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8 days ago

Magellan has decided to make party baskets for the fundraiser. Balloons are sold in bags of 20, party horns are sold in bags of

10, and there are 8 candy bars in packages. How many of each should he buy so there ate an equal number of balloons, horns and candy bars in each basket

Mathematics

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Jerry buys a pack of pencils that cost $3 David buys 4 sets of markers each set of marker also cost 3 what is the total cost of

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The aggregate expense for the markers is 12.

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3 months ago

The equation of the tangent plane to the ellipsoid x2/a2 + y2/b2 + z2/c2 = 1 at the point (x0, y0, z0) can be written as xx0 a2

PIT_PIT [12445]

Answer:

The tangent plane equation for the hyperboloid

$\frac{xx_0}{a^2}+\frac{yy_0}{b^2}-\frac{zz_0}{c^2}=1$ .

Step-by-step explanation:

We have

The ellipsoid's equation is

$\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$

The equation for the tangent plane at the point $\left(x_0,y_0,z_0\right)$

$\frac{xx_0}{a^2}+\frac{yy_0}{b^2}+\frac{zz_0}{c^2}=1$ (Given)

The hyperboloid's equation is

$\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}=1$

F(x,y,z)= $\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}[c^2}$

$F_x=\frac{2x}{a^2},F_y=\frac{2y}{b^2},F_z=-\frac{2z}{c^2}$

$(F_x,F_y,F_z)(x_0,y_0,z_0)=\left(\frac{2x_0}{a^2},\frac{2y_0}{b^2},-\frac{2z_0}{c^2}\right)$

The tangent plane equation at point $\left(x_0,y_0,z_0\right)$

$\frac{2x_0}{a^2}(x-x_0)+\frac{2y_0}{b^2}(y-y_0)-\farc{2z_0}{c^2}(z-z_0)=0$

The tangent plane equation for the hyperboloid is

$\frac{2xx_0}{a^2}+\frac{2yy_0}{b^2}-\frac{2zz_0}{c^2}-2\left(\frac{x_0^2}{a^2}+\frac{y_0^2}{b^2}-\frac{z_0^2}{c^2}\right)=0$

The tangent plane equation

$2\left(\frac{xx_0}{a^2}+\frac{yy_0}{b^2}-\frac{zz_0}{c^2}\right)=2$

Hence, the required tangent plane equation for the hyperboloid is

$\frac{xx_0}{a^2}+\frac{yy_0}{b^2}-\frac{zz_0}{c^2}=0$

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3 months ago

In how many ways can you receive four cards of the same face value and one card from the other 48 available cards?

Zina [12379]

A deck contains 13 groups of 4 cards, indicating 13 unique ways to select four cards sharing the same face value. Any subsequent card drawn will necessarily represent a different face value. Consequently, the total combinations for selecting 5 cards—4 of which share the same face value and 1 diverging—amount to 13 x 48.

13 x 48 = 624.

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2 months ago

Kevin drew a triangle with angle measures of 30 degrees and 40 degrees and side measures of 5 cm, 7cm, and 8 cm. Explain, using

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He created a scalene triangle.
A scalene triangle has sides and angles that do not measure alike.

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3 months ago

Read 2 more answers