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mina [271]
3 years ago
12

a) The curve with equation y2 = x3 + 3x2 is called the Tschirnhausen cubic. Find an equation of the tangent line to this curve a

t the point (1, 2). y = Correct: Your answer is correct. (b) At what points does this curve have horizontal tangents? (x, y) = -2 Incorrect: Your answer is incorrect. (smaller y-value) (x, y) = 2 Incorrect: Your answer is incorrect. (larger y-value)
Mathematics
1 answer:
Neporo4naja [7]3 years ago
6 0

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

\implies x(x+2)=0\implies x=0 or -2

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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alexgriva [62]
<h2>Answer:</h2>

<em>Rounded to the nearest hundredth the volume of the composite figure is:</em>

<em>1308 33 cubic millimeters</em>

<h2>Explanation:</h2>

Hello! I wrote the complete question in a comment above. The volume of a cylinder is defined as:

V_{c}=\pi r^2 h \\ \\ r:radius \\ \\ h:height

While the volume of half a sphere is:

V_{hs}=\frac{2}{3}\pi r^3

Since we have 2 half spheres, then the volume of these is the same as the volume of a sphere:

V_{s}=\frac{4}{3}\pi r^3

Then, the composite figure is:

V=\pi r^2 h +\frac{4}{3}\pi r^3 \\ \\ V=\pi r^2(h+\frac{4}{3}r)

The radius of the cylinder is the same of the radius of each half sphere. So:

r=5mm \\ \\ h=10mm \\ \\ \\ V=(3.14) (5)^2((10)+\frac{4}{3}(5)) \\ \\ V=25(3.14)(10+\frac{20}{3}) \\ \\ \boxed{V\approx 1308.33mm^3}

7 0
2 years ago
The answer I got is not one of the options, and I am very confused, because now I don't know what to do?
Effectus [21]
<span>A’(2, -4); B’(7, -9); C’(-2, -9)
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4 0
3 years ago
if i supposedly got 2 cats and trained them to bring me quarters and they did and supposedly everyday i got 10 quarters how much
ivanzaharov [21]

Answer:

After a year you would have $1,825

Step-by-step explanation:

Amount for one cat a day in cents

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Amount for both cats for a year dollars

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8 0
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Stolb23 [73]
Im thinking it would be odd because when you multiply 2 odd numbers youre result is usually odd 
5 0
3 years ago
Read 2 more answers
Need help please guys.
KengaRu [80]

Answer: x= 21.6

Step-by-step explanation:

12^2  + 18^2  =x^2

144 + 324 =x^2

468  = x^2

c=  21.633  

To the nearest tenth place  is c= 21.6

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