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2 years ago

Henry ate 3/8 of a sandwich. Keith ate 4/8 of the same sandwich. How much more of the sandwich did Keith eat than Henry?

Mathematics

1 answer:

ludmilkaskok [199]2 years ago

6 0

4/8-3/8=1/8more

Therefore Keith at 1/8 more of the sandwich than Henry.

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Evaluate the line integral, where c is the given curve. (x + 9y) dx + x2 dy, c c consists of line segments from (0, 0) to (9, 1)

viktelen [127]

$\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=\int_C\langle x+9y,x^2\rangle\cdot\underbrace{\langle\mathrm dx,\mathrm dy\rangle}_{\mathrm d\mathbf r}$

The first line segment can be parameterized by $\mathbf r_1(t)=\langle0,0\rangle(1-t)+\langle9,1\rangle t=\langle9t,t\rangle$ with $0\le t\le1$ . Denote this first segment by $C_1$ . Then

$\displaystyle\int_{C_1}\langle x+9y,x^2\rangle\cdot\mathbf dr_1=\int_{t=0}^{t=1}\langle9t+9t,81t^2\rangle\cdot\langle9,1\rangle\,\mathrm dt$
$=\displaystyle\int_0^1(162t+81t^2)\,\mathrm dt$
$=108$

The second line segment ( $C_2$ ) can be described by $\mathbf r_2(t)=\langle9,1\rangle(1-t)+\langle10,0\rangle t=\langle9+t,1-t\rangle$ , again with $0\le t\le1$ . Then

$\displaystyle\int_{C_2}\langle x+9y,x^2\rangle\cdot\mathrm d\mathbf r_2=\int_{t=0}^{t=1}\langle9+t+9-9t,(9+t)^2\rangle\cdot\langle1,-1\rangle\,\mathrm dt$
$=\displaystyle\int_0^1(18-8t-(9+t)^2)\,\mathrm dt$
$=-\dfrac{229}3$

Finally,

$\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=108-\dfrac{229}3=\dfrac{95}3$

5 0

3 years ago

Find the y-intercept for the parabola defined by

olasank [31]

Answer:

(0,6)

Step-by-step explanation:

because a point that lies on y axis has the coordinates of its x = 0.

the therm without the x in the equation of the parabola indicate where it intercepts the y axis

6 0

2 years ago

Solve the following simultaneous linear equations.<br>2x + y = 5<br>4x – 3y = -10

Jet001 [13]

Answer:

(1/2,4)

Step-by-step explanation:

First, determine y in first equation: 2x+y=5 or y=5-2x

replace value of y determined in first equation (5-2x) into 2nd equation

4x-3(5-2x)=-10

4x-15+6x=10

10x=5

x=1/2

put value of x into either equation to solve for y so

2(1/2)+y=5

1+y=5

y=4

answer: x=1/2, y=4

check answer by substituting x and y into either equation:

4x-3y=-10

4(1/2)-3(4)=-10

2-12=-10

-10=-10

2x+y=5

2(1/2)+4=5

1+4=5

5=5

7 0

2 years ago

Mr. Ahmed has 9 water heaters for his apartment buildings. each heater weighs 32 kilograms. How many grams do all 9 water heater

iris [78.8K]

Multiply 32X 9 = 288kg

they asked you to convert the kilograms to grams so divide the 288kg by a 1000= 0.288grams

8 0

2 years ago

Does 2x+15+x equal 180 or 90? Someone pls help.

tatyana61 [14]

Answer:

Its 180!

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers