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2 years ago

What is the quotient of 2 divided by 1/2?

Mathematics

2 answers:

SVEN [57.7K]2 years ago

8 0

Answer:

The answer is 4

Step-by-step explanation:

ad-work [718]2 years ago

3 0

Answer: 4

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The table shows values for functions f(x) and g(x) .

mart [117]

Answer:

-3 and -4

Step-by-step explanation:

f(x) = g(x) will be the input or x value at which f and g have the same output or y value. Look in the table where two numbers repeat right next to each other.

−6 −4 1

−5 0 2

−4 4 4

−3 8 8

−2 12 16

−1 16 32

0 20 64

The solution to f(x)=g(x) is both x = -4 and x=-3.

5 0

2 years ago

Direct variations need help

Solnce55 [7]

Answer:

Part 11) The table represent a direct variation. The equation is $y=18x$

Part 12) The table represent a direct variation. The equation is $y=0.4x$

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Part 11)

For x=0.5, y=9

Find the value of k

$k=y/x$ -----> $k=9/0.5=18$

For x=3, y=54

Find the value of k

$k=y/x$ -----> $k=54/3=18$

For x=-2, y=-36

Find the value of k

$k=y/x$ -----> $k=-36/-2=18$

For x=1, y=18

Find the value of k

$k=y/x$ -----> $k=18/1=18$

For x=-8, y=-144

Find the value of k

$k=y/x$ -----> $k=-144/-8=18$

The values of k is the same for each ordered pair

therefore

The table represent a direct variation

The linear equation is

$y=18x$

Part 12)

For x=-5, y=-2

Find the value of k

$k=y/x$ -----> $k=-2/-5=2/5=0.40$

For x=3, y=1.2

Find the value of k

$k=y/x$ -----> $k=1.2/3=0.40$

For x=-2, y=-0.8

Find the value of k

$k=y/x$ -----> $k=-0.8/-2=0.4$

For x=10, y=4

Find the value of k

$k=y/x$ -----> $k=4/10=0.4$

For x=20, y=8

Find the value of k

$k=y/x$ -----> $k=8/20=0.4$

The values of k is the same for each ordered pair

therefore

The table represent a direct variation

The linear equation is

$y=0.4x$

8 0

2 years ago

Subtract (8x + 6) - (x + 4)

Zigmanuir [339]

Answer:

(8x + 6) - (x + 4)

8x+6-x-4

8x-x+6-4

7x+2

8 0

3 years ago

Read 2 more answers

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.