Hey there!
Area= length*width.
6.2 is the length and 3.7 is the width
3.7 *6.2= 22.94 yd^2
I hope this helps!
~kaikers
I assume you're supposed to establish the identity,
cos(A) cos(2A) cos(4A) = 1/8 sin(8A) / sin(A)
Recall the double angle identity for sine:
sin(2<em>x</em>) = 2 sin(<em>x</em>) cos(<em>x</em>)
Then you have
sin(8A) = 2 sin(4A) cos(4A)
sin(8A) = 4 sin(2A) cos(2A) cos(4A)
sin(8A) = 8 sin(A) cos(A) cos(2A) cos(4A)
==> sin(8A)/(8 sin(A)) = cos(A) cos(2A) cos(4A)
as required.
Answer:
- dimensions: 12 ft by 5 ft
- area: 60 ft²
Step-by-step explanation:
Let x represent the shorter dimension in feet. Then the longer one is x+7 and the Pythagorean theorem tells us the relation of these to the diagonal is ...
x² + (x+7)² = 13²
2x² +14x + 49 = 169 . . . . eliminate parentheses
x² +7x -60 = 0 . . . . . subtract 169 and divide by 2
(x +12)(x -5) = 0 . . . . factor the equation
x = -12 or +5 . . . . . . . only the positive value of x is useful here.
The short dimension is 5 ft, so the long dimension is 12 ft. The area is their product, 60 ft².
_____
<em>Comment on finding the area</em>
The quadratic equation above can be rearranged and factored as ...
x(x +7) = 60
Since the dimensions of the garden are x and (x+7), this product is the garden's area. This equation tells us the area is 60. We don't actually have to find the dimensions.
Answer:
-2
Step-by-step explanation:
Distribute
2
(
3
+
4
)
+
2
=
4
+
3
{\color{#c92786}{2(3x+4)}}+2=4+3x
2(3x+4)+2=4+3x
6
+
8
+
2
=
4
+
3
{\color{#c92786}{6x+8}}+2=4+3x
6x+8+2=4+3x
2
Add the numbers
6
+
8
+
2
=
4
+
3
6x+{\color{#c92786}{8}}+{\color{#c92786}{2}}=4+3x
6x+8+2=4+3x
6
+
1
0
=
4
+
3
6x+{\color{#c92786}{10}}=4+3x
6x+10=4+3x
3
Rearrange terms
6
+
1
0
=
4
+
3
6x+10={\color{#c92786}{4+3x}}
6x+10=4+3x
6
+
1
0
=
3
+
4
6x+10={\color{#c92786}{3x+4}}
6x+10=3x+4
4
Subtract
1
0
10
10
from both sides of the equation
6
+
1
0
=
3
+
4
6x+10=3x+4
6x+10=3x+4
6
+
1
0
−
1
0
=
3
+
4
−
1
0
6x+10{\color{#c92786}{-10}}=3x+4{\color{#c92786}{-10}}
6x+10−10=3x+4−10
5
Simplify
Subtract the numbers
Subtract the numbers
6
=
3
−
6
6x=3x-6
6x=3x−6
6
Subtract
3
3x
3x
from both sides of the equation
6
=
3
−
6
6x=3x-6
6x=3x−6
6
−
3
=
3
−
6
−
3
6x{\color{#c92786}{-3x}}=3x-6{\color{#c92786}{-3x}}
6x−3x=3x−6−3x
7
Simplify
Combine like terms
Combine like terms
3
=
−
6
3x=-6
3x=−6
8
Divide both sides of the equation by the same term
3
=
−
6
3x=-6
3x=−6
3
3
=
−
6
3
\frac{3x}{{\color{#c92786}{3}}}=\frac{-6}{{\color{#c92786}{3}}}
33x=3−6
9
Simplify
Cancel terms that are in both the numerator and denominator
Divide the numbers
=
−
2
