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4 years ago

Pls help a brother out!

Mathematics

2 answers:

Leviafan [203]4 years ago

3 0

Answer:

12 maybe the ANSWER.

hope it helps you

LenaWriter [7]4 years ago

3 0

Answer:

Range = (-∞ , 6]

Step-by-step explanation:

Write down the inequality and then solve it to get the required solution.

Let's say "x" is the certain number.

4 + 3x <= 2x + 10

x <= 6

That's it, Best Regards!

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HELP MEeeeeeeeee g: R² → R a differentiable function at (0, 0), with g (x, y) = 0 only at the point (x, y) = (0, 0). Consider<im

GrogVix [38]

(a) This follows from the definition for the partial derivative, with the help of some limit properties and a well-known limit.

• Recall that for $f:\mathbb R^2\to\mathbb R$ , we have the partial derivative with respect to $x$ defined as

$\displaystyle \frac{\partial f}{\partial x} = \lim_{h\to0}\frac{f(x+h,y) - f(x,y)}h$

The derivative at (0, 0) is then

$\displaystyle \frac{\partial f}{\partial x}(0,0) = \lim_{h\to0}\frac{f(0+h,0) - f(0,0)}h$

• By definition of $f$ , $f(0,0)=0$ , so

$\displaystyle \frac{\partial f}{\partial x}(0,0) = \lim_{h\to0}\frac{f(h,0)}h = \lim_{h\to0}\frac{\tan^2(g(h,0))}{h\cdot g(h,0)}$

• Expanding the tangent in terms of sine and cosine gives

$\displaystyle \frac{\partial f}{\partial x}(0,0) = \lim_{h\to0}\frac{\sin^2(g(h,0))}{h\cdot g(h,0) \cdot \cos^2(g(h,0))}$

• Introduce a factor of $g(h,0)$ in the numerator, then distribute the limit over the resulting product as

$\displaystyle \frac{\partial f}{\partial x}(0,0) = \lim_{h\to0}\frac{\sin^2(g(h,0))}{g(h,0)^2} \cdot \lim_{h\to0}\frac1{\cos^2(g(h,0))} \cdot \lim_{h\to0}\frac{g(h,0)}h$

• The first limit is 1; recall that for $a\neq0$ , we have

$\displaystyle\lim_{x\to0}\frac{\sin(ax)}{ax}=1$

The second limit is also 1, which should be obvious.

• In the remaining limit, we end up with

$\displaystyle \frac{\partial f}{\partial x}(0,0) = \lim_{h\to0}\frac{g(h,0)}h = \lim_{h\to0}\frac{g(h,0)-g(0,0)}h$

and this is exactly the partial derivative of $g$ with respect to $x$ .

$\displaystyle \frac{\partial f}{\partial x}(0,0) = \lim_{h\to0}\frac{g(h,0)-g(0,0)}h = \frac{\partial g}{\partial x}(0,0)$

For the same reasons shown above,

$\displaystyle \frac{\partial f}{\partial y}(0,0) = \frac{\partial g}{\partial y}(0,0)$

(b) To show that $f$ is differentiable at (0, 0), we first need to show that $f$ is continuous.

• By definition of continuity, we need to show that

$\left|f(x,y)-f(0,0)\right|$

is very small, and that as we move the point $(x,y)$ closer to the origin, $f(x,y)$ converges to $f(0,0)$ .

We have

$\left|f(x,y)-f(0,0)\right| = \left|\dfrac{\tan^2(g(x,y))}{g(x,y)}\right| \\\\ = \left|\dfrac{\sin^2(g(x,y))}{g(x,y)^2}\cdot\dfrac{g(x,y)}{\cos^2(g(x,y))}\right| \\\\ = \left|\dfrac{\sin(g(x,y))}{g(x,y)}\right|^2 \cdot \dfrac{|g(x,y)|}{\cos^2(x,y)}$

The first expression in the product is bounded above by 1, since $|\sin(x)|\le|x|$ for all $x$ . Then as $(x,y)$ approaches the origin,

$\displaystyle\lim_{(x,y)\to(0,0)}\frac{|g(x,y)|}{\cos^2(x,y)} = 0$

So, $f$ is continuous at the origin.

• Now that we have continuity established, we need to show that the derivative exists at (0, 0), which amounts to showing that the rate at which $f(x,y)$ changes as we move the point $(x,y)$ closer to the origin, given by

$\left|\dfrac{f(x,y)-f(0,0)}{\sqrt{x^2+y^2}}\right|,$

approaches 0.

Just like before,

$\left|\dfrac{\tan^2(g(x,y))}{g(x,y)\sqrt{x^2+y^2}}\right| = \left|\dfrac{\sin^2(g(x,y))}{g(x,y)}\right|^2 \cdot \left|\dfrac{g(x,y)}{\cos^2(g(x,y))\sqrt{x^2+y^2}}\right| \\\\ \le \dfrac{|g(x,y)|}{\cos^2(g(x,y))\sqrt{x^2+y^2}}$

and this converges to $g(0,0)=0$ , since differentiability of $g$ means

$\displaystyle \lim_{(x,y)\to(0,0)}\frac{g(x,y)-g(0,0)}{\sqrt{x^2+y^2}}=0$

So, $f$ is differentiable at (0, 0).

3 0

3 years ago

Plz I need Answer For It Will give Good Rating

avanturin [10]

Answer:

Step-by-step explanation:

1. Find where the line crosses on the y-axis

2. Find two corresponding points on the graph and do the rise/run method, which in this problem is 4/1 or 4( 4÷1= 4)

- When the line is like this / you rise from up and run to the right(positive), but when it is like this \ you rise from down and run to left (negative)

Ps: You should have taken the picture at a different angle 'cause I can see what you looks like and see part of your room.

Hope I was helpful =)

7 0

3 years ago

Solve equation <img src="https://tex.z-dn.net/?f=%5Cfrac%7Bk-4%7D%7B3%7D%20%3D%203" id="TexFormula1" title="\frac{k-4}{

3241004551 [841]

k-4/3= 3

Mutiply both sides by 3 .

(3)(k-4/3)= (3)(3)

Cross out 3 and 3 , divide by 3 and then becomes k-4= 9

Move -4 to the other side

Sign changes from -4 to +4

k-4+4= 9+4

k= 13

Answer: k= 13

6 0

3 years ago

How to find the mad of the set of data?

kramer

Answer:

add up all numbers

then divide that number by the amount of numbers.

Step-by-step explanation:

mad is basically finding the average of a set of numbers.

and how do you do that?

first, add up all numbers

ex: 1, 5,3,10,6,20,15,15,14 --> this adds up to 90.

then divide that number by the amount of numbers.

count how much numbers ehere are: there are 9 numbers.

divide 90 by 9 and the mad/average is 10.

plz give brainliestttt

5 0

3 years ago

Read 2 more answers

Sally gets paid $15.00 dollars per hour for a 40-hour work week and y dollars for each hour she works over 40 hours. What is the

Anna35 [415]

The equation x = 600 + 8y represents the earnings of Sally if she works 48 hours.

Step-by-step explanation:

Sally gets paid $15.00 dollars per hour for a 40-hour weekly work.
She gets y dollars for each extra hour she works over 40 hours.

The equation can be framed as :

Let,

x be the total pay she could get for 48 hours.
The amount she earned for 40 hours = 40 × $15 ⇒ $600
The amount she earned for extra hours = 8 × y ⇒ 8y

The equation is given as,

Total earnings = amount earned for 40 hours + amount for extra 8 hours.

⇒ x = 600 + 8y

Therefore, the equation x = 600 + 8y represents the earnings of Sally if she works 48 hours.

4 0

3 years ago