Answer:
x = -2
Step-by-step explanation:
- 3 x - 6x = -18x
- 4 - 18x + 9 = 41
9 - 4 = 5
- 18x + 5 = 41
- 18x = 41 - 5
- 18x = 36
36 divided by -18 is -2
Answer:
a
Step-by-step explanation:
Answer:
The boat is approaching the dock at rate of 2.14 ft/s
Step-by-step explanation:
The situation given in the question can be modeled as a triangle, please refer to the attached diagram.
A rope attached to the bow of the boat is drawn in over a pulley that stands on a post on the end of the dock that is 5 feet higher than the bow that means x = 5 ft.
The length of rope from bow to pulley is 13 feet that means y = 13 ft.
We know that Pythagorean theorem is given by
![x^{2} + y^{2} = z^{2}](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%20y%5E%7B2%7D%20%3D%20z%5E%7B2%7D)
Differentiating the above equation with respect to time yields,
![2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 2z\frac{dz}{dt}](https://tex.z-dn.net/?f=2x%5Cfrac%7Bdx%7D%7Bdt%7D%20%20%2B%202y%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%202z%5Cfrac%7Bdz%7D%7Bdt%7D)
![x\frac{dx}{dt} + y\frac{dy}{dt} = z\frac{dz}{dt}](https://tex.z-dn.net/?f=x%5Cfrac%7Bdx%7D%7Bdt%7D%20%20%2B%20y%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%20z%5Cfrac%7Bdz%7D%7Bdt%7D)
dx/dt = 0 since dock height doesn't change
![y\frac{dy}{dt} = z\frac{dz}{dt}](https://tex.z-dn.net/?f=y%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%20z%5Cfrac%7Bdz%7D%7Bdt%7D)
![\frac{dy}{dt} = \frac{z}{y} \frac{dz}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%20%5Cfrac%7Bz%7D%7By%7D%20%5Cfrac%7Bdz%7D%7Bdt%7D)
The rope is being pulled in at a rate of 2 feet per second that is dz/dt = 2 ft/s
First we need to find z
z² = (5)² + (13)²
z² = 194
z = √194
z = 13.93 ft
So,
![\frac{dy}{dt} = \frac{z}{y} \frac{dz}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%20%5Cfrac%7Bz%7D%7By%7D%20%5Cfrac%7Bdz%7D%7Bdt%7D)
![\frac{dy}{dt} = \frac{13.93}{13}(2)](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%20%5Cfrac%7B13.93%7D%7B13%7D%282%29)
![ft/s](https://tex.z-dn.net/?f=ft%2Fs)
Therefore, the boat is approaching the dock at rate of 2.14 ft/s
Answer:
the answer is X
Step-by-step explanation:
it is x
Answer:
Step-by-step explanation:
The formula for determining simple interest is expressed as
I = PRT/100
Where
P represents the principal or initial amount invested or collected as a loan.
R represents interest rate.
T represents the duration of time in years before the loan is bald back.
From the information given,
P = 1290
I = 5.75
Since there are 365 days in a year,
t = 65/365 = 0.1781 years
Therefore,
5.75 = (1290 × r × 0.1781)/100
5.75 = 229.749r/100 = 2.29749r
r = 5.75/2.29749
r = 2.5027
Rounding to the nearest percent,
r = 3%