Answer:
We can see that for this case the vertex is [tex] V= (0,0)[/tex]
The values for a and b are:
[tex] a = \sqrt{169}=13, b= \sqrt{25}=1[/tex]
Then the ellipse have the major axis on x.
In order to find the two foci we need to use the following formula:
[tex] c =\sqrt{a^2 -b^2}[/tex]
And replacing we got:
[tex] c =\sqrt{169-25}= \pm 12[/tex]
And then the two foci are (12,0) and (-12,0)
And the covertex are on this case (-13,0) (13,0) and (0,5) (0,-5) on the y axis
Step-by-step explanation:
For this problem we have the following equation given:
[tex]\frac{x^2}{169} + \frac{y^2}{25}= 1[/tex]
If we compare this with the general expression of an ellipse given by:
[tex] \frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}= 1[/tex]
We can see that for this case the vertex is [tex] V= (0,0)[/tex]
The values for a and b are:
[tex] a = \sqrt{169}=13, b= \sqrt{25}=1[/tex]
Then the ellipse have the major axis on x.
In order to find the two foci we need to use the following formula:
[tex] c =\sqrt{a^2 -b^2}[/tex]
And replacing we got:
[tex] c =\sqrt{169-25}= \pm 12[/tex]
And then the two foci are (12,0) and (-12,0)
And the covertex are on this case (-13,0) (13,0) and (0,5) (0,-5) on the y axis
A table of values of a linear function is shown below. Find the output when the input is N. Type your answer in the space provide
Answer:
[tex] -3n - 7 [/tex]
Step-by-step explanation:
Considering the linear function represented in the table above, to find what output an input "n" would give, we need to first find an equation that defines the linear function.
Using the slope-intercept formula, y = mx + b, let's find the equation.
Where,
m = the increase in output ÷ increase in input = [tex] \frac{-13 - (-10)}{2 - 1} [/tex]
[tex] m = \frac{-13 + 10}{1} [/tex]
[tex] m = \frac{-3}{1} [/tex]
[tex] m = -3 [/tex]
Using any if the given pairs, i.e., (1, -10), plug in the values as x and y in the equation formula to solve for b, which is the y-intercept
[tex] y = mx + b [/tex]
[tex] -10 = -3(1) + b [/tex]
[tex] -10 = -3 + b [/tex]
Add 3 to both sides:
[tex] -10 + 3 = -3 + b + 3 [/tex]
[tex] -7 = b [/tex]
[tex] b = -7 [/tex]
The equation of the given linear function can be written as:
[tex] y = -3x - 7 [/tex]
Or
[tex] f(x) = -3x - 7 [/tex]
Therefore, if the input is n, the output would be:
[tex] f(n) = -3n - 7 [/tex]
Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 11 ft high
Answer:
0.0526ft/minStep-by-step explanation:
Since the gravel being dumped is in the shape of a cone, we will use the formula for calculating the volume of a cone.
Volume of a cone V = πr²h/3
If the diameter and the height are equal, then r = h
V = πh²h/3
V = πh³/3
If the gravel is being dumped from a conveyor belt at a rate of 20 ft³/min, then dV/dt = 20ft³/min
Using chain rule to get the expression for dV/dt;
dV/dt = dV/dh * dh/dt
From the formula above, dV/dh = 3πh²/3
dV/dh = πh²
dV/dt = πh²dh/dt
20 = πh²dh/dt
To calculate how fast the height of the pile is increasing when the pile is 11 ft high, we will substitute h = 11 into the resulting expression and solve for dh/dt.
20 = π(11)²dh/dt
20 = 121πdh/dt
dh/dt = 20/121π
dh/dt = 20/380.133
dh/dt = 0.0526ft/min
This means that the height of the pile is increasing at 0.0526ft/min
Help!! It’s much appreciated in this time
Answer: D. y = (x - 3)² + 2
Step-by-step explanation:
Inverse is when you swap the x's and y's and solve for y.
y = [tex]\sqrt{x-2}[/tex] + 3
Swap: x = [tex]\sqrt{y-2}[/tex] + 3
Solve: x - 3 = [tex]\sqrt{y-2}[/tex]
(x - 3)² = [tex](\sqrt{y-2})^2[/tex]
(x - 3)² = y - 2
(x - 3)² + 2 = y
amanda teaches the art of quilling to 4 students. These students each teach art of quilling to 4 other students. If this process continues for 5 generation after amanda, BLANK people other than amanda will know the art of qiulling
Answer:
1024
Step-by-step explanation:
4 * 4 * 4 * 4 * 4
The ratio of boys to girls in Jamal's class is 3:2. If four more girls join the class, there will be the same number of boys and girls. What is the number of boys in the class?
Answer:
4 boys
Step-by-step explanation:
Let x represent boys and y represent girls
Hence, x : y = 3 : 2
x/y = 3/2
2x = 3y ------ (1)
x/y + 4 = 3/3
3x = 3(y + 4)
3x = 3y + 12 --------- (2)
From (1): x = 3y/2
Substitute x into (2) we have:
9y/2 = 3y + 12
9y = 6y + 24
9y - 6y = 24
3y = 24
∴ y = 8
From (2) : 3x = 24 - 12 = 12
∴ x = 4
Hence there Four boys
Calculate the side lengths a and b to two decimal places
A. a= 10.92 b=14.52 <--- My answer
B. a= 11 b= 15
C. a=4.18 b=3.15
D. a= 11.40 b=13.38
Answer:
Option (D)
Step-by-step explanation:
In the picture attached,
An obtuse angle triangle ABC has been given.
By applying Sine rule in the triangle,
[tex]\frac{\text{SinB}}{b}=\frac{\text{SinA}}{a}=\frac{\text{SinC}}{c}[/tex]
Since, m∠A + m∠B + m∠C = 180°
45° + 110° + m∠C = 180°
m∠C = 180°- 155° = 25°
[tex]\frac{\text{Sin110}}{b}=\frac{\text{Sin45}}{a}=\frac{\text{Sin25}}{7}[/tex]
[tex]\frac{\text{Sin110}}{b}=\frac{\text{Sin45}}{a}=0.060374[/tex]
[tex]\frac{\text{Sin110}}{b}=0.060374[/tex]
b = [tex]\frac{\text{Sin110}}{0.060374}[/tex]
b = 15.56
b ≈ 15.56
[tex]\frac{\text{Sin45}}{a}=0.060374[/tex]
a = [tex]\frac{\text{Sin45}}{0.060374}[/tex]
a = 11.712
a = 11.71
Therefore, Option (D) will be the answer.
Perform the indicated operation. kyz * 1/kyz answer choices is 0 1 and k^2 y^2 z^2
Answer:
1
Step-by-step explanation:
[tex]\frac{kyz}{1}*\frac{1}{kyz} =\frac{kyz}{kyz}=1[/tex]
Please HELP best answer will receive a BRAINLIEST. Given the probability density function f ( x ) = 1/3 over the interval [ 4 , 7 ] , find the expected value, the mean, the variance and the standard deviation.
Answer:
[tex] E(X) =\int_{4}^7 \frac{1}{3} x[/tex]
[tex] E(X) = \frac{1}{6} (7^2 -4^2) = 5.5[/tex]
Now we can find the second moment with this formula:
[tex] E(X^2) =\int_{4}^7 \frac{1}{3} x^2[/tex]
[tex] E(X^2) = \frac{1}{9} (7^3 -4^3) = 31[/tex]
And the variance for this case would be:
[tex] Var(X)= E(X^2) -[E(X)]^2 = 31 -(5.5)^2 = 0.75[/tex]
And the standard deviation is:
[tex] Sd(X)= \sqrt{0.75}= 0.866[/tex]
Step-by-step explanation:
For this case we have the following probability density function
[tex] f(x)= \frac{1}{3}, 4 \leq x \leq 7[/tex]
And for this case we can find the expected value with this formula:
[tex] E(X) =\int_{4}^7 \frac{1}{3} x[/tex]
[tex] E(X) = \frac{1}{6} (7^2 -4^2) = 5.5[/tex]
Now we can find the second moment with this formula:
[tex] E(X^2) =\int_{4}^7 \frac{1}{3} x^2[/tex]
[tex] E(X^2) = \frac{1}{9} (7^3 -4^3) = 31[/tex]
And the variance for this case would be:
[tex] Var(X)= E(X^2) -[E(X)]^2 = 31 -(5.5)^2 = 0.75[/tex]
And the standard deviation is:
[tex] Sd(X)= \sqrt{0.75}= 0.866[/tex]
Enter your answer in the box
____
Answer:
[tex]\boxed{2144}[/tex]
Step-by-step explanation:
The sum can be found by adding the parts:
[tex]\sum\limits_{n=1}^{32}{(4n+1)}=4\sum\limits_{n=1}^{32}{n}+\sum\limits_{n=1}^{32}{1}=4\cdot\dfrac{32\cdot 33}{2}+32\\\\= 2112+32=\boxed{2144}[/tex]
__
The sum of numbers 1 to n is n(n+1)/2.
About 9% of the population has a particular genetic mutation. 600 people are randomly selected.
Find the standard deviation for the number of people with the genetic mutation in such groups of 600.
Answer:
The mean for all such groups randomly selected is 0.09*800=72.
Step-by-step explanation:
The value of the standard deviation is 7.
What is the standard deviation?Standard deviation is defined as the amount of variation or the deviation of the numbers from each other.
The standard deviation is calculated by using the formula,
[tex]\sigma = \sqrt{Npq}[/tex]
N = 600
p = 9%= 0.09
q = 1 - p= 1 - 0.09= 0.91
Put the values in the formulas.
[tex]\sigma = \sqrt{Npq}[/tex]
[tex]\sigma = \sqrt{600 \times 0.09\times 0.91}[/tex]
[tex]\sigma[/tex] = 7
Therefore, the value of the standard deviation is 7.
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If C(x) is the cost of producing x units of a commodity, then the average cost per unit is c(x) = C(x)/x. Consider the cost function C(x) given below. C(x) = 54,000 + 130x + 4x3/2 (a) Find the total cost at a production level of 1000 units. (Round your answer to the nearest cent.) $ (b) Find the average cost at a production level of 1000 units. (Round your answer to the nearest cent.) $ per unit (c) Find the marginal cost at a production level of 1000 units. (Round your answer to the nearest cent.) $ per unit (d) Find the production level that will minimize the average cost. (Round your answer to the nearest whole number.) units (e) What is the minimum average cost? (Round your answer to the nearest dollar.) $ per unit
Answer:
Step-by-step explanation:
Given that:
If C(x) = the cost of producing x units of a commodity
Then;
then the average cost per unit is c(x) = [tex]\dfrac{C(x)}{x}[/tex]
We are to consider a given function:
[tex]C(x) = 54,000 + 130x + 4x^{3/2}[/tex]
And the objectives are to determine the following:
a) the total cost at a production level of 1000 units.
So;
If C(1000) = the cost of producing 1000 units of a commodity
[tex]C(1000) = 54,000 + 130(1000) + 4(1000)^{3/2}[/tex]
[tex]C(1000) = 54,000 + 130000 + 4( \sqrt[2]{1000^3} )[/tex]
[tex]C(1000) = 54,000 + 130000 + 4(31622.7766)[/tex]
[tex]C(1000) = 54,000 + 130000 + 126491.1064[/tex]
[tex]C(1000) = $310491.1064[/tex]
[tex]\mathbf{C(1000) \approx $310491.11 }[/tex]
(b) Find the average cost at a production level of 1000 units.
Recall that :
the average cost per unit is c(x) = [tex]\dfrac{C(x)}{x}[/tex]
SO;
[tex]c(x) =\dfrac{(54,000 + 130x + 4x^{3/2})}{x}[/tex]
Using the law of indices
[tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex]
[tex]c(1000) = \dfrac{54000}{1000}+ 130 + {4(1000)^{1/2}}[/tex]
c(1000) =$ 310.49 per unit
(c) Find the marginal cost at a production level of 1000 units.
The marginal cost is C'(x)
Differentiating C(x) = 54,000 + 130x + 4x^{3/2} to get C'(x) ; we Have:
[tex]C'(x) = 0 + 130 + 4 \times \dfrac{3}{2} \ x^{\dfrac{3}{2}-1}[/tex]
[tex]C'(x) = 0 + 130 + 2 \times \ {3} \ x^{\frac{1}{2}}[/tex]
[tex]C'(x) = 0 + 130 + \ {6}\ x^{\frac{1}{2}}[/tex]
[tex]C'(1000) = 0 + 130 + \ {6} \ (1000)^{\frac{1}{2}}[/tex]
[tex]C'(1000) = 319.7366596[/tex]
[tex]\mathbf{C'(1000) = \$319.74 \ per \ unit}[/tex]
(d) Find the production level that will minimize the average cost.
the average cost per unit is c(x) = [tex]\dfrac{C(x)}{x}[/tex]
[tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex]
the production level that will minimize the average cost is c'(x)
differentiating [tex]c(x) =\dfrac{54000}{x} + 130 + 4x^{1/2}[/tex] to get c'(x); we have
[tex]c'(x)= \dfrac{54000}{x^2} + 0+ \dfrac{4}{2 \sqrt{x} }[/tex]
[tex]c'(x)= \dfrac{54000}{x^2} + 0+ \dfrac{2}{ \sqrt{x} }[/tex]
Also
[tex]c''(x)= \dfrac{108000}{x^3} -x^{-3/2}[/tex]
[tex]c'(x)= \dfrac{54000}{x^2} + \dfrac{4}{2 \sqrt{x} } = 0[/tex]
[tex]x^2 = 27000\sqrt{x}[/tex]
[tex]\sqrt{x} (x^{3/2} - 27000) =0[/tex]
x= 0; or [tex]x= (27000)^{2/3}[/tex] = [tex]\sqrt[3]{27000^2}[/tex] = 30² = 900
Since production cost can never be zero; then the production cost = 900 units
(e) What is the minimum average cost?
the minimum average cost of c(900) is
[tex]c(900) =\dfrac{54000}{900} + 130 + 4(900)^{1/2}[/tex]
c(900) = 60 + 130 + 4(30)
c(900) = 60 +130 + 120
c(900) = $310 per unit
Help ASAP it’s Math I need this rightnow 31 points
Answer:
AC (b)
Step-by-step explanation:
Since 10 is half of 20, you have to find the variable closest to the middle. Which in this case, is C. So, your awnser is B. (AC)
Answer:
[tex]\boxed{\sf C}[/tex]
Step-by-step explanation:
The whole segment is [tex]\sf \sqrt {20}[/tex], we can see that AD is approximately 75% of the segment AE.
[tex]75\%*\sqrt{20} = 3.354102[/tex]
[tex]\sqrt{10}= 3.162278[/tex]
AC is almost half of AE.
[tex]\frac{\sqrt{20} }{2} = 2.2360679775[/tex]
[tex]\sqrt{10} = 3.16227766017[/tex]
It isn’t close to the option C.
Simplify the expression . 39*x / 13
Answer:
3x
Step-by-step explanation:
39*x / 13
39/13 * x
3*x
3x
Answer:
3x
Step-by-step explanation:
We are given the expression:
39*x /13
We want to simplify this expression. It can be simplified because both the numerator (top number) and denominator (bottom number) can be evenly divided by 13.
(39*x /13) / (13/13)
(39x/13) / 1
3x / 1
When the denominator is 1, we can simply eliminate the denominator and leave the numerator as our answer.
3x
The expression 39*x/13 can be simplified to 3x
Find the value of a A.130 B.86 C.58 D.65
Answer:
Option (B)
Step-by-step explanation:
If two chords intersect inside a circle, measure of angle formed is one half the sum of the arcs intercepted by the vertical angles.
Therefore, 86° = [tex]\frac{1}{2}(a+c)[/tex]
a + c = 172°
Since the chords intercepting arcs a and c are of the same length, measures of the intercepted arcs by these chords will be same.
Therefore, a = c
⇒ a = c = 86°
Therefore, a = 86°
Option (B) will be the answer.
If jimmy has 15 apples and give 7 to gohn how many does jimmy have?
Answer:
Hey there!
Jimmy has 15-7, or 8 apples left.
Hope this helps :)
W varies inversely as the square root of x when x=4 w=4 find when x=25
Answer:
8/5
Step-by-step explanation:
w = k / √x
4 = k / √4
k = 8
w = 8 / √x
w = 8 / √25
w = 8/5
I need to know if the following questions are true or false
Answer:
False
Step-by-step explanation:
To find <A, we can do 5x - 80 = 3x + 20.
As we simplify, we will get 2x = 100, which is x = 50
Therefore, <A will be 50 degrees and not 45 degrees.
Also, if you need y, you can do:
3y - 7 = y + 7
2y = 14
y = 7
Click on the solution set below until the correct one is displayed.
Answer:
{ } or empty set.
Step-by-step explanation:
The solutions should be where the two lines intersect, but in this case, the parallel lines never intersect. That means that they have no solutions.
Hope this helps!
Answer:
{ } or empty set
Step-by-step explanation:
It's because these lines are parallel so they don't intersect to give you a coordinate.
(SAT Prep) In the given figure, a║b. What is the value of x? A. 70° B. 45° C. 80° D. 65° I NEED THIS FAST PLZZZZZZ!!!!!!!!!!!!
Answer:
70
Step-by-step explanation:
You have to find the vertical of x. To the right of the vertical, we see that there is an angle of 25 (since the 25 up top corresponds to that blank angle). Once you add 25 + 85 + x = 180 (since this is a straight line), we see that x is 70, and its vertical is also 70.
Construct the confidence interval for the population mean mu. c = 0.90, x = 16.9, s = 9.0, and n = 45. A 90% confidence interval for mu is:______.
Answer:
The 90% confidence interval for population mean is [tex]14.7 < \mu < 19.1[/tex]
Step-by-step explanation:
From the question we are told that
The sample mean is [tex]\= x = 16.9[/tex]
The confidence level is [tex]C = 0.90[/tex]
The sample size is [tex]n = 45[/tex]
The standard deviation
Now given that the confidence level is 0.90 the level of significance is mathematically evaluated as
[tex]\alpha = 1-0.90[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the standardized normal distribution table. The values is [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
The reason we are obtaining critical values for [tex]\frac{\alpha }{2}[/tex] instead of that of [tex]\alpha[/tex] is because [tex]\alpha[/tex] represents the area under the normal curve where the confidence level 1 - [tex]\alpha[/tex] (90%) did not cover which include both the left and right tail while [tex]\frac{\alpha }{2}[/tex] is just considering the area of one tail which is what we required calculate the margin of error
Generally the margin of error is mathematically evaluated as
[tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]MOE = 1.645* \frac{ 9 }{\sqrt{45} }[/tex]
[tex]MOE = 2.207[/tex]
The 90% confidence level interval is mathematically represented as
[tex]\= x - MOE < \mu < \= x + MOE[/tex]
substituting values
[tex]16.9 - 2.207 < \mu < 16.9 + 2.207[/tex]
[tex]16.9 - 2.207 < \mu < 16.9 + 2.207[/tex]
[tex]14.7 < \mu < 19.1[/tex]
Consider two consecutive positive integers such that the square of the second integer added to 3 times the first is equal to 105
Answer:
8 and 9
Step-by-step explanation:
If x is the smaller integer, and x + 1 is the larger integer, then:
(x + 1)² + 3x = 105
x² + 2x + 1 + 3x = 105
x² + 5x − 104 = 0
(x + 13) (x − 8) = 0
x = -13 or 8
Since x is positive, x = 8. So the two integers are 8 and 9.
17. What is the most likely outcome of decreasing the wavelength of incident light on a diffraction grating? A. lines become narrower B. distance between lines increases C. lines become thicker D. distance between lines decreases
When the wavelength of a diffraction grating is decreased, the distance between lines decreases.
What is a diffraction grating?The diffraction grating is used to carry out interference experiments. It consists of a number of small lines that are constructed to be close to each other and produce an interference pattern.
The outcome of decreasing the wavelength of incident light on a diffraction grating is that the distance between lines decreases.
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50 points + brainliest!
Answer:
( x+2) ^2 = 11
x =1.32,-5.32
Step-by-step explanation:
x^2 + 4x -7 = 0
Add the constant to each side
x^2 + 4x -7+7 = 0+7
x^2 + 4x = 7
Take the coefficient of the x term
4
Divide by 2
4/2 =2
Square it
2^2 = 4
Add this to each side
x^2 + 4x +4 = 7+4
Take the 4/2 as the term inside the parentheses
( x+2) ^2 = 11
Take the square root of each side
sqrt( ( x+2) ^2) =±sqrt( 11)
x+2 = ±sqrt( 11)
Subtract 2 from each side
x = -2 ±sqrt( 11)
To the nearest hundredth
x =1.32
x=-5.32
Answer:
[tex](x+2)^2=11[/tex]
[tex]x=-2 \pm \sqrt{11}[/tex]
Step-by-step explanation:
[tex]x^2+4x-7=0[/tex]
[tex]x^2+4x=7[/tex]
[tex]x^2+4x+4=7+4[/tex]
[tex](x+2)^2=11[/tex]
[tex]x+2=\pm\sqrt{11}[/tex]
[tex]x=-2 \pm \sqrt{11}[/tex]
Which point is a solution to the inequality shown in this graph?
Answer: A, (0, -3)
Step-by-step explanation:
Inequalities, once graphed, take the form of the image you attached:
Linear inequalities are straight lines, sometimes dotted and sometimes solid, with shading on one side of the line.
Any point in the shading is a correct solution to the inequality.
When the line is solid, any point on the line is a solution to the inequality.When the line is dotted, only the shaded area past the line includes solutions - points on the line are not solutions.In this case, the line is solid, so any point on the line is a solution to the inequality.
Looking at answer choice A: (0, -3), it lies on the line as the y-intercept.
The correct choice is A.
A crew clears brush at a rate 2/3 acre in 2 days. How long will it take the same crew to clear the entire plot of 4 acres?
Answer:
It takes the crew 12 days to clear the bush.
Step-by-step explanation:
Given clears 2/3 acres / 2 days, or 1/3 acre per day
Time to clear 4 acres
= 4 / (1/3)
= 4 * (3/1)
= 12 days
What are the expressions for length, width, and height?
Volume = length width height
V = _____ _____ _____
For odyyseyware
Answer:
[tex]\boxed{V=lwh}[/tex]
Step-by-step explanation:
The formula for volume of a cuboid is:
[tex]V=lwh[/tex]
[tex]volume = length \times width \times height[/tex]
Answer:
V = l w h
Step-by-step explanation:
Volume of a Cuboid = Length × Width × Height
Where l = length, w = width and h = height
When the input is 4, the output of f(x) = x + 21 is
Answer:
25Step-by-step explanation:
When the input is 4, the output of f(x) = x + 21 is f(4).
Substitute x = 4 to f(x):
f(4) = 4 + 21 = 25
Answer:
25
Step-by-step explanation:
We can find the output by plugging in 4 as x into the function:
f(x) = x + 21
f(4) = 4 + 21
f(4) = 25
Please answer this correctly without making mistakes
Answer:
3/11
Step-by-step explanation:
There are eleven equal parts.
So the denominator is 11.
He copies 8 parts on Sunday.
11-8=3.
He copied 3 parts on Saturday.
Hope this helps ;) ❤❤❤
At a deli counter, there are sandwiches with meat and vegetarian sandwiches. Kira is at the counter buying sandwiches for a picnic. In how many ways can she choose sandwiches if fewer than must be vegetarian sandwiches
Answer:
The number ways to choose between meat and vegetarian sandwiches can be computed using computation technique.
Step-by-step explanation:
There are two types of sandwiches available at the deli counter. The possibility of combinations can be found by computation technique of statistic. It is assumed that order does not matter and sandwiches will be selected at random. The sandwiches can be arranged in any order and number ways can be found by 2Cn.
A hotel rents 210 rooms at a rate of $ 60 per day. For each $ 2 increase in the rate, three fewer rooms are rented. Find the room rate that maximizes daily revenue.
Answer:
r=$14,400
The hotel should charge $120
Step-by-step explanation:
Revenue (r)= p * n
where,
p = price per item
n = number of items sold
A change in price leads to a change in number sold
A variable to measure the change in p and n needs to be introduced
Let the variable=x
Such that
p + x means a one dollar price increase
p - x means a one dollar price decrease
n + x means a one item number-sold increase
n - x means a one item number-sold decrease
for each $2 price increase (p + 2x) there are 3 fewer rooms are rented (n-3x)
know that at $60 per room, the hotel rents 210 rooms
r = (60 + 2x) * (210 - 3x)
=12,600-180x+420x-6x^2
=12,600+240x-6x^2
r=2100+40x-x^2
= -x^2 +40x+2100=0
Solve the quadratic equation
x= -b +or- √b^2-4ac / 2a
a= -1
b=40
c=2100
x= -b +or- √b^2-4ac / 2a
= -40 +or- √(40)^2 - (4)(-1)(2100) / (2)(-1)
= -40 +or- √1600-(-8400) / -2
= -40 +or- √ 1600+8400 / -2
= -40 +or- √10,000 / -2
= -40 +or- 100 / -2
x= -40+100/-2 OR -40-100/-2
=60/-2 OR -140/-2
= -30 OR 70
x=70
The quadratic equation has a maximum at x=70
p+2x
=60+2(30)
=60+60
=$120
r= (60 + 2x) * (210 - 3x)
={60+2(30)}*{(210-3(30)}
r=(60+60)*(210-90)
=120*120
=$14,400