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2 answers:
Since the triangles are similar, the ratio of the sides of larger triangle to the smaller triangle is a constant.
That constant =
Since the sides are in that constant proportion, the area of the triangles will also be in proportion.
(Area of larger triangle) over (Area of smaller triangle) =
= 123.6 ≈ 124
Hence, to the nearest whole number the area of smaller triangle is 124 <span>ft</span>²<span>.</span>
That constant =
Since the sides are in that constant proportion, the area of the triangles will also be in proportion.
(Area of larger triangle) over (Area of smaller triangle) =
Hence, to the nearest whole number the area of smaller triangle is 124 <span>ft</span>²<span>.</span>
Answer:
Area of the smaller triangle 74 ft².
Step-by-step explanation:
Given : The triangles are similar. The area of the larger triangle is 206 ft^2.
To find : Find the area of the smaller triangle to the nearest whole number.
Solution : We have given that triangles are similar and area of the larger triangle is 206 ft^2.
By the similar triangles property : .
Then Side of triangle 1 = 15 ft .
Side of triangle 2 = 9 ft.
Area of triangle 1 = 206 ft².
Let area of triangle 2 = x.
Then ,
Ratio of sides = =
.
.
On cross multiplication :
206 * 9 = 25 *x
1854 = 25 * x .
On dividing by 25
x = 74.16 ft².
Therefore, Area of the smaller triangle 74 ft².
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Try this option:
1. Common view of hyperbola equation is:
2. hyperbolas are: 2x²+4x-5y²-10y+57=0 and -x²+12x+3y²+7y+11=0.
1. Common view of hyperbola equation is:
2. hyperbolas are: 2x²+4x-5y²-10y+57=0 and -x²+12x+3y²+7y+11=0.
This question can be solved primarily by L'Hospital Rule and the Product Rule.
I) Product Rule and L'Hospital Rule:
![y= \lim_{x \to 0} \frac{[2xcos(x)-x^2sin(x)]-2sin(x)cos(x)}{4x^3}](https://tex.z-dn.net/?f=y%3D%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B%5B2xcos%28x%29-x%5E2sin%28x%29%5D-2sin%28x%29cos%28x%29%7D%7B4x%5E3%7D%20)
II) Product Rule and L'Hospital Rule:
![y= \lim_{x \to 0} \frac{[-2xsin(x)+2cos(x)]-[2xsin(x)+x^2cos(x)]-[2cos^2(x)-2sin^2(x)]}{12x^2} \\ y= \lim_{x \to 0} \frac{2cos(x)-4xsin(x)-x^2cos(x)-2cos^2(x)+2sin^2(x)}{12x^2}](https://tex.z-dn.net/?f=y%3D%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B%5B-2xsin%28x%29%2B2cos%28x%29%5D-%5B2xsin%28x%29%2Bx%5E2cos%28x%29%5D-%5B2cos%5E2%28x%29-2sin%5E2%28x%29%5D%7D%7B12x%5E2%7D%20%5C%5C%20y%3D%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B2cos%28x%29-4xsin%28x%29-x%5E2cos%28x%29-2cos%5E2%28x%29%2B2sin%5E2%28x%29%7D%7B12x%5E2%7D)
III) Product Rule and L'Hospital Rule:
![]y= \alpha + \beta \\ \\ \alpha =\lim_{x \to 0} \frac{-2sin(x)-[4sin(x)+4xcos(x)]-[2xcos(x)-x^2sin(x)]}{24x} \\ \beta = \lim_{x \to 0} \frac{4sin(x)cos(x)+4sin(x)cos(x)}{24x} \\ \\ y = \lim_{x \to 0} \frac{-6sin(x)-4xcos(x)-2xcos(x)+x^2sin(x)+8sin(x)cos(x)}{24x}](https://tex.z-dn.net/?f=%5Dy%3D%20%5Calpha%20%2B%20%5Cbeta%20%5C%5C%20%5C%5C%20%5Calpha%20%3D%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B-2sin%28x%29-%5B4sin%28x%29%2B4xcos%28x%29%5D-%5B2xcos%28x%29-x%5E2sin%28x%29%5D%7D%7B24x%7D%20%5C%5C%20%5Cbeta%20%3D%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B4sin%28x%29cos%28x%29%2B4sin%28x%29cos%28x%29%7D%7B24x%7D%20%5C%5C%20%20%5C%5C%20y%20%3D%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B-6sin%28x%29-4xcos%28x%29-2xcos%28x%29%2Bx%5E2sin%28x%29%2B8sin%28x%29cos%28x%29%7D%7B24x%7D)
IV) Product Rule and L'Hospital Rule:
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V) Using the Definition of Limit:
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II) Product Rule and L'Hospital Rule:
III) Product Rule and L'Hospital Rule:
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