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2 years ago

Which equation could be represented by the number line

Mathematics

1 answer:

guapka [62]2 years ago

3 0

Answer:

Step-by-step explanation:

I took the test

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1 1/11 rewrite each number as a single fraction greater then one

mafiozo [28]

Answer:

12/11

Step-by-step explanation:

11/11=1

1/11=1/11

11/11+1/11=12/11

7 0

2 years ago

Consider F and C below. F(x, y, z) = y2 sin(z) i + 2xy sin(z) j + xy2 cos(z) k C: r(t) = t2 i + sin(t) j + t k, 0 ≤ t ≤ π (a) Fi

Liono4ka [1.6K]

Answer:

a) $f (x,y,z)= xy^2\sin(z)$

b) $\int_C F \cdot dr =0$

Step-by-step explanation:

Recall that given a function f(x,y,z) then $\nabla f = (\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z})$ . To find f, we will assume it exists and then we will find its form by integration.

First assume that F = $\nabla f$ . This implies that

$\frac{\partial f}{\partial x} = y^2\sin(z)$ if we integrate with respect to x we get that

$f(x,y,z) = xy^2\sin(z) + g(y,z)$ for some function g(y,z). If we take the derivative of this equation with respect to y, we get

$\frac{\partial f}{\partial y} = 2xy\sin(z) + \frac{\partial g}{\partial y}$

This must be equal to the second component of F. Then

$2xy\sin(z) + \frac{\partial g}{\partial y}=2xy\sin(z)$

This implies that $\frac{\partial g}{\partial y}=0$ , which means that g depends on z only. So $f(x,y,z) = xy^2\sin(z) + g(z)$

Taking the derivative with respect to z and making it equal to the third component of F, we get

$xy^2\cos(z)+\frac{dg}{dz} = xy^2\cos(z)$

which implies that $\frac{dg}{dz}=0$ which means that g(z) = K, where K is a constant. So

$f (x,y,z)= xy^2\sin(z)$

b) To evaluate $\int_C F \cdot dr$ we can evaluate it by using f. We can calculate the value of f at the initial and final point of C and the subtract them as follows.

$\int_C F \cdot dr = f(r(\pi))-f(r(0))$

Recall that $r(\pi) = (\pi^2, 0, \pi)$ so $f(r(\pi)) = \pi^2\cdot 0 \cdot \sin(\pi) = 0$

Also $r(0) = (0, 0, 0)$ so $f(r(0)) = 0^2\cdot 0 \cdot \sin(0) = 0$

So $\int_C F \cdot dr =0$

5 0

2 years ago

Round 653 , 500 653,500653, comma, 500 to the nearest thousand.

Jlenok [28]

Answer:

Do you mean to round the number 653,500,653,500,653,500? Or do you mean to round the number 653,500? If so, for 653,500, the digit in the thousand's place is 5, so it's already rounded to the nearest thousands place.

Step-by-step explanation:

5 0

2 years ago

Use a model to divide. 1/4 ÷ 5 1/20 4/5 1 1/4 20

Lera25 [3.4K]

Answer:

$\frac{1}{4} \div 5 \\ = \frac{1}{20}$