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V125BC [204]
3 years ago
7

2 pipes running together can fill a cistern in 3 1÷3 min.if one pipe takes 3 min more than the other to fill it,find the time in

which each pipe would fill the cistern
Mathematics
1 answer:
charle [14.2K]3 years ago
8 0
It takes one pipe x minutes, the other pipe x+3 minutes
the portion filled per minute is by one pipe is 1/x, by the second pipe 1/(x+3)

when two pipes running together:
3&1/3[1/x+1/(x+3)] =1, 1 means the whole cistern
solve for x: 3&1/3(x+3) +3 1/3(x)=x(x+3)
6 &2/3 x +10 =x^2+3x
x^2- (3&2/3) x-10=0
3x^2-11x-30=0

this cannot be factored, so use the quadratic equation: 
x is about 5.5
x+3=8.5
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Which describes the behavior of the function f(x)= tan^-1(x)?
Fantom [35]

Answer:

Third Option

Step-by-step explanation:

We know that the function tan(x) is defined as y=\frac{sin(x)}{cos(x)}. Since the denominator is cos(x) then we know that  cos(x)=0  when x=\frac{\pi}{2}

We also know that the division by 0 is not defined. Therefore, the limit of y=tan(x) when "x" tends to \frac{\pi}{2} is infinite.

The function tan^{-1}(x) is the inverse of tan(x)

By definition, if we have a function f(x), its domain will be equal to the range of its inverse function f^{-1}(x). If f(3)=8, then f^{-1}(8)=3

This also happens for the function tan^{-1}(x)

If when x \to \frac{\pi}{2}, tan(x) \to \infty then when x \to \infty, tan^{-1}x \to \frac{\pi}{2}

Then, the answer is:

x \to \infty, f(x) \to \frac{\pi}{2}

7 0
3 years ago
X/3-15=-2 solve for x
Otrada [13]

Answer:

x = 45

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

x/3-(15)=0

Step  1  : <u>Simplify</u>

\frac{x}{3}      

Equation at the end of step  1  :

\frac{x}{3} -  15  = 0    

Step  2  :

<u>Rewriting the whole as an Equivalent Fraction :</u>

Subtracting a whole from a fraction

Rewrite the whole as a fraction using  3  as the denominator :            

15=\frac{15}{1} =\frac{15*3}{3}

<u>Equivalent fraction :</u> The fraction thus generated looks different but has the same value as the whole

<u>Common denominator : </u>The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

\frac{x-(15*3)}{3} =\frac{x-45}{3}

Equation at the end of step  2  :

\frac{x-45}{3} =0

Step  3  :

When a fraction equals zero :

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

\frac{x-45}{3}*3=0*3

Now, on the left hand side, the  3  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  x-45  = 0

Solving a Single Variable Equation :

<u>Solve  :</u>    x-45 = 0

Add  45  to both sides of the equation :

x = 45

One solution was found :

x = 45

3 0
3 years ago
Find the slope of the line that passes through (10,8) and (8,0).​
N76 [4]

Answer:

The slope of the line that passes through points ( -10, -8 ) and ( -8, -16 ) is -4.

Explanation:

Points given = ( -10, -8) and ( -8, -16)

Slope = ?

( -10, -8 ) : x1 = -10 and y1 = -8

( -8, -16 ) : x2 = -8 and y2 = -16

We know,

slope = y2 - y1 / x2 - x1

Slope = -16 - ( -8) / -8 - (-10)

slope = -16 + 8 / -8 + 10

slope = -8 / 2

slope = -4

Therefore,  slope of the line that passes through points ( -10, -8 ) and ( -8, -16 ) is -4.

Step-by-step explanation:

3 0
3 years ago
There are 9 people going on a trip. They purchased coach tickets for $160, and first class tickets for $1180. The total budget t
Savatey [412]

Answer:

Step-by-step explanation:

Given

There are 9 people going on a trip

They purchased coach tickets =$160

first class tickets =$1180

total budget to spend = $4500

Let coach tickets=X

So first class tickets=9-x

160x+1180(9-x)=4500

160+10620-1180x=4500

160x-1180x=4500-10620

-1020x=-6120

X=6120/1020

X=6

So answer

Coach tickets=X=6

First class tickets=(9-x)

=3.

4 0
3 years ago
Xiaoming is making cookies. Each batch of cookies uses3 eggs. If Xiaoming has 20 eggs, and assuming he has enough of the other i
koban [17]

Answer:

6

Step-by-step explanation:

3(1)=3       3(2)=6          3(3)=9      3(4)=12     3(5)=15

3(6)=18     3(7)=21         3(8)=24

----------------------------------------------------

3(6)=18 is closest to 20

so the greatest number of batches Xiaoming can make is 6.

7 0
3 years ago
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