No Alan did not break even
Alan incured a loss of 6.25 %
<em><u>Solution:</u></em>
Given that,
Alan bought two bikes
He sold one to Beth for $300 taking a 25% loss
He also sold one to Greta for $300 making a 25% profit
When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then the seller always incurs a loss
Which is given as:

Here, x = 25

Thus the loss percentage is 6.25 %
I attached the picture associated with this question.
Answer:x = 2
y = 5
Explanation:ABCD is a parallelogram. This means that each two opposite sides are equal.
This means that:1- AB = CD2y + 1 = 7x - 3 ...........> equation I
2- AD = BC3x = y + 1
This can be rewritten as:y = 3x - 1............> equation II
Substitute with equation II in equation I and solve for x as follows:2y + 1 = 7x - 3 ...........> equation I
2(3x - 1) + 1 = 7x - 3
6x - 2 + 1 = 7x - 3
6x - 1 = 7x - 3
7x - 6x = -1 + 3
x = 2
Substitute with x in equation I to get y as follows:y = 3x - 1
y = 3(2) - 1
y = 6 - 1
y = 5
Hope this helps :)
Answer:
3y + 2x = 5
Step-by-step explanation:
3x-2y = -2
2y = 3x + 2
y = (3/2)x + 1
Slope is 3/2
Slope of the Perpendicular line is -2/3
y = (-2/3)x + c
x = -2 , y = 3
3 = (-2/3)(-2) + c
3 = 4/3 + c
c = 3 - 4/3 = 5/3
y = (-2/3)x + 5/3
3y = -2x + 5
3y + 2x = 5
Answer:
(-1.703, 2.396)
(1.37, 6.493)
Step-by-step explanation:
We can easily solve this question by using a plotting tool or any graphing calculator,
The solution to the system of equation is given by the intersection points between the graphs of
y1 = −x^2 + x + 7
y2 = x^2 + 3x + 7
Please, see attached picture below.
The solutions are:
(-1.703, 2.396)
(1.37, 6.493)
Answer:
Equation of tangent plane to given parametric equation is:

Step-by-step explanation:
Given equation
---(1)
Normal vector tangent to plane is:


Normal vector tangent to plane is given by:
![r_{u} \times r_{v} =det\left[\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\cos(v)&sin(v)&0\\-usin(v)&ucos(v)&1\end{array}\right]](https://tex.z-dn.net/?f=r_%7Bu%7D%20%5Ctimes%20r_%7Bv%7D%20%3Ddet%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Chat%7Bi%7D%26%5Chat%7Bj%7D%26%5Chat%7Bk%7D%5C%5Ccos%28v%29%26sin%28v%29%260%5C%5C-usin%28v%29%26ucos%28v%29%261%5Cend%7Barray%7D%5Cright%5D)
Expanding with first row

at u=5, v =π/3
---(2)
at u=5, v =π/3 (1) becomes,



From above eq coordinates of r₀ can be found as:

From (2) coordinates of normal vector can be found as
Equation of tangent line can be found as:
