Tutor profile: Amy W.
"八仙过海 ----- 各显神通" 是： A）俗语 B）谚语 C）歇后语 D）成语
The correct answer is C. This is because 歇后语 is a type of Chinese proverb that contains two elements. The first part describes a novel or story type scenario. The second part describes a thereof situation. Similar to english phrases such as "an apple a day, keeps the doctor away".
A regular hexagon is drawn with a perimeter of 180cm. Find the area.
A regular hexagon has 6 sides of equal length. The perimeter is found by adding the lengths of all 6 sides of the hexagon. Therefore, one side of the regular hexagon has a length of (180cm)/(6) = 30 cm. A regular hexagon can be divided into 6 congruent equilateral triangles by drawing a line connecting opposite vertices. The height of any one of the equilateral triangle can be found using the pythagorean theorem. The height = sqrt((30cm^2) - (15cm^2)) = 25.98cm. The height is also the apothem as it is perpendicular to the side and starts from the center. The formula for the area of a regular polygon is (0.5)(perimeter * apothem). Therefore the area of the given regular hexagon is (0.5)(180 cm * 25.98cm) = 2338.2 cm^2
Solve for the unknown variable x: 3^(x+ 5) + 3^x = 177876
The product of rules for exponents states that (a^x)(a^y) = a^(x+y). Therefore 3^(x+ 5) = (3^x)(3^5). The equation is now (3^x)(3^5) + 3^x = 177876. We see that on the left hand side of the equation, both the first term and second term have 3^x, therefore by distribution we can "take it out". The equation is now (3^x)(3^5 + 1) = 177876. We can simplify the equation by calculating 3^5 + 1. The equation is now (3^x)(244) = 177876. To find the value of x, we need to isolate x, so we will divide 244 on both sides of the equation. The equation is now (3^x) = 729. We can now use log to solve for x by converting the exponential form to the logarithmic form. The equation is now log3(729) = x. We will solve for x by using the change of bases formula. So now x = (ln(729))/(ln(3)). Thus, x = 6.
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