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2 years ago

Which inequality is best represented by the graph? Picture down below

Mathematics

1 answer:

pshichka [43]2 years ago

5 0

Answer: D

Step-by-step explanation:

When you convert the equation to y-intercept form it becomes y > $\frac{1}{2}$ x +3 and the sign is > because the line is dotted and the shaded portion is above the graph.

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3-3x6+2= what is the right answer?

Kamila [148]

Use PEMDAS:-

3 - 3 × 6 + 2 = ?
3 - 18 + 2 = ?
-15 + 2 =
-13

3 - 3 × 6 + 2 = -13.

8 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 diameter of a sphere is 4 centimeters. Which represents the volume of the sphere?

soldier1979 [14.2K]

Answer:

32 $\pi$ /3 cm³

Step-by-step explanation:

If the diameter is 4 cm, then the radius is 2 cm.

Use the sphere volume formula:

V = 4/3 $\pi$ r³

Plug in the radius and solve:

V = 4/3 $\pi$ (2)³

V = 4/3 $\pi$ (8)

V = 32 $\pi$ /3

So, the volume of the sphere is 32 $\pi$ /3 cm³

3 0

3 years ago

Find out what make 30 with only the number 1,3,5,7,9,11,13,15

Mrrafil [7]

Answer:

Step-by-step explanation:

7 + 3 + 5 + 15 = 30

6 0

3 years ago

Read 2 more answers

A fair spinner has 10 equal sections: 3 red, 3 blue and 4 green. It is spun twice. What is the probability of getting not green

Nonamiya [84]

Answer:

0.24

Step-by-step explanation:

Probability is the ratio of the number of possible outcome to the number of total outcome. The probability that an even will happen or not happen is 1.

Given that the spun has 10 sections 3 red, 3 blue and 4 green, the probability of not getting green

= (3 + 3)/(3 + 3 + 4)

= 6/10

The probability of getting green

= 4/10

Hence the probability of getting not green then green

= 6/10 * 4/10

= 24/100

= 0.24

4 0

3 years ago