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2 years ago

18x - 77=1 X - 7y=-33

Mathematics

1 answer:

SIZIF [17.4K]2 years ago

4 0

Answer:

x=-33+7y

then putting value of x

18(-33+7y)-77=1

-594+126y-77=1

-671+126y=1

126y=670

y=670/126

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Two cars are traveling down the highway with the same speed. If the first car increases its speed by 1km/hr, and the other car d

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Answer:

The speed of the cars is $32 \frac{km}{h}$

Step-by-step explanation:

First we must first have the clear concept that $speed=\frac{distance}{time}$ or $s=\frac{d}{t}$

Our question is the speed of the cars then the variable to clear will be s.

Let's raise the equation for each car taking into account that we have the following data:

Car 1: $s_{1}=s+1$ , $t_{1}=2$ and $d_{1}= d_{2}$

Car 1: $s_{2}=s-10$ , $t_{2}=3$ and $d_{1}= d_{2}$

The two cars travel the same distance so we will raise the distance formula for each car and then match them.

<em>Car 1</em>

$d_{1}=s_{1}*t_{1}$

$d_{1}=(s+1)*2$

$d_{1}=2s+2$

<em>Car 2</em>

$d_{2}=s_{2}*t_{2}$

$d_{2}=(s-10)*3$

$d_{2}=3s.30$

$d_{1}=d_{2}$

$2s+2=3s-30$

$2+30=3s-2s$

$32=s$

The speed of the cars is 32 km/hr

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3 years ago

Amira is painting a rectangular banner 2 1/4 yards wide in the cafeteria. The banner will have a blue background. Amira has enou

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Area of a rectangle:
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The height of a banner is 2/3 yard.

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3 years ago

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Answer: only has one solution

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2 years ago

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Paladinen [302]

Answer:

Rate of change = 18/√74

Step-by-step explanation:

The rate of change of f at x_o in the direction of the unit vector v is given by: ∇f(x_o) × v

Now, for us to get the direction of the unit vector, since we are told that f(x, y, z) = xyz in the direction normal to the surface yx² + xy² + yz² = 3, we will use; g(x, y, z) = yx² + xy² + yz² = 3 and k =3 to give;

∇g(x,y,z) = (2xy + y², (x² + 2xy + z²), 2yz)

So;

∇g(1, 1, 2) = (2(1 × 1) + 1²) , (1² + 2(1 × 1) + 2²), 2(1 × 2))

This gives;

∇g(1, 1, 2) = (3, 7, 4)

Now,

||∇g(1, 1, 2)|| = √(3² + 7² + 4²)

||∇g(1, 1, 2)|| = √74

Normal vector would be given by the formula;

v = [∇g(1, 1, 2)]/[||∇g(1, 1, 2)||]

Thus;

v = (3, 7, 4)/√74

Let's not forget that our ∇f(1, 1, 2) = (1, 1, 2)

Thus, rate of change is given by;

∇f(1, 1, 2) × v = (1, 1, 2) × (3, 7, 4)/√74

This gives;

Rate of change = [(1 × 3) + (1 × 7) + (2 × 4)]/√74 = 18/√74

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