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2 years ago

Without multiplying, tell whether the product 0.644 x 0.25 will be greater than 1 or less than 1? Explain how you know.

Mathematics

2 answers:

stepladder [879]2 years ago

7 0

Answer:

Less than 1

Step-by-step explanation:

As 0.644 and 0.25 are less than 1, then

$0.644=\frac{1}{p}$

$0.25=\frac{1}{q}$

where p and q are greater than 1

then

$0.644\times0.24=\frac{1}{p.q}$

But p.q is greater than 1, so 1/(p.q) is smaller than 1

Marat540 [252]2 years ago

3 0

Answer:

Less than 1

Step-by-step explanation:

Both the number are less than 1, i.e 0.64 and 0.25.

Hence, the result will always be less than 1 and will be in zeros.

If you write both numbers in fraction, the denominator will be greater than the numerator, hence the resulting fraction will be less than 1.

Hope this helps.

Good luck and thankyou.

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In 2005, out of every 50 employees at a company were women. If there are total company employees, estimate the number of women

myrzilka [38]

Answer:

9248

Step-by-step explanation:

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1 year ago

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3 years ago

The tangent to the circle x^2+y^2=18 is parallel to the tangent x+y=6

liubo4ka [24]

Answer:

y = -x - 6

Step-by-step explanation:

If we are looking for the equation of the line tangent to the circle, we have to find the first derivative of the circle function. If that tangent line is to be parallel to the given tangent line, we need to find the slope of the the given tangent line and make sure the slope of the line we are looking for is the same. First let's find the slope of the given tangent. If the given tangent is x+y=6, then to find the slope, solve for y:

y = -x + 6. So the slope of that line, and also the slope of the tangent we are solving for, is -1. Hold that thought while we find the derivative of the function. Using implicit differentiation, we find the derivative to be:

$2x+2y\frac{dy}{dx}=0$

Solving for the slope (dy/dx) gives us:

$2y\frac{dy}{dx}=-2x$ and

$\frac{dy}{dx}=\frac{-2x}{2y}$ so

$\frac{dy}{dx}=-\frac{x}{y}$

Subbing in the value of the slope we found:

$-1=-\frac{x}{y}$ so

-y = -x or, equivalently,

y = x. Now that we know that y and x are the same value, we can go back to the original circle to find out what they both are by substitution. If y = x, we make the substution:

If $x^2+y^2=18$ , then

$y^2+y^2=18$ and

$2y^2=18$ and

$y^2=9$ so

y = ±3

We will choose the negative root (you'll see why in a second) and sub that in for both y and x since y and x are th same number. Going back to the fact that the slope is -1:

y - (-3) = -1(x - (-3)) simplifies a bit to:

y + 3 = -x - 3 which gives us, in slope-intercept form:

y = -x - 6

That is the equation of the tangent to the circle that is parallel to the given tangent.

If we would have chosen the principle (or positive) root of 3, our equation would have looked like this:

y - 3 = -1(x - 3) and

y = -x + 3 + 3 so

y = -x + 6. Notice that that is the EXACT SAME EQUATION as the given tangent. That's why we have to pick the negative 3 as our root.

Good luck in your calculus class! Make sure you post your questions in here! Many of us LOVE the challenge of calculus!

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