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3 years ago

Calculate The Constant of Proportionality (k) and Write an Equation for the line in the Graph Below:

Mathematics

1 answer:

S_A_V [24]3 years ago

7 0

Answer:

k = ½

Equation => $y = \frac{1}{2}x$

Step-by-step explanation:

Constant of proportionality (k) = y/x

Using a point on the graph, (6, 3),

k = y/x = 3/6 = ½

k = ½

Equation of the line:

Plug in the value of k into $y = kx$ (slope-intercept form of equation for proportional relationship)

Thus:

$y = \frac{1}{2}x$

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4² - 3 + 7<br>pemdas please

mezya [45]

Answer:

Step-by-step explanation:

4^2= 16

16+7=23

23-3=20

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3 years ago

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What is the volume in cubic feet of a cylinder with a radius of 6 and a height of 24.

NikAS [45]

Hey! Here you are, hope this helps...

Formula: π*r^2*h

r = 6 r^2 = 36

h = 24

π*36*24 = V

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4 years ago

Events A and B are independent. The probability of A occurring is 2/5. The probability of B occurring is 1/4. What is P(Aand B)

Elena L [17]

Answer:

The value of P(A and B) is 1/10

Step-by-step explanation:

In case of independent events, the probability of one event doesn't depend on the probability of other events.

Therefore, for an independent events

P(A and B) = P(A) × P(B)

P(A and B) = 2/5 × 1/4

P(A and B) =2/20

P(A and B) =1/10

Therefore, the value of P(A and B) is 1/10

6 0

3 years ago

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Find the outward flux of the vector field f=(x3,y3,z2) across the surface of the region that is enclosed by the circular cylinde

ahrayia [7]

Use the divergence theorem.

$\mathbf f(x,y,z)=(x^3,y^3,z^3)\implies \nabla\cdot\mathbf f=3(x^2+y^2+z^2)$

Calling the closed region $\mathcal R$ and its boundary the surface $\partial\mathcal R$ , we have by the divergence theorem,

$\displaystyle\underbrace{\iint_{\partial\mathcal R}\mathbf f\cdot\mathrm d\mathbf S}_{\text{flux}}=\iiint_{\mathcal R}\nabla\cdot\mathbf f\,\mathrm dV$

We set up the volume integral in cylindrical coordinates, using

$\begin{cases}x=u\cos v\\y=u\sin v\\z=w\end{cases}\implies\mathrm dV=u\,\mathrm du\,\mathrm dv\,\mathrm dw$

$\displaystyle\iiint_{\mathcal R}\nabla\cdot\mathbf f\,\mathrm dV=3\int_{w=0}^{w=6}\int_{v=0}^{v=2\pi}\int_{u=0}^{u=8}(u^2\cos^2v+u^2\sin^2v+w^2)u\,\mathrm du\,\mathrm dv\,\mathrm dw$
$=6\pi\displaystyle\int_{w=0}^{w=6}\int_{u=0}^{u=8}(u^3+uw^2)\,\mathrm du\,\mathrm dw=50,688\pi$

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3 years ago

Decide whether each table could represent a proportional relationship. If the relationship could be proportional, what would be

musickatia [10]

Answer:

I'm not sure but I've attched a link that can help you calculate unit rates: https://www.calculatorsoup.com/calculators/math/unit-rate-calculator.php

Step-by-step explanation:

Hope this helps

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3 years ago