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RideAnS [48]
3 years ago
8

Which graph represents y = RootIndex 3 StartRoot x + 6 EndRoot minus 3? in a test plese help fast

Mathematics
1 answer:
Oxana [17]3 years ago
4 0

Answer:

Graph (a)

Step-by-step explanation:

Given

y = \sqrt[3]{x+ 6} -3

Required

The graph

First, calculate y, when x = 0

y = \sqrt[3]{0+ 6} -3

y = \sqrt[3]{6} -3

y = -1.183

The above value of y implies that the graph is below the origin when x = 0. Hence, (c) and (d) are incorrect because they are above the origin

<em>Also, only the first graph passes through point (0,-1.183). Hence, graph (a) is correct</em>

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I really need help with this. You can answer this at any time if you want.​
Tcecarenko [31]

Answer:

1. a 3d rectangle

2. 40 in cubed

3. repeat

4. another repeat

Step-by-step explanation:

8 0
3 years ago
For each vector field f⃗ (x,y,z), compute the curl of f⃗ and, if possible, find a function f(x,y,z) so that f⃗ =∇f. if no such f
butalik [34]

\vec f(x,y,z)=(2yze^{2xyz}+4z^2\cos(xz^2))\,\vec\imath+2xze^{2xyz}\,\vec\jmath+(2xye^{2xyz}+8xz\cos(xz^2))\,\vec k

Let

\vec f=f_1\,\vec\imath+f_2\,\vec\jmath+f_3\,\vec k

The curl is

\nabla\cdot\vec f=(\partial_x\,\vec\imath+\partial_y\,\vec\jmath+\partial_z\,\vec k)\times(f_1\,\vec\imath+f_2\,\vec\jmath+f_3\,\vec k)

where \partial_\xi denotes the partial derivative operator with respect to \xi. Recall that

\vec\imath\times\vec\jmath=\vec k

\vec\jmath\times\vec k=\vec i

\vec k\times\vec\imath=\vec\jmath

and that for any two vectors \vec a and \vec b, \vec a\times\vec b=-\vec b\times\vec a, and \vec a\times\vec a=\vec0.

The cross product reduces to

\nabla\times\vec f=(\partial_yf_3-\partial_zf_2)\,\vec\imath+(\partial_xf_3-\partial_zf_1)\,\vec\jmath+(\partial_xf_2-\partial_yf_1)\,\vec k

When you compute the partial derivatives, you'll find that all the components reduce to 0 and

\nabla\times\vec f=\vec0

which means \vec f is indeed conservative and we can find f.

Integrate both sides of

\dfrac{\partial f}{\partial y}=2xze^{2xyz}

with respect to y and

\implies f(x,y,z)=e^{2xyz}+g(x,z)

Differentiate both sides with respect to x and

\dfrac{\partial f}{\partial x}=\dfrac{\partial(e^{2xyz})}{\partial x}+\dfrac{\partial g}{\partial x}

2yze^{2xyz}+4z^2\cos(xz^2)=2yze^{2xyz}+\dfrac{\partial g}{\partial x}

4z^2\cos(xz^2)=\dfrac{\partial g}{\partial x}

\implies g(x,z)=4\sin(xz^2)+h(z)

Now

f(x,y,z)=e^{2xyz}+4\sin(xz^2)+h(z)

and differentiating with respect to z gives

\dfrac{\partial f}{\partial z}=\dfrac{\partial(e^{2xyz}+4\sin(xz^2))}{\partial z}+\dfrac{\mathrm dh}{\mathrm dz}

2xye^{2xyz}+8xz\cos(xz^2)=2xye^{2xyz}+8xz\cos(xz^2)+\dfrac{\mathrm dh}{\mathrm dz}

\dfrac{\mathrm dh}{\mathrm dz}=0

\implies h(z)=C

for some constant C. So

f(x,y,z)=e^{2xyz}+4\sin(xz^2)+C

3 0
4 years ago
The backboard of the basketball hoop forms a right triangle with the supporting rods, as shown. Use the
svlad2 [7]

Answer:

9.14 inches.

Step-by-step explanation:

From the question,

Assuming the diagram attached, is similar to diagram required to support the question,

From the diagram,

Applying pythagoras theorem

a² = b²+c²...................... Equation 1

Where a = 13.4 in, b = x in, c = 9.8 in.

Substitute these values into equation 1

13.4² = x²+9.8²

x² = 13.4²-9.8²

x² = 179.56-96.04

x² = 83.52

x = √(83.52)

x = 9.14 inches

Hence the distance between the rods is 9.14 inches

8 0
3 years ago
Hai has 24 video games. Six of his games are sports related and the rest are role-playing games. Which ratio represents the numb
Ierofanga [76]
The total number of Games.....TNG=24
Sports Related Games...............SRG=06
Role Playing Games.....................RPG=18 (24-6)

The ratio of Role Playing Games to Total Number of Games=RPG:TNG
18:24
3:4 is the answer.  A ratio is actually a concept related to Division. Here in 18:24 you can divide both sides by 6 to reach the answer 3:4.


3 0
4 years ago
Read 2 more answers
Twice the sum of a number and 3 is equal to three times the difference of the number and 7. Find the number
Agata [3.3K]

Answer:

The number is 27

Step-by-step explanation:

Let us change the word statement to an algebraic equation

→ Assume that the number is x

→ Twice the sum of a number and 3, means add x by 3, then multiply the sum by 2

→ The algebraic expression is 2(x + 3)

→ Three times the difference of the number and 7, means subtract x and 7, then multiply the difference by 3

→ The algebraic expression is 3(x - 7)

→ Equate the two expressions

∴ 2(x + 3) = 3(x - 7)

→ Simplify each side

∵ 2(x + 3) = 2(x) + 2(3) = 2x + 6

∵ 3(x - 7) = 3(x) - 3(7) = 3x - 21

∴ 2x + 6 = 3x - 21

Let us solve the equation to find x

→ Subtract 6 from both sides

∴ 2x + 6 - 6 = 3x -21 - 6

∴ 2x = 3x - 21

→ Subtract 3x from both sides

∴ 2x - 3x = 3x - 3x - 27

∴ -x = -27

→ Divide both sides by -1

∴ x = 27

The number is 27

6 0
3 years ago
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