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alekssr [168]
3 years ago
12

The temperature at a point (x, y) on a flat metal plate is given by t(x, y) = 23/(8 + x2 + y2), where t is measured in °c and x,

y in meters. find the rate of change of temperature with respect to distance at the point (1, 1) in the x-direction and the y-direction.
Mathematics
1 answer:
Firlakuza [10]3 years ago
5 0
∂t/∂x = -46x/(8 +x² +y²)²
∂t/∂y = -46y/(8 +x² +y²)²

At (x, y) = (1, 1)
.. ∂t/∂x = -46/100
.. ∂t/∂y = -46/100
You might be interested in
The 5th term in a geometric sequence is 40. The 7th term is 10. What is (are) the possible value(s) of the 4th term?
Lena [83]

Answer:

possible values of 4th term is 80 & - 80

Step-by-step explanation:

The general term of a geometric series is given by

a(n)=ar^{n-1}

Where a(n) is the nth term, r is the common ratio (a term divided by the term before it) and n is the number of term

  • Given, 5th term is 40, we can write:

ar^{5-1}=40\\ar^4=40

  • Given, 7th term is 10, we can write:

ar^{7-1}=10\\ar^6=10

We can solve for a in the first equation as:

ar^4=40\\a=\frac{40}{r^4}

<em>Now we can plug this into a of the 2nd equation:</em>

<em>ar^6=10\\(\frac{40}{r^4})r^6=10\\40r^2=10\\r^2=\frac{10}{40}\\r^2=\frac{1}{4}\\r=+-\sqrt{\frac{1}{4}} \\r=\frac{1}{2},-\frac{1}{2}</em>

<em />

<em>Let's solve for a:</em>

<em>a=\frac{40}{r^4}\\a=\frac{40}{(\frac{1}{2})^4}\\a=640</em>

<em />

Now, using the general formula of a term, we know that 4th term is:

4th term = ar^3

<u>Plugging in a = 640 and r = 1/2 and -1/2 respectively, we get 2 possible values of 4th term as:</u>

ar^3\\1.(640)(\frac{1}{2})^3=80\\2.(640)(-\frac{1}{2})^3=-80

possible values of 4th term is 80 & - 80

3 0
3 years ago
2. Given: HM = VM, and ZH and cV Triangle congruence criteria,
STALIN [3.7K]
Answer: SAS is the correct criteria

Explanation:

Angles VMU and GMH are congruent by the Vertical Angles Theorem. Given that angles UVM and GHM are congruent because they are both right angles, we now have two pairs of corresponding angles. Also given that sides HM and VM are congruent, we now have two corresponding pairs of congruent angles and a pair of congruent sides.Therefore, your best option is the ASA postulate, which states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. Therefore, we have a corresponding angle, a corresponding side, and another corresponding angle in triangle GHM, which is congruent to its corresponding angle, a corresponding side, and another corresponding angle in triangle UVM.
3 0
3 years ago
Line AB intersects line CD at point F, with a ray FE forming a right angle EFB. What angle relationship best describes angles AF
vova2212 [387]

Based on the positions of angles AFC and EFC, the relationship between them is a Complimentary angle.

<h3>How are AFC and EFC related?</h3>

Angles AFC and EFC are complimentary angles because complimentary angles are angles that add up to 90 degrees.

Looking at the shape, Line FC divides the right angle to create angles AFC and EFC so when these are added together, they equal 90 degrees.

In conclusion, angles AFC and EFC are complimentary.

Find out more on complimentary angles at brainly.com/question/20728641.

#SPJ1

4 0
2 years ago
How much is 21 hundreds
Dmitrij [34]
21 hundreds would be 2100
5 0
2 years ago
Read 2 more answers
12x5 – 10x2 + x – 45
qaws [65]
(a)
12x  ^{5}    - 10x ^{2}  + x - 45
(b)we have 4 terms in this expression.
(c)+12 is the leading coefficient in
12x ^{5}

(d) constant is -45
6 0
3 years ago
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