How to construct linear equations Q2b) Q11 and Q13?


I've found the formula for a which is #r=(v+mu)/(m+1)#. But I could construct equation for c without getting a bizarre answer.
For questions 11, I got the equation 10x+5(41-2x)=205 but x=0 in this case.

And lucky last questions 13
I did x=Apollo y=aph and z=ad
Z=x+7200 y=x-4000
So we have x+x+7200-400=303200
And go x=98800, complete different to the answer. Can't someone please correct my mistake? And I will love you forever:)

Answer 1

2(b) #m=v/u#
(11) We have #10# pieces of length #12m# and #5# pieces of length #17m#.
(13) Mr. Aphrodite earn #$96000#, Mr. Apollo earns #$100000# and Mr. Adonis earns #$107200#

2(b)

As #1/v+1/u=2/r#, we have #1/v-1/r=1/r-1/u#
or #(r-v)/(vr)=(u-r)/(ru)#
i.e. #(r-v)/(u-r)=(vr)/(ru)=v/u#
or #m=(v-r)/(r-u)=v/u#
(11) let there be #10# pieces of length #x# and #5# pieces of length #y#.
As total length is #205m#, we have #10x+5y=205# or dividing by #5#
#2x+y=41# ..................(A)
Further, as three pieces of size #x# exceed two pieces of size #y# by #2#, we have
#3x-2y=2# ..................(B)
Now multiplying (A) by #2# and adding to (B), we get
#4x+2y+3x-2y=82+2# i.e. #7x=84# and #x=12#
and putting this in (A) we get #2xx12+y=41# or ##24+y=41#
i.e. #y=41-24=17#
Hence, we have #10# pieces of length #12# and #5# pieces of length #17#.

(13)

Let Mr. Aphrodite earn #x#, then Mr. Apollo earns #x+$4000# and Mr. Adonis earns #(x+$4000)+$7200# or #x+$11200#
As their total earnings are #$303200#, we have
#x+x+4000+x+11200=303200#
or #3x+15200=303200#
or #3x=303200-15200=28800#
and #x=288000/3=96000#
Hence, Mr. Aphrodite earn #$96000#, then Mr. Apollo earns #$96000+$4000=$100000# and Mr. Adonis earns #$100000+$7200# or #$107200#.
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Answer 2

To construct linear equations Q2b), Q11, and Q13, follow these steps:

  1. Q2b):

    • Identify the slope (m) and y-intercept (b) from the given information or context.
    • Write the equation in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
  2. Q11):

    • Determine two points that lie on the line.
    • Calculate the slope (m) using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
    • Choose one of the points and use it to solve for the y-intercept (b) using the formula: y = mx + b.
  3. Q13):

    • If the equation represents a line passing through the origin (0,0), the equation will be in the form y = mx, where m is the slope.
    • If the equation represents a line parallel to the y-axis, it will be in the form x = c, where c is a constant.
    • If the equation represents a line parallel to the x-axis, it will be in the form y = c, where c is a constant.

Ensure to substitute the appropriate values and constants into the equations to form the desired linear equations for Q2b), Q11, and Q13.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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