

\displaystyle \int_0^3 f(x) \, dx = \frac12 \times 3 \times 5 = \boxed{\frac{15}2}

b) The integral is zero since the areas under the curve over [3, 4] and [4, 5] are equal but opposite in sign. In other words, on the interval [3, 5], f(x) is symmetric and odd about x = 4, so

\displaystyle \int_3^5 f(x) \, dx = \int_3^4 f(x) \, dx + \int_4^5 f(x) \, dx = \int_3^4 f(x) \, dx - \int_3^4 f(x) \, dx = \boxed{0}

c) The integral over [5, 9] is the negative of the area of a rectangle with length 9 - 5 = 4 and height 5, so

\displaystyle \int_5^9 f(x) \, dx = -4\times5 = -20

Then by linearity, we have

\displaystyle \int_0^9 f(x) \, dx = \left\{\int_0^3 + \int_3^5 + \int_5^9\right\} f(x) \, dx = \frac{15}2 + 0 - 20 = \boxed{-\frac{25}2}

8 0
2 years ago
2x-5y+5z=-10<br> 5x-4y+3z=-19<br> X-y+5z=17
yarga [219]

Answer:

x = -125/71 , y = 448/71 , z = 356/71

Step-by-step explanation:

Solve the following system:

{2 x - 5 y + 5 z = -10 | (equation 1)

5 x - 4 y + 3 z = -19 | (equation 2)

x - y + 5 z = 17 | (equation 3)

Swap equation 1 with equation 2:

{5 x - 4 y + 3 z = -19 | (equation 1)

2 x - 5 y + 5 z = -10 | (equation 2)

x - y + 5 z = 17 | (equation 3)

Subtract 2/5 × (equation 1) from equation 2:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - (17 y)/5 + (19 z)/5 = (-12)/5 | (equation 2)

x - y + 5 z = 17 | (equation 3)

Multiply equation 2 by 5:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - 17 y + 19 z = -12 | (equation 2)

x - y + 5 z = 17 | (equation 3)

Subtract 1/5 × (equation 1) from equation 3:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - 17 y + 19 z = -12 | (equation 2)

0 x - y/5 + (22 z)/5 = 104/5 | (equation 3)

Multiply equation 3 by 5:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - 17 y + 19 z = -12 | (equation 2)

0 x - y + 22 z = 104 | (equation 3)

Subtract 1/17 × (equation 2) from equation 3:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - 17 y + 19 z = -12 | (equation 2)

0 x+0 y+(355 z)/17 = 1780/17 | (equation 3)

Multiply equation 3 by 17/5:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - 17 y + 19 z = -12 | (equation 2)

0 x+0 y+71 z = 356 | (equation 3)

Divide equation 3 by 71:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - 17 y + 19 z = -12 | (equation 2)

0 x+0 y+z = 356/71 | (equation 3)

Subtract 19 × (equation 3) from equation 2:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - 17 y+0 z = (-7616)/71 | (equation 2)

0 x+0 y+z = 356/71 | (equation 3)

Divide equation 2 by -17:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x+y+0 z = 448/71 | (equation 2)

0 x+0 y+z = 356/71 | (equation 3)

Add 4 × (equation 2) to equation 1:

{5 x + 0 y+3 z = 443/71 | (equation 1)

0 x+y+0 z = 448/71 | (equation 2)

0 x+0 y+z = 356/71 | (equation 3)

Subtract 3 × (equation 3) from equation 1:

{5 x+0 y+0 z = (-625)/71 | (equation 1)

0 x+y+0 z = 448/71 | (equation 2)

0 x+0 y+z = 356/71 | (equation 3)

Divide equation 1 by 5:

{x+0 y+0 z = (-125)/71 | (equation 1)

0 x+y+0 z = 448/71 | (equation 2)

0 x+0 y+z = 356/71 | (equation 3)

Collect results:

Answer: {x = -125/71 , y = 448/71 , z = 356/71

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