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4 years ago

12

supoose that x^4 +y^4=82. 1) Use the method of implicit differentiation to find dy/dx. 20 Find the equation of the tangent line

at the point (x,y)= (-1,-3).

1 answer:

Mkey [24]4 years ago

3 0

Since d/dx f(y) = (dy/dx)(d/dy f(y)), by differentiating the equation wrt x on both side, 4x^3 + 4y^3(dy/dx) = 0, dy/dx = -(x/y)^3.

At (-1,-3), dy/dx = -1/27
Equation of tangent: y - y1 = m(x - x1) where x1 and y1 are coordinates of a point.
y + 3 = -1/27(x + 1)

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$Volume = 3052.08\ in^3$ -- Sphere

<em>Best Buy: Sphere Clay</em>

Step-by-step explanation:

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Solid Shapes: Cone, Cylinder, Sphere

Cost of Cone Clay = $12

Cost of Cylinder Clay = $30

Cost of Sphere Clay = $28

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Determine the volume of each shape

Which is the best buy

<h2>CONE</h2><h3>Calculating Volume</h3>

The volume of a cone is calculated as thus;

$Volume = \frac{1}{3}\pi r^2h$

From the attached diagram

Radius, r = 9 inches; Height, h = 12 inches and $\pi = 3.14$

Substitute these values in the above formula;

$Volume = \frac{1}{3} * 3.14 * 9^2 * 12$

$Volume = \frac{3052.08}{3}$

$Volume = 1017.36\ in^3$

<h3>Calculating Volume:Price Ratio</h3>

The unit cost of the cone is calculated as thus;

$Volume:Price = \frac{Volume}{Total\ Cost}$

Where

$Volume = 1017.36\ in^3$

$Total\ Cost = \$12$ (Given)

$Volume:Price = \frac{1017.36\ in^3}{\$ 12}$

$Volume:Price = 84.78 in^3/\$$

$Volume:Price = 84.78 in^3:\$1$

<h2>CYLINDER</h2><h3>Calculating Volume</h3>

The volume of a cylinder is calculated as thus;

$Volume = \pi r^2h$

From the attached diagram

Radius, r = 9 inches; Height, h = 12 inches and $\pi = 3.14$

Substitute these values in the above formula;

$Volume = 3.14 * 9^2 * 12$

$Volume = 3052.08\ in^3$

<h3>Calculating Volume:Price Ratio</h3>

The unit cost of the cone is calculated as thus;

$Volume:Price = \frac{Volume}{Total\ Cost}$

Where

$Volume = 3052.08\ in^3$

$Total\ Cost = \$30$ (Given)

$Volume:Price = \frac{3052.08\ in^3}{\$ 30}$

$Volume:Price = 101.736\ in^3/\$$

$Volume:Price = 101.736\ in^3:\$1$

<h2>SPHERE</h2><h3>Calculating Volume</h3>

The volume of a sphereis calculated as thus;

$Volume = \frac{4}{3}\pi r^3$

From the attached diagram

Radius, r = 9 inches; and $\pi = 3.14$

Substitute these values in the above formula;

$Volume = \frac{4}{3} * 3.14 * 9^3$

$Volume = \frac{9156.24}{3}$

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<h3>Calculating Volume-Price ratio</h3>

The unit cost of the cone is calculated as thus;

$Volume:Price = \frac{Volume}{Total\ Cost}$

Where

$Volume = 3052.08\ in^3$

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$Volume:Price = \frac{3052.08\ in^3}{\$ 28}$

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3 years ago