Answer:
0.492
Step-by-step explanation:
According to the given situation, the calculation of Δy and dy is shown below:-
![y = e^x, x = o, \Delta x = 0.6](https://tex.z-dn.net/?f=y%20%3D%20e%5Ex%2C%20x%20%3D%20o%2C%20%5CDelta%20x%20%3D%200.6)
![dy = f'(x) = e^x](https://tex.z-dn.net/?f=dy%20%3D%20f%27%28x%29%20%3D%20e%5Ex)
![dy = e^x dx](https://tex.z-dn.net/?f=dy%20%3D%20e%5Ex%20dx)
![= e^x (0.4)](https://tex.z-dn.net/?f=%3D%20e%5Ex%20%280.4%29)
![dy = 0.4e^x](https://tex.z-dn.net/?f=dy%20%3D%200.4e%5Ex)
![\Delta y = f(0.4) - f(0)](https://tex.z-dn.net/?f=%5CDelta%20y%20%3D%20f%280.4%29%20-%20f%280%29)
![= e^{0.4} - e^0](https://tex.z-dn.net/?f=%3D%20e%5E%7B0.4%7D%20-%20e%5E0)
Now we use the scientific calculator or spreadsheet to determine the exponential value
= 1.491824698 - 1
= 0.491824698
or
= 0.492
Therefore for computing the Δy and dy we simply applied the above formula.
Hence, the answer is 0.4918
Answer:
Option (2)
Step-by-step explanation:
Since, rotation of any figure is a rigid transformation, side lengths and measure of angles of the image polygon after rotation will remain same.
NP = N'P'
Coordinates of N → (5, 9)
Coordinates of P → (7, 9)
Formula of distance between two points
and
is,
d = ![\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
By this formula length of NP = ![\sqrt{(7-5)^2+(9-9)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%287-5%29%5E2%2B%289-9%29%5E2%7D)
= 2 units
Therefore, Option (2) will be the correct option.
Answer: D. It depends on the cost of the shirt as to which coupon will help John pay the lowest price.
Step-by-step explanation:
You do not know how much a 20% discount is unless you know the price of the shirt. This can be more or less than $20, so you don’t know.
Hope this helps!
Answer:
See a solution process below:
Explanation:
Let's call the number of miles driven we are looking for
m
.
The the total cost of ownership for the first car model is:
12000
+
0.1
m
The the total cost of ownership for the second car model is:
14000
+
0.08
m
We can equate these two expressions and solve for
m
to find after how many miles the total cost of ownership is the same:
12000
+
0.1
m
=
14000
+
0.08
m
Next, we can subtract
12000
and
0.08
m
from each side of the equation to isolate the
m
term while keeping the equation balanced:
−
12000
+
12000
+
0.1
m
−
0.08
m
=
−
12000
+
14000
+
0.08
m
−
0.08
m
0
+
(
0.1
−
0.08
)
m
=
2000
+
0
0.02
m
=
2000
Now, we can divide each side of the equation by
0.02
to solve for
m
while keeping the equation balanced:
0.02
m
0.02
=
2000
0.02
0.02
m
0.02
=
100000
After 100,000 miles the total cost of ownership of the two cars would be the same.