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3 years ago

If 1/4x +2y= 11/4 and - 6y - x = 7, what is half of y?

Mathematics

1 answer:

ioda3 years ago

8 0

Answer:

y/2 = 4.5

Step-by-step explanation:

1/4x + 2y = 11/4

distribute by 4 to eliminate fractions

x + 8y = 11

+ -x - 6y = 7

2y = 18

y = 9

half of 9 = 4 1/2

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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

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

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

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

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3 years ago

Clare used 25% less butter this month than last month when baking holiday treats. If she used 240 tablespoons of butter last mon

max2010maxim [7]

Answer:

180 tablespoons

Step-by-step explanation:

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240-60=180

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3 years ago

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3 years ago

Two equivalent equations of the line in point slope form for (-4,8) and (0,5)

34kurt

Answer:

Equation of line 1 is 3 X - 4 Y = 20

Equation of line 2 is 3 X + 4 Y = 20

Step-by-step explanation:

Given co ordinates of points as,

( -4 , 8) and (0 , 5)

From the given two points we can determine the slop of a line

I. e slop (m) = $\frac{(y2 - y1)}{(x2 - x1)}$

Or, m = $\frac{(5 - 8)}{(0 + 4)}$

So, m = $\frac{(-3)}{(4)}$

Now equations of line can be written as ,

Y - y1 = m ( X - x1)

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Y - 8 = $\frac{(-3)}{(4)}$ (X + 4)

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Again with points ( 0 , 5)

Y - 5 = $\frac{(-3)}{(4)}$ ( X - 0)

So, Equation of line 2 is 3 X + 4 Y = 20

Hence Equation of line 1 is 3 X - 4 Y = 20 and Equation of line 2 is 3 X + 4 Y = 20 Answer

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4 years ago