Rewrite the boundary lines <em>y</em> = -1 - <em>x</em> and <em>y</em> = <em>x</em> - 1 as functions of <em>y </em>:
<em>y</em> = -1 - <em>x</em> ==> <em>x</em> = -1 - <em>y</em>
<em>y</em> = <em>x</em> - 1 ==> <em>x</em> = 1 + <em>y</em>
So if we let <em>x</em> range between these two lines, we need to let <em>y</em> vary between the point where these lines intersect, and the line <em>y</em> = 1.
This means the area is given by the integral,
The integral with respect to <em>x</em> is trivial:
For the remaining integral, integrate term-by-term to get
Alternatively, the triangle can be said to have a base of length 4 (the distance from (-2, 1) to (2, 1)) and a height of length 2 (the distance from the line <em>y</em> = 1 and (0, -1)), so its area is 1/2*4*2 = 4.
The taxes on an item costs $164 *4,7/%
T=$7,78
Answer:
x= 
Step-by-step explanation:
Applying the trigonometry ratios, we have:
a. CD = 63.6
b. CD = 33.8
c. CD = 16.1
d. CD = 15.9
<h3>What are the Trigonometry Ratios?</h3>
The trigonometry ratios are used to find a length or angle in any right triangle. They are:
- SOH, which is sin ∅ = opp/hyp
- CAH, which is cos ∅ = adj/hyp
- TOA, which is tan ∅ = opp/adj
a. ∅ = 32°
hyp = 75
adj = CD
Apply CAH:
cos 32 = CD/75
CD = cos 32 × 75
CD = 63.6
b. ∅ = 56°
opp = 28
hyp = CD
Apply SOH:
sin 56 = 28/CD
CD = 28/sin 56
CD = 33.8
c. ∅ = 43°
opp = 15
adj = CD
Apply TOA:
tan 43 = 15/CD
CD = 15/tan 43
CD = 16.1
d. ∅ = 27°
hyp = 35
opp = CD
Apply SOH:
sin 27 = CD/35
CD = sin 27 × 35
CD = 15.9
Learn more about the trigonometry ratios on:
brainly.com/question/10417664
Answer:
Length = 12 inches
Width = 14 inches
Step-by-step explanation:
Formula for perimeter of a rectangle is;
P = 2(L + W)
Where;
L is length
W is width
We are told that the length is 2 inches shorter than its width. Thus;
L = (W - 2)
Thus,perimeter is now;
P = 2(W - 2 + W)
P = 2(2W - 2)
P = 4W - 4
We are told that the perimeter is 52. Thus;
4W - 4 = 52
4W = 52 + 4
4W = 56
W = 56/4
W = 14 inches
From L = (W - 2) ;
L = 14 - 2
L = 12 inches
