Tutor profile: Sophie Y.
Subject: Basic Math
Given that 5cm on a map represents 1km on actual ground: a. Calculate the scale of the map in the form of 1:n. Where n is an integer b. The length of a road is 8km. Find the length, in cm, of the line on the map which represents this road.
Solution to a: Given that 5cm on map --> 1km on actual ground, we can express this as a ratio >>5cm: 1km As the question asks for the form 1:n, simplify 5cm into 1 by dividing this by 5. >>1cm: 0.2km Since n needs to be an integer, convert 0.2km into cm. (Q: Why cm instead of m? A: This is to ensure that both numbers are in the same units so that the ratio is accurate.) >>0.2km = 200m = 20000 cm Thus, 1: 20000. Solution to b: (TIP: You don't have to use the ratio found in a. Because the length of the road is given in km, you can use the initial information to solve for the answer much faster!) >>5cm: 1km Since 8km = 1km *8, 5cm*8= 40cm. The length of the line on the map is 40cm.
Why does calcium carbonate decompose less readily on heating than beryllium carbonate?
Metal carbonates decompose when heated. In general, all carbonates in Group II undergo thermal decomposition to give metal oxide and carbon dioxide (g). However, some carbonates are more reactive than others. Upon heating, these are the chemical reactions taking place: BeCO3 (s) –> BeO (s) + CO2 (g) CaCO3 (s) –> CaO (s) + CO2 (g) Down Group 2 of the periodic table, the thermal stability of the carbonates increases. This trend exists because the trend in the polarizing abilities of the positively charged Group II cation and negatively charged carbonate The polarizing ability of the positive Group II cation decreases down the group. The bigger the cation, the same charge has to be spread over a larger volume of space. Its charge density will be lower which will cause less distortion to nearby negative ions. When a cation with a high charge density comes close to the carbonate ion, the carbonate ion gets polarized. The carbonate ion and Group II cation then form ionic bonds. The amount of heat needed to break these ionic bonds apart increases with stronger ionic bonds. As the Ca2+ cation has a stronger charge density than the Be2+ cation, the ionic bond in calcium carbonate is stronger than that in beryllium carbonate. Thus more heat is required to decompose calcium carbonate and it decomposes less readily.
Solve for x and y in 3*x+2*y= 36 and 5*x + 4*y = 64
First, solve for x using the first equation. >>3*x = 36-2*y Divide by 3 to get x in terms of y. >>x = 12-2*y/3 Plug x into the second equation. >> 5*(12-2*y/3) + 4*y = 64 Simplifying by multiplying across and separating the xs on the left and numbers on the right. >>60-10*y/3 + 4*y = 64 >> 8*y/12 = 64-60 >> 8*y/12= 4 >>8*y = 48 >>y=6 Plug this into the first equation to solve for x >>3*x + 2*6 =36 >>3*x =24 >>x =8 Thus, x = 8 and y = 6.
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