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3 years ago

Px + qy = r 2px - qy = 2r When solving this system of equations, x =

Mathematics

2 answers:

VladimirAG [237]3 years ago

8 0

Px + qy = r
2px - qy = 2r
----------------add
3px = 3r

x = 3r/3p
x = r/p

expeople1 [14]3 years ago

8 0

You just add the equations:
px + qy = r
2px - qy = 2r
3px = 3r
divide by 3
px = r
divide by p
x = (r)/(p)

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3 years ago

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3 years ago

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Find the components of the vertical force Bold Upper Fequalsleft angle 0 comma negative 8 right anglein the directions parallel

nydimaria [60]

Answer with Step-by-step explanation:

We are given that

F=<0,-8>=0i-8j=-8j

$\theta=\frac{\pi}{3}$

The component of force is divided into two direction

1.Along the plane

2.Perpendicular to the plane

1.The vector parallel to the plane will be= $r=cos\frac{\pi}{3}i-sin\frac{\pi}{3}j=\frac{1}{2}i-\frac{\sqrt 3}{2}j$

By using $cos\frac{\pi}{3}=\frac{1}{2},sin\frac{\pi}{3}=\frac{\sqrt 3}{2}$

Force along the plane will be= $\mid F_x\mid=F\cdot r$

Force along the plane will be = $\mid F_x\mid=F\cdot (\frac{1}{2}i-\frac{\sqrt 3}{2}j)=-8j\cdot(\frac{1}{2}i-\frac{\sqrt 3}{2}j)=8\times \frac{\sqrt 3}{2}=4\sqrt 3$ N

By using $i\cdot i=j\cdoty j=k\cdot k=1,i\cdot j=j\cdot k=k\cdot i=j\cdot i=k\cdot j=i\cdot k=0$

Therefore, force along the plane= $\mid F_x\mid(\frac{1}{2}i-\frac{\sqrt 3}{2}j)=4\sqrt 3(\frac{1}{2}i-\frac{\sqrt 3}{2}j)$

2.The vector perpendicular to the plane= $r=-sin\frac{\pi}{3}-cos\frac{\pi}{3}=-\frac{\sqrt 3}{2}i-\frac{1}{2}j$

The force perpendicular to the plane= $\mid F_y\mid=F\cdot r=-8j(-\frac{\sqrt 3}{2}i-\frac{1}{2}j)$

The force perpendicular to the plane= $4$ N

Therefore, $F_y=4(-\frac{\sqrt 3}{2}i-\frac{1}{2}j)$

Sum of two component of force= $F_x+F_y=4\sqrt 3(\frac{1}{2}i-\frac{\sqrt 3}{2}j)+4(-\frac{\sqrt 3}{2}i-\frac{1}{2}j)$

Sum of two component of force= $2\sqrt 3i-6j-2\sqrt3 i-2j=-8j$

Hence,sum of two component of forces=Total force.

6 0

3 years ago

A factory produces 60005/12

ycow [4]

Answer:

$About\ 193 \frac{209}{372} \ tons\ of \ steel$

Step-by-step explanation:

Given the amount of tons of steel produced monthly by a factory to be 6000 5/12 tons, to determine their daily production, we need to use the conversion;

Maximum of 31 days = 1 month

This means that the steel company produces 6000 5/12 tons of steel in 31 days.

6000 5/12 tons = 31 dsays

72,005/12 tons = 31 days

in a day, the company will therefore produce approx. (72,005/12)/31 tons of steel.

(72,005/12)/31 = 72,005/12 * 1/31

= 72,005/12*31

= 72,005/372

= 193 209/372 tons of steel.

Hence, the factory produces about $193 \frac{209}{372}$ tons of steel daily

6 0

3 years ago