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3 years ago

An 8ft length of 4 inch wide crown molding costs $14. How much will it cost to buy 32 ft of crown molding?

Mathematics

1 answer:

miskamm [114]3 years ago

6 0

It will cost $56 to buy 32 ft of crown molding.

Explanation

Suppose, the cost of 32 ft of crown molding is $x$ dollar.

Given that, 8 ft length crown molding costs $14.

According to the ratio of "length" of crown molding to the "cost", the equation will be.......

$\frac{8}{14}= \frac{32}{x}\\ \\ 8x=14*32=448\\ \\ x=\frac{448}{8}=56$

So, it will cost $56 to buy 32 ft of crown molding.

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You normally sell 72 tacos for every 50 people that stop by your taco truck . How many tacos would you expect to sell if 275 cam

Naya [18.7K]

Answer:

about 396 tacos

Step-by-step explanation:

First, figure out how many per person.

72 tacos / 50 people = about 1.44 (per person)

275 * 1.44 = about 396 tacos

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3 years ago

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The sum of three consecutive even numbers is one hundred sixty - two.

Alenkasestr [34]

Answer:

Step-by-step explanation:

Let x represent the smallest of the three numbers. Then the other two are (x+2) and (x+4). Their sum is ...

x + (x+2) +(x+4) = 162

3x = 156 . . . . . . . . . . . .subtract 6

x = 156/3 = 52

The smallest of the three numbers is 52.

___

I like to work problems like this by considering the average number. Here, the average of the three numbers is 162/3 = 54, the middle number of the three. Then the smallest of the three consecutive even numbers is 2 less, or 52.

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2 years ago

The roof of a tower in a castle is shaped like a cone. The height of the roof is 30 ft, and the radius of the base is 15 ft. Wha

xz_007 [3.2K]

Answer:

The area of the roof: ≈2287.44 ft^2, the lateral area of the roof:≈1580.58 ft^2

Step-by-step explanation:

The area of the roof is computed by the equation of the area of a cone:
A = πr(r + $\sqrt{h^{2}+r^(2) }$ )
(r: radius, h: height, πr^2 is the area of the base of the cone, πr $\sqrt{h^{2}+r^(2) }$ is the lateral area of the cone). So:

A = $15\pi (15 + \sqrt{30^{2} +15^{2} } )$ ≈ 2287.44 ft^2.

As I stated earlier, the lateral area of the roof can be computed:

A $L$ = $15\pi \sqrt{30^{2} +15^{2} }$ ≈ 1580.58 ft^2.

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2 years ago

Use Stokes' Theorem to evaluate C F · dr F(x, y, z) = xyi + yzj + zxk, C is the boundary of the part of the paraboloid z = 1 − x

Serggg [28]

I assume $C$ has counterclockwise orientation when viewed from above.

By Stokes' theorem,

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

so we first compute the curl:

$\vec F(x,y,z)=xy\,\vec\imath+yz\,\vec\jmath+xz\,\vec k$

$\implies\nabla\times\vec F(x,y,z)=-y\,\vec\imath-z\,\vec\jmath-x\,\vec k$

Then parameterize $S$ by

$\vec r(u,v)=\cos u\sin v\,\vec\imath+\sin u\sin v\,\vec\jmath+\cos^2v\,\vec k$

where the $z$ -component is obtained from

$1-(\cos u\sin v)^2-(\sin u\sin v)^2=1-\sin^2v=\cos^2v$

with $0\le u\le\dfrac\pi2$ and $0\le v\le\dfrac\pi2$ .

Take the normal vector to $S$ to be

$\vec r_v\times\vec r_u=2\cos u\cos v\sin^2v\,\vec\imath+\sin u\sin v\sin(2v)\,\vec\jmath+\cos v\sin v\,\vec k$

Then the line integral is equal in value to the surface integral,

$\displaystyle\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

$=\displaystyle\int_0^{\pi/2}\int_0^{\pi/2}(-\sin u\sin v\,\vec\imath-\cos^2v\,\vec\jmath-\cos u\sin v\,\vec k)\cdot(\vec r_v\times\vec r_u)\,\mathrm du\,\mathrm dv$

$=\displaystyle-\int_0^{\pi/2}\int_0^{\pi/2}\cos v\sin^2v(\cos u+2\cos^2v\sin u+\sin(2u)\sin v)\,\mathrm du\,\mathrm dv=\boxed{-\frac{17}{20}}$

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3 years ago

50 is 40% of what number

DENIUS [597]

50 / 0.40 = 125

To check your answer, 125 * 0.4 = 50

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2 years ago

Read 2 more answers