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2 years ago

Write the equation of a line that passes through the point (-8,2) and is parallel to the line 3x-2y=12

Mathematics

1 answer:

arlik [135]2 years ago

7 0

Answer:

Step-by-step explanation:

-2y = -3x + 12

2y = 3x - 12

y = 3/2x - 6

y - 2 = 3/2(x + 8)

y - 2 = 3/2x + 12

y = 3/2x + 14

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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:

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

So the ratio of the area of the circle to the original square is:

$\begin{aligned}\textsf{area of circle} & :\textsf{area of square}\\\sf \dfrac{1}{4}\pi s^2 & : \sf s^2\\\sf \dfrac{1}{4}\pi & : 1\end{aligned}$

Given:

side length (s) = 6 in
radius (r) = 6 ÷ 2 = 3 in

$\implies \sf \textsf{Area of square}=6^2=36\:in^2$

$\implies \sf \textsf{Area of circle}=\pi \cdot 3^2=28\:in^2\:\:(nearest\:whole\:number)$

Ratio of circle to square:

$\implies \dfrac{28}{36}=\dfrac{7}{9}$

5 0

2 years ago

If ΔΡQR

frozen [14]

Answer:

If y varies directly as x^3 and y=36 when x=7, find y if x=4? (Round answer to the nearest hundredth) , find y if x=4 x = 4 . (Round off your answer to the nearest hundredth.)

Step-by-step explanation:

6 0

3 years ago

The processing speed of a certain computer is 10¹¹ instructions per second. Another computer has a processing speed that is 10³

Mashcka [7]

“Times as fast” means you need to multiply the original speed (10^11) by how many times faster the faster processor works:

10^11 instructions/second • 10^3 faster = 10^14 instructions/second

The key is “___ times as fast”.

7 0

2 years ago

Calculate the resistance of a 270-cm length of copper wire with a 0.030-cm2 cross-sectional area. ( = 1.8 · 10-6 ohm-cm) R = ___

devlian [24]

Answer:

Given:-

The length of copper wire (L) = 270 cm

Area of cross-sectional (A) = 0.030 $cm^2$