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3 years ago

The formula in finding the area of a circle can be derived usin the perimeter of a rectangle

Mathematics

1 answer:

Alex777 [14]3 years ago

4 0

Yes absolutely as if you just take a circle and break the circle from the centre point into pieces such that the no

of pieces formed is infinite and and then when you take the pieces of the circle and arrange them in the form of rectangle then the area of the rectangle obviously equal to the area of circles.For better understanding I had attached a picture with the answer

Hope it helps

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Use the geometric mean to find the 7th term in a geometric sequence if the 6th term is 12 and the 8th term is 27. 20 19.5 18 17

Lesechka [4]

A₆ =12

a₇ = ?? = x

a₈ 27

In this case x is the geometric mean & as per the formula
geometric mean of 2 numbers =√(a₆ * a₈) = √(12*27)
& x=18.
Proof:
Find the common ratio between a₇ & a₆ ==> = ( x) / 12
now find the common ration between a₈ & a₇ ===> =27 / (x)
x/12 = 27/x ===> x² = 12*27 ==> x² = 324 & x =√324 = 18

7 0

4 years ago

The BP station sold gas for $2.49 per gallon. This week their gas prices are $2.61 a gallon. What was the percent increase in ga

Karolina [17]

Answer:

.12%

Step-by-step explanation

2.61-2.49= 0.12

.12%

5 0

3 years ago

A plane flying horizontally at an altitude of 3 mi and a speed of 440 mi/h passes directly over a radar station. find the rate a

Amiraneli [1.4K]

Let α represent the acute angle between the horizontal and the straight line from the plane to the station. If the 4-mile measure is the straight-line distance from the plane to the station, then
sin(α) = 3/4
and
cos(α) = √(1 - (3/4)²) = (√7)/4

The distance from the station to the plane is increasing at a rate that is the plane's speed multiplied by the cosine of the angle α. Hence the plane–station distance is increasing at the rate of
(440 mph)×(√7)/4 ≈ 291 mph

8 0

3 years ago

John made a triangle with all three sides the same length, 1 \frac{2}{3} ft. What is the perimeter of the triangle?

UNO [17]

Answer:

5 ft

Step-by-step explanation:

If all sides are of the same length, we can multiply the value of one side by 3, because a triangle has three sides (and the perimeter is all sides added together), to find the perimeter.

$1\frac{2}{3}$ × 3

$1\frac{2}{3}$ can be rewritten as $\frac{5}{3}$ , so:

$\frac{5}{3}$ × $\frac{3}{1}$

$= \frac{15}{3}$

The numerator & denominator share a common factor of 3, so:

5 ft is the final answer/perimeter.

hope this helps!

7 0

2 years ago

A certain brand of dinnerware set comes in three colors: red, white, and blue. Twenty percent of customers order the red set, 45

denis23 [38]

Answer:

a) 0.20

b) 0.45

c) 0.65

d) Yes

e) Yes

f) Z = X + Y (except when X = 1 and Y = 1)

This is because the successes of X and Y are mutually exclusive events but their failures aren't. X and Y cannot both be 1.

Step-by-step explanation:

Probability of a red set = 20% = 0.20

Probability of a white set = 45% = 0.45

Probability of a blue set = 35% = 0.35

Probability of the single set being a red or white set = 20% + 45% = 65% = 0.65

P(X=1) = 0.20, P(X=0) = 1 - 0.2 = 0.80

P(Y=1) = 0.45, P(Y=0) = 1 - 0.45 = 0.55

P(Z=1) = 0.65, P(Z=0) = 1 - 0.65 = 0.35

a) pX = P(X=1) = 0.20

b) pY = P(Y=1) = 0.45

c) pZ = P(Z=1) = 0.65

d) Since only one order is being considered at a time, it isn't possible to order red & white set in a single set, hence, both X and Y cannot both be successes (equal to 1) at the same time. But they can both be failures (both equal to 0) if a blue set is ordered. The successes of X and Y are mutually exclusive events but their failures aren't

e) Is pZ = pX + pY

pX = 0.2, pY = 0.45, pZ = 0.65

Hence, this statement is correct!

f) Z = X + Y

Let's check all the probabilities

when X = 1 and Y = 1, Z = 1

1 ≠ 1 + 1

when X = 0 and Y = 1, Z = 1

1 = 0 + 1

when X = 1 and Y = 0, Z = 1

1 = 1 + 0

when X = 0 and Y = 0, Z = 0

0 = 0 + 0

Hence, Z = X + Y (except when X = 1 and Y = 1)

This is because the success of X and Y are mutually exclusive events but their failures aren't.

8 0

3 years ago