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3 years ago

The ratio of the numerator and denominator of a rational number is 2 : 7 and

Mathematics

1 answer:

Nadya [2.5K]3 years ago

4 0

Answer:

6/21.

Step-by-step explanation:

let the rational number be 2x/7x.

2x + 4 / 7x - 2 = 10 /19

Cross multiply:

19(2x + 4) = 10(7x - 2)

38x + 76 = 70x - 20

96 = 70x - 38x

32x = 96

x = 3.

So the rational number is 2*3/ 7*3

= 6/21.

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Which whole numbers fall betweeen .53 and 2.5

Aloiza [94]

Whole numbers are 0,1,2,3 etc. so it would be 1 and 2

6 0

3 years ago

In 2000, the circulation of a local newspaper was 3,250. In 2001, its circulation was 3,640. In 2002, the circulation was 4,100.

vodka [1.7K]

Percent increase from 2000 to 2001 is 12% and from 2001 to 2002 is 12.6%. Thus period of 2001 to 2002 has higher increase percentage.

Solution:

Given that,

Total circulation of local newspaper in 2000 = 3250

Total circulation of local newspaper in 2001 = 3640

Total circulation of local newspaper in 2002 = 4100

Finding percent of increase in the newspaper’s circulation from 2000 to 2001:

$\text { Percent increase from } 2000 \text { to } 2001=\frac{\text { change in circulation from 2001 - 2000 }}{\text { circulation in } 2000} \times 100$

$\begin{array}{l}{=\frac{3640-3250}{3250} \times 100} \\\\ {=\frac{390}{3250} \times 100=12 \%}\end{array}$

Finding percent of increase in the newspaper’s circulation from 2001 to 2002:

$\begin{array}{l}{\text { Percent increase from } 2001 \text { to } 2002=\frac{\text { change in circulation }}{\text {circulation in } 2001} \times 100} \\\\ {=\frac{4100-3640}{3640} \times 100} \\\\ {=\frac{460}{3640} \times 100=12.6 \%}\end{array}$

As we can see 12% < 12.6%

So period of 2001 to 2002 has higher increase percentage.

7 0

3 years ago

Show that the line integral is independent of path by finding a function f such that ?f = f. c 2xe?ydx (2y ? x2e?ydy, c is any p

Juli2301 [7.4K]

I'm reading this as

$\displaystyle\int_C2xe^{-y}\,\mathrm dx+(2y-x^2e^{-y})\,\mathrm dy$

with $\nabla f=(2xe^{-y},2y-x^2e^{-y})$ .

The value of the integral will be independent of the path if we can find a function $f(x,y)$ that satisfies the gradient equation above.

You have

$\begin{cases}\dfrac{\partial f}{\partial x}=2xe^{-y}\\\\\dfrac{\partial f}{\partial y}=2y-x^2e^{-y}\end{cases}$

Integrate $\dfrac{\partial f}{\partial x}$ with respect to $x$ . You get

$\displaystyle\int\dfrac{\partial f}{\partial x}\,\mathrm dx=\int2xe^{-y}\,\mathrm dx$
$f=x^2e^{-y}+g(y)$

Differentiate with respect to $y$ . You get

$\dfrac{\partial f}{\partial y}=\dfrac{\partial}{\partial y}[x^2e^{-y}+g(y)]$
$2y-x^2e^{-y}=-x^2e^{-y}+g'(y)$
$2y=g'(y)$

Integrate both sides with respect to $y$ to arrive at

$\displaystyle\int2y\,\mathrm dy=\int g'(y)\,\mathrm dy$
$y^2=g(y)+C$
$g(y)=y^2+C$

So you have

$f(x,y)=x^2e^{-y}+y^2+C$

The gradient is continuous for all $x,y$ , so the fundamental theorem of calculus applies, and so the value of the integral, regardless of the path taken, is

$\displaystyle\int_C2xe^{-y}\,\mathrm dx+(2y-x^2e^{-y})\,\mathrm dy=f(4,1)-f(1,0)=\frac9e$

8 0

3 years ago

What is the value of each of the numbers one by one 7 and 6 and 9

zubka84 [21]

I may not fully understand the question but the value of 7 is 7. The value of 6 is 6 and the value of 9 is 9.

3 0

3 years ago

Katya measured the growth of a plant seeding. The seedling grew 1/3 inch by the end of the first week and another 5/6 inch by th

snow_tiger [21]

Answer: 1 1/6

Step-by-step explanation: I just used simple addition and then you should get the answer above becyase they ask the growth which was displayed

5 0

2 years ago