Answer:
5 km
Step-by-step explanation:
It helps to draw a diagram.
The triangle between Stamford, Newport, and Amanda's house is a right triangle with one leg of length 12 and hypotenuse 13. The Pythagorean theorem can be used to find the remaining leg:
13² = 12² + (distance to Newport)²
169 -144 = (distance to Newport)²
√25 = 5 = distance to Newport
Newport is 5 km from Amanda's house.
_____
It can be useful to remember this right triangle. 5-12-13 right triangles show up in a number of algebra and geometry problems.
Answer:
- a) 125,220,046 barrels
- b) 71.25 years
Step-by-step explanation:
<u>Oil consumption:</u>
<u>Rate of increase of consumption:</u>
<u>Total reserves </u>
- 155*2000000 = 310000000 barrels
a) ....................................................................................
<u>Total oil consumption at the end of 42 years:</u>
- 2,000,000
- 2,000,000*1.02 =
- 2.000,000*1.02^2
- ...
- 2,000,000*1.02^41
<u>Sum</u>:
- 2000000*(1 + 1.02+ 1.02^2+ ...+ 1.02^41) =
- 2000000*(1.02^41 - 1)/(1.02 - 1) = 125,220,046 barrels
b) ....................................................................................
<u>Oil reserves will last:</u>
- 2000000*(1.02^x - 1)/(1.02 - 1) = 310000000
- (1.02^x - 1)/0.02 = 155
- 1.02^x - 1 = 155*0.02
- 1.02^x =1 +3.1
- 1.02^x = 4.1
- x log 1.02 = log 4.1
- x = log 4.1 /log 1.02
- x = 71.25 years
1 cup = 128 grams
X cups = 96 grams
Cross multiply
128X = 1*96
X=96/128 cups = 6/8 = 3/4 cups.
If she has already added 1/2 cups, then she needs to add (3/4-1/2)=1/4 cup more sugar.
Also please remind her to do the calculations before adding ingredients to avoid ruining a recipe.
x+y=120_______1
x=4*y_________2
x=4y
substitute 4y for x in equation 1
`4y+y=120
5y=120
eliminate the coefficient of y
y=120/5
y=24
now,input 24 for y in equation 2
`x=4y
x=4*24
x=96
thus, the numbers are
96 and 24
