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4 years ago

Determine whether the lines are parallel, perpendicular or neither:

Mathematics

1 answer:

11Alexandr11 [23.1K]4 years ago

8 0

Answer:

They are parallel lines

Step-by-step explanation:

Firsr you have to put both of the equations in slope intercept form which is y=mx+b and line 1 that would be 4y=3x+12 then you divide the slope and the y-intercept by 4 to get ride of the 4 in front of the y and it would equal y=3/4x+3 and for line 2 you do the same and that put into slope intercept form would be 2y=1.5x-14 so you do the same and divide the slope and the y-intercept by 2 which would equal y=0.75x-7 and 3/4 in decimal form would be 0.75. since the slopes are the same the lines would be parallel

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the dimensions of a triangular prism are shown in the diagram.What is the volume of the triangular prism in cubic centimeters

bonufazy [111]

Answer:

Answer:

1632 cm³

Step-by-step explanation:

½(12×8)×34

= 1632

Step-by-step explanation:

7 0

2 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

PLS HELP DUE SOON!!!!:(

Len [333]

Answer:

I don't know how to answer question 1, but the answer from question 2 is x=5

Step-by-step explanation:

The triangle shown is an isosceles triangle because it has two congruent sides. The base angles of isosceles triangles are congruent so ∠y=∠x. since the ∠x is 52 the ∠y is also 52. We subtract the measure of angles x and y in order to find the measure of the third angle. 180-(52+52) or 180-104 is 76. this means that 14x=6=76. All we have to do to get the answer now is solve. 76-6 is 70 and 70 divided by 14 is 5. x=5.

5 0

3 years ago

What are all the exact solutions of -3tan^2(x)+1=0? Give your answer in radians.

goldenfox [79]

$\displaystyle\\
 -3\tan^2x + 1 = 0\\\\
 -3\tan^2x = -1\\\\
\tan^2x = \frac{-1}{-3} \\\\
\tan^2x = \frac{1}{3} ~~~~~ \Big|~\sqrt{~~~} \\\\
\sqrt{\tan^2x} = \sqrt{\frac{1}{3}} \\\\
\tan x = \Big| \frac{1}{ \sqrt{3} } \Big|\\\\
\tan x = \Big| \frac{\sqrt{3}}{ 3 } \Big|\\\\
\tan x = \frac{\sqrt{3}}{ 3 }~~~\Longrightarrow~~x_1= \frac{\pi}{6} + k\pi,~~k \in N \\\\ 
\tan x = -\frac{\sqrt{3}}{ 3 }~~~\Longrightarrow~~x_2= \pi-\frac{\pi}{6} + k\pi = \frac{5\pi}{6} + k\pi,~~k \in N \\\\ 
$

4 0

3 years ago

Read 2 more answers

I need help with question 16

Contact [7]

The answers to the questions are C=11 and D=3

5 0

3 years ago