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2 years ago

10 men can do the work in 8 days. how many men should be reduced to finish the work in 10 days

Mathematics

1 answer:

e-lub [12.9K]2 years ago

7 0

If Reducing 2 men will bbe enough too finish the work in 10 days

For rate of work use the formualar

rate of work = quantity of work / duration

10 men can do the work at a rate of = 1 / 8

x men can do same work at a rate of = 1 / 10

x * ( 1 / 8 ) = 10 * ( 1 / 10 )

x = 1 * 8 = 8

therefore 8 men can do the work in 10 days

number of men reduced = 10 men - 8 men = 2 men

Hope it helped

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Use exponent property of logs.

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The football team need to buy Gatorade for Saturdays big game . They have two option. The first option us they can buy it pre-ma

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The question is incomplete. Here is the complete question.

The football team needed to buy Gatorade for Saturday's big game. They have two options. The first option is they can buy it pre-made in 48 ounces bottles for $3.84 for each bottle. Or they can buy packets and mix with water. Each packet makes 64 ounces and will cost $4.80.

a) Find the cost per ounce of each.

b) Which size costs less?

c) The team will need to buy 192 ounces of Gatorade. How much do you save using the choice from answer b?

Answer: a) Pre-made: $0.08 cost per ounce; Packet: $0.075 cost per ounce

b) Packets

c) Save $0.96.

Step-by-step explanation:

a) Cost per ounce:

Pre-made:

$\frac{3.84}{48}$ = 0.08

Packet:

$\frac{4.8}{64}$ = 0.075

b) Comparing costs per ounce, packets costs less than pre-made.

c) Buying packets, the cost will be:

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3 years ago

Find the mass and the center of mass of a wire loop in the shape of a helix (measured in cm: x = t, y = 4 cos(t), z = 4 sin(t) f

Sholpan [36]

Answer:

Mass

$\sqrt{17}(\displaystyle\frac{8\pi^3}{3}+32\pi)$

Center of mass

Coordinate x

$\displaystyle\frac{(\displaystyle\frac{(2\pi)^4}{4}+32\pi)}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}$

Coordinate y

$\displaystyle\frac{16\pi}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}$

Coordinate z

$\displaystyle\frac{-16\pi}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}$

Step-by-step explanation:

Let W be the wire. We can consider W=(x(t),y(t),z(t)) as a path given by the parametric functions

x(t) = t

y(t) = 4 cos(t)

z(t) = 4 sin(t)

for 0 ≤ t ≤ 2π

If D(x,y,z) is the density of W at a given point (x,y,z), the mass m would be the curve integral along the path W

$m=\displaystyle\int_{W}D(x,y,z)=\displaystyle\int_{0}^{2\pi}D(x(t),y(t),z(t))||W'(t)||dt$

The density D(x,y,z) is given by

$D(x,y,z)=x^2+y^2+z^2=t^2+16cos^2(t)+16sin^2(t)=t^2+16$

on the other hand

$||W'(t)||=\sqrt{1^2+(-4sin(t))^2+(4cos(t))^2}=\sqrt{1+16}=\sqrt{17}$

and we have

$m=\displaystyle\int_{W}D(x,y,z)=\displaystyle\int_{0}^{2\pi}D(x(t),y(t),z(t))||W'(t)||dt=\\\\\sqrt{17}\displaystyle\int_{0}^{2\pi}(t^2+16)dt=\sqrt{17}(\displaystyle\frac{8\pi^3}{3}+32\pi)$

The center of mass is the point $(\bar x,\bar y,\bar z)$

where

$\bar x=\displaystyle\frac{1}{m}\displaystyle\int_{W}xD(x,y,z)\\\\\bar y=\displaystyle\frac{1}{m}\displaystyle\int_{W}yD(x,y,z)\\\\\bar z=\displaystyle\frac{1}{m}\displaystyle\int_{W}zD(x,y,z)$

We have

$\displaystyle\int_{W}xD(x,y,z)=\sqrt{17}\displaystyle\int_{0}^{2\pi}t(t^2+16)dt=\\\\=\sqrt{17}(\displaystyle\frac{(2\pi)^4}{4}+32\pi)$

$\bar x=\displaystyle\frac{\sqrt{17}(\displaystyle\frac{(2\pi)^4}{4}+32\pi)}{\sqrt{17}(\displaystyle\frac{8\pi^3}{3}+32\pi)}=\displaystyle\frac{(\displaystyle\frac{(2\pi)^4}{4}+32\pi)}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}$

$\displaystyle\int_{W}yD(x,y,z)=\sqrt{17}\displaystyle\int_{0}^{2\pi}4cos(t)(t^2+16)dt=\\\\=16\sqrt{17}\pi$

$\bar y=\displaystyle\frac{16\sqrt{17}\pi}{\sqrt{17}(\displaystyle\frac{8\pi^3}{3}+32\pi)}=\displaystyle\frac{16\pi}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}$

$\displaystyle\int_{W}zD(x,y,z)=4\sqrt{17}\displaystyle\int_{0}^{2\pi}sin(t)(t^2+16)dt=\\\\=-16\sqrt{17}\pi$

$\bar z=\displaystyle\frac{-16\sqrt{17}\pi}{\sqrt{17}(\displaystyle\frac{8\pi^3}{3}+32\pi)}=\displaystyle\frac{-16\pi}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}$

3 0

3 years ago

10 men can do the work in 8 days. how many men should be reduced to finish the work in 10 days​

10 men can do the work in 8 days. how many men should be reduced to finish the work in 10 days