Answers
Answer:
sin(α+β)/sin(α-β) ==(tan α+tan β)/(tan α-tan β )
Step-by-step explanation:
We have to complete
sin(α+β)/sin(α-β) = ?
The identities that will be used:
sin(α+β)=sin α cos β+cos α sin β
and
sin(α-β)=sin α cos β-cos α sin β
Now:
= sin(α+β)/sin(α-β)
=(sin α cos β+cos α sin β)/(sin α cos β-cos α sin β)
In order to bring the equation in compact form we wil divide both numerator and denominator with cos α cos β
= (((sin α cos β+cos α sin β))/(cos α cos β ))/(((sin α cos β-cos α sin β))/(cos α cos β))
=((sin α cosβ)/(cos α cos β )+(cos α sin β)/(cos α cos β ))/((sin α cos β)/(cos α cos β )-(cos α sin β)/(cos α cos β))
=(sin α/cos α + sin β/cos β )/(sin α/cos β - sin β/cos β)
=(tan α+tan β)/(tan α-tan β )
So,
sin(α+β)/sin(α-β) ==(tan α+tan β)/(tan α-tan β)
Related Questions
Use the equation of the water level of the river represented by the equation y=-4x + 170, where x represents the
number of years and y represents the total feet. What points are located on the line?
Check all that apply.
(170,0)
(0,170)
(12, 126)
(50,30)
(5, 150)
(60,-70)
Answers
Answer:
(0,170) and (60,-70) and (5, 150)
Step-by-step explanation:
To see if a given point is on the line or not, you just have to enter the x value (first value in the parenthesis) and see if the function returns the correct y value (second number in the parenthesis).
f(x) = -4x + 170
(170,0) => -4 (170) + 170 = -680 + 170 = 510. NO, not equal to 0.
(0,170) => -4 (0) + 170 = 0 + 170 = 170. YES
(12, 126) => -4 (12) + 170= -48 + 170= 122. No, not equal to 126.
(50,30) => -4(50) + 170 = -200 + 170 = 130. No, not equal to 30.
(5, 150) => -4(5) + 170 = -20 + 170 = 150. YES
(60,-70) => -4(60) + 170 = -240 + 170 = -70. YES
Answer:
(0,170) and (60,-70) and (5, 150)
Step-by-step explanation:
Select the margin of error that corresponds to the sample mean that corresponds to each population:
A population mean of 25, a standard deviation of 2.5, and margin of error of 5%
1. 30
2. 25
3. 20
Answers
Answer:
25
Step-by-step explanation:
which expression or expressions have thw same value a as 12. 2
Answers
Answer:
B, C
Step-by-step explanation:
The values of the expressions are ...
A:
20^2 -18^2 = (20 -18)(20 +18) = 2·38 = 4·19 ≠ 12^2 = 4·36
__
B:
8(4^2) +2^4 = 8(4^2) +4^2 = (8+1)·4^2 = (3·4)^2 = 12^2
__
C:
15^2 -3^4 = 15^2 -9^2 = (15 -9)(15 +9) = 6·24 = 6·2·12 = 12^2
Drag and drop a statement or reason to each box to complete the proof.
Given: parallelogram MNPQ
Prove: ∠N≅∠Q
Answers
Answer:
1. MN≅QP
MQ≅NP
2. MP≅MP
3. SSS congruence postulate
4. ∠N≅∠Q
5. CPCTC
Step-by-step explanation:
1. As per the property of parallelogram that opposite sides are congruent, in given case of parallelogram MNPQ the opposite sides
MN≅QP and MQ≅NP.
2. The reflexive property of congruence states that a line or a geometrical figure is reflection of itself and is congruent to itself. Hence in given case of parallelogram MNPQ
MP≅MP
3. SSS congruence postulate stands for Side-Side-Side congruence postulate, it states that when three adjacent sides of two triangle are congruent then the two triangles are congruent. In given case of parallelogram MNPQ, as the sides MN≅Q, MQ≅NP and MP≅MP hence
ΔMQP≅ΔPNM
5. As proven in part 4 that ΔMQP is congruent to ΔPNM, so as per the property of CPCTC (congruent parts of congruent triangles are congruent)
∠N≅∠Q
5. CPCTC stands for congruent parts of congruent triangles are congruent.
!
Which of the following represent(s) an equation of the line passing through the points A(5, 6) and B(4, 8). Select all that apply.
Answers
For this case we have that the equation of a straight line in the form of an intersection is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cutoff point with the y axis
We found the slope:
[tex]m = \frac {y2-y1} {x2-x1} = \frac {8-6} {4-5} = \frac {2} {- 1} = - 2[/tex]
So, the line is:
[tex]y = -2x + b[/tex]
We find the cut point by substituting a point:
[tex]8 = -2 (4) + b\\8 = -8 + b\\b = 8 + 8\\b = 16[/tex]
Finally, the equation is:
[tex]y = -2x + 16[/tex]
We can also have the equation of the point-slope form:
[tex]y-y_ {0} = m (x-x_ {0})[/tex]
Where:
[tex](x_ {0}, y_ {0}) = (4,8)[/tex]represents a point:
So:
[tex]y-8 = -2 (x-4)[/tex]
ANswer:
[tex]y-8 = -2 (x-4)\\y = -2x + 16[/tex]
write a function to model the situation.
a box is w inches wide. the box is twice as long as it is wide and 3.5 times as tall as it is wide. write a function to model the volume (v) of the box in cubic inches as a function of its width.
please help and thank you!
Answers
Answer:
v(w) = 7w³
Step-by-step explanation:
The formula for the volume of a cuboid (rectangular prism, or box) is ...
V = LWH . . . . . . where L represent length, W represents width, and H represents height
The problem statement tells you that for a box of width w (in inches), the length is 2w, and the height is 3.5w. Using these values in the formula, we have ...
V = (2w)(w)(3.5w)
V = 7w³
Written as a function v(w), volume as a function of width, this is ...
v(w) = 7w³
Find all values of k for which the equation 3x2−(k+2)x+k−1=0 has no solutions.
Answers
Answer:
there are solutions for all values of k
Step-by-step explanation:
In order for there to be no real solutions, the value of the discriminant must be negative. For this equation, the discriminant is ...
(-(k+2))^2 -4(3)(k-1)
We want to find values of k for which this is negative:
(k^2 +4k +4) -12k +12 < 0
k^2 -8k +16 < 0
(k -4)^2 < 0
A square is never negative, so there are no values of k that result in the equation having no solutions.
I got 140 as my answer before but it said it was incorrect.
Answers
[tex]\bf \begin{bmatrix} 11&-8\\-1&12 \end{bmatrix}\implies \stackrel{Determinant}{(11\cdot 12)-(-1\cdot -8)}\implies 132-(8)\implies 124[/tex]
recall, minus * minus = plus.
Need help! Geometry!
Answers
Answer:
(x, y) ⇒ (-y, x)
Step-by-step explanation:
You can see that the points (1, 2) and (3, 5) get mapped to (-2, 1) and (-5, 3), respectively. That is, the old value y, when negated, is the new value of x; and the old value of x is the new value of y.
___
I find it easier to think of a 270° CW rotation as being the same as a 90° CCW rotation.
Someone help please.
Answers
Answer:
$27
Step-by-step explanation:
If the table was marked up 125%, you can find the retail price of it this way:
20 + 1.25(20) = retail price
$45 = retail price.
To find 40% off of that, use
$45 - .4($45) = sale price
$27 = sale price (aka discount price)
A bus picks Trish up at 9 o’clock. She ate breakfast one hour and 30 minutes earlier. What time did Trish eat breakfast?
Answers
Trish ate her yummy breakfast at 7:30 :)
Answer:
7:30 am
Step-by-step explanation:
Subtract 90 minutes from 9:00 am to determine what time Trish ate breakfast.
By 6 months, cubs can eat their adult diet of bamboo and fiber biscuits. An adult red panda might eat 1,100 grams of food per day made up of 23% biscuits, 73% bamboo, and the rest in fruit. Write and evaluate an expression to calculate how many grams of fruit an adult red panda eats in 3 weeks?
Answers
Explanation:
First we need to find the amount of the diet that is fruit. (It is what is not biscuits or bamboo.) The quantity is given per day, so we need to multiply that by the number of days in 3 weeks.
(1 - 23% -73%)·(1100 g/day)·(7 day/week)·(3 week) = (44 g/day)·(21 day)
= 924 g . . . . of fruit
If possible, please help me with this problem. I do not understand what method and such.
Answers
Answer:
14 m^2
Step-by-step explanation:
The method used to find the area of this trapezoid is to put the given numbers into the formula for the area of a trapezoid. That formula is ...
A = (1/2)(b1 +b2)h
where b1 and b2 are the lengths of the parallel bases, and h is the perpendicular distance between them.
The figure shows you that b1 and b2 are 5 m and 2 m (in no particular order) and h is 4 m. Putting these numbers into the formula gives ...
A = (1/2)(5 m + 2m)(4 m) = (1/2)(28 m^2) = 14 m^2
8. Janine has 3/5
of a pound of peanuts to divide equally between 2 friends.
a. What is the weight of peanuts in pounds that each friend will
receive?
b. One of Janine's friends already had 3/4 pounds of peanuts before Janine gave her more. However, this friend wants to end with 2 pounds of peanuts. How much more pounds of peanuts does this friend need to get to end up with 2 pounds of peanuts?
Answers
Answer:
Part a) Each friend will receive [tex]\frac{3}{10}\ pounds[/tex]
Part b) [tex]\frac{19}{20}\ pounds[/tex] or [tex]0.95\ pounds[/tex]
Step-by-step explanation:
Part a)
we know that
To calculate the weight of peanuts in pounds that each friend will
receive, divide the total pounds of peanuts by two
so
[tex]\frac{(3/5)}{2}=\frac{3}{10}\ pounds[/tex]
Part b)
Let
x-----> pounds of extra peanuts the friend needs to end up with 2 pounds of peanuts
we know that
[tex]2=x+\frac{3}{10}+\frac{3}{4}[/tex]
Solve for x
[tex]x=2-(\frac{3}{10}+\frac{3}{4})[/tex]
Multiply by 40 both sides
[tex]40x=80-(12+30)[/tex]
[tex]40x=38[/tex]
[tex]x=\frac{38}{40}\ pounds[/tex]
Simplify
[tex]x=\frac{19}{20}\ pounds[/tex] or [tex]x=0.95\ pounds[/tex]
Which relationship describes angles 1 and 2
Answers
Answer: First option and Third option
Step-by-step explanation:
You can observe in the figure that the angle 1 and the angle 2 have a common vertex and a common side. These kind of angles are known as "adjacent angles".
You can observe that the intersection of the lines forms four equal anles wich are right angles (Angles of 90 degrees). Thererefore, the angles 1 and 2 and also "complementary angles", because the sum of them is 90 degrees.
Then, the answers are the first option and the third option.
Amira pulls a 3 pound wagon 4 feet. How much work has she done?
3 ft-lbs.
4 ft-lbs.
7 ft-lbs.
12 ft-lbs.
Answers
Answer:
12 ft-lbs is your answer
12ft-lbs that she has done
Find the area of a parallelogram if a base and corresponding altitude have the indicated lengths.
Base 1 1/2 feet, altitude 6 inches.
Answers
Answer:
The area of the parallelogram is 108 inches² OR 0.75 foot²
Step-by-step explanation:
* Lets revise the properties of the parallelogram
- Each two opposite bases are are parallel
- Each two opposite bases are equal in length
- Each two opposite angles are equal in measure
- Each two adjacent angles are supplementary (their sum = 180°)
- Its two diagonals bisect each other
- Each base has an altitude (height) drawn from the opposite
base to it
* Look to the attached figure to more understand
- The area of the parallelogram is the product of the length of one
of its base and the corresponding altitude (height)
∵ Area = B1 × H1 ⇒ OR ⇒ Area = B2 × H2
∵ B1 = 1 1/2 feet
∵ H1 = 6 inches
- The base and the height have different units, so we must
change the unit of one of them to the other
∵ 1 foot = 12 inches
∵ B1 = 1 1/2 = 1.5 feet
∴ B1 = 1.5 × 12 = 18 inches
∴ A = 18 × 6 = 108 inches²
* The area of the parallelogram is 108 inches²
OR
∵ B1 = 1 1/2 = 1.5 feet
∵ H1 = 6 inches
∴ H1 = 6 ÷ 12 = 1/2 = 0.5 foot
∴ A = 1.5 × 0.5 = 0.75 foot²
* The area of the parallelogram is 0.75 foot²
Answer:
108 square inches
Step-by-step explanation:
We know that the formula of area of a parallelogram is given by:
A = base × altitude
Since here we have different units for base and altitude, so either we will change the base to inches or the altitude to feet.
Base = [tex]1\frac{1}{2} ft = 1.5 ft[/tex]
[tex]\frac{1}{1.5ft} =\frac{12inches}{x}[/tex]
Base (x) = 18 inches
Substituting the values in the above formula to get:
Area of parallelogram = 18 × 6 = 108 square inches
A sixth grade teacher can grade 25 HW assignments in 20 minutes. Is he working at a faster rate or slower rate than grading 36 HW assignments in 30 minutes?
Answers
Answer:
im not sure but he is grading assignments at a faster rate
Step-by-step explanation:
25/20=1.25 so 1.25 mins per hw assignment
36/30=1.20 so 1.20 mins per hw assignment
it takes him 5 more seconds to grade 36 hw assignments so he's going at a faster rate
hope this helps :)
what is 6tens + 6 ones
Answers
Answer:
66
6 x 10=60
6 x 1=6
60+6=66
Have a good day!!! <3 Hope this helped ma dude :)
Graph the image of the figure after a dilation with a scale factor of 2 centered at (−7, −2) .
Use the Polygon tool to graph the quadrilateral by connecting all its vertices.
Answers
Answer:
See image and explanation
Step-by-step explanation:
Point (-7,-2) is the center of dilation. The scale factor is 2.
If point A has coordinates (-3,-2), then its image point H has coordinates (1,-2).
If point B has coordinates (-6,2), then its image point E has coordinates (-5,6).
If point C has coordinates (-4,3), then its image point F has coordinates (-1,8).
If point D has coordinates (-1,1), then its image point G has coordinates (5,4).
Answer:
hope this helps :)
Step-by-step explanation:
Mrs. Varner deposited q dollars in a bank account that has been earning annual interest. The total value of the account is based on the function f(x) = q • 1.025x, where x represents the number of years the money has been in the account. If no deposits or withdrawals are made after the initial deposit, which equation represents the total value of the account 5 years from now? f(x) = q • 1.025x + 5 f(x) = q • 1.025x + 5 f(x) = q • 1.025x – 5 f(x) = q • 1.025x – 5
Answers
Answer:
f(x) = q • 1.025x + 5
Step-by-step explanation:
Mrs. Varner deposited q dollars in a bank account that has been earning annual interest.
The total value of the account is based on the function f(x) = q • 1.025x
where x represents the number of years the money has been in the account.
If no deposits or withdrawals are made after the initial deposit, the equation that represents the total value of the account 5 years from now is :
f(x) = q • 1.025x + 5
Answer:
b
Step-by-step explanation:
Use the Divergence Theorem to calculate the surface integral S F · dS; that is, calculate the flux of F across S. F(x, y, z) = (cos(z) + xy2) i + xe−z j + (sin(y) + x2z) k, S is the surface of the solid bounded by the paraboloid z = x2 + y2 and the plane z = 4.
Answers
The divergence of the vector field [tex]\vec F[/tex] is
[tex]\nabla\cdot\vec F=y^2+0+x^2=x^2+y^2[/tex]
By the divergence theorem,
[tex]\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\iiint_V(x^2+y^2)\,\mathrm dV[/tex]
where [tex]V[/tex] denotes the region with boundary [tex]S[/tex]. Convert to cylindrical coordinates:
[tex]x=u\cos v[/tex]
[tex]y=u\sin v[/tex]
[tex]z=z[/tex]
The integral is then
[tex]\displaystyle\int_0^{2\pi}\int_0^2\int_{u^2}^4u^3\,\mathrm du\,\mathrm dv=\frac{32\pi}3[/tex]
Using the Divergence Theorem, the flux of the vector field F across the surface S can be calculated by finding the dot product of F and the outward-pointing unit normal vector to the surface. This concept is similar to that of a Gaussian surface in physics, which is used to analyze the flux of electric fields.
Explanation:In this problem, you are required to use the Divergence Theorem in order to calculate a surface integral, specifically the flux of the vector field F across a defined surface S. At a basic level, the Divergence Theorem states that the flux of a vector field through a closed surface is equal to the triple integral of the divergence of the field over the volume enclosed by the surface.
In this specific scenario, we have the vector field F(x, y, z) = (cos(z) + xy²) i + xe⁻ᶻ j + (sin(y) + x²z) k, and the surface S is bounded by the paraboloid z = x² + y² and the plane z = 4. To calculate the surface integral, you would first express these surfaces parametrically and then find the outward pointing unit normal vector to the surface. The dot product of F and this normal vector will give the amount of F flowing across an infinitesimal element of the surface, which when integrated over the entire surface, yields the flux of F across S.
This process is similar to the concept of Gaussian surface, which is used to calculate the flux of an electric field. In both cases, we're examining how a field interacts with a defined space or volume.
Learn more about Divergence Theorem here:https://brainly.com/question/31272239
#SPJ3
a car gets 36 miles to the gallon. How many miles can the car travel on six and ¾ gallon of gasoline?
Answers
For this case we have a mixed number given by:
[tex]6 \frac {3} {4} = \frac {6 * 4 + 3 * 1} {4} = \frac {27} {4}[/tex]
We make a rule of three to get the miles that the car can travel.
36 ---------> 1
x ------------> [tex]\frac {27} {4}[/tex]
Where "x" represents the variable that gives the number of miles that the car can travel with [tex]\frac{27}{4}[/tex]gallons of gasoline
[tex]x = \frac {\frac {27} {4} * 36} {1}\\x = 243[/tex]
So, the car can travel 243 miles
ANswer:
243 miles
Use the graph to determine the number of solutions the system has. x=4 y=x+3
Answers
Answer:
Final answer is x=4, y=7.
Step-by-step explanation:
Questions says to use the graph to determine the number of solutions the system has. where system of equations are x=4 and y=x+3
any equation of the form x=k is a vertical line crossing x-axis at k.
So x=4 is a vertical line crossing x-axis at 4.
y=x+3 has slope m=1 and y-intercept b=3
So it passes through point (0,3) and for slope m=1, rise 1 up then 1 right to get new point.
Then final graph is given as shown in the picture.
We can see that both lines intersect at point (4,7).
Hence final answer is x=4, y=7.
PLEASE HELP AND THANK YOU
Answers
Answer:
• n(t) = 150·2^t . . . . . . . . . . . . number of cells after t minutes
• a(t) = π(0.25 +0.50t)^2 . . . . area in cm^2 after t minutes
• d(t) = n(t)/a(t) = (2400·2^t)/(π(1+2t)^2)
Step-by-step explanation:
The number of cells (n(t)) is described by an exponential function of time (t) with an initial value of 150 and a growth factor of 2 each minute:
n(t) = 150·2^t . . . . . . n in cells; t in minutes
___
The area of the culture is given by ...
a(t) = π·(r(t))^2 . . . . where r(t) is the radius as a function of time.
The radius is linearly increasing with a rate of increase of 0.50 cm/min, so can be described by ...
r(t) = 0.25 +0.50t
Then the area is ...
a(t) = π·(0.25 +0.50t)^2
A factor of 0.25 can be removed from inside parentheses to make this be ...
a(t) = (π/16)(1 +2t)^2 . . . . . a in cm^2; t in minutes
___
The density is the number of cells divided by the area:
d(t) = n(t) / a(t) = 150·2^t/((π/16)(1 +2t)^2)
Simplifying a bit, this is ...
d(t) = (2400/π)(2^t)/(1 +2t)^2 . . . . . d in cells/cm^2; t in minutes
solve the system of equations using elimination. –9x – 2y = –115 –6x + 2y = –110
Answers
The answers are:
[tex]x=15\\y=-10[/tex]
Why?Solving systems of equations using elimination means multiplying/dividing the factors of the given equations in order to reduce variables and make the isolating process simpler, so, solving we have:
We are given the equations:
[tex]\left \{ {{-9x-2y=-115} \atop {-6x+2y=-110}} \right.[/tex]
We have that the terms that contains the variable "y" are equal with opposite signs, so, we can eliminate both directly, and then, isolate the variable "x", so, solving we have:
[tex]\left \{ {{-9x-2y=-115} \atop {-6x+2y=-110}} \right\\\\\left \{ {{-9x=-115} \atop {-6x=-110}} \right\\\\-9x-6x=-115-110\\\\-15x=-225\\\\x=\frac{-225}{-15}=25[/tex]
Now, that we know "x" we need to substitute it into any of the given equations in order to find "y", so, substituting we have:
[tex]-9x-2y=-115\\\\-9*(15)-2y=-115\\\\-135+115=2y\\\\2y=-20\\\\y=\frac{-20}{2}=-10[/tex]
Hence, we have that:
[tex]x=15\\y=-10[/tex]
Have a nice day!
ANSWER
(15,-10)
EXPLANATION
The given equations are:
–9x – 2y = –115 ...(1)
–6x + 2y = –110...(2)
Add equation (1) from equation (2) to eliminate y.
-9x+-6x=-110+-115
This implies that,
-15x=-225
Divide both sides by -15
[tex]x = 15[/tex]
Put the value of x into equation (2) to find y.
[tex] - 6(15 ) + 2y = - 110[/tex]
[tex] - 90+ 2y = - 110[/tex]
[tex]2y = - 110 + 90[/tex]
[tex]2y = - 20[/tex]
[tex]y = - 10[/tex]
The solution is (15,-10)
Find the coordinates of the points of intersection of the graphs without building them: 5x–4y=16 and x–2y=6
Answers
[tex]\bf \begin{cases} 5x-4y=16\\ \cline{1-1} x-2y=6\\ \boxed{x}=6+2y \end{cases}~\hspace{7em}\stackrel{\textit{substituting \underline{x} in the first equation}}{5\left( \boxed{6+2y} \right)-4y=16} \\\\\\ 30+10y-4y=16\implies 30+6y=16\implies 6y=-14 \\\\\\ y=-\cfrac{14}{6}\implies y=-\cfrac{7}{3}\implies \blacktriangleright y=-2\frac{1}{3} \blacktriangleleft \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{since we know that}}{x=6+2y}\implies x=6+2\left( -\cfrac{7}{3} \right)\implies x=6+\left(-\cfrac{14}{3} \right) \\\\\\ x=6-\cfrac{14}{3}\implies x=\cfrac{18-14}{3}\implies x=\cfrac{4}{3}\implies \blacktriangleright x=1\frac{1}{3} \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left( 1\frac{1}{3} ~,~-2\frac{1}{3}\right)~\hfill[/tex]
(6x – 4) – (2x + 8) is equivalent to:
A. 4(x + 4)
B. 4(x – 1)
C. 4(x – 3)
D. 4(x – 12)
Show Your Work
Answers
Answer:
C. 4(x – 3)
Step-by-step explanation:
(6 x - 4) - (2 x + 8)
6 x - 4 - 2 x - 8
4 x - 12
Factor
4 ( x - 3 )
+4. +4
0. 12
(6x) - (2x+12)
-2x -2x
4x. 0
4x-12
4÷12= 3
4(x-3)
Solve the exponential equation. 125^7x-2 = 150.
A.) -0.1375
B.) 2.1483
C.) 0.4234
D.) 0.4340
Answers
Answer:
D
Step-by-step explanation:
You need to get the x out of the position in which is currently sitting, which is exponential. The only way to get an exponent out from that position is to take the log of both sides. The power rule of logs allows us to move the exponent down in front of the log. Like this:
7x - 2 log (125)=log(150)
Now you want to divide both sides by log(125) to get the 7x - 2 all by itself:
[tex]7x-2=\frac{log(150)}{log(125)}[/tex]
Do that on your calculator and you'll get this:
7x - 2 = 1.037760918
Add 2 to both sides to get
7x = 3.037760918
then divide both sides by 7:
x = .4339 which rounds to .4340
Answer:
D.) -0.1375
Step-by-step explanation:
Help me with ixl please
Answers
Answer:
$5.82
Step-by-step explanation:
A markup or markdown of p% on a price causes that price to be multiplied by ...
(1 + p/100)
The price after the markup 115% is ...
$7.74(1 + 115/100)
And the price after that has been marked down 65% is ...
$7.74(1 +115/100)(1 -65/100) = $7.74×2.15×0.35 ≈ $5.82
The discount price was $5.82.