Anybody knows all of them?
1 answer:
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Answer:
6√3 ±3 ≈ {7.392, 13.392}
Step-by-step explanation:
The length of AB is the long side of a right triangle with hypotenuse CD and short side (AC -BD). The desired radius values will be half the length of EF, with AE added or subtracted.
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<h3>length of AB</h3>Radii AC and BD are perpendicular to the points of tangency at A and B. They differ in length by AC -BD = 12 -9 = 3 units.
A right triangle can be drawn as in the attached figure, where it is shaded and labeled with vertices A, B, C. Its long leg (AB in the attachment) is the long leg of the right triangle with hypotenuse 21 and short leg 3. The length of that leg is found from the Pythagorean theorem to be ...
AB = √(21² -3²) = √432 = 12√3
<h3>tangent circle radii</h3>This is the same as the distance EF. Half this length, 6√3, is the distance from the midpoint of EF to E or F. The radii of the tangent circles to circles E and F will be (EF/2 ±3). Those values are ...
6√3 ±3 ≈ {7.392, 13.392}
Answer:
The number of big pictures are 49 and number of small pictures are 48 .
Step-by-step explanation:
Let us assume that the number of big pictures are x .
Let us assume that the number of small pictures are y .
As given
Big pictures are 56$ each small ones are 34$.
97 were sold at the total of $4,376.
Equations becomes
x + y = 97
56x + 34y = 4376
Multiply x + y = 97 by 56 and subtracted from 56x + 34y = 4376 .
56x - 56x + 34y - 56y = 4376 - 5432
-22y = - 1056
22y = 1056
y = 48
Put value of y in the equation x + y = 97
x + 48 =97
x = 97 - 48
x = 49
Therefore the number of big pictures are 49 and number of small pictures are 48 .