Answer:
P = $80
Step-by-step explanation:
I = P*r*t
P = I/rt
Where,
simple interest, I = $20
Interest rate, r = 5%
Time, t = 5 years
P = I / rt
= 20 / 5% * 5
= 20 / 0.05 * 5
= 20 / 0.25
= 80
P = $80
Answer:
2r (1 + √3)
Step-by-step explanation:
Circle O₁ is tangent to AB. Let's call the point of intersection point D. If we draw a radius from the center O₁ to D, we know this forms a right angle.
△ABC is an equilateral triangle, so we know m∠A = 60°. If we draw a line from A to O₁, we know that bisects the angle, so m∠DAO₁ = 30°.
So △DAO₁ is a 30-60-90 triangle. We can find the length AD:
AD = r √3
Now on the other side, circle O₃ is tangent to AB. Let's call the point of intersection point E. We know it's the same triangle we found earlier, so:
EB = r √3
And finally, we can draw a rectangle connecting O₁, O₃, E, and D. The distance between O₁ and O₃ is 2r, so:
DE = 2r.
Therefore:
AB = r√3 + 2r + r√3
AB = 2r√3 + 2r
AB = 2r (1 + √3)
Here's a graph showing the steps. Hopefully this helps, let me know if you have questions!
desmos.com/calculator/hgaonfzxsm
If you're using the app, try seeing this answer through your browser: brainly.com/question/2887301—————
Solve the initial value problem:
dy——— = 2xy², y = 2, when x = – 1. dxSeparate the variables in the equation above:

Integrate both sides:


Take the reciprocal of both sides, and then you have

In order to find the value of
C₁ , just plug in the equation above those known values for
x and
y, then solve it for
C₁:
y = 2, when
x = – 1. So,


Substitute that for
C₁ into (i), and you have

So
y(– 2) is

I hope this helps. =)
Tags: <em>ordinary differential equation ode integration separable variables initial value problem differential integral calculus</em>
Step-by-step answer:
Given:
mean, mu = 200 m
standard deviation, sigma = 30 m
sample size, N = 5
Maximum deviation for no damage, D = 100 m
Solution:
Z-score for maximum deviation
= (D-mu)/sigma
= (100-200)/30
= -10/3
From normal distribution tables, the probability of right tail with
Z= - 10/3
is 0.9995709, which represents the probability that the parachute will open at 100m or more.
Thus, by the multiplication rule, the probability that all five parachutes will ALL open at 100m or more is the product of the individual probabilities, i.e.
P(all five safe) = 0.9995709^5 = 0.9978565
So there is an approximately 1-0.9978565 = 0.214% probability that at least one of the five parachutes will open below 100m
Answer:
B. Carl yearns more per hour
C. put line through points (1,15) and 3,45) on graph and you will have Carl's earnings per hr.
Step-by-step explanation:
Louis earns 12$ per hr (y=12x)
Carl yearns 15$ per hr (y=15x)
to find what carl yearns hourly you divide 45 by 3 which is 15.
(Explaination of answer for question b)
C isnt hard once you find y=15x.