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3 years ago

How many solutions does the equation have?

Mathematics

1 answer:

kherson [118]3 years ago

7 0

Answer:

there is one solution if I am right and math is my best so .

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Evaluate the line integral, where C is the given curve. (x + 6y) dx + x2 dy, C C consists of line segments from (0, 0) to (6, 1)

Dima020 [189]

Split $C$ into two component segments, $C_1$ and $C_2$ , parameterized by

$\mathbf r_1(t)=(1-t)(0,0)+t(6,1)=(6t,t)$

$\mathbf r_2(t)=(1-t)(6,1)+t(7,0)=(6+t,1-t)$

respectively, with $0\le t\le1$ , where $\mathbf r_i(t)=(x(t),y(t))$ .

We have

$\mathrm d\mathbf r_1=(6,1)\,\mathrm dt$

$\mathrm d\mathbf r_2=(1,-1)\,\mathrm dt$

where $\mathrm d\mathbf r_i=\left(\dfrac{\mathrm dx}{\mathrm dt},\dfrac{\mathrm dy}{\mathrm dt}\right)\,\mathrm dt$

so the line integral becomes

$\displaystyle\int_C(x+6y)\,\mathrm dx+x^2\,\mathrm dy=\left\{\int_{C_1}+\int_{C_2}\right\}(x+6y,x^2)\cdot(\mathrm dx,\mathrm dy)$

$=\displaystyle\int_0^1(6t+6t,(6t)^2)\cdot(6,1)\,\mathrm dt+\int_0^1((6+t)+6(1-t),(6+t)^2)\cdot(1,-1)\,\mathrm dt$

$=\displaystyle\int_0^1(35t^2+55t-24)\,\mathrm dt=\frac{91}6$

6 0

3 years ago

GRADE 10 MATH QUESTION

xxTIMURxx [149]

Answer:

the shortest route is from cabin site to B

Step-by-step explanation:

see my attachment

4 0

3 years ago

Read 2 more answers

a rectangle has an area of 34 sqaure feet. A larger rectangle has an area of 124 sqaure feet. what is the percent increase of th

amid [387]

Answer:

The difference in areas:

124 - 34 = 90 square feet

Percent increase:

90/34*100% = 264.71%

5 0

3 years ago

Which expression has the fewest number of significant figures

Brums [2.3K]

Answer:

18.3

18.3 only has three significant figures while the other numbers have more

5 0

3 years ago

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Solve the inequality. -1.5(4x+1) ≥ 45-25(x+1)

777dan777 [17]

Answer:

x ≥ 21.5/19

Step-by-step explanation:

-1.5(4x + 1) ≥ 45 - 25(x + 1)

-6x - 1.5 ≥ 45 - 25x - 25

-6x + 25x ≥ 45 - 25 + 1.5

19x ≥ 21.5

x ≥ 21.5/19

3 0

2 years ago