Use the Chain Rule to find dz/dt. 5 + x2 + y2, x = 4 In(t), y = cos(t) Z= dz dt II Need Help? Read It Watch It
Answers
To find dz/dt using the chain rule, we first need to find the partial derivatives of z with respect to x and y:
∂z/∂x = 2x
∂z/∂y = 2y
Next, we can use the chain rule to find dz/dt by substituting the given values of x and y and taking the derivative with respect to t:
dz/dt = ∂z/∂x * dx/dt + ∂z/∂y * dy/dt
Substituting x = 4 ln(t) and y = cos(t):
dz/dt = 2(4 ln(t)) * (1/t) + 2(cos(t)) * (-sin(t))
Simplifying:
dz/dt = (8/t)ln(t) - 2cos(t)sin(t)
Therefore, the value of dz/dt is (8/t)ln(t) - 2cos(t)sin(t).
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Related Questions
What is the relationship between ∠a and ∠b?Choose 1 answer:A. Vertical anglesB. Complementary anglesC. Supplementary anglesD. None of the above
Answers
Answer:
C. Supplementary angles
Explanation:
Angles a and b are on the straight line AC.
Recall that the sum of angles on a straight line is 180 degrees.
If two angles add up to 180 degrees, they are said to be Supplementary.
Hence angles a and b are Supplementary angles.
(a) The area of a rectangular parking lot is 6279 m². If the length of the parking lot is 91 m, what is its width? Width of the parking lot:
Answers
Answer:
The width of the parking is 69 meters
Step-by-step explanation:
Rectangle area = L*W
6279 = 91*W
Widht = 6279/91
W = 69 m
A ball is dropped from a cliff that is 135 m high.
The relationship between the height of the ball,
h, in metres, and time, t, in seconds, can be
represented by the equation h = –4.9t
2 + 135.
Which is closest to the height of the ball after
2.1 seconds?
Answers
Answer:
113 feet
Step-by-step explanation:
I will assume you meant h = -4.9t^2 + 135; "t2" is incorrect.
To answer this question, to find the height of the ball after 2.1 seconds, substitute 2.1 for t in the above equation:
h(2.1) = -4.9(2.1)^2 + 135. This becomes -21.6 + 135, or 113.4.
The closest result to the height of the ball after 2.1 seconds is 113 feet.
I NEED HELP WITH THIS PLS HELP!!!
Answers
Answer:
29.7 m^3
Step-by-step explanation:
Hope this helps
A formula containing the entry =j$7 is copied to a cell three columns to the right and four rows down. how will the entry display in its new location?
Answers
In its new location, the entry will display as =M$7.
When a formula containing the entry =J$7 is copied to a cell three columns to the right and four rows down, certain adjustments occur. The entry has a dollar sign ($) before the row number, which means the row reference remains fixed during copying, while the column reference adjusts relatively.
For the row adjustment, copying four rows down from J$7 results in the new row reference being 7 + 4 = 11.
For the column adjustment, copying three columns to the right from J$7 means that the column reference moves three letters to the right, resulting in the new column reference being M.
Combining the adjusted row and column references, we get =M$7 as the entry displayed in its new location.
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On Tuesday, the number of orange cakes Aadil needs in his sample is 5 correct to the nearest whole number. Aadil takes at random a cake from the 750 cakes made on Tuesday. b) What is the lower bound of the probability that the cake is an orange cake, giving your answer as a decimal?
Answers
Answer:
A) 210 B) 0.18
Step-by-step explanation:
got it right
–8( — 10и + би — 7) – 10и
Answers
Answer:
22и + 56
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Parenthesis (add)
-8(-4и - 7) - 10и
Step 2: Distribute (multiply)
32и + 56 - 10и
Step 3: Combine like terms (и)
22и + 56
Find the general term T(n) of the sequence -1, 2, 5, 8, .... a. T(n) = 3n - 4 b. T(n) = 4n - 3 c. T(n) = n-2 d. T(n)=4-3n
Answers
To find the general term of the sequence -1, 2, 5, 8, ..., we need to examine the pattern in the terms.
Looking at the sequence, we can observe that each term is obtained by adding 3 to the previous term. Therefore, the common difference between consecutive terms is 3.
We can start with the initial term, -1, and then add multiples of the common difference (3) to find subsequent terms.
Starting with n = 1:
T(1) = -1 + (1 - 1) × 3 = -1 + 0 × 3 = -1
Starting with n = 2:
T(2) = -1 + (2 - 1) × 3 = -1 + 1 × 3 = 2
Starting with n = 3:
T(3) = -1 + (3 - 1) × 3 = -1 + 2 × 3 = 5
Starting with n = 4:
T(4) = -1 + (4 - 1) × 3 = -1 + 3 × 3 = 8
From the pattern, we can see that each term can be obtained by multiplying n - 1 by 3 and then subtracting 1.
Therefore, the general term T(n) of the sequence -1, 2, 5, 8, ... can be expressed as:
T(n) = 3(n - 1) - 1
Simplifying this expression, we get:
T(n) = 3n - 3 - 1
T(n) = 3n - 4
So the correct option is a. T(n) = 3n - 4.
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Mr.Richardson would like to build a planter surrounded by a brick path
Answers
Answer: It is 128
Step-by-step explanation: Byee stay safe: Wear your mask, drink water and stan bts
also can I have brainliest
According to a government agency, 18.6% of the population of a certain country smoked in 2016. In 2018, a random sample of 612 citizens of that country was selected, 97 of whom smoked. Complete parts
Answers
The 99% confidence interval for the proportion in 2018 is given as follows:
(0.1205, 0.1965).
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In which the variables used to calculated these bounds are listed as follows:
\(\pi\) is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The critical value for the 99% confidence interval using the z-distribution is given as follows:
z = 2.575.
The parameters for this problem are given as follows:
\(n = 612, \pi = \frac{97}{612} = 0.1585\)
The lower bound of the interval is given as follows:
\(0.1585 - 2.575 \times \sqrt{\frac{0.1585(0.8415)}{612}} = 0.1205\)
The upper bound of the interval is given as follows:
\(0.1585 + 2.575 \times \sqrt{\frac{0.1585(0.8415)}{612}} = 0.1205\)
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factorise and divide: (3y^8 - 4y^6 + 5y^4) ÷ y^3
Answers
Answer:
\( \star→ \: { \sf{ \frac{ \{ {3y}^{8} - {4y}^{6} + {5y}^{4} \}}{ {y}^{3} } }} \\ \)
• factorization:
\( \star→ \: { \sf{ \frac{ {y}^{3}(3y {}^{5} - 4 {y}^{3} + 5 {y} }{ {y}^{3} }}} \\ \\ \star→ \: { \sf{ \frac{ {y}^{3} }{ {y}^{3} } .^{}(3y {}^{5} - 4 {y}^{3} + 5 {y}}})\)
• divide:
\( = { \boxed{ \boxed{ \sf{y(3 {y}^{4} - 4 {y}^{2} + 5)}}}}\)
affu it so hard question please help me
\( \frac{x - 1}{ {x}^{2} - 3x + 2 } + \frac{x - 2}{ {x}^{2} - 5x + 6} + \frac{x - 5}{ {x}^{2} - 8x + 15} \)
Answers
9514 1404 393
Answer:
(3x-7)/(x^2-5x+6)
Step-by-step explanation:
Not particularly hard, just tedious. You need to factor all the quadratics, cancel common factors, and combine terms using a common denominator.
\(\dfrac{x-1}{x^2-3x+2}+\dfrac{x-2}{x^2-5x+6}+\dfrac{x-5}{x^2-8x+15}\\\\=\dfrac{x-1}{(x-1)(x-2)}+\dfrac{x-2}{(x-2)(x-3)}+\dfrac{x-5}{(x-3)(x-5)}=\dfrac{1}{x-2}+\dfrac{1}{x-3}+\dfrac{1}{x-3}\\\\=\dfrac{1}{x-2}+\dfrac{2}{x-3}=\dfrac{(x-3)+2(x-2)}{(x-2)(x-3)}=\dfrac{x-3+2x-4}{x^2-5x+6}\\\\\boxed{\dfrac{3x-7}{x^2-5x+6}}\)
Answer:
\(\rm \displaystyle \frac{3x - 7}{ {x}^{2} - 5x + 6 } \)
Step-by-step explanation:
we would like to simplify the following:
\( \rm\displaystyle \frac{x - 1}{ {x}^{2} - 3x + 2 } + \frac{x - 2}{ {x}^{2} - 5x + 6} + \frac{x - 5}{ {x}^{2} - 8x + 15}\)
to simplify algebraic expression the first step is to figure out the LCM of the denominator in order to do so we can factor the denominators therefore factor the denominators and work out the LCM
\(\rm\displaystyle \frac{x - 1}{ (x - 1)(x - 2)} + \frac{x - 2}{ (x - 2)(x - 3)} + \frac{x - 5}{(x - 5)(x - 3)}\)
reduce fraction:
\(\rm\displaystyle \frac{1}{ x - 2} + \frac{1}{ x - 3} + \frac{1}{x - 3}\)
figure out the LCM and divide it by the denominator and multiply the result with the numerator which yields:
\(\rm\displaystyle \frac{1}{ x - 2} + \frac{1}{ x - 3} + \frac{1}{x - 3} \\ \\ \displaystyle \frac{x - 3 + x - 2 + x - 2}{(x - 2)(x - 3)} \)
simplify addition:
\(\rm \displaystyle \frac{3x - 7}{(x - 2)(x - 3)} \)
further expansion if necessary:
\(\rm \displaystyle \frac{3x - 7}{ {x}^{2} - 5x + 6 } \)
if you jog 1 mile in 10 minutes how many miles do you run in a minute
Answers
Answer:
.1 mi/min
Step-by-step explanation:
Hilton Head Island is about 12 miles long. Susan has a map that shows the island. If the scale on the map is 1 inch = 1/2 mile, what is the length of the island on Susan's map?
Answers
Answer:
20 inches long
Step-by-step explanation:
if 1inch=1/2 miles
then,1/2×12
___________
1
=1/2×12
=24 inches
can you make a square with 24 tiles? Why or Why not?
Answers
Answer:
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
You want to know if 24 tiles can be used to make a square.
Aspect ratio24 tiles can be made into rectangles of different aspect ratios:
1 × 24
2 × 12
3 × 8
4 × 6
If the aspect ratio of a tile matches any of these, then 24 tiles can be used to make a square.
For example, a 2×3 tile shape can be arranged in rows of 6 tiles along the "2" dimension and 4 tiles along the "3" dimension. Then the total side length in each case is ...
6×2 = 12 = 4×3
and the resulting figure is a square.
Hole in the middle24 square tiles can be arranged in a 5×5 array with a missing tile in the middle spot. That array will be square.
Similarly, they can be arranged in a square outline that has 7 tiles on each side (5 between the corner tiles).
24 square tiles cannot be used to make a solid square. For that, you need a square number of tiles.
1
A line segment has the endpoints (-7,-4) and (9,8). What are the coordinates of the
midpoint of this line segment?
Answers
4 x + 6 < − 6 Help me please
Answers
Answer:
x<-3
Step-by-step explanation:
Let's do this step by step:
1) isolate 4x : 4x<-6-6
2) so then we get : 4x<-12
3) isolate x : x< -12/4
WHICH GETS YOU TO: x<-3
Answer:
4x + 6 < -6 = x < −3
The value of x = -2 or greater
In a binomial situation, n=18 and π=0.60. Determine the expected
value
Answers
The expected value in a binomial situation with n = 18 and π = 0.60 is E(X) = np = 18 * 0.60 = 10.8.
In a binomial situation, the expected value, denoted as E(X), represents the average or mean outcome of a random variable X. It is calculated by multiplying the number of trials, denoted as n, by the probability of success for each trial, denoted as π.
In this case, we are given n = 18 and π = 0.60. To find the expected value, we multiply the number of trials, 18, by the probability of success, 0.60.
n = 18 (number of trials)
π = 0.60 (probability of success for each trial)
To find the expected value:
E(X) = np
Substitute the given values:
E(X) = 18 * 0.60
Calculate the expected value:
E(X) = 10.8
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Please answer honestly! <3
Answers
Evaluate by finding the value of x. 2/3x = 24
Answers
Answer:
x = 36
Step-by-step explanation:
given three points that lie on the parabola, find the equation that represents this parabola in standard form
Answers
The equation that represents this parabola in standard form is y = x²
Find the equation that represents this parabola in standard formFrom the question, we have the following parameters that can be used in our computation:
(0,0) , (1,1) and (-1, 1)
A parabola in standard form is represented as
y = ax² + bx + c
Using the points, we have
(0)²a + (0)b + c = 0
c = 0
Next, we have
(1)²a + (1)b + 0 = 1
a + b = 1
(-1)²a + (-1)b + 0 = 1
a - b = 1
Add the equations
2a = 2
a = 1
So, we have
1 + b = 1
b = 0
This means that the equation is y = x²
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Question
Given three points that lie on the parabola, find the equation that represents this parabola in standard form
(0,0) , (1,1) and (-1, 1)
find product6,372x75
Answers
Answer:
i like c ock
Step-by-step explanation:
Simplify 10 times the square root of quantity 3 x end quantity plus 4 times the square root of quantity 3 x end quantity plus 5 times the square root of quantity 3 x end quantity.
Answers
The value of the expression is 19 times the square root of quantity 3 x end quantity
How to simplify the expression?The expression is given as:
10 times the square root of quantity 3 x end quantity plus 4 times the square root of quantity 3 x end quantity plus 5 times the square root of quantity 3 x end quantity.
Rewrite the expression properly:
10 * √3x + 4 * √3x + 5 * √3x
Evaluate the product
10 √3x + 4√3x + 5√3x
Evaluate the sum
19√3x
This can be rewritten as:
19 times the square root of quantity 3 x end quantity
Hence, the value of the expression is 19 times the square root of quantity 3 x end quantity
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What is the volume?
4.2 mm
4.2 mm
4.2 mm
Answers
Answer:
74.088 mm^3
Step-by-step explanation:
V = l * w * h
V = 4.2 * 4.2 * 4.2
V = 74.088 mm^3
Betty correctly determined that the ordered pair (–3, 5) is a solution to the system of linear equations 6 x 5 y = 7 and x 4y = 17. Based on this information, which statement is correct? (–3, 5) satisfies neither the equation 6x 5y = 7 nor the equation x 4y = 17. (–3, 5) satisfies the equation 6x 5y = 7 but not the equation x 4y = 17. (–3, 5) satisfies the equation x 4y = 17 but not the equation 6x 5y = 7. (–3, 5) satisfies both the equation 6x 5y = 7 and the equation x 4y = 17.
Answers
(–3, 5) satisfies both the equation 6x+ 5y = 7 and the equation x +4y = 17.
Given thatBetty correctly determined that the ordered pair (–3, 5) is a solution to the system of linear equations 6 x + 5 y = 7 and x + 4y = 17.
We have to determineBased on this information, which statement is correct?
According to the questionIf a system of equations of two variables has a single solution (x, y), then both equations must be satisfied for x and y.
We are given the system:6 x + 5 y = 7
x + 4y = 17
The ordered pair (–3, 5) is a solution to the system of linear equations.
\(=\rm 6x +5y=17\\\\6\times (-3) + 5 \times 5 \\\\ =-18 + 25 = 7\\\\ And\\\\ x+4y = 7 \ -3 + 4\times 5\\\\ -3+20 \\\\ = 17\)
Hence, (–3, 5) satisfies both the equation 6x+ 5y = 7 and the equation x +4y = 17.
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Answer:
I believe the answer is D
Step-by-step explanation:
Cathy wants to pack 100 gifts. The packaging includes a closed box made out of cardboard. The dimensions of the box are 11cm Long , 8cm wide and 8cm high. In square centimeters l, what is the minimum amount it cardboard Cathy needs to package all the gifts?
Answers
Answer:
\(10800\ \text{cm}\)
Step-by-step explanation:
l = Length = 11 cm
w = Width = 8 cm
h = Height = 8 cm
Perimeter of cardboard required for one box is
\(4(l+w+h)=4(11+8+8)\\ =108\ \text{cm}\)
There are 100 gifts to pack so the total amount of cardboard needed would be
\(108\times 100=10800\ \text{cm}\)
So, the minimum amount of cardboard Cathy needs to package all the gifts is \(10800\ \text{cm}\).
find the mode of give data
14,12,8,7,12,12,14,8,12,8,12,7
\(class8\)
Answers
Hey there!
FACT:MODE is the number you see MORE THAN once in your particular data plot/set.
⎯⎯ ୨YOUR SET ୧ ⎯⎯
14, 12, 8, 7, 12, 12, 14, 8, 12, 8, 12, 7
⎯⎯୨ BREAKING DOWN the SET୧⎯⎯
14 is seen TWO times
12 is seen FIVE times
8 is seen THREE times
7 is seen TWO times
Therefore, your answer is: 12
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
There are 12 crayons in a box. How many boxes will be needed for 8 children if each child gets 7 crayons?
please awnser whover awnsers get 100 points
Answers
Each child gets =7×8=56crayoms
One box contains 12 crayonsTotal boxes
56/124.66Round to next whole as we can't have depict
5 boxesAnswer:
5 boxes
Step-by-step explanation:
There are 12 crayons in one box.
So,8×7=56
56crayons
Then divide 56 and 12
56 ÷12 =4.66
Round of 4.66 and u will get 5
So,the answer is 5 boxes
Help me ASAP!!!!!
See picture attached
Answers
n=18 is the correct answer to the question
Jim takes out a mortgage for 30 years at an interest rate of 2. 49% and his monthly repayments are $986. 50. What is the principal loan amount? Round your answer to the nearest ten thousand dollars. Do NOT round until you have calculated the final answer
Answers
The principal mortgage amount is $220,000.
To compute the principal loan amount, we need to apply the compound interest formulation for a loan:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
Where M is the monthly reimbursement, P is the primary mortgage amount, i is the month-to-month interest charge, and n is the range of months.
First, we need to calculate the month-to-month interest charge:
i = 2.49% / 12 = 0.02075
Subsequent, we want to calculate the range of months:
n = 30 years x 12 months/year = 360 months
Now we are able to plug in the given values:
$986.50 = P [ 0.02075(1 + 0.02075)^360 ] / [ (1 + 0.02075)^360 – 1]
Solving for P, we get:
P = $221,114.07
Rounding to the nearest ten thousand dollars, the principal mortgage amount is $220,000.
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