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3 years ago

A student attempted to generate an equivalent expression using the distributive property, as shown below:

Mathematics

2 answers:

Schach [20]3 years ago

5 0

It is 6 was not multiplied by 3
The answer should be 6(m+3)= 6m+ 18

Fantom [35]3 years ago

5 0

Answer:

THE ANSWER IS D

Step-by-step explanation:

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Find a parametrization, using cos(t) and sin(t), of the following curve: The intersection of the plane y= 5 with the sphere

Elenna [48]

Answer:

The parametrization, of the given curve is $x = 10 cos(t) \ \ ,z = 10 sin(t)$

Step-by-step explanation:

From the question we are given the function

$x^2 + y^2 + z^2 = 125$

At y= 5

$x^2 + 5^2 +z^2 =125$

$x^2 + z^2 = 100$

$x^2 + z^2 = 10^2$

Converting the above to it polar equation we have

$x = 10 cos(t) \ \ ,z = 10 sin(t)$

6 0

3 years ago

8. You are paid a commission plus $5.40 per hour with time and a half overtime

Elanso [62]

9514 1404 393

Answer:

$491.65

Step-by-step explanation:

The pay for the first 8 hours is $5.40 per hour × 8 hours = $43.20. Hours over 8 are paid at 1.5 × $5.40 = $8.10 per hour. There are at least 8 hours every day for the 6-day week. There are hours over 8 on Monday, Wednesday, Thursday, and Friday totaling 7 hours of overtime.

The amount of sales is more than $3000, so 4% will be paid on $3000, and 5% will be paid on the $1115 in excess of $3000.

So, the gross pay is ...

$43.20 × 6 + 8.10 × 7 = $315.90 . . . . wages

$3000 × .04 +1115 × .05 = $175.75 . . . commission

$315.90 +1.75.75 = $491.65 . . . . gross pay for the week

_____

It can be less tedious to let a spreadsheet do the calculations.

6 0

2 years ago

Evaluate the surface integral ModifyingBelow Integral from nothing to nothing Integral from nothing to nothing With Upper S f (x

kykrilka [37]

Parameterize $S$ by

$\vec s(u,v)=6\cos u\sin v\,\vec\imath+6\sin u\sin v\,\vec\jmath+6\cos v\,\vec k$

with $0\le u\le2\pi$ and $0\le v\le\frac\pi2$ . Take a normal vector to $S$ ,

$\dfrac{\partial\vec s}{\partial v}\times\dfrac{\partial\vec s}{\partial u}=36\cos u\sin^2v\,\vec\imath+36\sin u\sin^2v\,\vec\jmath+36\cos v\sin v\,\vec k$

which has norm

$\left\|\dfrac{\partial\vec s}{\partial v}\times\dfrac{\partial\vec s}{\partial u}\right\|=36\sin v$

Then the integral of $f(x,y,z)=x^2+y^2$ over $S$ is

$\displaystyle\iint_Sx^2+y^2\,\mathrm dS=\iint_S\left((6\cos u\sin v)^2+(6\sin u\sin v)^2\right)\left\|\frac{\partial\vec s}{\partial v}\times\frac{\partial\vec s}{\partial u}\right\|\,\mathrm du\,\mathrm dv$