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2 years ago

At Shower and Body Works, there are different sizes of lotion dispensers. Two of the

Mathematics

1 answer:

natali 33 [55]2 years ago

3 0

Answer:

2.5 times

Step-by-step explanation:

From the diagram attached below;

let's calculate the volume of each bottle;

SO for bottle X;

we have ;

Volume of X = $\dfrac{1}{2}*2*1*6$

Volume of X = $6 \ \ in^3$

Volume of Y = $\dfrac{1}{2}*3*2.5*4$

Volume of Y = $15 \ \ in^3$

The ratio of Y to X can help us to determine how many times more lotion is in Bottle Y than in Bottle X; So taking their ratio ; we have:

$\mathbf{\dfrac{volume \ of \ Y }{volume\ of \ X} = \dfrac{15}{6} }$

= 2.5 times

Thus; Bottle Y has 2.5 times more lotion than Bottle X

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The tangents to the curve with equation y = x^3-3x at the points A and B with x coordinates −1 and 4 respectively meet at the po

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Answer:

$\displaystyle C=\left(\frac{26}{9}, 2\right)$

Step-by-step explanation:

We need to find the equation of the tangent lines of Points A and B.

Differentiate the equation:

$\displaystyle \frac{dy}{dx}=3x^2-3$

Point A has an x-coordinate of -1. Hence, the slope of its tangent line is:

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$\displaystyle \frac{dy}{dx}\Big|_{x=4}=3(4)^2-3=45$

Find the y-coordinate of Point B:

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Thus, Point B is at (4, 52).

So, the tangent line at Point B is:

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Simplify:

$y=45x-128$

Point C occurs at the intersections of the tangent lines of Points A and B. Set the two equations equal to each other and solve for x:

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We acquire:

$\displaystyle x=\frac{26}{9}$

Since one of our equations is y = 2, the y-coordinate is 2.

Hence, Point C is:

$\displaystyle C=\left(\frac{26}{9}, 2\right)$

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