Subtract 4 from each side
Divide both sides by 5
Take square root of both sides
Add 3 to both sides
Check the picture below.
well, we want only the equation of the diametrical line, now, the diameter can touch the chord at any several angles, as well at a right-angle.
bearing in mind that <u>perpendicular lines have negative reciprocal</u> slopes, hmm let's find firstly the slope of AB, and the negative reciprocal of that will be the slope of the diameter, that is passing through the midpoint of AB.
![\bf A(\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{5}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{1}}}\implies \cfrac{-3}{4} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{slope of AB}}{-\cfrac{3}{4}}\qquad \qquad \qquad \stackrel{\textit{\underline{negative reciprocal} and slope of the diameter}}{\cfrac{4}{3}}](https://tex.z-dn.net/?f=%5Cbf%20A%28%5Cstackrel%7Bx_1%7D%7B1%7D~%2C~%5Cstackrel%7By_1%7D%7B4%7D%29%5Cqquad%20B%28%5Cstackrel%7Bx_2%7D%7B5%7D~%2C~%5Cstackrel%7By_2%7D%7B1%7D%29%20~%5Chfill%20%5Cstackrel%7Bslope%7D%7Bm%7D%5Cimplies%20%5Ccfrac%7B%5Cstackrel%7Brise%7D%20%7B%5Cstackrel%7By_2%7D%7B1%7D-%5Cstackrel%7By1%7D%7B4%7D%7D%7D%7B%5Cunderset%7Brun%7D%20%7B%5Cunderset%7Bx_2%7D%7B5%7D-%5Cunderset%7Bx_1%7D%7B1%7D%7D%7D%5Cimplies%20%5Ccfrac%7B-3%7D%7B4%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bslope%20of%20AB%7D%7D%7B-%5Ccfrac%7B3%7D%7B4%7D%7D%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Cstackrel%7B%5Ctextit%7B%5Cunderline%7Bnegative%20reciprocal%7D%20and%20slope%20of%20the%20diameter%7D%7D%7B%5Ccfrac%7B4%7D%7B3%7D%7D)
so, it passes through the midpoint of AB,
so, we're really looking for the equation of a line whose slope is 4/3 and runs through (3 , 5/2)
Answer:
Step-by-step explanation:
Area of a Semi Circle
Area = 1/2 pi r^2
r = d/2
r = 3/2
r = 1.5
Area = 1/2 3.14 * 1.5^2
Area = 1/2 * 3.14 * 2.25
Area = 3.5325
Area of Rectangle
L = 12 Yd
W = 4 Yd
Area = L * W
Area = 12 * 4<u> = 48 </u>
Total Area = 51.5325
Answer:
3. 43.96 cm
4. 81.64 ft
Step-by-step explanation:
3. The formula for the circumference of a circle in terms of radius is ...
C = 2πr
When π is approximated by 3.14, this becomes ...
C ≈ 6.28r
The only answer choice even close to 6.28×(7 cm) is the one shown above.
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4. The formula for the circumference of a circle in terms of diameter is ...
C = πd
When π is approximated by 3.14, this becomes ...
C ≈ 3.14d
The only answer choice anywhere close to 3.14×(26 ft) is the one shown above.
_____
<em>Comment on the solution</em>
For questions like these, you only need to be able to estimate the answer to 1 or 2 significant digits. The answer choices are not so close together as to cause any confusion.
6×7 = 42, so the answer will be a few more than 42.
3×26 = 78, so the answer will be within a few numbers larger than that.
In each case, the answer is the largest value on the list. The other choices differ by a factor of 2, so aren't even close.
