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Sophie [7]
3 years ago
13

The difference between two positive integers is 4 and the difference between their reciprocal is 1/24 , find the 2 integers .

Mathematics
2 answers:
marishachu [46]3 years ago
8 0
X - y = 4 
1/y - 1/x = 1/24 
x = y + 4 
1/y - 1/(y + 4) = 1/24 
(y + 4)/y - 1 = (y + 4)/24 
y/y + 4/y - 1 = y/24 + 1/6 
4/y = y/24 + 1/6 
4 = y^2/24 + y/6 
96 = y^2 + 4y 
y^2 + 4y -96 = 0 
(y + 12)(y - 8) = 0 

The numbers are 8 and 12
Over [174]3 years ago
7 0
Heres the answer
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sike
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Given that sin x = cos 2x find the value of x​
natali 33 [55]

Answer:

The most straightforward way to obtain the expression for cos(2x) is by using the "cosine of the sum" formula: cos(x + y) = cosx*cosy - sinx*siny. cos(2x) = cos² (x) - (1 - cos²(x)) = 2cos²(x) - 1. = 2cos²(x) - 1.

Step-by-step explanation:

7 0
2 years ago
Consider the function f(x)= 2/5x-4
Gre4nikov [31]

Answer: a) \frac{5}{2}x+10=f^{-1}(x)=g(x)

Step-by-step explanation:

Since we have given that

f(x)=\frac{2}{5}x-4

a.) Find the inverse of f(x) and name it g(x).

Let f(x) = y

So, it becomes

y=\frac{2}{5}x-4

Switching x to y , we get

x=\frac{2}{5}y-4

5x=2y-20\\\\5x+20=2y\\\\\frac{5x+20}{2}=y\\\\\frac{5}{2}x+10=y\\\\\frac{5}{2}x+10=f^{-1}(x)=g(x)

b) . Use composition to show that f(x) and g(x) are inverses of each other.

\mathrm{For}\:f=\frac{2}{5}x-4\:\\\\\mathrm{substitute}\:x\:\mathrm{with}\:g\left(x\right)=\frac{5}{2}x+10\\\\=\frac{2}{5}\left(\frac{5}{2}x+10\right)-4\\\\=x

Similarly,

\mathrm{g\left(x\right)=\frac{5}{2}x+10,\:f\left(x\right)=\frac{2}{5}x-4,\:g\left(x\right)\circ \:f\left(x\right)}\\\\\mathrm{For}\:g=\frac{5}{2}x+10\:\mathrm{substitute}\:x\:\mathrm{with}\:f\left(x\right)=\frac{2}{5}x-4\\\\=\frac{5}{2}\left(\frac{2}{5}x-4\right)+10\\\\=x

so, both are inverses of each other.

c) Draw the graphs of f(x) and g(x) on the same coordinate plane.

As shown below in the graph , Since for inverse function we need an axis of symmetry i.e. y=x

And both f(x) and g(x) are symmetry to y=x.

∴ f(x) and g(x) are inverses of each other.


5 0
3 years ago
Write the list of integers in increasing order from left to right.12, -4, -9,2, -2.
kotykmax [81]

we have the list

12, -4, -9,2, -2

rewrite in increasing order from left to right

The answer is

<h2>-9,-4,-2,2,12</h2>
5 0
1 year ago
2 over 5 (x − 4) = 2x.
Sav [38]
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5 0
3 years ago
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AleksandrR [38]

Step-by-step explanation:

12x + 3(x - 4) + 2x

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HOPE IT HELPS U

8 0
3 years ago
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