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3 years ago

14

Anyone know what the answer is?

1 answer:

Citrus2011 [14]3 years ago

3 0

It’s been a minute but I think it’s x=3

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For what real values of does the quadratic 12x^2+kx+27=0 have nonreal roots

bija089 [108]

Answer:

k<±36

Step-by-step explanation:

Δ<0 (no real roots)

b²-4ac<0

k²-4x12x27<0

k²-1296<0

k²<1296

k<±36

3 0

2 years ago

I'm really having trouble simplifying trigonometric expressions, I understand the identities, but sometimes I get stuck, and rea

Karolina [17]

$\bf \cfrac{sin(t)+tan(t)}{tan(t)}\impliedby \textit{distributing the denominator}
\\\\\\
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8 0

3 years ago

How many servings can be made from 108 cups of punch when you mix 18 cups of pineapple juice, 36 cups of orange juice and 54 cup

Alinara [238K]

Answer:

14

Step-by-step explanation:

5 0

3 years ago

A torus is formed by rotating a circle of radius r about a line in the plane of the circle that is a distance R (> r) from th

jeyben [28]

Consider a circle with radius $r$ centered at some point $(R+r,0)$ on the $x$ -axis. This circle has equation

$(x-(R+r))^2+y^2=r^2$

Revolve the region bounded by this circle across the $y$ -axis to get a torus. Using the shell method, the volume of the resulting torus is

$\displaystyle2\pi\int_R^{R+2r}2xy\,\mathrm dx$

where $2y=\sqrt{r^2-(x-(R+r))^2}-(-\sqrt{r^2-(x-(R+r))^2})=2\sqrt{r^2-(x-(R+r))^2}$ .

So the volume is

$\displaystyle4\pi\int_R^{R+2r}x\sqrt{r^2-(x-(R+r))^2}\,\mathrm dx$

Substitute

$x-(R+r)=r\sin t\implies\mathrm dx=r\cos t\,\mathrm dt$

and the integral becomes

$\displaystyle4\pi r^2\int_{-\pi/2}^{\pi/2}(R+r+r\sin t)\cos^2t\,\mathrm dt$

Notice that $\sin t\cos^2t$ is an odd function, so the integral over $\left[-\frac\pi2,\frac\pi2\right]$ is 0. This leaves us with

$\displaystyle4\pi r^2(R+r)\int_{-\pi/2}^{\pi/2}\cos^2t\,\mathrm dt$

Write

$\cos^2t=\dfrac{1+\cos(2t)}2$

so the volume is

$\displaystyle2\pi r^2(R+r)\int_{-\pi/2}^{\pi/2}(1+\cos(2t))\,\mathrm dt=\boxed{2\pi^2r^2(R+r)}$

6 0

2 years ago

Can someone help with this one

natali 33 [55]

Since the base is 4x4, and the height is 2, you'll use the 2 as the height of the netting and the 4 as the length. so, it will be 2x4 which is 8ft^2

4 0

2 years ago