Answer:
The volume of cone = Maximum holding of glass = 60 cube cm(cm^3)
Step-by-step explanation:
Cone formula:
The radius is 3cm and Volume is 60cm^3.
if pi =~ 3 So the "h" is 6.66 cm.
"h" is distance from cone's head to its base.
The "H"( height of glass) = 6.66 + 7 = 13.6 =~ 14
The unit rate of the parachutist change in height is 11 feet per second.
• In Mathematics, Unitary method is a technique for solving a question by first finding the value of a single unit and then finding the required value by multiplying the number by value of single unit .
• We use unitary method to find the ratio of one thing with respect to other thing.
• There are two types of unitary method one is Direct Variation and the other is Inverse variation.
We have the rate of descend as 44 feet in 4 sec.
So, in 1 second it will be = 44 / 4 = 11 feet.
Which is the unit rate.
Therefore, the unit rate of descend for the parachutist is 11 feet per second.
Learn more about unit rate here:
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5/8- I think that is the right answer
The lengths of sides of a 30°-60°-90° triangle have the ratio 1 : √3 : 2. Multiplying these values by 5 tells you the sides have the lengths 5 : 5√3 : 10.
The length x of the middle-length side is ...
c. 5√3
Answer:
y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1
Step-by-step explanation:
y" + y' + y = 1
This is a second order nonhomogenous differential equation with constant coefficients.
First, find the roots of the complementary solution.
y" + y' + y = 0
r² + r + 1 = 0
r = [ -1 ± √(1² − 4(1)(1)) ] / 2(1)
r = [ -1 ± √(1 − 4) ] / 2
r = -1/2 ± i√3/2
These roots are complex, so the complementary solution is:
y = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t)
Next, assume the particular solution has the form of the right hand side of the differential equation. In this case, a constant.
y = c
Plug this into the differential equation and use undetermined coefficients to solve:
y" + y' + y = 1
0 + 0 + c = 1
c = 1
So the total solution is:
y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1
To solve for c₁ and c₂, you need to be given initial conditions.
