Answer:
287 pounds
Step-by-step explanation:
1212 X 2= 2424
2424-2137= 287
Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) = 9 sin(xy), (0, 8)
Answer:
The magnitude is [tex]\Delta f(0,8) = 72[/tex]
The direction is [tex]i[/tex] i.e toward the x-axis
Step-by-step explanation:
From the question we are told that
The function is [tex]f(x, y) = 9sin(xy) \ \ \[/tex]
The point considered is [tex](0,8 )[/tex]
Generally the maximum rate of change of f at the given point and the direction is mathematically represented as
[tex]\Delta f(x,y) = [\frac{\delta f(x,y)}{\delta x } i + \frac{\delta f(x,y)}{\delta y } j ][/tex]
[tex]\Delta f(x,y) = [\frac{\delta (9sin(xy))}{\delta x} i + \frac{\delta (9sin(xy))}{\delta y} i ][/tex]
[tex]\Delta f(x,y) = [9y cos (x,y) i + 9xcos (x,y) j][/tex]
At [tex](0,8 )[/tex]
[tex]\Delta f (0,8) = [9(8) cos(0* 8)i + 9(8) sin(0* 8)j ][/tex]
[tex]\Delta f (0,8) = 72 i [/tex]
Select two rays that contain QP
Step-by-step explanation:
the line QP is a part of the line PR and PN
-5 = -a/36 plz hellllpppppp
Answer:
180
Step-by-step explanation:
-5= -a/36
-5*36= -a
-180= -a
180 = a
The Louvre Pyramid. designed by architect I.M. Pei is?made of glass and metal and serves as the main entrance to the museum. The diagonal part of the of the structure, from the top of the pyramid to the ground, measures 85 ft. and half the distance of the base measures 51 ft. How tall is pyramid? Round to the nearest foot.
Answer: 68 ft
Step-by-step explanation:
Use Pythagorean Theorem: x² + y² = d²
51² + h² = 85²
h² = 85² - 51²
h² = 4624
[tex]h=\sqrt{4624}[/tex]
h = 68
A company manufactures and sells x television sets per month. The monthly cost and price-demand equations are C(x)=74,000+80x and p(x)=300− x 30, 0≤x≤9000. (A) Find the maximum revenue. (B) Find the maximum profit, the production level that will realize the maximum profit, and the price the company should charge for each television set. (C) If the government decides to tax the company $5 for each set it produces, how many sets should the company manufacture each month to maximize its profit? What is the maximum profit? What should the company charge for each set?
Answer:
a) $675000
b) $289000 profit,3300 set, $190 per set
c) 3225 set, $272687.5 profit, $192.5 per set
Step-by-step explanation:
a) Revenue R(x) = xp(x) = x(300 - x/30) = 300x - x²/30
The maximum revenue is at R'(x) =0
R'(x) = 300 - 2x/30 = 300 - x/15
But we need to compute R'(x) = 0:
300 - x/15 = 0
x/15 = 300
x = 4500
Also the second derivative of R(x) is given as:
R"(x) = -1/15 < 0 This means that the maximum revenue is at x = 4500. Hence:
R(4500) = 300 (4500) - (4500)²/30 = $675000
B) Profit P(x) = R(x) - C(x) = 300x - x²/30 - (74000 + 80x) = -x²/30 + 300x - 80x - 74000
P(x) = -x²/30 + 220x - 74000
The maximum revenue is at P'(x) =0
P'(x) = - 2x/30 + 220= -x/15 + 220
But we need to compute P'(x) = 0:
-x/15 + 220 = 0
x/15 = 220
x = 3300
Also the second derivative of P(x) is given as:
P"(x) = -1/15 < 0 This means that the maximum profit is at x = 3300. Hence:
P(3300) = -(3300)²/30 + 220(3300) - 74000 = $289000
The price for each set is:
p(3300) = 300 -3300/30 = $190 per set
c) The new cost is:
C(x) = 74000 + 80x + 5x = 74000 + 85x
Profit P(x) = R(x) - C(x) = 300x - x²/30 - (74000 + 85x) = -x²/30 + 300x - 85x - 74000
P(x) = -x²/30 + 215x - 74000
The maximum revenue is at P'(x) =0
P'(x) = - 2x/30 + 215= -x/15 + 215
But we need to compute P'(x) = 0:
-x/15 + 215 = 0
x/15 = 215
x = 3225
Also the second derivative of P(x) is given as:
P"(x) = -1/15 < 0 This means that the maximum profit is at x = 3225. Hence:
P(3225) = -(3225)²/30 + 215(3225) - 74000 = $272687.5
The money to be charge for each set is:
p(x) = 300 - 3225/30 = $192.5 per set
When taxed $5, the maximum profit is $272687.5
Answer:
b) $289000 profit,3300 set, $190 per set
Find the maximum rate of change of f(x,y)=ln(x2+y2) at the point (-2, 2) and the direction in which it occurs.
The maximum rate of change of function [tex]f(x,y)=ln(x^2+y^2)[/tex] is [tex]\frac{\sqrt(2)}{2}[/tex] and the direction is [tex](\frac{-1}{2}, \frac{1}{2})[/tex]
Given data:
To find the maximum rate of change of the function [tex]f(x,y)=ln(x^2+y^2)[/tex] at the point (-2, 2), calculate the gradient vector (∇f) and evaluate it at that point.
The gradient vector is a vector that points in the direction of the steepest ascent of the function and its magnitude represents the rate of change of the function at that point.
To find the gradient vector (∇f), calculate the partial derivatives of f(x, y) with respect to x and y:
[tex]\frac{df}{dx} = \frac{(2x)}{ (x^2 + y^2)}[/tex]
[tex]\frac{df}{dy} = \frac{(2y)}{ (x^2 + y^2)}[/tex]
Evaluating these partial derivatives at the point (-2, 2):
[tex]\frac{df}{dx}_{-2,2}=-1/2[/tex]
[tex]\frac{df}{dy}_{-2,2}=--1/2[/tex]
So, the gradient vector (∇f) at the point (-2, 2) is (∇f) = (-1/2, 1/2).
The maximum rate of change of the function occurs in the direction of the gradient vector (∇f). Therefore, the direction in which the maximum rate of change occurs is in the direction of the vector (-1/2, 1/2).
Note that the magnitude of the gradient vector (∇f) represents the maximum rate of change. In this case, the magnitude of (∇f) is:
|∇f| = [tex](\frac{-1}{2}^2 + \frac{1}{2}^2)[/tex]
= √(1/4 + 1/4)
= √(1/2)
= 1/√(2)
[tex]=\frac{\sqrt(2)}{2}[/tex]
Hence, the maximum rate of change of f(x, y) at the point (-2, 2) is [tex]\frac{\sqrt(2)}{2}[/tex], and it occurs in the direction of the vector [tex](\frac{-1}{2}, \frac{1}{2})[/tex].
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3. |-9n-3|<6
help please
Answer:
n> −1 and n < 1/3
Step-by-step explanation:
What is the answer for -3(-5) - 16?
Answer:
-1
Step-by-step explanation:
-3x(-5)-16
15-16
-1
Do the phrases 6 less a number y and 6 less than a number y mean the same thing? Explain. A. No, they do not both mean the same thing. 6 less a number y can be represented by the expression 6 - y. 6 less than a number y can be represented by the expression y - 6. B. Yes, they both mean the same thing. They can also both be represented by the expression y - 6.
Answer:
B. Yes, they both mean the same thing. They can also both be represented by the expression y - 6.
Step-by-step explanation:
They are the same I think because 6 less than a number y means 6 less than y so y-6. 6 less a number y is the same.
Evaluate 2 - (-4) + 3 + (-6) - (-2)
Answer:
5
Step-by-step explanation:
Remember:
Two negatives make a positive
A negative flips a sign
2 - (-4) + 3 + (-6) - (-2)
=
2+4+3-6+2
9-6+2
=5
Six college buddies bought each other Christmas gifts. They spent:________.1. $178.622. $247.583. $228.454. $176.645. $180.226. $268.45What was the mean amount spent? Round answer to the nearest cent.a. $243.96b. $213.30c. $319.95d. $255.96
Answer:
B. $213.30
Step-by-step explanation:
Mean amount spent on Christmas gifts = Σx / n
Where,
Σ= sum of
x= cost of each Christmas gifts
n= number of Christmas gift
Mean amount spent on Christmas gifts = Σx / n
= ( $178.622 + $247.583 + $228.454 + $176.645 + $180.226 + $268.45 ) / 6
= $1,279.98 / 6
= $213.33
Round to the nearest cent
= $213.30
Option b is the correct answer
Consider the following data on 20 chemical reactions, with Y = chromatographic retention time (seconds) and X = molecular weight (gm/mole).Retention Time and Molecular Weight Name Retention Time Molecular Weight alpha-pinene 234.50 136.24 Cyclopentene 95.27 68.12 p-diethylbenzene 284.00 134.22 Decane 250.60 142.29 Toluene 174.00 92.14 Benzene 135.70 78.11 2-methylpentane 97.24 86.18 2,3 dimethylbutane 100.70 86.18 1,7-octadiene 172.20 110.20 1,2,4-trimethylbenzene 262.70 120.19 2,3,4-trimethylpentane 160.98 114.23 ethylcyclohexane 195.07 112.22 Limonene 271.50 136.24 methylcyclohexane 153.57 98.19 m-diethylbenzene 281.50 134.22 2,3-dimethylpentane 131.83 100.20 2,2-dimethylbutane 89.34 86.18 Pentane 78.00 72.15 Isooctane 136.90 114.23 Hexane 106.00 86.18 11.value:Required information(a) Write the fitted regression equation. (Negative amount should be indicated by a minus sign.) y = x +ReferenceseBook & ResourcesWorksheetDifficulty: MediumLearning Objective: 12-02Visual Displays and Correlation AnalysisSimple RegressionRegression TerminologyOrdinary Least Squares FormulasTests for SignificanceChapter Exercises12.value:Required information(b) Calculate R2. R2
Answer: (a) y = 2.7394x - 118.1368
(b) R² = 0.8215 or 82.15%
Step-by-step explanation: Regression line is the best line that relates the variables in the data.
To calculate the fitted regression equation:
1) Calculate average of x-values ([tex]x_{i}[/tex]) and average of y-values ([tex]y_{i}[/tex]);
2) Calculate the slope, b, by doing:
[tex]b=\frac{\Sigma (x-x_{i})(y-y_{i})}{\Sigma (x-x_{i})^{2}}[/tex]
3) Calculate y-intercept, a, by doing:
[tex]a=y_{i}-bx_{i}[/tex]
4) Then, it gives regression equation: y = bx + a
For the data on chemical reactions:
(a) [tex]b=\frac{ [(136.24-105.3955)+...+(86.18-105.3955)].[(234.5-170.58)+...+(106-170.58)]}{(136.24-105.3955)^{2}+...+(86.18-105.3955)^{2}}[/tex]
b = 2.7394
[tex]a=170.58-2.7394(105.3955)[/tex]
a = -118.1368
y = 2.7394x - 118.1368
The fittest regression equation is y = 2.7394x - 118.1368.
(b) R is correlation coefficient and measures the strength of the relationship between the variables. It is calculated as:
[tex]R=\frac{n\Sigma(xy)-(\Sigma x)(\Sigma y)}{\sqrt{[n\Sigma x^{2}-(\Sigma x^{2})][n\Sigma y^{2}-(\Sigmay^{2})]} }[/tex]
For this fit, R = 0.9064
The variable R² is the coefficient of determination, is the square of correlation coefficient and is usually stated as a percent.
What the variable represents is the percent of variation in the dependent variable (y) explained by the variation in the independent variable (x).
For this fit:
[tex]R^{2} = 0.9064^{2}[/tex]
[tex]R^{2} =[/tex] 0.8215
What it entails is that 82.15% of the variation of retention time is due to the molecular weight of each chemical compound.
Complete the equation involving x. Order terms like the physical situation, and don't simplify. A 6 foot wide painting should be centered on a 10 foot wide wall. How many feet (x) should be on each side of the painting?
Answer:
2 feet
Step-by-step explanation:
Given the question :
A 6 foot wide painting should be centered on a 10 foot wide wall. How many feet (x) should be on each side of the painting?
Width of painting = 6 foot
Width of wall = 10 foot
Since the painting is required to be centered on the wall, hence the space left on euth side of the wall after placing the painting should be equal.
Therefore,
Difference between painting width and wall width :
(10 - 6) foot = 4 foot
Hence, number of feet (x) on either side of the wall:
4 feet / 2 = 2 feet
HELPPPPPPPPPPPP ILL MARK BRAINLESTTTT PLZZZZZZZZZ
Answer:
5 + -155 = -150
Step-by-step explanation:
"A number sentence is a mathematical sentence, made up of numbers and signs." - splashlearn.com
To make one, pick a random number, add a math sign (+, -, ×, ÷), add another number, and put the corresponding answer to the numbers and symbol. For example: 6 - 2 = 4
For this specific question start with the answer (-150). Then add an equals sign: -150 =
Then pick a random number that isn't too dramatic, like 5. Add five to the number sentence: -150 = 5
Next pick a math symbol. Add it to the number sentence: -150 = 5 +
Lastly, pick another number that would make sense in this situation:
-150 = 5 + -155
Switch it around and you're done: 5 + -155 = -150
Find the area of the figure.(sides meet at right angles.)
Answer:
48
Step-by-step explanation:
not sure
The area of the figure is equal to 75 inches²
What is the area of the rectangle?The formula for area is equal to the product of the length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides.
Given: The length and breadth of the larger rectangle as 15 , 6 respectively
And area of the interior rectangle that forms a part of the larger rectangle is given by : Area (smaller)=3×5
= 15 inches²
While Area of the larger rectangle that contains the smaller rectangle is
= 15×6
=90 inches²
Thus the required area is = 90-15
=75 inches²
Hence, The area of the required rectangle is given by 75 inches²
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Helppppppppppppp!!!!!!!
Answer:
1.368
Step-by-step explanation:
[tex]2ln(x-1)=-2\\\\\text{divide by 2}\\\\ln(x-1)=-1\\\text{take the exponential}\\\\x-1=e^{-1}\\\\\Large \boxed{\sf \bf x = 1+\dfrac{1}{e}}[/tex]
Thanks
a woman can walk two miles per hour faster down the trail to cochita lake than she can on the return trip uphill. It takes her two hours to get to the lake and four hours to return. What is the distance of the trail?
Answer:
8 miles
Step-by-step explanation:
Downhill
speed = s+2
time = 2 h
then distance d = (s+2)2....i
Uphill
speed = s
time = 4 h
then distance d= 4s...ii
According to question i = ii
⇒(s+2)2 =4s
s = 2 miles/h
then distance d = 2×4 = 8 miles [from eq. ii]
Solve for x. 12x - 17 = 5x + 19
Answer:
x = [tex]\frac{36}{7}[/tex]
Step-by-step explanation:
Given
12x - 17 = 5x + 19 ( subtract 5x from both sides )
7x - 17 = 19 ( add 17 to both sides )
7x = 36 ( divide both sides by 7 )
x = [tex]\frac{36}{7}[/tex]
can someone please help me
Answer:
E
Step-by-step explanation:
\sqrt 6 is an irrational number, as it cannot be written as the ratio of 2 numbers.
It is also a real number, as it does not include the square root of a negative number.
Therefore, E is the correct option.
z(y+y); use y=3, and z=3
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{18}}}}}[/tex]
Step-by-step explanation:
Given, y = 3 , z = 3
[tex] \sf{z(y + y)}[/tex]
Plug the value of y and z
⇒[tex] \sf{3(3 + 3)}[/tex]
Add the numbers : 3 and 3
⇒[tex] \sf{3 \times 6}[/tex]
Multiply the numbers : 3 and 6
⇒[tex] \sf{18}[/tex]
Hope I helped!
Best regards! :D
Is #50 right? We got an answer of 44 square inches for #50
Answer:
44 inches
Step-by-step explanation:
Yes, it is 44, but it's just 44 in, not square inches. Square inches is for area, and you're just measuring the length for perimeter.
Split 84 into two parts so that one part is five times the other part.
Answer:
x+5x=84
6x=84
6x/6=84/6
x=14
so therefore
14+5(14)
14+70
The numbers are 14 and 70
The two parts are x = 70 and y = 14
We have a 2 - digit number - 84.
We have to split it into two parts such that one part is five times the other part.
Divide 24 into two parts such that second part is 3 times the first part.Assume the two numbers to be x and y.
x + y = 24
A/Q -
y = 3x
x + 3x =24
4x = 24
x = 6
and y = 3 x 6 = 18.
According to question, we have -
Number = 84
Assume the first part be x.
Then, the other part = [tex]\frac{x}{5}[/tex]
Therefore -
x + [tex]\frac{x}{5}[/tex] = 84
5x + x = 84 x 5
6x = 420
x = 70
and
y = [tex]\frac{x}{5} =\frac{70}{5}[/tex] = 14
Hence, the two parts are x = 70 and y = 14
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is -3 out of 11 an integer
Answer:
for 11 to be an integer, 11 has to be a whole number. Furthermore, for 11 to be an integer, you should be able to write 11 without a fractional or decimal component. 11 is a whole number that can be written without a fractional component, thus 11 is an integer
Step-by-step explanation:
i’ve posted this a lot already and i keep getting it wrong can you help pls?
Answer: See below; x=1/6
Step-by-step explanation:
This problem may seem intimidating, but all you need to know are your exponent rules. Let's first work inside the parenthesis. Since the bases are the same, we can directly subtract the exponents.
[tex]\frac{3}{4} -\frac{3}{8}[/tex] [common denominator]
[tex]\frac{6}{8} -\frac{3}{8}[/tex] [subtract]
[tex]\frac{3}{8}[/tex]
Now, our new answer is [tex](3^\frac{3}{8} )^\frac{4}{9}[/tex].
Unfortunately, the answer is asking for an exponent with a single base. One of the properties is when the exponents are separated by parenthesis, you multiply them together.
[tex]\frac{3}{8} *\frac{4}{9}[/tex] [cross cancel to simplify]
[tex]\frac{1}{2} *\frac{1}{3}[/tex] [multiply]
[tex]\frac{1}{6}[/tex]
Our final answer is [tex]3^\frac{1}{6}[/tex].
The value is x is [tex]\frac{1}{6}[/tex] since [tex]3^\frac{1}{6}[/tex] is equal to [tex]3^x[/tex], we know that [tex]x=\frac{1}{6}[/tex].
A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 5% vinegar, and the second brand contains 15% vinegar. The chef wants to make 240 millimeters of a dressing that is 13% vinegar. How much of each brand should she use?
Answer:
48 mL 5% vinegar, 192 mL 15% vinegar
Step-by-step explanation:
If x is volume of 5% vinegar, and y is volume of 15% vinegar, then:
x + y = 240
0.05 x + 0.15 y = 0.13 (240)
Solve with substitution:
0.05 x + 0.15 (240 − x) = 0.13 (240)
0.05 x + 36 − 0.15 x = 31.2
0.10 x = 4.8
x = 48
y = 192
2x + y = 11...(1)
5x-2y= 5...(2)
Given the above system of two equations in two variables, which one of the following equations does
NOT have the same solutions for x and y?
A 7x - y = 16
B 12x + 3y = 40
Cx-y= -2
D 12x – 3y = 21
Answer is B
basically you wrote the answer
Answer is B
Answer:
Well since u know the answer (LOL) its B
Step-by-step explanation:
U already solved it so u know how!
What is the value of x in both a & b?
Answer:
I've pretty much already solved this, in my discussion above:
| 3 | = 3
| –3 | = 3
So then x must be equal to 3 or equal to –3.
But how am I supposed to solve this if I don't already know the answer? I will use the positive / negative property of the absolute value to split the equation into two cases, and I will use the fact that the "minus" sign in the negative case indicates "the opposite sign", not "a negative number".
For example, if I have x = –6, then "–x " indicates "the opposite of x" or, in this case, –(–6) = +6, a positive number. The "minus" sign in "–x" just indicates that I am changing the sign on x. It does not indicate a negative number. This distinction is crucial!
Whatever the value of x might be, taking the absolute value of x makes it positive. Since x might originally have been positive and might originally have been negative, I must acknowledge this fact when I remove the absolute-value bars. I do this by splitting the equation into two cases. For this exercise, these cases are as follows:
a. If the value of x was non-negative (that is, if it was positive or zero) to start with, then I can bring that value out of the absolute-value bars without changing its sign, giving me the equation x = 3.
b. If the value of x was negative to start with, then I can bring that value out of the absolute-value bars by changing the sign on x, giving me the equation –x = 3, which solves as x = –3.
Then my solution
Answer:
7 and [tex]\frac{16}{5}[/tex]
Step-by-step explanation:
(a)
Δ ABC and Δ ADE are similar thus the ratios of corresponding sides are equal
[tex]\frac{AB}{AD}[/tex] = [tex]\frac{AC}{AE}[/tex] , substitute values
[tex]\frac{2}{4}[/tex] = [tex]\frac{x}{x+7}[/tex] ( cross- multiply )
4x = 2(x + 7) ← distribute
4x = 2x + 14 ( subtract 2x from both sides )
2x = 14 ( divide both sides by 2 )
x = 7
---------------------------------------------
(b)
Δ ABC and Δ CDF are similar thus ratios of corresponding sides are equal
[tex]\frac{AB}{CD}[/tex] = [tex]\frac{BC}{DF}[/tex] , substitute values
[tex]\frac{2}{5}[/tex] = [tex]\frac{x}{8}[/tex] ( cross- multiply )
5x = 16 ( divide both sides by 5 )
x = [tex]\frac{16}{5}[/tex]
Write the expression and give the solution from the information given on the number line. ( First blank is for your number sentence and the second blank is for your answer)
Answer:
0-3+5=2
Step-by-step explanation:
It starts in 0
The first line moves three spaces to the left so that's -3
the second line moves 5 spaces to the right so that's +5
add all up
0-3+5=2
Answer:
2
Step-by-step explanation:
1st line 0 → -3 = -3
2nd line -3 → 2 = 5
sum = 0 + (-3) + 5 = 2
i need help please... im really confused
when we divides m(x) ÷n(x) quotient and remainder is
Find the volume of the solid generated when R (shaded region) is revolved about the given line. x=6−3sec y, x=6, y= π 3, and y=0; about x= 6
Answer:
[tex]V=9\pi\sqrt{3}[/tex]
Step-by-step explanation:
In order to solve this problem we must start by graphing the given function and finding the differential area we will use to set our integral up. (See attached picture).
The formula we will use for this problem is the following:
[tex]V=\int\limits^b_a {\pi r^{2}} \, dy[/tex]
where:
[tex]r=6-(6-3 sec(y))[/tex]
[tex]r=3 sec(y)[/tex]
a=0
[tex]b=\frac{\pi}{3}[/tex]
so the volume becomes:
[tex]V=\int\limits^\frac{\pi}{3}_0 {\pi (3 sec(y))^{2}} \, dy[/tex]
This can be simplified to:
[tex]V=\int\limits^\frac{\pi}{3}_0 {9\pi sec^{2}(y)} \, dy[/tex]
and the integral can be rewritten like this:
[tex]V=9\pi\int\limits^\frac{\pi}{3}_0 {sec^{2}(y)} \, dy[/tex]
which is a standard integral so we solve it to:
[tex]V=9\pi[tan y]\limits^\frac{\pi}{3}_0[/tex]
so we get:
[tex]V=9\pi[tan \frac{\pi}{3} - tan 0][/tex]
which yields:
[tex]V=9\pi\sqrt{3}[/tex]]