If represented in a stem-and-leaf plot, what would be the stem of the number 1457?

Dr.Lamb is mixing a solution for his next patient. He has a cylindrical test tube which is 4 inches across on the inside. The de

SSSSS [86.1K]

Answer: There are 34.35 liters left in the test tube.

Step-by-step explanation:

Since we have given that

Depth of the tube = 9 inches

Circumference of base=4 inches

As we know the formula of circumference ,

$Circumference=2\pi r\\\\4=2\times \frac{22}{7}\times r\\\\4\times{7}{22\times 2}=r\\\\\frac{7}{11}=r$

Now, we need to find the volume of tube is given by

$\text{ Volume of test tube }=\pi r^2h\\\\\text{ Volume of test tube }=\frac{22}{7}\times \frac{7}{11}\times \frac{7}{11}\times 9\\\\\text{ Volume of test tube }=\frac{126}{11}=11.45\ inches^3$

Since we have also given that,

Of 1 cubic inch of space holds 3 liters of water,

So,

$1\text{ cubic inch}=3\text{ liters}\\\\11.45\text{ cubic inches}=3\times 11.45=34.35\text{ liters}$

Hence, there are 34.35 liters left in the test tube.

6 0

3 years ago

Will there be more thaan one relay exchange between 2 consecutive tenths of a mile

kondor19780726 [428]

Yes there will be more than one

6 0

3 years ago

How do you find slope

alisha [4.7K]

Step-by-step explanation:

Hi there!

To find slope you use the change of y over change of x formula. You first need to ordered pairs to plug into the equation.

Formula:

(Y1-Y2)/(X1-X2)

7 0

3 years ago

Read 2 more answers

Find all points on the portion of the plane x+y+z=5 in the first octant at which f(x, y, z) = xy2z2 has a maximum value.

irina1246 [14]

Lagrange multipliers:

$L(x,y,z,\lambda)=xy^2z^2+\lambda(x+y+z-5)$

$L_x=y^2z^2+\lambda=0$
$L_y=2xyz^2+\lambda=0$
$L_z=2xy^2z+\lambda=0$
$L_\lambda=x+y+z-5=0$

$\lambda=-y^2z^2=-2xyz^2=-2xy^2z$

$-y^2z^2=-2xyz^2\implies y=2x$ (if $y,z\neq0$ )

$-y^2z^2=-2xy^2z\implies z=2x$ (if $y,z\neq0$ )

$-2xyz^2=-2xy^2z\implies z=y$ (if $x,y,z\neq0$ )

In the first octant, we assume $x,y,z>0$ , so we can ignore the caveats above. Now,

$x+y+z=5\iff x+2x+2x=5x=5\implies x=1\implies y=z=2$

so that the only critical point in the region of interest is (1, 2, 2), for which we get a maximum value of $f(1,2,2)=16$ .

We also need to check the boundary of the region, i.e. the intersection of $x+y+z=5$ with the three coordinate axes. But in each case, we would end up setting at least one of the variables to 0, which would force $f(x,y,z)=0$ , so the point we found is the only extremum.