Answer:
No solution.
Step-by-step explanation:
Simplify. Combine like terms:
-10 = -14v + 14v
-10 = (-14v + 14v)
-10 = (0)
-10 ≠ 0 ∴ no solution is your answer.
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Answer:
Step-by-step explanation:
Let the rent be x
<u>Discounted rent </u>
<u>Increase applied</u>
<u>Final rent:</u>
- (x - 50) + 10% = (x - 50)*1.1
<u>We know this is equal to x + 5% = 1.05x, comparing now</u>
- 1.1(x - 50) = 1.05x
- 1.1x - 1.05x = 55
- 0.05x = 55
- x = 55/0.05
- x = $1100
To evaluate
![\lim_{\theta \to 0} \frac{\sin\theta}{\theta}](https://tex.z-dn.net/?f=%20%5Clim_%7B%5Ctheta%20%5Cto%200%7D%20%20%5Cfrac%7B%5Csin%5Ctheta%7D%7B%5Ctheta%7D%20)
First, we input 0, for theta in the function to obtain:
![\frac{\sin0}{0} = \frac{0}{0}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%5Csin0%7D%7B0%7D%20%3D%20%5Cfrac%7B0%7D%7B0%7D%20)
This is an indeterminate form.
So, we apply L'Hopital's rule by differentiating the numerator and the denominator as follows:
Total number of stocks bought = 20
Rate at which each stocks were bought = 31 1/2
= 63/2
Rate at which 20 stocks were bought = 20 * (63/2) dollars
= 10 * 63 dollars
= 630 dollars
Rate at which each stocks were sold = 35 1/4
= 141/4 dollars
Rate at which 20 stocks were sold = 20 * (141/4) dollars
= 5 * 141 dollars
= 705 dollars
Then
Amount of profit made by selling 20 stocks = (705 - 630) dollars
= 75 dollars
So the total amount of profit made is $75. The correct option in regards to the given question is option "D".
Answer:
The distance of the helicopter from the bristol is approximately 1<u>2.81 miles</u>
Step-by-step explanation:
Given:
Helicopter flies 10 miles east of bristol.
Then the helicopter flies 8 miles North before landing.
To find the direct distance between the helicopter and bristol.
Solution:
In order to find the distance of the helicopter from the bristol before landing, we will trace the path of the helicopter
The helicopter is first heading 10 miles east of bristol and then going 8 miles due north.
On tracing the path of the helicopter we find that the direct distance of the helicopter from the bristol is the hypotenuse of a right triangle formed by enclosing the path of the helicopter.
Applying Pythagorean theorem to find the hypotenuse of the triangle.
![Hypotenuse^2=Short\ leg^2+Shortest\ leg^2](https://tex.z-dn.net/?f=Hypotenuse%5E2%3DShort%5C%20leg%5E2%2BShortest%5C%20leg%5E2)
![Hypotenuse^2=10^2+8^2](https://tex.z-dn.net/?f=Hypotenuse%5E2%3D10%5E2%2B8%5E2)
![Hypotenuse^2=100+64\\Hypotenuse^2=164](https://tex.z-dn.net/?f=Hypotenuse%5E2%3D100%2B64%5C%5CHypotenuse%5E2%3D164)
Taking square root both sides.
![\sqrt{Hyptenuse^2}=\sqrt{164}\\Hypotenuse = 12.81\ miles](https://tex.z-dn.net/?f=%5Csqrt%7BHyptenuse%5E2%7D%3D%5Csqrt%7B164%7D%5C%5CHypotenuse%20%3D%2012.81%5C%20miles)
Thus, the distance of the helicopter from the bristol is approximately 12.81 miles