Answer:
The perimeter of the shape is of 40.56 units.
Step-by-step explanation:
Perimeter of a shape:
The perimeter of a shape is the sum of the lengths of all its sides.
In this question:
The sides are a = 9.60, b = 9.33, c = 4.46, d = 8.56, e = 8.61.
So
The perimeter of the shape is of 40.56 units.
Answer:The axis of symmetry is x=-4
The domain is all real numbers
The function is negative over (-6,-2)
Step-by-step explanation:
Its right
Answer:
$92.55
Step-by-step explanation:
Substitute the value of x, which is in weeks, to 12.
so y = 0.91(12) + 103.47
y = 92.55
<span>
10. Rewrite with only sin x and cos x.sin 2x - cos 2x</span>
sin2x =
2sinxcosx<span>
cos2x = (cosx)^2 - (sinx)^2 = 2(cosx)^2 -1 = 1-
2(sinx)^2</span>
sin2x- cos2x=2sinxcosx-(1- 2(sinx)^2=2sinxcosx-1+2(sinx)^2
sin2x- cos2x=2sinxcosx-1+2(sinx)^2
<span>
the answer is the letter <span>
b) 2 sin x cos2x - 1
+ 2 sin2x</span></span>
11. Find the exact value by using a half-angle identity. sin 22.5°Using the half angle formula you get:sin2(θ)=12[1−cos(2θ)]if θ=22.5° then 2θ=45°so you get:sin2(22.5°)=12[1−cos(45°)]sin2(22.5°)=12[1−√2/2]=2−√24and square root both sides:sin(22.5°)=±√2−√24=±0.382so
sin(22.5°)=0.382the answer is the letter D) one half times the square root of quantity two minus square root of two
15. Verify the identity. cot x minus pi divided by two. = -tan x
Cot(x-pi/2)=-tan(x)
sin(A − B) = sin A cos B − cos A sin B
sin(x – pi/2) = sin x cos (pi/2) − cos x sin (pi/2)=-cosx
cos(A − B) = cos A cos B − sin A sin B
cos(x− pi/2) = cos x cos pi/2 − sin x sin pi/2=-sinx
Cot(x-pi/2)=cos(x-pi/2)/sin(x-pi/2)
= (-sinx)/(-cosx)=-tanx--------------ok
Answer:
(a) Increasing:
and Decreasing:
(b) The local minimum and maximum values are -16 and 16 respectively.
(c) The inflection points are 
Step-by-step explanation:
The function provided is:
(a)
Then, ![f'(x)=-16cos(x)sin(x)-16cos(x)=-16cos(x)[1+sin(x)]](https://tex.z-dn.net/?f=f%27%28x%29%3D-16cos%28x%29sin%28x%29-16cos%28x%29%3D-16cos%28x%29%5B1%2Bsin%28x%29%5D)
Note, 
Then, 
for 
.
Also 
.
Thus, f (x) is increasing for,
And f (x) is decreasing for,
(b)
From part (a) f (x) changes from decreasing to increasing at 
and from increasing to decreasing at 
.
The local minimum value is:
The local maximum value is:
(c)
Compute the value of f'' (x) as follows:
![f''(x)=16sin(x)[1+sin(x)]-16cos^{2}(x)\\\\=16sin(x)+16sin^{2}(x)-16[1-sin^{2}(x)]\\\\=32sin^{2}(x)+16sin(x)-16\\\\=16[2sin(x)-1][sin (x)+1]](https://tex.z-dn.net/?f=f%27%27%28x%29%3D16sin%28x%29%5B1%2Bsin%28x%29%5D-16cos%5E%7B2%7D%28x%29%5C%5C%5C%5C%3D16sin%28x%29%2B16sin%5E%7B2%7D%28x%29-16%5B1-sin%5E%7B2%7D%28x%29%5D%5C%5C%5C%5C%3D32sin%5E%7B2%7D%28x%29%2B16sin%28x%29-16%5C%5C%5C%5C%3D16%5B2sin%28x%29-1%5D%5Bsin%20%28x%29%2B1%5D)
So,
And,
Thus, f (x) is concave upward on 
and concave downward on 
.
If 
, then f (x) will be:
If 
, then f (x) will be:
The inflection points are .
