Answer:
The distance from point A to given line is: 2√5 or 4.472 units
Step-by-step explanation:
Given equation of line is:
And the point is:
The standard form of equation of line is:
Converting the given equation into standard form
The distance of a point (x1,y1) from a line is given by the formula:
In the given details,
A = -1, B = 2, C = -14
x1 = -14, y1 = 5
Putting the values in the formula
Hence,
The distance from point A to given line is: 2√5 or 4.472 units
72 blue, 42 red beads
beads are used to make identical necklaces
<h3>Find</h3>(a) the greatest number of necklaces that can be made
(b) the number of each color bead in each necklace
<h3>Solution</h3>You can write and factor the equation
... necklaces = 72 blue + 42 red
... necklaces = 6(12 blue + 7 red)
where 6 is the greatest common factor (GCF) of 72 and 42.
(a) You can make up to 6 identical necklaces. 6 is the largest common factor of 72 and 42. If you were to try to make more, they could not be identical.
(b) Each necklace can consist of 12 blue and 7 red beads. These are the numbers obtained when the total bead count is divided into 6 equal groups.
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There are several ways you can find the GCF of two numbers. For small numbers, it is generally feasible to use your knowledge of multiplication tables and factors to choose the largest common factor of two numbers. You can also use Euclid's algorithm, which is to repeatedly compute
... (largest number) modulo (smallest number)
until the result is zero. The final "smallest number" is the GCF.
Here, that looks like
... 72 mod 42 = 30
... 42 mod 30 = 12
... 30 mod 12 = 6
... 12 mod 6 = 0 . . . . . . . so 6 is the GCF
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Of course, you know that
... 72 = 2³×3²
... 42 = 2×3×7
so, the largest set of common factors is 2×3 = 6.
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Your graphing calculator may have a function for computing the greatest common divisor (GCD), too. The TI-84 does, for example.
Answer:
Choice B is correct
Step-by-step explanation:
The eccentricity of the conic section is given as 4 and thus the conic section is a hyperbola. Hyperbolas are the only conic sections with an eccentricity greater than 1.
Next, the directrix of this hyperbola is located at y = -6 implying that the hyperbola will be opening upwards. Consequently, the polar equation of this hyperbola will be of the form;
The value of k in the numerator is the product of eccentricity and the absolute value of the directrix;
k= 4*6 = 24
The polar equation is thus given by alternative B
