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3 years ago

How many solutions does this equation have? d − 3 = –3 + d

1 answer:

4 0

It has an infinite amount of solutions.

Explanation:
d-3 = -3+d which can be arranged as: d-3=d-3
Since they are equal to each other, no matter what number you input, your solution will be the same which means that there are an infinite amount of solutions. Let’s put this to the test and put in 5 for d. 5-3=5-3 is 2=2. They are equal to each other which means: infinite solution.

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2 years ago

The price of a gallon went from $0.64 to $0.68 per gallon. What was the percent of increase in the price of a gallon?

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Step-by-step explanation:

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2 years ago

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A particle begins at point (1, 2) and is moving along the line segment joining (1, 2) to (3, 4). Initially, what is the rate of

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Answer:

Initially, that is, at (1,2), the rate of increase of the function in the direction given = 0

Hence the function is neither increasing nor decreasing initially in the given direction.

Step-by-step explanation:

f(x,y) = 2x² - y²

Rate of Change of the function = ∇f = (fₓ, fᵧ)

And we're told to find the rate of change in a particular direction = ∇f.û

We first obtain the unit vector in that direction, û

Direction = (3,4) - (1,2) = (2,2)

Uni vector = vector/magnitude

Vector = 2î + 2j

magnitude = √(2² + 2²) = √8 = 2 √2

(2î + 2j)/(2√2) = (1/√2)î + (1/√2)j = û

Unit vector in the direction = (1/√2, 1/√2)

f = 2x² - y²

At (1,2)

fₓ = ∂f/∂x = 4x = 4

fᵧ = ∂f/∂y = -2y = -4

∇f = (4,-4)

∇f.û = (4î - 4j).((1/√2)î + (1/√2)j) = (4/√2) - (4/√2) = 0

If it was positive, then the function is increasing, if it was negative, the function is decreasing. Zero means neither of them.

Hence the function is neither increasing nor decreasing initially in the given direction.

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2 years ago

The sum of the lengths of two opposite sides of the circumscribed quadrilateral is 10 cm, and its area is 12 cm2. Find the radiu

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Answer:

1.2 cm

Step-by-step explanation:

The area of sircumscribed quadrilateral over a circle is equal to

$A=s\cdot r,$

where s is semi-perimeter of the quadrilateral and r is the radius of the circle.

Use property of circumscribed quadrilateral: The sums of the opposite sides are equal.

So, if the sum of two opposite sides of the circumscribed quadrilateral is 10 cm, then the sum of another two sides is also 10 cm and the perimeter of the quadrilateral is 20 cm. Hence,

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Now,

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3 years ago

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