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3 years ago

Use the diagram to answer the questions.

Mathematics

1 answer:

emmasim [6.3K]3 years ago

3 0

Answer:

Line m is not parallel to Line n.

Line m is perpendicular to Line k

Step-by-step explanation:

1. Calculate slopes of n and m. N = -2 and M = -7/4. The two slopes aren't the same thus they are not parallel

2. Slope of m = -7/4 and k = 4/7. By definition of perpendicular these two fit the description. (to be perpendicular, k = -1/m

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(see image for question)

almond37 [142]

Answer:

Hans has done a mistake in the second step.

The correct answer is:

5x^2+13x-6=0

5x^2+15x-2x-6x=0 - 5. -6=-30 -30=15. -2

5x(1+3x)-2x(1+3x)=0

(5x-2x)(1+3x)=0

5-2x=0 1+3x=0

x=5/2 x=-1/3

4 0

3 years ago

haru rides his bike from his home for 30 minutes at a fast pace. He stops to rest for 20 minutes, and then continues riding in t

Bezzdna [24]

Using the given information and what we know about linear equations, we will find the sketch below.

<h3>How to sketch a graph?</h3>

Here we need to analyze each part separately.

In a coordinate axis where the y-axis represents distance and the x-axis represents time, we will have that:

First, we know that he rides for 30 minutes at a given speed, this will be represented with an increasing linear function.

Then he stops for 20 minutes, this is represented with a horizontal line.

Finally, he returns the motion, but slower than before, so the slope of this line will be smaller than the first one.

So for 0 to 30 we have an increasing linear equation, then for 30 to 50 we have a constant horizontal line, then for 50 to 80 we have another increasing linear equation

The sketch can be seen below.

If you want to learn more about linear equations, you can read:

brainly.com/question/4074386

6 0

2 years ago

G verify that the divergence theorem is true for the vector field f on the region

Alenkasestr [34]

$\mathbf f(x,y,z)=\langle z,y,x\rangle\implies\nabla\cdot\mathbf f=\dfrac{\partial z}{\partial x}+\dfrac{\partial y}{\partial y}+\dfrac{\partial x}{\partial z}=0+1+0=1$

Converting to spherical coordinates, we have

$\displaystyle\iiint_E\nabla\cdot\mathbf f(x,y,z)\,\mathrm dV=\int_{\varphi=0}^{\varphi=\pi}\int_{\theta=0}^{\theta=2\pi}\int_{\rho=0}^{\rho=6}\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=288\pi$

On the other hand, we can parameterize the boundary of $E$ by

$\mathbf s(u,v)=\langle6\cos u\sin v,6\sin u\sin v,6\cos v\rangle$

with $0\le u\le2\pi$ and $0\le v\le\pi$ . Now, consider the surface element

$\mathrm d\mathbf S=\mathbf n\,\mathrm dS=\dfrac{\mathbf s_v\times\mathbf s_u}{\|\mathbf s_v\times\mathbf s_u\|}\|\mathbf s_v\times\mathbf s_u\|\,\mathrm du\,\mathrm dv$
$\mathrm d\mathbf S=\mathbf s_v\times\mathbf s_u\,\mathrm du\,\mathrm dv$
$\mathrm d\mathbf S=36\langle\cos u\sin^2v,\sin u\sin^2v,\sin v\cos v\rangle\,\mathrm du\,\mathrm dv$

So we have the surface integral - which the divergence theorem says the above triple integral is equal to -

$\displaystyle\iint_{\partial E}\mathbf f\cdot\mathrm d\mathbf S=36\int_{v=0}^{v=\pi}\int_{u=0}^{u=2\pi}\mathbf f(x(u,v),y(u,v),z(u,v))\cdot(\mathbf s_v\times\mathbf s_u)\,\mathrm du\,\mathrm dv$
$=\displaystyle36\int_{v=0}^{v=\pi}\int_{u=0}^{u=2\pi}(12\cos u\cos v\sin^2v+6\sin^2u\sin^3v)\,\mathrm du\,\mathrm dv=288\pi$

as required.

3 0

3 years ago

What is 23 in simplest form

rodikova [14]

23 or 23/1 or 23.0

Hope this helps ;)
Please don't forget to mark as brainliest answer

5 0

3 years ago

Anita bought these supplies for school 5 packs of pencils that cost 0.79 each 8 pens for 1.19 each what was the total cost of th

Snezhnost [94]

Answer:

14.38

Step-by-step explanation:

1. multiply the 5 packs of pencils times 0.79 each (5x0.79 = 3.95)

2. multiply the 8 packs of pens times 1.19 each (8x1.19=9.52)

3. add the total of pens and pencils together (3.95+9.52=13.44)

4. multiply 13.44 times 7% sales tax (13.44x.07=0.94)

5. add the total plus the sales tax (13.44+0.94=14.38

5 0

3 years ago