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Delvig [45]
2 years ago
9

If you know that a < b, and both a and b are positive numbers, then what must be true about the relationship between the oppo

sites of these numbers? Explain.
Mathematics
2 answers:
NikAS [45]2 years ago
7 0

Answer:

Step-by-step explanation:

A is closest to 0

Ymorist [56]2 years ago
6 0

Answer:

The number further left on a number line is the smaller number. For positive numbers, the number closest to zero is smaller. For negative numbers, the number closest to zero is larger. If a is less than b, and they are both positive, then a is closer to 0 than b. The opposite of a is also closer to zero than the opposite of b, so the opposite of a must be larger than the opposite of b.

Step-by-step explanation:

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An element with mass 730 grams decays by 28.8% per minute. How much of the element is remaining after 10 minutes, to the nearest
trasher [3.6K]
\bf \qquad \textit{Amount for Exponential Decay}\\\\&#10;A=P(1 - r)^t\qquad &#10;\begin{cases}&#10;A=\textit{accumulated amount}\\&#10;P=\textit{initial amount}\to &730\\&#10;r=rate\to 28.8\%\to \frac{28.8}{100}\to &0.288\\&#10;t=\textit{elapsed time}\to &10\\&#10;\end{cases}&#10;\\\\\\&#10;A=730(1-0.288)^{10}\implies A=730(0.712)^{10}
6 0
2 years ago
Read 2 more answers
se the function to show that fx(0, 0) and fy(0, 0) both exist, but that f is not differentiable at (0, 0). f(x, y) = 9x2y x4 + y
alexandr1967 [171]

Answer:

It is proved that f_x, f_y exixts at (0,0) but not differentiable there.

Step-by-step explanation:

Given function is,

f(x,y)=\frac{9x^2y}{x^4+y^2}; (x,y)\neq (0,0)

  • To show exixtance of f_x(0,0), f_y(0,0) we take,

f_x(0,0)=\lim_{h\to 0}\frac{f(h+0,k+0)-f(0,0)}{h}=\lim_{h\to 0}\frac{\frac{9h^2k}{h^4+k^2}-0}{h}\\\therefore f_x(0,0)=\lim_{h\to 0}\frac{9hk}{h^4+k^2}=\lim_{h\to 0}\frac{9k}{h^3+\frac{k^2}{h}}=0    exists.

And,

f_y(0,0)=\lim_{k\to 0}\frac{f(h,k)-f(0,0)}{k}=\lim_{k\to 0}\frac{9h^2k}{k(h^4+k^2)}=\lim_{k\to 0}\frac{9h^2}{h^4+k^2}=\frac{9}{h^2}   exists.

  • To show f(x,y) is not differentiable at the origin cheaking continuity at origin be such that,

\lim_{(x,y)\to (0,0)}\frac{9x^2y}{x^4+y^2}=\lim_{x\to 0\\ y=mx^2}\frac{9x^2y}{x^4+y^2}=\frac{9x^2\times m x^2}{x^4+m^2x^4}=\frac{9m}{1+m^2}  where m is a variable.

which depends on various values of m, therefore limit does not exists. So f(x,y) is not continuous at (0,0). Hence it is not differentiable at (0,0).

4 0
2 years ago
Grace has 1.35 pounds of strawberries, 1.4 pounds of bananas, and some apples. She has more pounds of apples than pounds of stra
satela [25.4K]

Answer:

Grace could have 1.36 pounds, 1.37 pounds, 1.38 pounds or 1.39 pounds of apples.

Step-by-step explanation:

Let a represent pounds of apples.

We have been given that Grace has 1.35 pounds of strawberries. She has more pounds of apples than pounds of strawberries.

This means that a is greater than 1.35. We can represent this information in an inequality as:

a>1.35

We are also told that Grace has 1.4 pounds of bananas. She has fewer pounds of apples than pounds of bananas. This means that a is less than 1.4. We can represent this information in an inequality as:

a

Upon combining both inequalities, we will get:

1.35

Therefore, Grace could have 1.36 pounds, 1.37 pounds, 1.38 pounds or 1.39 pounds of apples.

6 0
2 years ago
Cecily is comparing two checking accounts. Checking account A has a monthly fee of $16 and a per-check fee of $0.08, while check
Tpy6a [65]

Answer:

(1) 0.08x + 16

(2) 0.08x + 16=0.12x + 14

Step-by-step explanation:

Checking account A has a monthly fee of $16 and a per-check fee of $0.08

Per check fee is a constant rate that is 0.08

Let x represents the number of checks Cecily writes per month

1 check fee = 0.08

x checks fee = 0.08x

monthly fee is $16 , we add that as well

So total monthly fee charges for account A  is

0.08x + 16

checking account B has monthly fee of $14 and a per-check fee of $0.12.

1 check fee = 0.12

x checks fee = 0.12x

monthly fee is $14 , we add that as well

So total monthly fee charges for account B  is

0.12x + 14

(2) To find number of checks write per month for the accounts to charge the same in fees

WE set both expression , account A = account B

0.08x + 16=0.12x + 14

Subtract 0.12x on both sides

-0.04x + 16 = 14

Now subtract 16 on both sides

-0.04x = -2

Divide by -0.04 on both sides

So x= 50



7 0
2 years ago
Write the fraction or mixed number as a percent. 43/25 = %
Stels [109]
This is a fraction, so treat it like one. Divide 43 and 25 and you'll get 1.72. Multiply that decimal value by 100 and that is your percent, 172%
5 0
2 years ago
Read 2 more answers
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