Answer:
The number of big pictures are 49 and number of small pictures are 48 .
Step-by-step explanation:
Let us assume that the number of big pictures are x .
Let us assume that the number of small pictures are y .
As given
Big pictures are 56$ each small ones are 34$.
97 were sold at the total of $4,376.
Equations becomes
x + y = 97
56x + 34y = 4376
Multiply x + y = 97 by 56 and subtracted from 56x + 34y = 4376 .
56x - 56x + 34y - 56y = 4376 - 5432
-22y = - 1056
22y = 1056
y = 48
Put value of y in the equation x + y = 97
x + 48 =97
x = 97 - 48
x = 49
Therefore the number of big pictures are 49 and number of small pictures are 48 .
8/7= 7/2x
2x= 16*7/8
2x =14
X=7
The maximum angle of repose is the<span> maximum angle at which a material can be piled without slumping. The material piled up will form a cone.
If we project the situation on a 2D plane, we get a triangle rectangle (see picture attached). We know one angle and the Opposite side (height) and we need to find the Adjacent side (radius).
Recalling trigonometry formulae:
tan</span>α = O / A
Solving for A:
A = O / tan<span>α
We can now substitute our data (O = 20):
</span>1) Sand, Bank Damp
<span>α = 45°
A = 20 / tan(45)
= 20
The radius is
20 feet.
</span>
2)Sand, Bank Dry
α = 35°
A = 20 / tan(35)
= 28.5629
The radius is
28.6 feet.
3) Sand, core
α = 41°
A = 20 / tan(41)
= 23.0074
The radius is
23 feet.
4) Sand, foundry prepared
α₁ = 30°
A₁ = 20 / tan(30)
= 34.6410
α₂ = 44°
A₂ = 20 / tan(44)
= 20.7106
The radius is between
20.7 and 34.6 feet.
5) Sand, Foundry shakeout
α = 39°
A = 20 / tan(39)
= 24.6979
The radius is
24.7 feet<span>.</span>
Total time = upstream time + downstream time
he rowed the same distance both ways.
upstream time = D/4
downstream time = D/6
total time = D/4 + D/6 = 3D/12 + 2D/12 = 5D/12 = 3 hours
D = 3*12/5 = 36/5 or 7.2 miles
where D is the one-way distance. The total distance he rowed is 2*D = 72/5 or 14.4 miles
