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The line 4x-3y=-12 is tangent at the point (-3,0) and the line 3x+4y=16 is tangent at the point (4,1). find the equation of the circle. solution) well you could first find the radius at (3,-4) since it is perpendicular to the tangentthat''s using two-points form: (for (0,0) and (3,-4) )y + 4 = [(-4 -0) / (3 - 0 )]* (x - 3)or, 3y + 12 = -4x + 12or, y = (-4/3) xlet m be the slope of the tangent, then:m * -4/3 = -1or, m = 3/4thus you use the equation:y - y, = m (x - x,)or, y + 4 = 3/4 (x - 3)or, 4y + 16 = 3x - 9or, 3x - 4y - 25 = 0that''s the slope you needof course, if you wanted to do it the shorter way, you could always use the formula:ax + by = r^2where (a,b) is the point (3,-4) and r is the radius squared, as in the circle''s equation x^2+y^2 = r^2, which is 25
Example of 3-D Coordinate System Example: Graph x = 3 in R, R 2 and R 3 . Solution In R we consist of a single coordinate system and thus x=3 is a point in a 1-D co
Volumes of Solids of Revolution / Method of Rings In this section we will begin looking at the volume of solid of revolution. We have to first describe just what a solid of rev
Theorem, from Definition of Derivative If f(x) is differentiable at x = a then f(x) is continuous at x =a. Proof : Since f(x) is differentiable at x = a we know, f'(a
Find out if each of the subsequent series are absolute convergent, conditionally convergent or divergent. Solution: (a) The above is the alternating harmonic ser
The index of industrial production This is a quantity index compiled by the government. This measures changes in the volume of production in main industries. The index is a ex
A 64-ounce bottle of detergent costs $3.20. What is the cost per ounce of detergent? To ?nd out the cost per ounce, divide the cost through the number of ounces; $3.20 ÷ 64 =
ther are 162 student in a school.20 of them are girls .how many are boy
A rescue and ?re squad places a 15 ft ladder against a burning building. If the ladder is 9 ft from the base of the building, how far up the building will the ladder reach? a. 8
I have a log that is 1/3 in mud and the rest of it is 6 meters long. How long is the entire log?
Properties of Dot Product u → • (v → + w → ) = u → • v → + u → • w → (cv → ) • w → = v → •(cw → ) = c (v → •w → ) v → • w → = w → • v →
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