Answer: 6 / √26
Step-by-step explanation:
Given that f(x, y, z) = xe^y + ye^z + ze^x
so first we compute the gradient vector at (0, 0, 0)
Δf ( x, y, z ) = [ e^y + ze^x, xe^y + e^z, ye^z + e^x ]
Δf ( 0, 0, 0 ) = [ e⁰ + 0(e)⁰, 0(e)⁰ + e⁰, 0(e)⁰ + e⁰ ] = [ 1+0 , 0+1, 0+1 ] = [ 1, 1, 1 ]
Now we were also given that V = < 4, 3, -1 >
so ║v║ = √ ( 4² + 3² + (-1)² )
║v║ = √ ( 16 + 9 + 1 )
║v║ = √ 26
It must be noted that "v" is not a unit vector but since ║v║ = √ 26, the unit vector in the direction of "V" is ⊆ = ( V / ║v║)
so
⊆ = ( V / ║v║) = [ 4/√26, 3/√26, -1/√26 ]
therefore by equation D⊆f ( x, y, z ) = Δf ( x, y, z ) × ⊆
D⊆f ( x, y, z ) = Δf ( 0, 0, 0 ) × ⊆ = [ 1, 1, 1 ] × [ 4/√26, 3/√26, -1/√26 ]
= ( 1×4 + 1×3 -1×1 ) / √26
= (4 + 3 - 1) / √26
= 6 / √26
Solve the system of linear equations and check any solutions algebraically.
Answer:
[tex]\boxed{\sf \ \ x = 9, \ y = -5, \ z = 5 \ \ }[/tex]
Step-by-step explanation:
Hello,
(1) 2x + 4y + z = 3
(2) x - 2y - 3z = 4
(3) x + y - z = -1
From (3) we can write z = x + y + 1 and we replace in (1)
2x + 4y + x + y + 1 = 3 <=> 3x + 5y = 3-1 =2
(1') 3x + 5y = 2
and we replace in (2)
x - 2y -3(x+y+1) = 4 <=> -2x -5y -3 = 4 <=> -2x -5y = 4 + 3 = 7
(2') -2x - 5y = 7
(1') + (2') gives
3x - 2x + 5y - 5y = 2 + 7 = 9
x = 9
we replace in (1')
3*9 + 5y = 2 <=> 27 + 5y = 2 <=> 5y = 2-27 = -25 <=> y = -25/5 = -5
y = -5
and then in (3)
9 - 5 - z = -1 <=> 4 - z = -1 <=> z = 4 + 1 = 5
z = 5
hope this helps
Answer:
work is shown and pictured
help i need to know pls
Answer:
7.8 =x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp / adj
tan 48 = x/7
7 tan 48 = x
7.774287604 = x
To the nearest tenth
7.8 =x
What is the image of the point by (-5,3) under a 270 rotation about the point (-7,-3)
Step-by-step explanation:
here, the given point is (-7,-3)
now, by the formula,
p(x,y)= p-1 (-y+a+b,x-a+b) ( p-1 is p das)
p(-5,3)= p-1 (-13,-1) is answer.
hope it helps..
Roberta sold goods costing $35,500, her expenses totaled $2,500 and her freight in totaled $750.
Her company's average stock of goods during the same period was $9,500.
The inventory turnover ratio for Roberta's company is
Answer:
Inventory turnover ratio is 3.74
explanation:
Inventory turnover is a ratio of the number of times a company's inventory is sold and replaced in a given period.
Inventory turn over ratio is calculated as ; Cost of goods sold ÷ Average stock of goods sold
= $35,500 / $9500
= 3.74
A factory manufactures chairs and tables, each requiring the use of three operations: cutting, assembly, and finishing. The first operation can use at most 40 hours; the second at most 42 hours; and the third at most 25 hours. A chair requires 1 hour of cutting, 2 hours of assembly, and 1 hour of finishing; a table needs 2 hours of cutting, 1 hour of assembly, and 1 hour of finishing. If the profit is $20 per unit for a chair and $30 for a table, what is the maximum revenue? Round your answer to the nearest whole number. Do not include a dollar sign or comma in your answer.
Answer:
z(max) = 650 $
x₁ = 10 units
x₂ = 15 units
Step-by-step explanation:
That is a linear programming problem, we will use a simplex method to solve it
Formulation:
Let´s call x₁ number of chairs and x₂ number of tables then :
Item (in hours) cutting assembly finishing Profit ($)
Chairs (x₁) 1 2 1 20
Tables (x₂) 2 1 1 30
Availability 40 42 25
Objective Function
z = 20*x₁ + 30x₂ ( to maximize) subject to:
x₁ + 2x₂ ≤ 40
2x₁ + x₂ ≤ 42
x₁ + x₂ ≤ 25
x₁ , x₂ >= 0
Using excel or any other software we find:
z(max) = 650
x₁ = 10
x₂ = 15
The chairs and tables manufactured by the factory is an illustration of linear programming, where the maximum revenue is 674
Let x represent chairs, and y represent tables
So, the given parameters are:
Cutting:
Chairs: 1 hourTable: 2 hoursHour available: 40So, the constraint is:
[tex]\mathbf{x + 2y \le 40}[/tex]
Assembly:
Chairs: 2 hoursTable: 1 hourHour available: 42So, the constraint is:
[tex]\mathbf{2x + y \le 42}[/tex]
Finishing:
Chairs: 1 hourTable: 1 hourHour available: 25So, the constraint is:
[tex]\mathbf{x + y \le 25}[/tex]
The unit profit on the items are:
Chairs: $20Table: $30So, the objective function to maximize is:
[tex]\mathbf{Max\ z = 20x + 30y}[/tex]
And the constraints are:
[tex]\mathbf{x + 2y \le 40}[/tex]
[tex]\mathbf{2x + y \le 42}[/tex]
[tex]\mathbf{x + y \le 25}[/tex]
[tex]\mathbf{x,y \ge 0}[/tex]
Using graphical method (see attachment for graph), we have the following feasible points:
[tex]\mathbf{(x,y) = \{(10,15),\ (17,8),\ (14.67, 12.67)\}}[/tex]
Calculate the objective function using the feasible points.
[tex]\mathbf{z = 20 \times 10 + 30 \times 15}[/tex]
[tex]\mathbf{z = 650}[/tex]
[tex]\mathbf{z = 20 \times 17 + 30 \times 8}[/tex]
[tex]\mathbf{z = 580}[/tex]
[tex]\mathbf{z = 20 \times 14.67+ 30 \times 12.67}[/tex]
[tex]\mathbf{z = 673.5}[/tex]
Approximate
[tex]\mathbf{z = 674}[/tex]
Hence, the maximum revenue is 674
Read more about linear programming at:
https://brainly.com/question/14225202
Help, Please. File attached this time. Sorry
Answer:
27 degrees
Step-by-step explanation:
Because there is a straight line, all of the angles shown add up to 180, so if you add up all the given angles and subtract it from 180, you will get your answer.
39+86+28=153
180-153=27
Hope this helps. If you have any follow-up questions, feel free to ask.
Have a great day! :)
A bag contains a collection of distinguishable marbles. The bag has two red marbles, three green ones, one lavender one, two yellows, and two orange marbles. HINT [See Example 7.] How many sets of four marbles include exactly two green marbles
Answer:
63
Step-by-step explanation:
Given that;
The bag has two red marbles, n(red) =2
three green ones marbles, n(green) = 3
one lavender one marbles, n(lavender) = 1
two yellows marbles, n(yellow ) = 2
two orange marbles. n(orange) = 2
number of non green marbles = 2+1+2+2 = 7
The objective is to find out how many sets of four marbles include exactly two green marbles
Since sets of four marbles contain exactly two green marbles, then N(select 2 from 3 marbles and 2 from 7 marbles)
= [tex]^3C_2 \times ^{7}C _2[/tex]
= [tex]\dfrac{3!}{2!(3-2)!} \times \dfrac{7!}{2!(7-2)!}[/tex]
= [tex]\dfrac{3*2!}{2!} \times \dfrac{7*6*5!}{2!(5)!}[/tex]
= [tex]3 \times 7\times 3[/tex]
= 63
What is the value of Sine theta in the diagram below?
Answer:
C) 24/25
Step-by-step explanation:
did the quiz and got it right
The value of the sine theta in the first quadrant in the diagram given is [tex]\mathbf{\dfrac{24}{25}}[/tex]
What is the trigonometric function in the first quadrant?The explanation of the trigonometric functions (i.e cosine, sine, tangent) in respect of point coordinates on the unit circle informs us of the signs and meanings of the trigonometric functions for each of the four(4) quadrants, depending on the signs of the x, as well as, y coordinates in each quadrant.
In the first quadrant;
cos(θ) > 0, sin(θ) > 0 andtan(θ) > 0Thus, we have a positive x and y-axis.
Taking the forms x and y, i.e. (x, y) = (cos θ, sin θ)
The value of sine theta in [tex]\mathbf{(\dfrac{7}{25}, \dfrac{24}{25} ) = \dfrac{24}{25} }[/tex]
Learn more about Trigonometric functions here:
https://brainly.com/question/24349828
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CAN ANYONE HELP ME THANKS FOR BRAINLIEST ANSWER PLEASE What one is the standard form of the equation y = – 1/4 x – 2? A. x + 4y = 8 B. x + 4y = – 2 C. x + 4y = – 8 D. –x + 4y = – 8
Answer:
The standard form of the equation of y = -1/4x - 2 is x + 4y = -8 which is C
The sum of the digits of a two-digit number is 5. If nine is subtracted from the number, the digits will be reversed. Find the Algebraic equation by replacing the tens digit with x.
Let a be the number in the 10s place and b in the 1s place. Then the original two-digit number is 10a + b.
The sum of the digits is 5:
a + b = 5
Subtract 9 from the original number, and we get the same number with its digits reversed:
(10a + b) - 9 = 10b + a
Simplifying this equation gives
9a - 9b = 9
or
a - b = 1
Add this to the first equation above:
(a + b) + (a - b) = 5 + 1
2a = 6
a = 3
Then
3 - b = 1
b = 2
So the original number is 32. Just to check, we have 3 + 2 = 5, and 32 - 9 = 23.
the solution of the equation 0=4+4(m+1) is
Answer:
[tex]\boxed{m = -2}[/tex]
Step-by-step explanation:
[tex]0 = 4+4(m+1)[/tex]
Resolving Parenthesis
[tex]0 = 4+4m + 4[/tex]
[tex]0 = 4m+8[/tex]
Subtracting 8 to both sides
[tex]-8 = 4m[/tex]
[tex]4m = -8[/tex]
Dividing both sides by 4
m = -8/4
m = -2
Step-by-step explanation:
4+4m+4= 0
4m+8=0
4m=-8
m= -8/4=-2
Consider a triangle ABC like the one below. Suppose that B=36°, C= 62°, and b= 40. (The figure is not drawn to scale.) Solve the triangle.
Round your answers to the nearest tenth.
If there is more than one solution, use the button labeled "or".
Answer:
A=82°
a= 67.4
c = 60.1
Step-by-step explanation:
For A
A+B+C =180°
A= 180-(B+C)
A= 180-(36+62)
A= 189-(98)
A= 82°
For a
a/sinA= b/sinB
a/sin82= 40/sin36
a= (40*sin82)/sin36
a=( 40*0.9903)/0.5878
a=67.39
Approximately = 67.4
For c
c/sinC= b/sinB
c= (sinC*b)/sinB
c= (sin62*40)/sin36
c =(0.8829*40)/0.5878
c = 60.08
Approximately = 60.1
Write the equation of the line in point-slope form that passes through (1, -4) and has a slope of 1/4.
Answer:
y + 4 =(1/4)(x - 1)
Step-by-step explanation:
The point slope equation is y - k = m(x - h), where (h, k) is the given point and m is the given slope.
In this particular case we have y + 4 =(1/4)(x - 1)
what equals 1+1= Why can't I see any answers help i logged off etc is it just me?
Answer:
1 + 1 = 2
Step-by-step explanation:
^
Answer:
no , it's happening to everyone , even I can't see it .
Given the radius of a circle is 7 cm, what is the circumference?
Answer:
14π or 43.96
Step-by-step explanation:
C = 2πr and we know that r = 7 so C = 14π or 43.96.
A=63°
C = 7.75 inch
B = 47°
Oblique Triangle
13. Refer to the oblique triangle shown. What's the length of side a? Round to the nearest hundredth of an inch.
O A. 7.75 inches
O B. 7.35 inches
O C.4.72 inches
O D. 6.03 inches
Answer:
B. 7.35 inches
Step-by-step explanation:
In the triangle:
A=63° c = 7.75 inch B = 47°Now we know that:
[tex]\angle A+\angle B+\angle C=180^\circ$ (Sum of angles in a \triangle)\\63^\circ+47^\circ+\angle C=180^\circ\\\angle C=180^\circ-(63^\circ+47^\circ)\\\angle C=70^\circ[/tex]
Using the Law of Sines
[tex]\dfrac{a}{\sin A} =\dfrac{c}{\sin C}\\\\\dfrac{a}{\sin 63^\circ} =\dfrac{7.75}{\sin 70^\circ} \\\\a=\dfrac{7.75}{\sin 70^\circ} \times \sin 63^\circ\\\\a=7.35$ inches (to the nearest hundredth of an inch)[/tex]
Answer:
B. 7.35 inches
Step-by-step explanation:
just use the law of sines
The sum of a number and 9 is subtracted from 60. The result is 10. Find the number.
Answer:
Number : 41
Step-by-step explanation:
Say that this number is x. The sum of this number ( x ) and 9 subtracted from 60 will be 10. Therefore we can create the following equation to solve for x,
60 - (x + 9) = 10,
60 - x - 9 = 10,
51 - x = 10,
- x = 10 - 51 = - 41,
x = 41
This number will be 41
Graph a line that contains the point (-7,-4)and has a slope of - 2/3
Hi there! :)
Answer:
Given the information, we can write an equation in slope-intercept form
(y = mx + b) to graph the line:
Plug in the slope for 'm', the y-coordinate of the point given for 'y', and the
x-coordinate given for 'x':
-4 = -2/3(-7) + b
-4 = 14/3 + b
Solve for b:
-12/3 = 14/3 + b
-12/3 - 14/3 = b
-26/3 = b
Therefore, the equation of the line is y = -2/3x - 26/3 (Graphed below)
Some points on the line include:
(-7, -4)
(-4, -6)
(0, -26/3)
(2, -10)
(5, -12)
Please show step by step working out of stationary points and points of inflection with the y coordinates (and sketch graph) for the equation y=x^4-36x^2
Answer:
See picture attached
Step-by-step explanation:
F(n)=6.5n+4.5 find the 5th term of the sequence defined by the given rule
Answer:
37
Step-by-step explanation:
To find the fifth term , we have to take the value of n as 5
So, F(5)= 6.5 (5) +4.5
= 32.5 + 4.5
= 37
A concert starts at 7:45pm and ends at 1:35 am. How long was the concert?
Answer:
The concert starts at 7:45 pm and ended at 1:35 am which mean the concert going on 5 hours and 50 minutes.
Find x and y, please solve with steps and leave answers in fraction form, THANK YOU
Answer:
Below
Step-by-step explanation:
Using the proprtionality relation:
● 8/10 =5/x
● (4*2)/(5*2) = 5/x
Simplify using 2
● 4/5 = 5/x
Multiply both sides by 5
● (4/5)*5 = (5/x)*5
● 4 = 25/x
Switch x and 4
● x= 25/4
■■■■■■■■■■■■■■■■■■■■■■■■■
Again use the proportionality relation but this time with y.
● 8/10 =7/y
8/10 = 4/5
● 4/5 = 7/y
Multiply both sides by 5
● (4/5)*5 =(7/y)*5
● 4 = 35/y
Switch 4 and y
● y = 35/4
In the figure below, YZA and YZX are right angles, XYZ and AYZ are congruent, and XZ = 10. What is the length of ?
A.
25
B.
20
C.
10
D.
5
Answer:
C. 10
Step-by-step explanation:
The given information tells you that triangles YZX and YZA are congruent, so ZA = ZX = 10.
Look at the number pattern shown below:3 × 17 = 5133 × 167 = 5511333 × 1667 = 555111What will be 33333 × 166667?
Answer:
33333 x 166667 = 5555511111
I think that is the answer you wanted
Step-by-step explanation:
166667
x 33333
5555511111
20
When converting from inches to feet, the measurement in inches, m, of an object varies directly with its measurement
in feet, f, with the constant of variation being 12.
What is the equation relating these two quantities?
Answer:
[tex]m=12f[/tex]
Step-by-step explanation:
The measurement in inches =m
The measurement in feet = f
We are told that: m varies directly with f
Written mathematically:
[tex]m\propto f[/tex]
Introducing the constant of variation, we have:
[tex]m=k f[/tex]
Given that: k=12
The equation relating these two quantities is:
[tex]m=12f[/tex]
helpppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answer:
4
Step-by-step explanation:
Answer:
1/8 < 1/6
Step-by-step explanation:
The top is divided into 8 and 1 part is shaded so 1/8
The bottom is divided into 6 and 1 part is shaded so 1/6
Comparing
1/8 < 1/6
Amber says that the data set is left-skewed because the box is farther to the left on the number line. (A) Is Amber correct? (B) Explain your reasoning.
A political analyst predicts Mr. Smith will only get 122 votes for mayor. If Mr. Smith only gets 57 votes, what is the political analyst's percent error?
Answer:
65%
Step-by-step explanation:
A bag contains two red marbles, four green ones, one lavender one, four yellows, and six orange marbles. HINT [See Example 7.] How many sets of four marbles include one of each color other than lavender
Answer:
192
Step-by-step explanation:
There are a total of 15 marbles . When the lavender is left out 14 remain.
Using combinations we find that each of the four color marbles can be chosen in the following way.
2C1*4C1*4C1*6C1= 2*4*4*6= 192
We select one of the two red marbles , one of the four green marbles, one of the four yellow marbles, one of the 6 orange marbles leaving the lavender out.. We apply combinations and then multiply to get the answer.
HELP PLEASE FOR 35 POINTS!!!! Solve the rational equation 3 divided by x equals quantity 4 times x plus 3 divided by x squared, and check for extraneous solutions.
Answer:
[tex]x=-3[/tex]
Step-by-step explanation:
So, we are given:
[tex]\frac{3}{x}=\frac{4x+3}{x^2}[/tex]
First, we should immediately rule out 0 as an answer. This is because the if [tex]x=0[/tex], the equation would be undefined.
[tex]x\neq 0[/tex]
Now, cross multiply.
[tex]3(x^2)=x(4x+3)[/tex]
[tex]3x^2=4x^2+3x[/tex]
Divide everything by x (and we can do this safely because we already know x cannot be equal to zero).
[tex]3x=4x+3[/tex]
[tex]-x=3[/tex]
[tex]x=-3[/tex]
We didn't run into any possibilities for extraneous solutions.