10. Aman plans to spend his January salary as

Mathematics

1 answer:

julia-pushkina [17]3 years ago

6 0

Answer:

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Lana has 3 bags with the same amount of marbles in them, totaling 12 marbles. Markus has 3 bags with the same amount of marbles

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Answer:

Markus has 6 marbles in each bag.

Step-by-step explanation:

Markus has 18 marbles and 3 bags

If you divide 18 marbles by 3 bags that would be 6 marbles in each bag.

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The answer and work is in the SS below

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A circle has the equation x^2+y^2+x-6y+9=0. Find the center and any x or y intercepts.

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We know:x^2+y^2+x−6y+9=0So, we complete the square as such:x^2+y^2+x−6y+9=x^2+x+y^2−6y+9=(x+1/2)^2+(y−3)^2=(1/2)^2=1/4

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From a piece of tin in the shape of a square 6 inches on a side, the largest possible circle is cut out. What is the ratio of th

wel

Answer:

$\sf \dfrac{1}{4} \pi \quad or \quad \dfrac{7}{9}$

Step-by-step explanation:

The width of a square is its side length.

The width of a circle is its diameter.

Therefore, the largest possible circle that can be cut out from a square is a circle whose diameter is equal in length to the side length of the square.

Formulas

$\sf \textsf{Area of a square}=s^2 \quad \textsf{(where s is the side length)}$

$\sf \textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}$

$\sf \textsf{Radius of a circle}=\dfrac{1}{2}d \quad \textsf{(where d is the diameter)}$

If the diameter is equal to the side length of the square, then:
$\implies \sf r=\dfrac{1}{2}s$

Therefore:

$\begin{aligned}\implies \sf Area\:of\:circle & = \sf \pi \left(\dfrac{s}{2}\right)^2\\& = \sf \pi \left(\dfrac{s^2}{4}\right)\\& = \sf \dfrac{1}{4}\pi s^2 \end{aligned}$