Answer:
a21 = -61
Step-by-step explanation:
(subtract to eliminate a₁)
9 = -3d
d = -3
-19 = a₁ + (6)(-3)
-1 = a
a21 = -1 + (21 - 1)(-3)
= -61
Triangle IUP has angles I=50, U=60, P=70. What side is the longest side of the triangle?
2 answers:
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Answer:
see below
Step-by-step explanation:
f(x) = −16x^2 + 24x + 16
Factor out -8
f(x) = -8( 2x^2-3x-2)
Factor
f(x) = -8 (x-2) ( 2 x+1)
Set equal to zero to find the x intercepts
0 = -8 (x-2) ( 2 x+1)
Using the zero product property
x-2 =0 2x+1 =0
x=2 2x=-1
x=2 x = -1/2
The x intercepts are
(2,0) and (-1/2,0)
The end behavior
Let x = -∞
f(x) = −16( -∞)^2 + 24( -∞) + 16
The squared term dominates
= −16( -∞)^2 = −16( ∞) = −( ∞)
It goes to -∞ as x goes to ( -∞)
Let x = ∞
f(x) = −16( ∞)^2 + 24( ∞) + 16
The squared term dominates
= −16( ∞)^2 = −16( ∞) = −( ∞)
It goes to -∞ as x goes to ( ∞)
We need the vertex, the zeros and the end behavior to graph the parabola
The vertex is 1/2 way between the zeros
(-1/2+2) /2 = 3/4
f(3/4) = -8 (3/4-2) ( 2 *3/4+1) = 25
We know it opens down since the x^2 term has a negative coefficient
we know that
In the graph the intersection both functions is the point when f(x)=g(x)
so
see the graph
the point of intersection both graphs is
that means
for the input value of
therefore
<u>the answer is</u>
the input value is
We can use the Pythagorean Trigonometric Identity which says:
Since we need to find sin(t), we have to solve for it:
Let's plug in the given cos(t) value:
And solve sin(t):
Simplify further:
And it all simplifies down to:
Since it's in the 4th quadrant, the sin(t) value is going to be negative. So, your final answer is:
Hope this helps!
Since we need to find sin(t), we have to solve for it:
Let's plug in the given cos(t) value:
And solve sin(t):
Simplify further:
And it all simplifies down to:
Since it's in the 4th quadrant, the sin(t) value is going to be negative. So, your final answer is:
Hope this helps!
Answer and explanation:
Please find attached answer and explanation
