9514 1404 393
Answer:
10
Step-by-step explanation:
The n-th triangular number is given by ...
t(n) = n(n+1)/2
We went to find n when t(n) = 55.
55 = n(n+1)/2
110 = n(n+1)
Adding 1/4 completes the square.
110.25 = (n +0.5)^2
√110.25 = n+0.5 . . . . . we are interested in the positive value of n
n = 10.5 -0.5 = 10
The triangular number that has 55 dots in its shape is the 10-th number.
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<em>Additional comment</em>
Here, we have gone to the trouble to formally complete the square to find the value of n. You may realize that it isn't really necessary to go to that trouble.
A reasonable estimate of the value of n is possible by considering that the product n(n+1) is a little more than n², so the value of n will be a little less than √110 ≈ 10.49. The nearest integer is 10, which is the answer we're looking for.
Answer:
$233.75
Step-by-step explanation:
2.75 x 15 = 41.25
275 - 41.25 = $233.75
Amy can estimate with 10% instead, so she can just simply move the decimal point of $9.11 to the right, and so it will be estimated to more than 91 cents.
Answer:
24
Step-by-step explanation:
You can use the Pythagorean Theorem to solve this:
The legs of the triangle are put into either a or b and the hypotenuse is put into c. In this case, they've already given you the hypotenuse, but now you need to find the leg:
2025 + 
= 2601
<em><u>Subtract 2025 from both sides:</u></em>
2025 + = 2601
-2025 -2025
_____________
= 576
<em><u>Square root:</u></em>
b = 24
Answer:
The coordinate axes divide the plane into four quadrants, labelled first, second, third and fourth as shown. Angles in the third quadrant, for example, lie between 180∘ and 270∘ &By considering the x- and y-coordinates of the point P as it lies in each of the four quadrants, we can identify the sign of each of the trigonometric ratios in a given quadrant. These are summarised in the following diagrams. &In the module Further trigonometry (Year 10), we saw that we could relate the sine and cosine of an angle in the second, third or fourth quadrant to that of a related angle in the first quadrant. The method is very similar to that outlined in the previous section for angles in the second quadrant.
We will find the trigonometric ratios for the angle 210∘, which lies in the third quadrant. In this quadrant, the sine and cosine ratios are negative and the tangent ratio is positive.
To find the sine and cosine of 210∘, we locate the corresponding point P in the third quadrant. The coordinates of P are (cos210∘,sin210∘). The angle POQ is 30∘ and is called the related angle for 210∘.
Step-by-step explanation:
