Y varies inversely with x
y = k/x
when y = 0.5, x = 3
0.5 = k/3
k = 0.5 x 3 = 1.5
k = 1.5
y = 1.5/x or y = 3/2x
Answer:
4
Step-by-step explanation:
Every year, the world grows by 1.1%. Converting to a decimal, we can divide by 100 to get 1.1% = 0.011. This means that the world grows by 0.011 exponentially each year. To put this into an expression, we can add 1 to our percentage to get 1.011. This represents 1 = 100% (the original population) and the growth of 1.1% = 0.011. We multiply the rate including the growth by the population to get the population after one year. After the first year, we have
population * 1.011 as the new population after one year. We do that for every year, so the second year's population is population*(1.011)*(1.011) and so on. If x represents the amount of years, then the population can be represented as
(original population)*1.011ˣ
Therefore, to get from 7 billion to 7.31 billion, we have
7 billion * 1.011ˣ = 7.31 billion
divide both sides by 7 billion to relatively isolate the x
1.011ˣ = 7.31/7
Another way of writing this is
log (base 1.011) (7.31/7) = x
≈ 3.96
Rounding to the nearest whole number, we get 4 as our answer
Second one where the wind is blowing 35 km/h east
this is velocity because it gives u both displacement over time and direction
There are 20 miles is Sheng from his home.
Annie's Attic does not have a proportional relationship but Bettie's Boutique does. The constant of proportionality at Betty's Boutique is 0.8.
Step-by-step explanation:
Step 1; To have a proportional relationship, if x's value varies, the y's value should also vary. If x increases, y increases correspondingly while if x decreases, y should also decrease.
Step 2; For Annie's Attic, the sale price = Original price - $5.
No matter what the value of the original price, there is only a difference of $5. Even if the price is increased to $100 the discount will only be $5. So this is not a proportional relationship.
Step 3; At Bettie's Boutique, they are having a 20% off sale. Whatever the cost, 20% is reduced. If bought for $15, price is $15 - 20% = $12. If bought for $25, the price will be $25 - 20% = $20.
If the original price is taken as x as the sale price is y, the relationship is given by; y = (100% - 20%) × x = 80% × x = 0.8 × x. So y = 0.8x. Here the constant of proportionality is 0.8.
