The diagram shows a logo made from 3 circles.
1 answer:
Answer:
% area of the shaded region = 33%
Step-by-step explanation:
Radius of the middle circle = 7 cm
Radius of the inner circle = 4 cm
Area of the middle circle = πr²
= π(7)²
= 49π
Area of the inner circle = π(4)²
= 16π
Area of the shaded region= 49π - 16π
= 33π
Area of the outermost circle = π(10)²
= 100π
% area of the shaded region =
=
= 33%
Therefore, area of the shaded region is 33% of the complete logo.
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Answer:
Step-by-step explanation:
First, we need to write the polynomial in descending order
Then, grab the term with the highest power from the polynomial and divide it by the term with highest power from the polynomial located at the other side of the division symbol (this polynomial would be x+5)
The result (4x^2 / x) = 4x
This term will be part of the solution, and will be use to start the process of division.
This process start with the previous obtained term (4x), which will be multiplied by the polynomial from the other side of the division symbol (x+5).
The result another is another polynomial
This new polynomial will be multiply by negative 1
The new polynomial is then added to the poly (4X^2+14x-9)
The result will constitute a new poly, that will be use as the remaining of the division.
Since, our remaining differs from zero, and we still have member to simplify, we repeat the step 1 using the remaining as the new poly that needs to by divided by (x+5).
The attached picture explains the whole procedure.
The hyperbola having both foci lying in the same quadrant is <u>(y - 16)²/9² - (x + 1)²/12² = 1</u>, making the <u>4th option</u> a right choice.
For the hyperbola with an equation of the form (x - h)²/a² - (y - k)²/b² = 1, the foci in on the points (h + c, k) and (h - c, k), where c = √(a² + b²).
For the hyperbola with an equation of the form (y - k)²/a² - (x - h)²/b² = 1, the foci in on the points (h, k + c) and (h, k - c), where c = √(a² + b²).
<u>Among the options</u>:
(a) (x - 24)²/24² - (y -1)²/7² = 1.
The equation is of the form (x - h)²/a² - (y - k)²/b².
h = 24, k = 1, a = 24, b = 7.
c = √(a² + b²) = √(24² + 7²) = √(576 + 49) = √625 = 25.
Thus, foci are at the points (h + c, k), (h - c, k) = (24 + 25, 1), (24 - 25, 1) = (49, 1), and (-1, 1), which are in different quadrants.
(b) (y - 12)²/5² - (x - 6)²/12² = 1.
The equation is of the form (y - k)²/a² - (x - h)²/b².
h = 6, k = 12, a = 5, b = 12.
c = √(a² + b²) = √(5² + 12²) = √(25 + 144) = √169 = 13.
Thus, foci are at the points (h, k + c), (h, k - c) = (6, 12 + 13), (6, 12 - 13) = (6, 25), and (6, -1), which are in different quadrants.
(c) (y - 16)²/15² - (x - 2)²/8² = 1.
The equation is of the form (y - k)²/a² - (x - h)²/b².
h = 2, k = 16, a = 15, b = 8.
c = √(a² + b²) = √(15² + 8²) = √(225 + 64) = √289 = 17.
Thus, foci are at the points (h, k + c), (h, k - c) = (2, 16 + 17), (2, 16 - 17) = (2, 33), and (2, -1), which are in different quadrants.
(d) (y - 16)²/9² - (x + 1)²/12² = 1.
The equation is of the form (y - k)²/a² - (x - h)²/b².
h = -1, k = 16, a = 9, b = 12.
c = √(a² + b²) = √(9² + 12²) = √(81 + 144) = √225 = 15.
Thus, foci are at the points (h, k + c), (h, k - c) = (-1, 16 + 15), (-1, 16 - 15) = (-1, 31), and (-1, 1), which are in the same quadrants (QUADRANT II).
Thus, the hyperbola having both foci lying in the same quadrant is <u>(y - 16)²/9² - (x + 1)²/12² = 1</u>, making the <u>4th option</u> a right choice.
Learn more about the foci of a hyperbola at
#SPJ4
For the options, refer the image.
