By about how much will g(x,y,z) = 3x + x cos z-y sin z+y change if the point P(x,y,z) moves from Po(1.-3,0) a distance of ds=0.1 unit toward the point P1 (-1,-1,2)?
Answers
The change in g is approximately -0.143 units. This can be answered by the concept of gradient vector.
The function g(x,y,z) is given as:
g(x,y,z) = 3x + x cos z - y sin z + y
To find the change in g as the point P(x,y,z) moves from Po(1,-3,0) to P1(-1,-1,2) by a distance of ds=0.1 unit, we can use the gradient of g and the direction of the movement towards P1. The gradient of g is given as:
∇g = [∂g/∂x, ∂g/∂y, ∂g/∂z]
= [3 + cos z, -sin z + 1, -x sin z - y cos z]
Evaluating the gradient at Po(1,-3,0), we get:
∇g(Po) = [3 + cos 0, -sin 0 + 1, -1(-3) sin 0 - (-3) cos 0]
= [4, 1, 0]
To determine the direction of the movement towards P1, we calculate the unit vector in the direction from Po towards P1:
u = [(P1 - Po)/ds]
= [(-2, 2, 2)/3.7417]
= [-0.5345, 0.5345, 0.7217]
where ds = distance between Po and P1 = √[(P1x - Pox)² + (P1y - Poy)² + (P1z - Poz)²] = √[(-2 - 1)² + (2 + 3)² + (2 - 0)²] = √29 ≈ 5.3852
Taking the dot product of ∇g(Po) and u, we get:
∇g(Po) · u = [4, 1, 0] · [-0.5345, 0.5345, 0.7217] = -1.3571
Therefore, the change in g as the point P moves from Po to P1 by a distance of ds=0.1 unit is approximately:
Δg = ∇g(Po) · u ds
= -1.3571 × 0.1
≈ -0.143
Hence, the change in g is approximately -0.143 units.
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Related Questions
What is ?1/3 X 15 I wasn’t paying attention
Answers
1/3 x 15/1 = 15/3 = 5/1 = 5
Answer
3
Step-by-step explanation:
1/3 times 15 ? is what i belive you are asking?
therefore it is three becasue it you multipy 15 by 1 then divide it by 5, 15 divide 5 is three
what is the value of A in 34×A=100
Answers
Answer:
A = 2.94
Step-by-step explanation:
You need to isolate the variable. This can be done by performing the same operation to each side to eliminate the unwanted term. In this case, you should divide both sides by 34. This removes the 34 from the left side while also doing the same thing to both sides of the equation.
When you divide 34 from 100, you are left with 2.94 on the right side. Because the only thing on the left side is the variable, this would be your answer.
1) Write your equation again so it’s easier to manipulate and change. 34 x A = 100.
2) Next, you can isolate, (or make the A variable on it’s own side of the equation), the variable
3) You can isolate the variable by dividing 34 on both sides. You divide because you are multiplying the variable A by 34 in the equation. And it can be rewritten as: 34A = 100 to what would now be: A = 100/34
4. Your final step is to divide 100 by 34, giving you the value of your variable.
100 / 34 = 2.941 or 2.9 for short.
I hope this helps, if you have any additional questions don’t hesitate to reach out to me.
The store is having a sale on 5 and a half pounds of gravel for $11.
What is the unit price?
Round to the nearest cent
Answers
Answer:
11/5.5= $2 per pound of gravel
Hope this helped :)
what expression best estimates -18 1/4 ÷ 2 2/3
a. 18÷3
b. -18÷3
c. -18÷(-3)
d. 18÷(-3)
Answers
You were recently hired by a company and will receive a starting salary of $45,000 per year. You will receive a $2,500 raise each year you are with the company. How much money will you earn altogether in the first 6 years?
Answers
Answer:
60,000
Step-by-step explanation:
So if you make 45,000 a year and you get a 2,500 raise all you need to do is add 45,000 and 2,500. Your answer for the first year is 47,500. Then you add another 2,500 to 47,500 which you will get 50,000 for your second year. The third year process is the same which is 52,500. You do this process until you get to the sixth year.
Re-write the equation 3 x minus y = 4 in slope-intercept form. a. y = 3 x minus 4 c. y = negative 3 x minus 4 b. y = 3 x 4 d. y = negative 3 x 4
Answers
The slope-intercept form of the equation of straight linr 3x - y = 4 is the option a) y = 3x - 4
The given equation is 3x - y = 4
The general slope-intercept form of a straight line is
y = mx + c
Here,
m is the slope of the straight line
and
c is the point at which x = 0 and the straight line intersects Y-axis, i.e the y-intercept
We are given
3x - y = 4
to make it to the form of the general equation we will bring 3x to RHS to get
-y = -3x + 4
removing the minus sign from y gives us the slope-intercept form
a) y = 3x - 4
Correct Question
Re-write the equation 3x - y = 4 in slope-intercept form.
a. y = 3x - 4
b. y = 3x + 4
c. y = -3x - 4
d. y = -3x + 4
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What's the numerator for the following
rational expression?
3 5 ?
+
k
74
k
k
Enter the correct answer.
Answers
The numerator for the given rational expression is 3 + 5k.
In the given rational expression, (3 + 5k) represents the numerator. The numerator is the part of the fraction that is located above the division line or the horizontal bar.
In this case, the expression 3 + 5k is the numerator because it is the sum of 3 and 5k. The term 3 is a constant, and 5k represents the product of 5 and k, which is a variable.
The numerator consists of the terms 3 and 5k, which are combined using addition (+). Therefore, the numerator can be written as 3 + 5k.
To clarify, the numerator is the value that contributes to the overall value of the fraction. In this case, it is the sum of 3 and 5k.
Hence, the correct answer for the numerator of the given rational expression (3 + 5k) / (74/k^2) is 3 + 5k.
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George and Charlotte have
150 marbles between them.
Charlotte gives George 10 of her marbles so that they
both have the same number of marbles.
How many marbles did they each have to start with?
Answers
Answer:
150:2=75
75+10=85
150-85=65
charlotte had 85 marbels and George had 65 marbels.
The number of prime factors of 3×5×7+7 is
Answers
The number of prime factors of 3×5×7+7 is 3.
To find the number of prime factors, we need to calculate the given expression:
3×5×7+7 = 105+7 = 112.
The number 112 can be factored as 2^4 × 7.
In the first step, we factor out the common prime factor of 7 from both terms in the expression. This gives us 7(3×5+1). Next, we simplify the expression within the parentheses to get 7(15+1). This further simplifies to 7×16 = 112.
So, the prime factorization of 112 is 2^4 × 7. The prime factors are 2 and 7. Therefore, the number of prime factors of 3×5×7+7 is 3.
In summary, the expression 3×5×7+7 simplifies to 112, which has three prime factors: 2, 2, and 7. The factor of 2 appears four times in the prime factorization, but we count each unique prime factor only once. Thus, the number of prime factors is 3.
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What is the domain and range of the graph?
Answers
Answer:
Not sure
i think the answer is 3
Models of inventory systems frequently consider the relationships among a beginning inventory,
a production quantity, a demand or sales, and an ending inventory. For a given
production period j, let
sj-1 = ending inventory from the previous period (beginning inventory for period j)
xj = production quantity in period j
dj = demand in period j
sj = ending inventory for period j
a. Write the mathematical relationship or model that shows ending inventory as a function
of beginning inventory, production, and demand.
b. What constraint should be added if production capacity for period j is given by Cj?
c. What constraint should be added if inventory requirements for period j mandate an
ending inventory of at least Ij?
Answers
a. This equation states that the ending inventory for period j (sj) is equal to the beginning inventory from the previous period (sj-1) plus the production quantity in period j (xj), minus the demand in period j (dj).
b. This constraint ensures that the production quantity in period j (xj) does not exceed the production capacity for that period (Cj).
c. This constraint ensures that the ending inventory for period j (sj) is greater than or equal to the required inventory level for that period (Ij).
a. The mathematical relationship or model that shows ending inventory as a function of beginning inventory, production, and demand can be represented as:
sj = sj-1 + xj - dj
This equation states that the ending inventory for period j (sj) is equal to the beginning inventory from the previous period (sj-1) plus the production quantity in period j (xj), minus the demand in period j (dj).
b. If the production capacity for period j is given by Cj, the constraint that should be added is:
xj ≤ Cj
This constraint ensures that the production quantity in period j (xj) does not exceed the production capacity for that period (Cj).
c. If inventory requirements for period j mandate an ending inventory of at least Ij, the constraint that should be added is:
sj ≥ Ij
This constraint ensures that the ending inventory for period j (sj) is greater than or equal to the required inventory level for that period (Ij).
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The International Space Station has 328 experiments in 15 different labs. What is the unit rate that
represents the amount of experiments in each lab? Round your answer to the nearest tenth.
a) 328 experiments per 15 labs
b) 21.8 experiments per lab
c) 49.2 experiments per lab
d) 21.9 experiments per lab
Answers
Rounded to nearest tenth is 21.9
So d.
What is the base of the expression 11^12?
3
11
12
21
Answers
Answer:
An exponential has the base at the bottom, or the lower portion. Think of "basement" to help remember this. The exponent is the number up top, so 12 is the exponent
therefore, the correct answer is 11
Answer:
The answer is B. 11
Step-by-step explanation:
11 is the base. 12 is the exponent. Hence why if it is worded, it is "11 to the power of 12"
Given:BC is congruent to DC, AB is congruent to ED, AG is congruent to EF. With the given information above, what is needed to prove that triangle ABF is congruent to triangle EDG
Answers
Answer:
To prove that triangle ABF is congruent to triangle EDG, we need to show that the three sides of triangle ABF are congruent to the corresponding three sides of triangle EDG.
Since we are given that BC is congruent to DC, AB is congruent to ED, and AG is congruent to EF, we can conclude that the three sides of triangle ABF are congruent to the corresponding three sides of triangle EDG. Therefore, triangle ABF is congruent to triangle EDG.
For a school fund-raiser, students sold T-shirts with the school logo for $14. PLEASE HELP!
They sold sweatshirts with the school logo for $20.
They sold 233 pieces of clothing and raised $3,748.
How many of each type of shirt did they sell at the fund-raiser?
Let x = the number of T-shirts sold.
Let y = the number of sweatshirts sold.
Answers
Answer:
The 3 problem
Step-by-step explanation:
Answer:
The answer is C) x+y = 233, 14x + 20y = 3748
Step-by-step explanation:
x(number of t-shirts sold) + y(number of sweatshirts sold) = 233 (total number of pieces of clothing sold)
14x (14 is the cost of each t-shirt and since x = number of t-shirts sold then it is 14x or 14 multiplied by number of t-shirts sold) + 20y (20 is the cost of each sweatshirt and since y = number of sweatshirts sold then it is 20y or 20 multiplied by number of sweatshirts sold) = 3748 (total of money raised)
Find the missing piece?
Answers
Answer:
7
Step-by-step explanation:
First use Pyth Theorem to find the length of the whole side.
8^2 + 20^2 = c^2
64 + 400 = c^2
21.54 = c
Round to 22
22 - 15 = 7
Is this a function or not a function?
(6, 3) (5, 3) (4, 3) (3, 3)
Answers
I need this ASAP
What is the volume to the nearest integer
Answers
Answer:
C
Step-by-step explanation:
How much higher is Veronica’s median score than James’s median score?
Answers
Answer:
12
Step-by-step explanation:
First, let's calculate both of the medians.
Veronica's Median: 141
James' Median: 129
And now, the only thing left for us to do is complete some simple subtraction.
141 - 129 = 12
Your answer is 12.
Answer:
so first you have to find out the median of both of the people. then you have to subtract both of the medians to find out how much veronicas is higher than the other guy
PLEASE HELP BRAINIEST!❤️
Answers
Answer:
B Q¹(1,2).............
Ten years ago, you could buy a loaf of bread for $1.21. Twenty years ago, you could buy a loaf of bread for $0.92.
Answers
Answer:
$0.29 is the price difference
Step-by-step explanation:
Ten years ago, you could buy a loaf of bread for $1.21. Twenty years ago, you could buy a loaf of bread for $0.92.
What is the slope of the line that passes through the points (10,3) and (7,0)? Write your answer in simplest form.
Answers
Given two points on a line, we can find its slope using the formula below
\(\begin{gathered} (x_1,y_1),(x_2,y_2) \\ \Rightarrow slope=\frac{y_2-y_1}{x_2-x_1} \end{gathered}\)Therefore, in our case,
\(\begin{gathered} (10,3),(7,0) \\ \Rightarrow slope=\frac{10-7}{3-0}=\frac{3}{3}=1 \end{gathered}\)Thus, the slope is equal to 1.
A small object at rest on a frictionless surface is attached to a wall by a frictionless spring. The object is pulled away from the wall to stretch the spring and
then released. The graph shows the displacement d, in centimeters, of the object from its resting position as a function of time t, in seconds, as the object
oscillates. Which of the following statement(s) is/are true?
Answers
A magazine atticle states that, at the end of a certain run, the speed of tho sled docreased from 1020 km/h to zero in 1.40 Part D What is a
2
, during this time? Express your answer in meters per second squared.
Answers
The acceleration of the sled is 202.54 m/s^2can be determined by calculating the change in velocity divided by the time taken. I
To find the acceleration of the sled, we need to calculate the change in velocity and divide it by the time taken.
The initial velocity is given as 1020 km/h. To convert this to meters per second, we need to multiply it by a conversion factor. Since 1 km/h is equal to 0.2778 m/s, the initial velocity can be calculated as:
Initial velocity = 1020 km/h * 0.2778 m/s = 283.536 m/s
The final velocity is given as 0 km/h, which is equal to 0 m/s.
The time taken is given as 1.40 seconds.
Using the formula for acceleration:
Acceleration = (Final velocity - Initial velocity) / Time taken
Acceleration = (0 m/s - 283.536 m/s) / 1.40 s
Simplifying this expression, we get:
Acceleration = -283.536 m/s / 1.40 s
Calculating this value, we find that the acceleration during this time is approximately -202.54 m/s².
Therefore, the acceleration of the sled, during this time, is approximately -202.54 m/s². The negative sign indicates that the sled is decelerating or slowing down.
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THIS IS FOR WHOEVER LIKES OR IS GOOD IN MATHS ITS confusing. I’ll brainlist if!!!
Answers
Answer:
jelly bean
Step-by-step explanation:
i cannot make a Venn-diagram on here so i will improvise
jelly bean | both | red
7 3 5
another way to do it is:
a jellybean=7 not a jellybean=4 a red jellybean=3 red but not a jelly bean=2 not a jelly bean or red= 2
alright last one- im very bad at this T-T 17 pointsss :)
Answers
A random sample of elementary school children in New York state is to be selected to estimate the proportion p who have received a medical examination during the past year. A random sample of 200 elementary school children indicated that 18 of them had received a medical examination in the past year.a)Find point estimate for p and also construct a 95% confidence interval for p.b) Using the information from the above sample, find the minimum sample size needed to estimate the population proportion p with 99% confidence. The estimate must be accurate to within .02 of p.
Answers
The minimum sample size needed to estimate the population proportion p with 99% confidence is 1359.
What is Random sample?
In statistics, a simple random sample is a subset of people chosen at random from a larger group, all of whom were chosen with the same probability. It is a procedure for randomly choosing a sample.
What is proportion?
A proportion is an equation that sets two ratios at the same value.
Given that;
p=18/200
95% means using 1.96
So, point estimate for p is ;
18/200+1.96*sqrt(18*182/200^3)
18/200-1.96*sqrt(18*182/200^3), 18/200+1.96*sqrt(18*182/200^3)
{0.0503372, 0.129663}
Using MoE equation:
.02=2.576*sqrt(18*182/200^2/n)
n=1358.6
n=1359
Hence, the population proportion p with 99% confidence is 1359.
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What is the following product? RootIndex 5 StartRoot 4 x squared EndRoot times RootIndex 5 StartRoot 4 x squared EndRoot.
Answers
You can use the fact that whenever bases are same, the product of such quantities end up getting their exponents added.
The product result of given expression is \(^5\sqrt{(2x)^4}\)
When does the power add in multiplication?Suppose you've got two values to multiply with each other and you have got both value's bases same, then the multiplication will end up with result being that base raised with sum of the exponents of both the initial values.
For example:
\(a^b \times ^c =a^{b+c}\)
How to find the product result for given expression?You can convert the roots to powers. Then you can use the fact that the bases are same and thus the powers will add.
Remember that if you've got xth root, then the power would be 1/x.
For our case, it will go like this:
\(^5\sqrt{4x^2} \times ^5\sqrt{4x^2} = \: ^5\sqrt{(2x)^2} \times ^5\sqrt{(2x)^2} = {((2x)^2)}^{\frac{1}{5}} \times {((2x)^2)}^{\frac{1}{5}} = (2x)^{\frac{2}{5}} \times (2x)^{\frac{2}{5}}\\\\ ^5\sqrt{4x^2} \times ^5\sqrt{4x^2} = (2x)^{\frac{2}{5} + \frac{2}{5}} = (2x)^{\frac{4}{5}} = \: ^5\sqrt{(2x)^4}\)
Thus, the final product result will be written as \(^5\sqrt{(2x)^4}\)
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Which set of values makes the inequality n > -5 true?
А
{-5, -5.5,-6)
B
{-5, -4.5, -3)
Ć
(-6,0,5)
D
{-6, -7,-8}
Answers
Answer:
the answer is c :)
Step-by-step explanation:
Find the value of x. Write your answer in simplest form. need help quick pls
Answers
Answer:
The value of x is approximately 5
Step-by-step explanation:
Answer:
x=6.36
Step-by-step explanation:
In a right triangle where the angles are 45, 45 and 90, the hypotenuse is equal to \(\sqrt{2}\) multiplied by the length of the legs. Knowing this, we can set up the following equation:
\(9=x\sqrt{2}\)
Multiply both sides by \(\sqrt{2}\)
\(9\sqrt{2} =x\sqrt{2}*\sqrt{2}\\9\sqrt{2} =2x\)
Divide both sides by 2
\(\frac{9\sqrt{2}}{2}=\frac{2x}{2}\\\frac{9\sqrt{2}}{2}=x\)
\(x=6.36\) (this answer is approximate)
Therefore, x is equal to 6.36.
I hope this helps!