If n denotes a number to the left of 0 on the number line such that the square of n is less than 1/100, then the reciprocal of n must be _______.A. less than -10B. between -1 and -1/10C. between -1/10 and 0D. between 0 and -1/10E. greater than 10
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Answer: E. Greater than 10
Step-by-step explanation:
First, know that number to the left of a number line are negative and the square of any negative number will be positive and a perfect square.
Since the square of the unknown number is less than 1/100 i.e 0.01 then the possible unknown number 'n' can be -0.01 itself, of which the square of -0.01 will give us 0.0001 (1/10,000) i.e a value less than 0.01.
The reciprocal of 1/10000 is 10,000 which is a value greater than 10.
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Not selecting an S.
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Answer:
a) Giving Reasons Why the Two Triangles are Similar
Similar triangles have the same shape but can be different sizes. For triangles to be similar, their matching angles must be equal, and their matching sides must have the same proportions.
In this problem, we have two triangles - one made by the tree, its shadow, and the line connecting the top of the tree to the end of the shadow. The other triangle is made the same way using the stick.
The bottom angle where the shadow meets the ground is 14 degrees for both triangles. Also, the vertical angles where the tree and stick meet the ground are both 90-degree right angles. Using those known angles, we can find the remaining top angles in each triangle, which are both 76 degrees (180 - 90 - 14 = 76).
Since the corresponding angles in the tree shadow triangle and the stick shadow triangle are all equal (14, 90, and 76 degrees), the two triangles have the same shape. This means the tree shadow triangle and stick shadow triangle are similar triangles.
b. Find the scale factor for the side lengths of the triangles.
The scale factor between two similar triangles is the ratio of their corresponding sides. In this case, you should use the length of the shadows to calculate the scale factor.
Since the shadow of the stick is 4m long and the shadow of the tree is 8m long, the scale factor from the tree's shadow to the stick's shadow is 4/8 = 0.5, or 1/2.
c. Find the height of the tree.
Given that the triangles are similar, and the scale factor is 1/2, the height of the tree would be twice the height of the stick because the stick's shadow is half the length of the tree's shadow.
So the height of the tree would be 2 * 1m = 2m.
Hope this helps! :)
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First, invert the 3/10.
3/10 = 10/3
Then multiply.
5/8 • 10/3 = 50/24
50/24 = 25/12
5/8 ÷ 3/10 = 25/12
5/8 x 10/3=
50/24=
25/12
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So you can do the cubic root of 512 or 3
The cubic root of 512 is 8.
The side length is eight
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