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Tatiana [17]
2 years ago
12

What do you have to do to this fraction before we can at the numerators ? 1/4 + 2/7​

Mathematics
1 answer:
motikmotik2 years ago
5 0

Answer:

you have to convert them to equivalent units (the same denominators)

Step-by-step explanation:

first, multiply  2 and 7 by 4.

now you have 8/21.

then, make the other fraction the same value.

multiply 1 and 4 by 7.

7/21.

now your equation is 7/21 + 8/21= 15/21.

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Use the Fundamental Theorem for Line Integrals to find Z C y cos(xy)dx + (x cos(xy) − zeyz)dy − yeyzdz, where C is the curve giv
Harrizon [31]

Answer:

The Line integral is π/2.

Step-by-step explanation:

We have to find a funtion f such that its gradient is (ycos(xy), x(cos(xy)-ze^(yz), -ye^(yz)). In other words:

f_x = ycos(xy)

f_y = xcos(xy) - ze^{yz}

f_z = -ye^{yz}

we can find the value of f using integration over each separate, variable. For example, if we integrate ycos(x,y) over the x variable (assuming y and z as constants), we should obtain any function like f plus a function h(y,z). We will use the substitution method. We call u(x) = xy. The derivate of u (in respect to x) is y, hence

\int{ycos(xy)} \, dx = \int cos(u) \, du = sen(u) + C = sen(xy) + C(y,z)  

(Remember that c is treated like a constant just for the x-variable).

This means that f(x,y,z) = sen(x,y)+C(y,z). The derivate of f respect to the y-variable is xcos(xy) + d/dy (C(y,z)) = xcos(x,y) - ye^{yz}. Then, the derivate of C respect to y is -ze^{yz}. To obtain C, we can integrate that expression over the y-variable using again the substitution method, this time calling u(y) = yz, and du = zdy.

\int {-ye^{yz}} \, dy = \int {-e^{u} \, dy} = -e^u +K = -e^{yz} + K(z)

Where, again, the constant of integration depends on Z.

As a result,

f(x,y,z) = cos(xy) - e^{yz} + K(z)

if we derivate f over z, we obtain

f_z(x,y,z) = -ye^{yz} + d/dz K(z)

That should be equal to -ye^(yz), hence the derivate of K(z) is 0 and, as a consecuence, K can be any constant. We can take K = 0. We obtain, therefore, that f(x,y,z) = cos(xy) - e^(yz)

The endpoints of the curve are r(0) = (0,0,1) and r(1) = (1,π/2,0). FOr the Fundamental Theorem for Line integrals, the integral of the gradient of f over C is f(c(1)) - f(c(0)) = f((0,0,1)) - f((1,π/2,0)) = (cos(0)-0e^(0))-(cos(π/2)-π/2e⁰) = 0-(-π/2) = π/2.

3 0
3 years ago
A x b = 400<br> a ÷ b = 4<br>how much is b​
laila [671]

Answer:

4 x 100 = 400

400 ÷100 = 4

B= 100

Step-by-step explanation:

8 0
3 years ago
What is the slope of the line that passes through the points (4, 9) and (1, 6)?
Aleksandr [31]

a = ( 1 , 6 )

b = ( 4 , 9 )

slope =  \frac{y(b) - y(a)}{x(b) - x(a)} \\

Now just need to put the coordinates in the above equation :

slope =  \frac{9 - 6}{4 - 1} \\

slope =  \frac{3}{3} \\

slope = 1

And we're done...♥️♥️♥️♥️♥️

5 0
3 years ago
What is the area, in square meters, of the trapezoid below
ahrayia [7]

Answer:

114.12

Step-by-step explanation:

A = (a+b)/2 ×h

= (6.2 + 25.5)/2 ×7.2

=114.12

8 0
2 years ago
3 out of 4 students in Nayo's class have brought in permission slips for the next field trip. There are 32 students in the class
Marina86 [1]
8
3/4
x/32

Solve for x, = 24

Subtract 24 from 32
Also another way
4 x n = 32
n = 8
3x8 = 24
Subtract and same result
5 0
3 years ago
Read 2 more answers
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