4)
In the graph we can see that the graph intersects the x axis at -5 & 1
So x = -5 or x= 1
Hence
x +5 = 0 or x -1 = 0
Multiplying them we get
(x+5)(x-1) are the correct factors
Option C) is the right answer
5)
We have
x² - 10x + 24=0
We need two numbers which add to give -10 & multiply to give 24.
The numbers are -6 & -4
We split the term -10x
We get
x² -6x-4x+24=0
x(x-6)-4(x-6)=0
(x-6)(x-4)=0
Using Zero Product rule
x-6 = 0 or x-4=0
x = 6 or x = 4
Option C) is the right answer.
Answer with Step-by-step explanation:
The given differential euation is
![\frac{dy}{dx}=(y-5)(y+5)\\\\\frac{dy}{(y-5)(y+5)}=dx\\\\(\frac{A}{y-5}+\frac{B}{y+5})dy=dx\\\\\frac{1}{100}\cdot (\frac{10}{y-5}-\frac{10}{y+5})dy=dx\\\\\frac{1}{100}\cdot \int (\frac{10}{y-5}-\frac{10}{y+5})dy=\int dx\\\\10[ln(y-5)-ln(y+5)]=100x+10c\\\\ln(\frac{y-5}{y+5})=10x+c\\\\\frac{y-5}{y+5}=ke^{10x}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D%28y-5%29%28y%2B5%29%5C%5C%5C%5C%5Cfrac%7Bdy%7D%7B%28y-5%29%28y%2B5%29%7D%3Ddx%5C%5C%5C%5C%28%5Cfrac%7BA%7D%7By-5%7D%2B%5Cfrac%7BB%7D%7By%2B5%7D%29dy%3Ddx%5C%5C%5C%5C%5Cfrac%7B1%7D%7B100%7D%5Ccdot%20%28%5Cfrac%7B10%7D%7By-5%7D-%5Cfrac%7B10%7D%7By%2B5%7D%29dy%3Ddx%5C%5C%5C%5C%5Cfrac%7B1%7D%7B100%7D%5Ccdot%20%5Cint%20%28%5Cfrac%7B10%7D%7By-5%7D-%5Cfrac%7B10%7D%7By%2B5%7D%29dy%3D%5Cint%20dx%5C%5C%5C%5C10%5Bln%28y-5%29-ln%28y%2B5%29%5D%3D100x%2B10c%5C%5C%5C%5Cln%28%5Cfrac%7By-5%7D%7By%2B5%7D%29%3D10x%2Bc%5C%5C%5C%5C%5Cfrac%7By-5%7D%7By%2B5%7D%3Dke%5E%7B10x%7D)
where
'k' is constant of integration whose value is obtained by the given condition that y(2)=0\\
Thus the solution of the differential becomes
Step-by-step explanation:
[ Refer to the attached file ]
( Slide to refer all files )
________________________________
• To solve Questions of type 11 we need to simplify the equation by using mathematical operations !!
• To solve Questions of type ( 13 , 15 and 17 ) we try to make the bar numeral to come other side of decimal
° and by subtracting we get the required fraction !!
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Answer:
y=2x-7
Step-by-step explanation:
The easiest way to answer this would be by using the slope-intercept form equation, y=mx+b. In this case, we can use our given in information to plug in values and find the equation.
Firstly, let's assess what know and what we don't:
Given the point (2,-3), we know that x=2 and y=-3. Now the slope for a perpendicular line can be found using a negative reciprocal, since the product of the slopes of both lines should equal -1. Therefore the slope must be 2.
All that's left is b, the y-intercept. To solve for this, we simply plug in what we have.
y=mx+b
-3=2(2)+b
-3=4+b
-3-4=b
-7=b
Now that we have b, we can write the equation:
y=2x-7
Shay and Alex went to pick apples. Alex picked 4 apples and Shay pick k apples.
.....hope that helps. Verbal statements are hard :3
