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3 years ago

Joe earns $4,100 per month and pays $870 each month in rent. Approximately what percent of his money is spent on rent?

Mathematics

1 answer:

Scorpion4ik [409]3 years ago

8 0

if we take 4100 to be the 100%, what is 870 off of it in percentage?

$\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 4100&100\\ 870&x \end{array}\implies \cfrac{4100}{870}=\cfrac{100}{x} \\\\\\ 4100x=87000\implies x=\cfrac{87000}{4100}\implies x=\cfrac{870}{41}\implies x\approx 21.22$

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21x =7?<br> A. x=3<br> B. None of these <br> C. x=147<br> D. x=28

Varvara68 [4.7K]

Answer: B

Step-by-step explanation:

To isolate x, you divide both sides by 21

21x=7

$\frac{21x}{21}=\frac{7}{21}$

x = 7/21

Simplify by dividing both the numerator and denominator by 7

x = 1/3

Since, 1/3 is not an option, B is the correct answer

6 0

2 years ago

A square pyramid and a cube have the same total surface area. The width of the cube is 8 centimeters. The base of the pyramid is

azamat

Answer:

Step-by-step explanation:

surface area of cube = 6×8² = 384 cm²

lateral area of pyramid = surface area of pyramid - base area

= 384 - 8²

= 320 cm²

area of triangular face = 320/4 = 80 = ½(base)(slant height) = ½(8)(slant height)

slant height = 20 cm

6 0

3 years ago

Find the absolute extrema for f(x,y)=4-x^2-y^4+1/2y^2 over the closed disk D:x^2+y^2 is less than or equal to 1

algol [13]

Find the critical points of $f(x,y)$ :

$\dfrac{\partial f}{\partial x}=-2x=0\implies x=0$

$\dfrac{\partial f}{\partial y}=y-4y^3=y(1-4y^2)=0\implies y=0\text{ or }y=\pm\dfrac12$

All three points lie within $D$ , and $f$ takes on values of

$\begin{cases}f(0,0)=4\\f\left(0,-\frac12\right)=\frac{65}{16}\\f\left(0,\frac12\right)=\frac{65}{16}\end{cases}$

Now check for extrema on the boundary of $D$ . Convert to polar coordinates:

$f(x,y)=f(\cos t,\sin t)=g(t)=4-\cos^2-\sin^4t+\dfrac12\sin^2t=3+\dfrac32\sin^2t-\sin^4t$

Find the critical points of $g(t)$ :

$\dfrac{\mathrm dg}{\mathrm dt}=3\sin t\cos t-4\sin^3t\cos t=\sin t\cos t(3-4\sin^2t)=0$

$\implies\sin t=0\text{ or }\cos t=0\text{ or }\sin t=\pm\dfrac{\sqrt3}2$

$\implies t=n\pi\text{ or }t=\dfrac{(2n+1)\pi}2\text{ or }\pm\dfrac\pi3+2n\pi$

where $n$ is any integer. There are some redundant critical points, so we'll just consider $0\le t< 2\pi$ , which gives

$t=0\text{ or }t=\dfrac\pi3\text{ or }t=\dfrac\pi2\text{ or }t=\pi\text{ or }t=\dfrac{3\pi}2\text{ or }t=\dfrac{5\pi}3$

which gives values of

$\begin{cases}g(0)=3\\g\left(\frac\pi3\right)=\frac{57}{16}\\g\left(\frac\pi2\right)=\frac72\\g(\pi)=3\\g\left(\frac{3\pi}2\right)=\frac72\\g\left(\frac{5\pi}3\right)=\frac{57}{16}\end{cases}$