Answer:
4.62 units
Step-by-step explanation:
Let's first find the length OR.
OR² = BR² + OB²
OR² = 5² + 12²
OR² = 25 + 144
OR² = 169
OR = 13
Let's find the area of triangle OBR.
Using the formula :
½bh
Where
b = BR
h = OB
Therefore, area of triangle OBR =
½ * BR * OB
= ½ * 5 * 12
= 30
From the diagram, triange OBR and OAR are parallel to each other, and they equal.
Thus, area of OBR = area of OAR
To find the length PA, we have :
Area of OAR = ½ * OR *PA
Let's make PA subject of the formula:
PA = 4.618 ≈ 4.62
PA = 4.62 units
Gustavo won, this question tries to trick you by adding more digits to Loreena.
Answer:
Large box weighs 18.25 kilograms
Small box weighs 15.25 kilograms
Step-by-step explanation:
A fruit company delivers its fruit in two types of boxes: large and small.
Let x = weight of large box.
Let y = weight of small box.
A delivery of 3 large boxes and 5 small boxes has a total weight of 131 kilograms. This means
3x + 5y = 131 - - - - - - - - - - -1
A delivery of 6 large boxes and 2 small boxes has a total weight of 140 kilograms.
This means 6x + 2y = 140 - - - - - - - 2
Solving equation 1 and equation 2 by elimination method,
Multiply equation 1 by 6 and equation 2 by 3
18x + 30y = 786
18x +6y = 420
24y = 366
y = 366/24 = 15.25
Put y = 15.25 in equation 1
3x + 5× 15.25 = 131
3x + 76.25 = 131
3x = 131 - 76.25
3x = 54.75
x = 54.75/3 = 18.25
The tank is filled up at a total rate of 10 gal/min, and currently contains 500 gal of solution. It can hold up to 1000 gal, so it will take time <em>t</em> to fill it up completely:
500 gal = (10 gal/min) <em>t</em>
<em>t</em> = (500 gal) / (10 gal/min)
<em>t</em> = 50 min
In that time,
(8 gal/min) (50 min) = 400 gal of cola
and
(2 gal/min) (50 min) = 100 gal of cherry syrup
are added to the tank, so that when it's full, the tank contains 850 gal of cola and 150 gal of syrup.
So 150 gal of the total 1000 gal of solution is cherry syrup, or (150 gal)/(1000 gal) = 15/100 = 15% of the mixture.
Answer:
204
Step-by-step explanation:
