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Cerrena [4.2K]
3 years ago
13

Diana uses 30 grams of coffee beans to make 48 fluid ounces of coffee. When company comes she makes 96 fluid ounces of coffee. H

ow many grams of coffee beans does Diana use when company comes?
Answers:

A.160

B.60

C.98.2

D.14.4
Mathematics
1 answer:
Komok [63]3 years ago
6 0

The answer is B. 48 x 2 = 96, 30 x 2 = 60.

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Find the equation of the tangent line to the curve (a lemniscate)
olya-2409 [2.1K]

Answer:

m=\frac{9}{13} and b=\frac{40}{13}

Step-by-step explanation:

The equation of curve is

2(x^2+y^2)^2=25(x^2-y^2)

We need to find the equation of the tangent line to the curve at the point (-3, 1).

Differentiate with respect to x.

2[2(x^2+y^2)\frac{d}{dx}(x^2+y^2)]=25(2x-2y\frac{dy}{dx})

4(x^2+y^2)(2x+2y\frac{dy}{dx})=25(2x-2y\frac{dy}{dx})

The point of tangency is (-3,1). It means the slope of tangent is \frac{dy}{dx}_{(-3,1)}.

Substitute x=-3 and y=1 in the above equation.

4((-3)^2+(1)^2)(2(-3)+2(1)\frac{dy}{dx})=25(2(-3)-2(1)\frac{dy}{dx})

40(-6+2\frac{dy}{dx})=25(-6-2\frac{dy}{dx})

-240+80\frac{dy}{dx})=-150-50\frac{dy}{dx}

80\frac{dy}{dx}+50\frac{dy}{dx}=-150+240

130\frac{dy}{dx}=90

Divide both sides by 130.

\frac{dy}{dx}=\frac{9}{13}

If a line passes through a points (x_1,y_1) with slope m, then the point slope form of the line is

y-y_1=m(x-x_1)

The slope of tangent line is \frac{9}{13} and it passes through the point (-3,1). So, the equation of tangent is

y-1=\frac{9}{13}(x-(-3))

y-1=\frac{9}{13}(x)+\frac{27}{13}

Add 1 on both sides.

y=\frac{9}{13}(x)+\frac{27}{13}+1

y=\frac{9}{13}(x)+\frac{40}{13}

Therefore, m=\frac{9}{13} and b=\frac{40}{13}.

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The tree frog population in your back yard doubles every two weeks. Currently, there are 10 frogs in your back yard. Assuming th
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There should be 80 but I'm not 100%.......
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Twenty men can cut thirty trees in four hours. If four men leave the job, how many
Mice21 [21]

Answer:

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Step-by-step explanation:

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\frac{q}{10} = 4\\q = 4 * 10\\q = 40

Answer: 40.

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