Answer and Step-by-step explanation:
SOLUTION:
Given function:
h (x, y, z) = ln (x2 + y2 – 1) + y +6z, p0(1, 1, 0)
Derivatives of the function:
∂h / ∂x = (1 / x2 + y2 -1). (2x)
= 2x / x2 + y2 -1
∂h/∂y = (1 / x2 + y2 – 1) (2y + 1)
= (2y / x2 + y2 -1) + 1
∂h / ∂z = 6
Now compute the partial derivatives:
∂h (1, 1, 0) / ∂x = 2(1) / 1 +1 -1
= 2
∂h(1, 1, 0) / ∂y =( 2(1) / 1 +1 -1) + 1
= 3
∂h (1, 1, 0) / ∂z = 6
Δh (1,1,0) = ( 2, 3, 6)
The definition of gradient is:
Δf (x, y, z) = (∂f / ∂x , ∂f / ∂y)
Put the coordinate values to arrive at solution:
Umax = Δh (1,1,0) / | Δh (1,1,0) |
= (2, 3, 6) / |2, 3, 6|
= (2, 3, 6) / √(22+33+62)
= (2, 3, 6) / √49
= (2, 3, 6) / 7
= (2/7 , 3/7, 6/7)
Umin = - U max = ( -2/7, -3/7, -6/7)
Compute direction by finding unit vector:
Du h max = Δh (1,1,0) . u max
= (2, 3, 6) . (2/7, 3/7, 6/7)
= 2(2/7) + 3(3/7) + 6(6/7)
= 4/7 + 9/7 +36/ 7
= 49 / 7
= 7
Du h min = -Du h max
= -7
A pallet full of soda contains 40 12-packs. The pallet itself weighs about 25 lbs and with
the pop weighs 410 lbs. How much does a can of pop weigh?
Answer:
0.802 lbs or 12.8 ounces(British).
Step-by-step explanation:
Weight of the pop = 410 - 25 = 385 lbs.
40 12-packs contains 40*12 = 480 cans,
So the weight of one can = 385 / 480
= 0.802 lbs
or about 12.8 ounces(British).
convert 3250 ml to L
Answer:
3250 milliliters transfers into 3.25 liters.
Describe a transformation that would make quadrilateral ABCD into a square
I NEED URGENT HELP PLEASE
Answer:
ok, relax and listen I’ve got this ok?
Step-by-step explanation:
You just move it up 4 squares to (2, 9), (10,9)
see?you got this I believe in you!!!
Tell whether the lines through the given points are parallel, perpendicular, or neither.
Line 1: (10,5), (-8, 9)
Line 2: (2, - 4), (11, - 6)
The slope of line 1 is.
The slope of line 2 is.
The two lines are...
use
[tex]y - y_{1} = \frac{ y_{2} - y_{1}}{x_{2} - x_{1}} \times (x_{2} - x_{1})[/tex]
slope is
[tex]m = \frac{ y_{2} - y_{1}}{x_{2} - x_{1}} \\[/tex]
[tex]if \: \: m_{1} = m_{2} \: \: lines \: are \: parallel \\ [/tex]
[tex]if\:m_{1} = - \frac{1}{m_{2}} \\ lines \: are \: perpendicular \: to \: each \: other[/tex]
Parallel lines have the same slope
The slope of line 1 is -2/9The slope of line 2 is -2/9The two lines are parallelThe slope of a line is calculated as:
[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]
The slope of line 1 is:
[tex]\mathbf{m_1 = \frac{9 - 5}{-8 - 10}}[/tex]
[tex]\mathbf{m_1 = \frac{4}{-18}}[/tex]
[tex]\mathbf{m_1 = -\frac{2}{9}}[/tex]
Hence, the slope of line 1 is -2/9
The slope of line 2 is:
[tex]\mathbf{m_2 = \frac{-6 - -4}{11 - 2}}[/tex]
[tex]\mathbf{m_2 = \frac{-2}{9}}[/tex]
[tex]\mathbf{m_2 = -\frac{2}{9}}[/tex]
Hence, the slope of line 2 is -2/9
The lines have the same slope.
Hence, the two lines are parallel
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If one angle of a set of vertical angles measures 63°, the sum of the vertical angles is °?
Answer:
126
Step-by-step explanation:
the answer is 126 degrees, °
Suppose a granola bar company estimates that its monthly cost is
C(c) = 500x2 + 400% and its monthly revenue is
R(x) = -0.62% + 80022 – 300x + 600, where x is in thousands of
granola bars sold. The profit is the difference between the revenue and the
cost.
What is the profit function, P(x)?
A. P(x) = -0.623 + 1300x2 + 100x + 600
B. P(x) = 0.62+ 300x2 – 700x + 600
C. P(x) = -0.6x3 + 300x2 – 700x + 600
D. P(2) = 0.623 – 300x2 + 700x - 600
Answer:
C. P(x) = -0.6x3 + 300x^2 – 700x + 600
Step-by-step explanation:
The profit function is P(x) = -0.6x³ + 300x² - 700x + 600.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Given,
Cost function, C(x) = 500x² + 400x
Revenue function, R(x) = -0.6x³ + 800x² - 300x + 600
Profit is the difference between the revenue and the cost.
Profit function is therefore the difference of revenue function and the cost function.
P(x) = R(x) - C(x)
P(x) = (-0.6x³ + 800x² - 300x + 600) - (500x² + 400x)
= -0.6x³ + 800x² - 300x + 600 - 500x² - 400x
= (-0.6x³) + (800x² - 500x²) + ( - 300x - 400x) + 600
= -0.6x³ + 300x² - 700x + 600
Hence the profit function of the granola bar company is P(x) = -0.6x³ + 300x² - 700x + 600.
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can someone help me
Answer:
The volume is 75
Step-by-step explanation:
because the volume is the width, length, and height, add them together.
Answer:
2700m
Step-by-step explanation:
you have to do L*W*H for both shapes then add
What proportion of these motors will last somewhere between 8 and 11 years
Answer: What Proportion Of These Motors Will Last Somewhere Between 8 And 11 Years? 2. What's The Probability That A Randomly Selected Motor Will Last More
the number of standard deviations a value is from the mean ... Suppose X ~ N(8, 1). ... Find the probability that a CD player will last between 2.8 and six years. a. ... A child who weighs 11 kg is one standard deviation above the mean of 10.2 kg. b. ... There is about a 68% chance that the number of heads will be somewhere.
Maria bought a blouse on sale for 30% off. The sale price was $28.76. What was the original price? Write an equation to model the situation and solve it. Use variable p for the original price. Round to the nearest hundredth.
Answer:
The original price is 37.38
Step-by-step explanation:
I'm tired and don't want to explain too much but you get 30 percent then add that number to the first price.
1. Utilice la función y=0.17% - 3.0 para encontrar lo siguiente.
a) Estime la pendiente de la recta tangente a la curva, donde x = 0,1,2,3.
Pendiente de la recta
Х
tangente
-1
O
1
3
b) ¿en qué intervalos aumenta la función? ¿En qué intervalos está disminuyendo?
c) ¿En qué intervalo o intervalos es positiva la pendiente de la recta tangente? ¿E
intervalo o intervalos es negativa la pendiente de la recta tangente? ¿Cuál es la c
estas preguntas y la parte (b)
c) ¿Dónde parece que la pendiente de la recta tangente es cero? ¿Qué propiedad
gráfica ocurren en estos puntos?
d) ¿Dónde parece la línea tangente aproximarse mejor a la curva? ¿Lo peor? ¿Qu
del gráfico parecen hacer que sea así?
According to the distributive property, 6(5 + 3) =
Answer:
48
Step-by-step explanation:
if given f(x)=2x+5 what is f(4)
Answer:
13
Step-by-step explanation:
f(4) means you plug in 4 for x so 2(4) + 5 = 8 +5 = 13
Answer: 13
Step-by-step explanation:
Plug 4 into the position of x in your equation and solve.
If the second term in a geometric sequence is -8 and the common ratio is 2, what is the value of the third term?
-4
-10
-16
Answer:-16
Step-by-step explanation:
The 3 in the 73.084 _ times the 3 in 65.732.
Answer:
it would be 3.0 times 0.03 so the answer is 0.9
A friend of yours was interested in computing a confidence interval for the mean student debt accumulated by NC State graduates during their undergraduate education. They collected a random sample of 40 students, and asked each how much student debt they had; all responded and responded honestly. A histogram of the data indicated it was normally distributed. They computed a 95% confidence interval of ($36,400, $41,650). However, they were unsatisfied with the margin of error, wanting a more precise interval. Referring to their ST 311 notes, they noted that in order to reduce the margin of error by half, they needed to increase their sample size by a factor of 4. So, they collected another random sample of 160 students and found another 95% confidence interval, which was much narrower, having a margin of error of $1,318. They are satisfied with the precision of the confidence interval, but are a little confused : it’s not quite half the original margin of error. Explain why the margin of error wasn’t quite reduced by a factor of 0.5. Be specific.
Answer:
Explained below.
Step-by-step explanation:
The (1 - α)% confidence interval for the population mean is:
[tex]CI=\bar x\pm z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}[/tex]
The margin of error for this interval is:
[tex]MOE= z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}[/tex]
The factors affecting the MOE are:
The sample size (n) is inversely proportional to the MOE, thus increasing n decreases the MOE and vice-versa. Variance (σ²) is the square of S.D. So if we increase σ² then σ increases. Since σ is directly proportional to MOE, increasing σ increases MOE. The confidence level is the value of (1 – α). If we increase the confidence level then the critical value increases and thus MOE also increases.Since the population standard deviation is not provided it is obvious the sample standard deviation is used to estimate the value of σ.
On increasing the value of σ the MOE will also increase.
As the sample size is inversely proportional, increasing the sample size by a factor of 4 will reduce the margin of error by half. But since σ is also increasing there are two factors affecting the MOE together.
Therefore reducing the MOE by more than half the original value.
What is NOT a way to write 52 + 80?
A.
50 + 2 + 80
B.
(50 + 80) + 2
c.
50 + 80 + 2 + 8
D.
50 + 2 + 80 + 0
Answer: C
Step-by-step explanation: 50+2+80+8 is not right
Side Length
(inches)
Perimeter
(inches)
0.5
2
7
?
20
Answer: The missing side is 10.5 inches
Step-by-step explanation:
Add the side lengths you know 0.5+2+ 7= 9.5
Subtract that from 20 20- 9.5 = 10.5
Don't forget to include the unit length,inches.
Find the slope of the line that passes through
the two given points: (2, 3) and (6, -13)
Answer:
-4
Step-by-step explanation:
-13-3=-16
6-2=4
-16/4=-4
Step-by-step explanation:
Hey there!
The points are; (2,3) as (X1,y1) and (6,-13) as (x2,y2)
Use the formula for slope.
[tex]slope(m) = \frac{y2 - y1}{x2 - x1} [/tex]
Put all values.
[tex]m = \frac{ - 13 - 3}{6 - 2} [/tex]
Simplify it to get answer.
[tex]m = \frac{ - 16}{4} [/tex]
Therefore, slope(m) = -4.
Hope it helps....
HHHHHHEEEEEELLLLLLPPPPPP!!!!!!
Answer:
Undefined
Step-by-step explanation:
if the line is like this __________________ then the slope is zero
If the line is vertical like up and down then the line is undefined.
Hope this helped!!!
Answer:
It is undefined slope so it would be x=3
Step-by-step explanation:
What is the solution to the system of equations?
{2x+3y=23
4x−5y=13
List the sides of triangle ABC from largest to smallest if m
give a verbal description of (7, ∞)
Geometry math question help please look at the attachment. :)
Answer:
x=20
Step-by-step explanation:
2x + 20 = 3x
-2x -2x
20 = x
3.1 plus 7.4 plus 6.9
Answer: 17.4
Step-by-step explanation:
There isn't much to it... it's basic addition.
I guess if you were not using a calculator you would set it up like this:
3.1
+7.4
+6.9
---------
17.4
Answer:
17.4
Step-by-step explanation:
if you estimate all of these you get 3,7, and 7, these(added together) are 17,
Susan paid for 6 shirts to be delivered.
Each shirt cost $15.00.
Susan paid $9.99 for delivery.
What is the total amount that Susan Paid?
Answer:
$99.99
Step-by-step explanation:
6 x 15 = 90
+ 9.99
6b.) Hence, or otherwise, evaluate g(f(3))
Answer:
-25
Step-by-step explanation:
g(f(3))= g(-5)
=4(-5)-5
= -20-5
=-25
Answer:
[tex]g(f(3))=-25[/tex]
Step-by-step explanation:
We have the two functions: [tex]f(x)=-2x+1[/tex] and [tex]g(x)=4x-5[/tex].
And we want to evaluate [tex]g(f(3))[/tex].
So, let's evaluate f(3) first. Substitute 3 into f(x). This yields:
[tex]f(3)=-2(3)+1[/tex]
Multiply and add:
[tex]f(3)=-6+1=-5[/tex]
So, our expression is now:
[tex]g(f(3))\Rightarrow g(-5)[/tex]
Substitute -5 for g(x):
[tex]g(-5)=4(-5)-5[/tex]
Multiply and subtract:
[tex]g(-5)=-20-5=-25[/tex]
Therefore:
[tex]g(f(3))=-25[/tex]
you have a blender mixed with raspberries,blueberries,ice, and water.Which of the following will NOT change when mixed together?
Answer: actually the mass
Step-by-step explanation: regardless on where you are the mass never change, it's the wait within a substance or a matter
20. A rectangle has a length of x + 2 meters and a width of 2x - 5. (A.APR.1)
A. Write an expression for the perimeter of the rectangle. Simplify your final answer.
B. Write an expression for the area of the rectangle. Simplify your final answer.
x + 2
2x - 5
A. Perimeter =
B. Area =
C. If x is 5, what is the perimeter? What is the area?
Rubric
2 pts - Two key elements are present
1 pt - One key element is present
O pts - No key elements are present
Answer:
A:
2(x + 2) + 2(2x - 5) =
2x + 4 + 4x - 10 =
6x - 6
perimeter = 6x - 6
B:
(x+2)(2x - 5) expand the brackets:
2x² - 5x + 4x - 10
area = 2x² - x - 10
C:
area = 6x - 6 = (6 x 5) - 6 = 30 - 6 = 24
perimeter = 2x² - x - 10 = (2 x 5²) - 5 - 10 = (2 x 25) - 5 - 10 = 50 - 5 - 10 = 35
brainliest please? x
Dina just accepted a new job. She expects to earn about $135 a week during the 34-week
school year and $450 a week during the remainder of the year. How much should Dina
earn next year?
A computer can perform 4.66 x 10^8 calculations per second, what is the performance of the computer in one minute?
any help is appreciated!!
Answer:
4.66 x 10^9
Step-by-step explanation:
The performance of the computer in one minute is 2.70x10¹⁰ per minute after performing unit conversion.
What is unit conversion?It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.
It is given that:
A computer can perform 4.66 x 10⁸ calculations per second,
As we know,
1 minute = 60 seconds
1 second = 1/60 minutes
The performance of the computer in one minute = 4.66 x 10⁸(1/(1/60))
The performance of the computer in one minute = 4.66x60x 10⁸
The performance of the computer in one minute = 279.6x10⁸
= 2.70x10¹⁰ per minute
Thus, the performance of the computer in one minute is 2.70x10¹⁰ per minute after performing unit conversion.
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