Determine whether each pair of functions are inverse functions. Picture attached.
2 answers:
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Answer:
Equation 1: r = <u>4</u> +( <u>3</u> * <u>cos theta</u> )
Equation 2: r = sqrt (<u> 5²</u> * <u>sin(2 theta)</u> )
Step-by-step explanation:
GRAPH 1:
The first graph is a dimpled limacon.
General equation for dimpled limacon:
r = a + b cos theta ∴ if dimple is along the x- axis
r = a + b sin theta ∴ if dimple is along the y-axis
y-intercept : { a, -a } = { 4, -4 } ∴ the points at which limacon intersects y-axis
Negative side of x-axis = ( a – b ) ⇒ 1
Positive side of x-axis = ( a + b ) ⇒ 7
Subtract the value of a from sum of a and b to find b:
b = 7 – 4 ⇒ 3
Equation1: r = <u>4</u> +( <u>3</u> * <u>cos theta</u> )
GRAPH 2:
The second graph is a lemniscates.
General equation for lemniscates is:
r² = a² cos(2theta) ∴ if petals of graph are on coordinate axis
r² = a² sin(2 theta) ∴ if petals of graph are not on coordinate axis
now, according to the graph:
a = 5 ⇒ a² = 25
angle of graph: cos2θ, simply divide 360° by 2:
⇒ 180°
The petals cannot be on coordinate axis, we start from 45° and then the next petal will be on:
45° + 180° = 225°
Since the graph is not on the coordinate axis, so
r² = 5² sin(2 theta) ⇒ r = sqrt ( 5² * sin(2 theta) )
Equation 2: r = sqrt (<u> 5²</u> * <u>sin(2 theta)</u> )
Answer:
16.7%
Step-by-step explanation:
Please check below attachment for sample space table
Firstly, we have the total number of possible results as 12
From the 12, the probability of flipping a head is 6/12
Rolling either a 3 or a 5 is the sum of places we have both divided by the possible total of 12
we have this as ; 2/12 + 2/12 = 4/12
The term ‘AND’ means we have to multiply the two probabilities as follows;
4/12 * 1/2 = 1/6 = 0.1667
To the nearest tenth, we have this as 16.67% which is 16.7%
