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2 years ago

Given: PRST square

Mathematics

1 answer:

yuradex [85]2 years ago

6 0

There is no difficulty in this problem until you construct the figures. How can we do it is shown in the attached picture. After drawing PRST, from the point P, we can draw PMKD and later we can complete PMCT as a result. From this picture, we can see that the side of PMCT is also a. Then, the area of this square is $A=a^{2}$

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Evaluate the line integral, where C is the given curve. C (x + yz) dx + 2x dy + xyz dz, C consists of line segments (1, 0, 1) to

Bess [88]

Parameterize the first line segment $C_1$ by

$\vec r(t)=(1,0,1)(1-t)+(2,4,1)t=(1+t,4t,1)$

and the second line segment $C_2$ by

$\vec s(t)=(2,4,1)(1-t)+(2,6,4)t=(2,4+2t,1+3t)$

both with $0\le t\le1$ . Then

$\displaystyle\int_{C_1}(x+yz)\,\mathrm dx+2x\,\mathrm dy+xyz\,\mathrm dz$

$\displaystyle=\int_0^1\bigg((1+5t)\cdot1+2(1+t)\cdot4+(1-t)4t\cdot0\bigg)\,\mathrm dt$

$=\displaystyle\int_0^1(9+13t)\,\mathrm dt=\frac{31}2$

and

$\displaystyle\int_{C_2}(x+yz)\,\mathrm dx+2x\,\mathrm dy+xyz\,\mathrm dz$

$\displaystyle=\int_0^1\bigg((2+(4+2t)(1+3t))\cdot0+2(2)\cdot2+2(4+2t)(1+3t)\cdot3\bigg)\,\mathrm dt$

$\displaystyle=\int_0^1(32+84t+36t^2)\,\mathrm dt=86$

Then

$\displaystyle\int_C(x+yz)\,\mathrm dx+2x\,\mathrm dy+xyz\,\mathrm dz=\frac{31}2+86=\boxed{\frac{203}2}$

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3 years ago

How can you determine if a number is a rational number?

FinnZ [79.3K]

A rational number is a number that can be written as a ratio. That means that it can be written as a fraction. The numerator and the denominator both need to be whole numbers for it to be rational. For example, 2 is a rational number because it can be written as the fraction 2/1.

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2 years ago

Please help me I don’t understand I have been working on this question for 14 minutes!!!m

ASHA 777 [7]

Answer:

<A = <B

=> 8x - 8 = 5x + 25

<=> 3x = 33

<=> x = 11

with x = 11 => mB = 5.11 + 25 = 55 + 25 = 80⁰

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2 years ago

Read 2 more answers

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PIT_PIT [208]

Answer: The answer is B

Step-by-step explanation:

Because it says its roaring like a freight train meaning it is loud and powerful like a train.

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2 years ago

What is the correct evaluation of 4x2 + 4x - 2y2 +3y, when x is equal to -2 and y is equal to 3?

____ [38]

Answer:

-1

Step-by-step explanation:

This all comes down to the substitution. I am assuming that (4x2) is meant to be 4x^2 so I will solve as that.

4(-2)^2 = 4(4) = 16

4(-2) = - 8

-2(3)^2 = -2(9) = -18

3(3) = 9

16-8-18+9= -1

7 0

1 year ago