Answer:
45 square centimeters
Step-by-step explanation:
The area of the triangle is given by ...
A = (1/2)bh
where b is the base, 2 cm + 3 cm = 5 cm, and h is the height, 6 cm.
A = (1/2)(5 cm)(6 cm) = 15 cm^2
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The area of the rectangle is given by ...
A = bh
where b is the base, 12 cm, and h is the height, 2.5 cm.
A = (12 cm)(2.5 cm) = 30 cm^2
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The area of the whole figure is the area of the triangle added to the area of the rectangle:
drawing area = 15 cm^2 + 30 cm^2 = 45 cm^2
X= 10
~because~
2x+5=8x, subtract 2x from both sides:
5=6x, divide 6 on both sides:
x=5/6, then rewrite the equation:
12(5/6)
x=10
Answer:
1 2/9 minutes
Step-by-step explanation:
55 mph
55 / 60 = 11/12
11/12 of a mile = 1 minute
45 mph
45 / 60 = 3/4
3/4 of a mile = 1 minute
11/12 divided by 3/4
11/12 * 4/3
We can cross-cancel
11/3 * 1/3 = 11/9 = 1 2/9
It takes 1 2/9 minutes for the hummingbird to cross the lake
Hope this helps!
(Please let me know if I did something wrong!)
Answer:
2
Step-by-step explanation:
Given g(x) = sin(x)-1/cos2(x), we are to find the limit if the function g(x) as g(x) tends to π/2
Substituting π/2 into the function
lim x-->π/2 sin(x)-1/cos 2(x)
= sin(π/2) - 1/cos(2)(π/2)
= 1 - 1/cosπ
= 1- 1/-1
= 1 -(-1)
= 1+1
= 2
Hence the limit of the function h(x) = sin(x)-1/cos2(x) as x--> π/2 is 2
The area ratio is the square of the linear dimension ratio. So if the merry-go-round base is circular, the area contains the square of the radius. If a polygon, the base can be divided into triangles. The area of each triangle involves the product of the base length and the height, so since both have the same change of length, the product will square the scaling ratio.
Let’s say the ratio of corresponding lengths is x:1 then the ratio of the base areas is x²:1.
The question doesn’t provide any figures.
Let’s put some in as an example. Let the actual merry-go-round be circular with a diameter of 20 feet, while the model is one foot in diameter. So the ratio of the actual ride and it’s model is 20:1. The area of the base of the actual ride is 100π sq ft. The area of the base of the model is π/4 sq ft. We expect the ratio of these areas to be 20²=400. 100π/(π/4)=400.
