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jenyasd209 [6]
1 year ago
7

John gave half of his stamps to Jim. Jim gave gave half of his stamps to Carla. Carla gave 1/4 of the stamps given to her to Tho

mas and kept the remaining 12. How many stamps did John start with?
Mathematics
1 answer:
Alexandra [31]1 year ago
8 0
This question wants you to reverse the operations that occurred.

Start with 12 stamps.

Divide this number by 3/4. This represents Carla giving 1/4 of the stamps to Thomas.

12 /  \frac{3}{4} = 16

Multiply this number by 2. This represents Jim giving half of the stamps to Carla.

16 * 2 = 32

Multiply this number by 2. This represents John giving half of his stamps to Jim.

32 * 2 = 64

John started out with 64 stamps.
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X-intercept has coordinates (x,0)
Y-intercept has coordinates (0,y)
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1 year ago
a) The curve with equation y2 = x3 + 3x2 is called the Tschirnhausen cubic. Find an equation of the tangent line to this curve a
Neporo4naja [7]

Answer:

Tangent at (1,2) has value \frac{15}{4}. And (-2, 4) is the point of intersection of horizontal tangent.

Step-by-step explanation:

Given curve equation,

y^2=x^3+3x^2\hfill (1)

To find tangent at (x,y)=(1,2) and point of intersection of horizontal tangent, differentiate (1) withrespect to x we get,

2y\frac{dy}{dx}=x^3+3x^2

\implies \frac{dy}{dx}=\frac{3(x^2+2x)}{2y}

At (1, 2), tangent line is,

\frac{dy}{dx}|_{(1,2)}}=\frac{15}{4}

To find point of intersection of horizontal tangent we have to do,

\frac{dy}{dx}=0

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Thus,

At x=0, y=0

but snce,

\lim_{y\to 0}\frac{dy}{dx}\to \infty

at (0,0) there exist a vertical tangent. And,

At x=-2, y=4.

Thus (-2, 4) is the point of intersection of horizontal tangent.

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2 years ago
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Step-by-step explanation:

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The answer is:

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The explanation for this answer is shown below:

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