4. The sum of the reciprocals of two consecutive even integers is 11/60.Find the integers.

Problem PageQuestion It takes an older pump twice as long to drain a certain pool as it does a newer pump. Working together, it

umka2103 [35]

Answer:

It will take 6 hours for the new pump to drain the pool.

Step-by-step explanation:

As the complete question is not given, the complete question is found online and is attached herewith

Let the rate of new pump is given as x=W/t_1

Let the rate of the old pump is given as y=W/t_2

it is given that the time t_2=2t_1

So by substituting the values of t_2 in the rate equation of y

y=W/2t_1

y=(W/t_1*2)=x/2

Also the total rate of both the pumps is given as W/t3 where t3 is given as 4 hours so the equation becomes

x+y=W/4

x+x/2=W/4

3x/2=W/4

As x=W/t_1

3W/2t_1=W/4

Now as W is same on both sides so

3/2t_1=1/4

12=2t_1

t_1=6 hours

So it will take 6 hours for the new pump to drain the pool.

7 0

3 years ago

Find the solution of the problem (1 3. (2 cos x - y sin x)dx + (cos x + sin y)dy=0.

lakkis [162]

Answer:

$2*sin(x)+y*cos(x)-cos(y)=C_1$

Step-by-step explanation:

Let:

$P(x,y)=2*cos(x)-y*sin(x)$

$Q(x,y)=cos(x)+sin(y)$

This is an exact differential equation because:

$\frac{\partial P(x,y)}{\partial y} =-sin(x)$

$\frac{\partial Q(x,y)}{\partial x}=-sin(x)$

With this in mind let's define f(x,y) such that:

$\frac{\partial f(x,y)}{\partial x}=P(x,y)$

and

$\frac{\partial f(x,y)}{\partial y}=Q(x,y)$

So, the solution will be given by f(x,y)=C1, C1=arbitrary constant

Now, integrate $\frac{\partial f(x,y)}{\partial x}$ with respect to x in order to find f(x,y)

$f(x,y)=\int\ 2*cos(x)-y*sin(x)\, dx =2*sin(x)+y*cos(x)+g(y)$

where g(y) is an arbitrary function of y

Let's differentiate f(x,y) with respect to y in order to find g(y):

$\frac{\partial f(x,y)}{\partial y}=\frac{\partial }{\partial y} (2*sin(x)+y*cos(x)+g(y))=cos(x)+\frac{dg(y)}{dy}$

Now, let's replace the previous result into $\frac{\partial f(x,y)}{\partial y}=Q(x,y)$ :

$cos(x)+\frac{dg(y)}{dy}=cos(x)+sin(y)$

Solving for $\frac{dg(y)}{dy}$

$\frac{dg(y)}{dy}=sin(y)$

Integrating both sides with respect to y:

$g(y)=\int\ sin(y) \, dy =-cos(y)$

Replacing this result into f(x,y)

$f(x,y)=2*sin(x)+y*cos(x)-cos(y)$

Finally the solution is f(x,y)=C1 :

$2*sin(x)+y*cos(x)-cos(y)=C_1$

7 0

3 years ago

Tell whether it is possible to draw a triangle with the given side lengths. 4 cm, 4 cm, 7 cm

Sati [7]

Yes it is because 4+4=8 and 8 is larger than 7

5 0

2 years ago

Read 2 more answers

Change each phrase into an algebraic expression

maks197457 [2]

Answer:

When translating phrases into algebraic expressions, you need to identify keywords and phrases which specifically refer to a mathematical operation (addition, subtraction, multiplication, and division). Usually, you can write out the algebraic expression of the verbal description in the order that it is said

3 0

2 years ago

2/3 to the fourth power

Stella [2.4K]

The correct answer is 16/81. Hope this helps.

5 0

3 years ago

Read 2 more answers