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3 years ago

7

Need help on number 11

1 answer:

elena55 [62]3 years ago

3 0

Hello!!

72% = n/25

n = 72% * 25

n = 18

Good luck :)

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Water is poured into a conical paper cup at the rate of 3/2 in3/sec. If the cup is 6 inches tall and the top has a radius of 6 i

Leto [7]

So.. hmm notice the picture below

r = h, due to similar triangles ratio, whatever "h" may be

now, we're given how much water is being poured into the cup per sec
namely dv/dt the volume's rate

so.. hmmm $\bf \textit{volume of a cone}=V=\cfrac{\pi r^2 h}{3}\quad however\implies r=h
\\\\\\
thus\implies V=\cfrac{\pi h^2 h}{3}\implies V=\cfrac{\pi h^3}{3}\\\\
------------------------\\\\
now
\\\\\\
\cfrac{dv}{dt}=\cfrac{\pi }{3}\cdot 3h^2\cdot \cfrac{dh}{dt}\implies \cfrac{dv}{dt}=\pi h^2\cdot \cfrac{dh}{dt}
\\\\\\
\cfrac{\frac{dv}{dt}}{\pi h^2}=\cfrac{dh}{dt}\quad 
\begin{cases}
\frac{dv}{dt}=\frac{3}{2}\\\\
\left. \frac{dh}{dt} \right|_{h=4}
\end{cases}\implies \cfrac{\frac{3}{2}}{\pi 4^2}=\cfrac{dh}{dt}$

8 0

3 years ago

PSYCHO15rus [73]

Answer:

61.74%

Step-by-step explanation

Find the vol of container one: Volume = Pi(r^2)(height) = 3.14159*81*10 = 2544.69 cu.ft.

Find the vol of container two: Pi(r^2)(height) = 1570.79 cu.ft.

Now the % of container A that is empty is

(1 - ((Volume A - Volume B)/Volume A))*100% = 61.73%

3 0

3 years ago

The equations that must be solved for maximum or minimum values of a differentiable function w=f(x,y,z) subject to two constrai

sammy [17]

The Lagrangian is

$L(x,y,z,\lambda,\mu)=x^2+y^2+z^2+\lambda(4x^2+4y^2-z^2)+\mu(2x+4z-2)$

with partial derivatives (set equal to 0)

$L_x=2x+8\lambda x+2\mu=0\implies x(1+4\lambda)+\mu=0$

$L_y=2y+8\lambda y=0\implies y(1+4\lambda)=0$

$L_z=2z-2\lambda z+4\mu=0\implies z(1-\lambda)+2\mu=0$

$L_\lambda=4x^2+4y^2-z^2=0$

$L_\mu=2x+4z-2=0\implies x+2z=1$

Case 1: If $y=0$ , then

$4x^2-z^2=0\implies4x^2=z^2\implies2|x|=|z|$

Then

$x+2z=1\implies x=1-2z\implies2|1-2z|=|z|\implies z=\dfrac25\text{ or }z=\dfrac23$

$\implies x=\dfrac15\text{ or }x=-\dfrac13$

So we have two critical points, $\left(\dfrac15,0,\dfrac25\right)$ and $\left(-\dfrac13,0,\dfrac23\right)$

Case 2: If $\lambda=-\dfrac14$ , then in the first equation we get

$x(1+4\lambda)+\mu=\mu=0$

and from the third equation,

$z(1-\lambda)+2\mu=\dfrac54z=0\implies z=0$

Then

$x+2z=1\implies x=1$

$4x^2+4y^2-z^2=0\implies1+y^2=0$

but there are no real solutions for $y$ , so this case yields no additional critical points.

So at the two critical points we've found, we get extreme values of

$f\left(\dfrac15,0,\dfrac25\right)=\dfrac15$ (min)

and

$f\left(-\dfrac13,0,\dfrac23\right)=\dfrac59$ (max)

5 0

4 years ago

Explain how to use the distributive property to create an expression that is equivalent to 2b + 5b

yuradex [85]

Answer:7b

Step-by-step explanation:

2b+5b

7b

3 0

4 years ago

Tell whether the angles are adjacent or vertical. Then find x

ki77a [65]

The Angles are adjacent and since they are both on a straight line it means that the sum of the angle is 180 degrees, so we get the equations:

$(6x) + (x - 2)=180\\7x = 182\\x=26$

So x = 26.

Hope that helps!

6 0

2 years ago