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2 years ago

100 POINTS!!!!!!!!!!

Mathematics

2 answers:

Vanyuwa [196]2 years ago

8 0

Answer:

x = 6 , x = 4

Step-by-step explanation:

A line parallel to a side of a triangle and intersecting the other 2 sides then divides those sides proportionally, that is

$\frac{x}{18}$ = $\frac{28-21}{21}$ = $\frac{7}{21}$ = $\frac{1}{3}$ ( cross- multiply )

3x = 18 ( divide both sides by 3 )

x = 6

(14)

$\frac{x+5}{15}$ = $\frac{5x+1}{35}$ ( cross- multiply )

15(5x + 1) = 35(x + 5) ← distribute parenthesis on both sides

75x + 15 = 35x + 175 ( subtract 35x from both sides )

40x + 15 = 175 ( subtract 15 from both sides )

40x = 160 ( divide both sides by 40 )

x = 4

Ne4ueva [31]2 years ago

5 0

the fiest answer is x=6 for the second one the answer is x=4

Step-by-step explanation:

x+15/5x+1 =15/35 then cross multiply

1st one

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Consider the line integral Z C (sin x dx + cos y dy), where C consists of the top part of the circle x 2 + y 2 = 1 from (1, 0) t

pashok25 [27]

Direct computation:

Parameterize the top part of the circle $x^2+y^2=1$ by

$\vec r(t)=(x(t),y(t))=(\cos t,\sin t)$

with $0\le t\le\pi$ , and the line segment by

$\vec s(t)=(1-t)(-1,0)+t(2,-\pi)=(3t-1,-\pi t)$

with $0\le t\le1$ . Then

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)$

$=\displaystyle\int_0^\pi(-\sin t\sin(\cos t)+\cos t\cos(\sin t)\,\mathrm dt+\int_0^1(3\sin(3t-1)-\pi\cos(-\pi t))\,\mathrm dt$

$=0+(\cos1-\cos2)=\boxed{\cos1-\cos2}$

Using the fundamental theorem of calculus:

The integral can be written as

$\displaystyle\int_C(\sin x\,\mathrm dx+\cos y\,\mathrm dy)=\int_C\underbrace{(\sin x,\cos y)}_{\vec F}\cdot\underbrace{(\mathrm dx,\mathrm dy)}_{\vec r}$

If there happens to be a scalar function $f$ such that $\vec F=\nabla f$ , then $\vec F$ is conservative and the integral is path-independent, so we only need to worry about the value of $f$ at the path's endpoints.