Answer:
12 inches
Step-by-step explanation:
Raj tested his new flashlight by shinning it on his bedroom wall the beam of the light can be described by the equation (x^2-2x) + (y^2-4y) - 31=0. how many inches wide is the beam of light on the wall
Solution
Given:
(x^2-2x) + (y^2-4y) - 31=0
By completing the square
(x^2-2x) + (y^2-4y) - 31=0
(x^2-2x+1-1) + (y^2-4y+4-4)-31=0
(x-1)^2 -1 + (y-2)^2 - 4 - 31=0
(x-1)^2 + (y-2)^2 - 1 - 4 - 31=0
(x-1)^2 + (y-2)^2 - 36=0
(x-1)^2 + (y-2)^2=36
Writing the equation in the form: (x-h)^2+(y-k)^2=r^2
(x-1)^2+(y-2)^2=6^2
From the above, r=6
Where,
r=radius
how wide is the diameter ?
radius=6
Diameter= 2 × radius
=2×6
=12 inches
The number that 7 belongs to is a rational number.
<h3>What is a rational number?</h3>
It should be noted that a rational number is a number that is expressed as the ratio of two integers.
In this case, the denominator should not be equal to zero, whereas an irrational number cannot be expressed in the form of fractions.
Rational numbers are terminating decimals but irrational numbers are non-terminating and non-recurring.
Therefore, the number that 7 belongs to is a rational number.
Learn more about numbers on:
brainly.com/question/4619309
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Answer:
904.78
Step-by-step explanation:
we have the radius, which is 6.
were trying to find the volume.
the foemula for the v of a sphere is 4/3(pi)r^3
so, multiply 4/3 times pi and we get 4.18879.
find 6^3, which is 216. multiply tyese two values, and we get 904.77864.
so, the volume of this sphere is around 904.78
Answer:
a) Parallel when a = -2/3
b) Perpendicular when a = 6
Explanation:
a) For two parallel lines slopes are equal.
So, 6y=−2x+4 and 2y=ax−5 parallel if they are slopes equal.
Slope of 6y=−2x+4, comparing with y = mx + c
So, m = -2/6 = =-1/3
For 6y=−2x+4 and 2y=ax−5 to b parallel we have slope of 2y=ax−5 equal to -1/3
Slope of 2y=ax−5
m = a/2
We have a/2 = -1/3
a = -2/3
b) For perpendicular lines product of slope is -1.
So we have
