The word or abbreviation that correctly completes the sentence is "yards." Three yards of the fabric cost $5.40.
The term "yards" is the appropriate unit of measurement for fabric, indicating the length or amount of fabric being referred to.
In the given sentence, the phrase "Three _____ of the fabric cost $5.40" indicates that a certain quantity or length of fabric is being discussed.
To express the amount of fabric, the correct unit of measurement is "yards." "Yards" is a commonly used term to quantify the length or amount of fabric, and it is often abbreviated as "yd."
Therefore, the correct completion of the sentence would be "Three yards of the fabric cost $5.40." This indicates that the price specified is for a total length of three yards of fabric.
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Give me...minutes and i'll be ready. a.few b.a few c.little d.a little
"Give me a few minutes and I'll be ready."
In this context, the correct phrase to use is "a few." When referring to a small number of minutes, we use the phrase "a few" to indicate a short amount of time. The word "few" is used to describe a small quantity. Therefore, when someone says "Give me a few minutes," they are asking for a short period of time to complete a task or prepare for something. It implies that they need just a small amount of time before they will be ready. So, if someone asks you to give them "a few minutes," it means they need a short amount of time to finish what they are doing.
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Considers F ( x , Y ) = ( 3 + 4 x Y two ) i + 4 x two Y j , C is the arc of the hyperbola Y = one x from the point ( one , one ) until the point ( two , one two ) Determine the potential function using the potential function determine ∫ C F d r along curve C.
The potential function φ(x, Y) for the vector field F(x, Y) = (3 + 4xY^2)i + 4x^2Yj is given by φ(x, Y) = 3x + 2x^2Y^2 + C1(Y) + C2(x). To calculate the integral ∫ C F · dr along curve C, we substitute the coordinates of the starting and ending points of the curve into φ(x, Y)
To determine the potential function, we need to find a scalar function φ(x, Y) such that the vector field F(x, Y) can be expressed as the gradient of φ, i.e., F(x, Y) = ∇φ.
Given F(x, Y) = (3 + 4xY^2)i + 4x^2Yj, we can find the potential function φ(x, Y) by integrating the components of F with respect to their respective variables:
φ(x, Y) = ∫ (3 + 4xY^2) dx + ∫ 4x^2Y dy
Integrating the first component with respect to x gives:
∫ (3 + 4xY^2) dx = 3x + 2x^2Y^2 + C1(Y),
where C1(Y) is the constant of integration with respect to x.
Integrating the second component with respect to Y gives:
∫ 4x^2Y dy = 2x^2Y^2 + C2(x),
where C2(x) is the constant of integration with respect to Y.
Combining the results, we have:
φ(x, Y) = 3x + 2x^2Y^2 + C1(Y) + C2(x).
To find the potential function along the curve C, we substitute the given values for x and Y, i.e., (1, 1) and (2, 1/2) into φ(x, Y) and subtract the values at the starting point from the values at the ending point:
∫ C F · dr = φ(2, 1/2) - φ(1, 1)
= (3(2) + 2(2)^2(1/2)^2 + C1(1/2) + C2(2)) - (3(1) + 2(1)^2(1)^2 + C1(1) + C2(1))
Simplifying further will yield the numerical value of the integral along the curve C.
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