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1 year ago

HELP PLEASE IM BEGGING PLEASEEE I NEED IT NOWWW

Mathematics

1 answer:

leonid [27]1 year ago

7 0

cylindrical-shaped aquarium is to be filled with water for the newly bought salt water fishes. How much salt water is needed if the aquarium has a 2 ft radius of its base and a height of 3 ft?

Volume = πr²h

V = (3.14) (2)² (3)

V = (3.14) (4) (3)

V = 37.68 ft³

37.68 ft³ of salt water is needed to fill the cylindrical aquarium.

Mr. Lee is buying a spherical water tank for his tomato plantation. How much water could be stored if the water tank has a radius of 2 meters?

Volume = (4/3) πr³

V = (4/3) (3.14) (2)³

V = (4/3) (3.14) (8)

V = (4/3) (25.12)

V = 33.493 m³

Mr. Lee can store 33.493 m³ of water in the spherical tank.

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Vectors AC and AC' are perpendicular, then

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Now, solve the system of two equations:

$\left\{\begin{array}{l}(2-x_A)(-2-x_A)+(6-y_A)(2-y_A)=0\\ \\(4-x_A)(1-x_A)+(3-y_A)(4-y_A)=0\end{array}\right.\\ \\\left\{\begin{array}{l}-4-2x_A+2x_A+x_A^2+12-6y_A-2y_A+y^2_A=0\\ \\4-4x_A-x_A+x_A^2+12-3y_A-4y_A+y_A^2=0\end{array}\right.\\ \\\left\{\begin{array}{l}x_A^2+y_A^2-8y_A+8=0\\ \\x_A^2+y_A^2-5x_A-7y_A+16=0\end{array}\right.$

Subtract these two equations:

$5x_A-y_A-8=0\Rightarrow y_A=5x_A-8$

Substitute it into the first equation:

$x_A^2+(5x_A-8)^2-8(5x_A-8)+8=0\\ \\x_A^2+25x_A^2-80x_A+64-40x_A+64+8=0\\ \\26x_A^2-120x_A+136=0\\ \\13x_A^2-60x_A+68=0\\ \\D=(-60)^2-4\cdot 13\cdot 68=3600-3536=64\\ \\x_{A_{1,2}}=\dfrac{60\pm8}{2\cdot 13}=\dfrac{34}{13},2$