Answer:
Savings % = 40%
Monthly income = Rs 20,600
Amount spend = Rs 12,360
Step-by-step explanation:
Let the percentage savings be 's'
Percentage savings = 60% + s = 100
s = 100 - 60
s = 40%
This is because, percentages sum up to hundred (100)
Let her monthly income be I
40/100 × I = 8240
40I/100 = 8240
40I = 824000
Divide both side by 40
I = Rs 20,600
Therefore her monthly income is Rs 20,600
Amount she spends
20,600 - 8240
= Rs 12,360
Or 60/100 × 20,600
= Rs 12,360
Answer:
15/56
Step-by-step explanation:
3*5=15 * 8*7=56
15/56
the answer is going to be 6.0
Step-by-step explanation:
1.5 + 1.5 = 3
3 + 3 = 6
Answer:
a) d(x)=![\sqrt{17x^{2} -12x+5}](https://tex.z-dn.net/?f=%5Csqrt%7B17x%5E%7B2%7D%20-12x%2B5%7D)
b)d'(x)=![\frac{17x-6}{\sqrt{17x^{2} -12x+5} }](https://tex.z-dn.net/?f=%5Cfrac%7B17x-6%7D%7B%5Csqrt%7B17x%5E%7B2%7D%20-12x%2B5%7D%20%7D)
c)The critical point is x=![\frac{6}{17}](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B17%7D)
d)Closest point is (
,![\frac{7}{17}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B17%7D)
Step-by-step explanation:
We are given the line
![y=4x-1](https://tex.z-dn.net/?f=y%3D4x-1)
Let a point Q(
) lie on the line.
Point P is given as P(2,0)
By distance formula, we have the distance D between any two points
A(
) and B(
) as
D=![\sqrt{(x_{1}-x_{2})^2 + (y_{1}-y_2)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_%7B1%7D-x_%7B2%7D%29%5E2%20%2B%20%28y_%7B1%7D-y_2%29%5E2%7D)
Thus,
d(x)=![\sqrt{(x-2)^2+(y-0)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x-2%29%5E2%2B%28y-0%29%5E2%7D)
But we have, ![y=4x-1](https://tex.z-dn.net/?f=y%3D4x-1)
So,
d(x)=![\sqrt{(x-2)^2+(4x-1)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x-2%29%5E2%2B%284x-1%29%5E2%7D)
Expanding,
d(x)=
- - - (a)
Now,
d'(x)= ![\frac{\frac{d}{dx} (17x^2-12x+5)}{2(\sqrt{17x^2-12x+5}) }](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7Bd%7D%7Bdx%7D%20%2817x%5E2-12x%2B5%29%7D%7B2%28%5Csqrt%7B17x%5E2-12x%2B5%7D%29%20%7D)
i.e.
d'(x)=
- - - (b)
Now, the critical point is where d'(x)=0
⇒
=0
⇒
- - - (c)
Now,
The closest point on the given line to point P is the one for which d(x) is minimum i.e. d'(x)=0
⇒![x=\frac{6}{17}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B6%7D%7B17%7D)
as ![y=4x-1](https://tex.z-dn.net/?f=y%3D4x-1)
⇒y=![\frac{7}{17}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B17%7D)
So, closest point is (
) - - -(d)
9514 1404 393
Answer:
A. (-3, -3) and (2,7)
Step-by-step explanation:
Read the points of intersection from the graph. They are ...
(-3, -3) and (2,7) . . . . matches choice A