Given:
The point is (6,2).
To find:
The image of given point after rotation of 270 degrees.
Solution:
Let the given point be P(6,2).
Rotation of 270 degrees means the figure is rotated 270 degrees counterclockwise about the origin. So, the rule of rotation is

Using this rule, we get

Therefore, the image of given point is (2,-6).
The light's coverage area is given mathematically as i.e. Area=
Given that a lighthouse casts a revolving beam of light as far as they peir and asked the area is covered.
The revolving beam of light covers the whole space i.e entirely 360°
I.e. it forms a circle-like region
Area of circle =
{ where r is the radius of circle}
Let's assume the distance traveled by light as "d"
as it forms a circular region, it forms a circle of radius "d"
Mathematical connection i.e. area of the region
⇒area of circular region=
{where d is the radius of region}
Learn more about area here:
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Answer:
The number of fringes at
is given as 20.
Step-by-step explanation:
Question
A Galapagos cactus finch population increases by half every decade. The number of finches is modeled by the expression
,
where d is the number of decades after the population was measured. Evaluate the expression for d = −2
Given :
The number of finches is modeled by the expression :
⇒ 
where
is the number of decades after the population was measured.
To evaluate the expression for d=-2
Solution:
In order to evaluate the given expression to find the number of finches at
, we will plugin
for
in the expression and simplify it.
Plugging in
in the expression:
⇒ 
Using negative exponent property. [
⇒ 
⇒ 
⇒
(Answer)
Thus, the number of fringes at
is given as 20.
This means the number of fringes two decades ago was 20.
Answer:
x = -4 , y = 3
Step-by-step explanation:
5x - 7y = -41 ... (i)
-3x - 5y = -3 ... (ii)
Multiplying (i) by -3 and (ii) by 5 ;
-15x + 21y = 123 ... (i)
-15x - 25y = -15 ... (ii)
Subtracting (i) by (ii) ;
0 + 46y = 138
46y = 138
y = 138 ÷ 46 = 3
Returning to equation (ii) ;
-3x - 5(3) = -3
-3x = -3 + 15
-3x = 12
x = -4