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3 years ago

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kennedy has 12 apples. together, she and Ariana have 42 apples. which diagram best represents the situation where A is the amoun

t of apples that Ariana has

1 answer:

Katarina [22]3 years ago

3 0

There is no diagram to chose from

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Can someone help me find the answers to this question

iVinArrow [24]

Answer should be b, not 100% sure

5 0

3 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

3 years ago

The perimeter of a rectangular garden is 37.5 feet. The width is x, and the length is 15 ft. Use the equation 2(x + 15) = 37.5 t

charle [14.2K]

Answer:

2.5

Step-by-step explanation:

37.5/15=2.5

3 0

3 years ago

Read 2 more answers

What number can cancel 15 and 10

Lena [83]

Answer:

Step-by-step explanation:

5 can cancel

5 0

3 years ago

Identify the k-value that makes the relationship shown in the table below proportional.

uysha [10]

Answer:

The value of k that makes the relationship shown in the table below proportional is $\mathbf{\frac{1}{2}}$

Step-by-step explanation:

The relation is proportional if $y=kx \:or\:k=\frac{y}{x}$

Putting values of x and y to find k.

For x =2 and y =1 k is: $k=\frac{y}{x}=\frac{1}{2}$

For x =4 and y =2 k is: $k=\frac{y}{x}=\frac{2}{4} =\frac{1}{2}$

For x =6 and y = 3 k is: $k=\frac{y}{x}=\frac{3}{6} =\frac{1}{2}$

For x = 8 and y = 4 k is: $k=\frac{y}{x}=\frac{4}{8} =\frac{1}{2}$

For x =10 and y = 5 k is: $k=\frac{y}{x}=\frac{5}{10} =\frac{1}{2}$

So, The value of k that makes the relationship shown in the table below proportional is $\mathbf{\frac{1}{2}}$

5 0

3 years ago