Answer:
$11,500 was invested at 13%.
$17,500 was invested at 4%
Step-by-step explanation:
This is a simple interest problem.
The simple interest formula is given by:
In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
After t years, the total amount of money is:
In this question:
Loans totaling 29,000.
P was invested at 13%
29000 - P was invested at 4%.
First investment:
Principal P.
Interest 13% = 0.13.
One year, so t = 1.
So
Second investment:
Principal 29000 - P.
Interest 4% = 0.04.
One year, so t = 1.
So
The total interest earned for both loans was $2,195.00.
This means that 
So
So we solve the following system:
$11,500 was invested at 13%.
29000 - 11500 = 17500
$17,500 was invested at 4%
Answer:
c. (4,3)
Step-by-step explanation:
If you look at all the rest of the coordinates, compared to (4,3). None of them are in the red area. They are either in the blue, or the orange. To be a solution it has to be in both areas, (the red). Hope this helps!
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>
Answer:
11/60
Step-by-step explanation:
It is convenient to use the relationship between sine, cosine, and tangent.
tan(x) = sin(x)/cos(x) = (11/61)/(60/61)
tan(x) = 11/60
Answer:
2.25
Step-by-step explanation:
-9/-4= 2.25
