7: The point B (-8,5) is dilated from the origin with a scale factor of 12 . What are the coordinates of B'? A (−6,3) B (−4,2.5
1 answer:
Answer:
The correct option is option B.
The coordinate of B' is (-4,2.5).
Step-by-step explanation:
Formula of dilation:
Image = (pre-image)×(scale factor)
Scale factor:
The amount by which the shrinks or grows is called " scale factor".
- If the scale factor less than 1 then the shape shrinks.
- If the sale factor equal to 1 then the shape remains same.
- If the scale factor greater than 1 then the shape enlarged.
Given point is B(-8,5)
Scale factor is .
The co-ordinate of image B is
=(-4,2.5)
The coordinate of B' is (-4,2.5).
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Answer:
Step-by-step explanation:
you can find where the first derivative is 0 to find the critical points
g'(x) = ( x^4 -5x^2 +4)' = 4x³-10x
g'(x) =0, make y =0 to find find where g'(x) is 0
4x³-10x =0 , factor 2x
2x(2x²-5)= 0 , each factor must be 0
2x= 0, so x= 0
2x²-5 =0, so x = ±√5/2
we now have 3 critical points -√5/2, 0, and √5/2
make intervals (-∞, -√5/2), (-√5/2, 0) , (0, √5/2) and (√5/2, +∞)
pick a point to test on each interval: -2, -1, 1 and 2 for example, and
calculate g'(x) = 4x³-10x at those points
for x= -2 we have 4(-2)³-10(-2) = -12 , negative number, decrease
for x= -1 we have 4(-1)³-10(-1) =6, positive number, increase
for x= 1 we have 4(1)³-10(1) = -6, negative number, decrease
for x= 2 we have 4(2)³-10(2) = 12, positive number, increase
we went from a decrease to an increase on intervals (-∞, -√5/2), (-√5/2, 0) so x= - √5/2 ≈ -1.58 is a minimum
we went from a decrease to an increase on intervals (0, √5/2), (√5/2, +∞) so
x= √5/2 ≈ 1.58 is a minimum as well
Answer:
336 squirrels
Step-by-step explanation:
-This is a Mark-Recapture method.
-The population is estimated using the formula:
where:
- N-is the estimated population size.
- M-is the number of individuals tagged
- C- is the total number captured the second time(both tagged and untagged)
- R-is the total number of tagged individuals recaptured.
#We substitute our values as follows to estimate N:
Hence, there are approximately 336 squirrels in the conservation area.
*population is always rounded up to the next whole number.