@bullseyes said:is it an equilateral triangle???
ya,you try with coordinates.It is equilateral with side 2a
@gnehagarg said:ya,you try with coordinates.It is equilateral with side 2a
A(0,a),B(0,-a),C(2a,0)
AB=2a
BC=sqrt(5)a, Ain't equilateral.
CA=2a
AB=2a
BC=sqrt(5)a, Ain't equilateral.
CA=2a
Good Morning question.
Given
AB=12, BC=18, AC=10
Both incircles touch at a common point E.
Can AD be determined? If yes, what's the length of it?
@chillfactor said:For last question, its trueAll three vertices of an equilateral triangle in a Cartesian plane can have integral coordinates. (True/False)
This is False. All three vertices of an equilateral triangle can never be integers.
@Torque024 said:Good Morning question.GivenAB=12, BC=18, AC=10Both incircles touch at a common point E.Can AD be determined? If yes, what's the length of it?
Check the attachement
@Torque024 said:Good Morning question.GivenAB=12, BC=18, AC=10Both incircles touch at a common point E.Can AD be determined? If yes, what's the length of it?
2sqrt(89)/3
BC = 18
12 -x + 2y + 10 -x = 18
x - y = 2
=> BD = 10
taking cosines of angle B for two triangles ABD and ABC
cosB = 12^2 + 18^2 - 10^2 / 2*12*18 = 12^2 + 10^2 - AD^2/ 2*12*10
solving the equation we get AD = 2sqrt(89)/3
The capitals of 4 partners a,b,c,d are in the ratio of 7:8:6:5.a's and c's capitals are there in the business for the entire year.if each partner kept his money invested in the business for a period which is more than 6 months and b and d together get 111/267 of the total profit ,then for how many months is d's capital invested?Please quote me !
The capitals of 4 partners a,b,c,d are in the ratio of 7:8:6:5.a's and c's capitals are there in the business for the entire year.if each partner kept his money invested in the business for a period which is more than 6 months and b and d together get 111/267 of the total profit ,then for how many months is d's capital invested?
Please quote me !
@Asfakul said:The capitals of 4 partners a,b,c,d are in the ratio of 7:8:6:5.a's and c's capitals are there in the business for the entire year.if each partner kept his money invested in the business for a period which is more than 6 months and b and d together get 111/267 of the total profit ,then for how many months is d's capital invested?Please quote me !
11months?
@Asfakul said:The capitals of 4 partners a,b,c,d are in the ratio of 7:8:6:5.a's and c's capitals are there in the business for the entire year.if each partner kept his money invested in the business for a period which is more than 6 months and b and d together get 111/267 of the total profit ,then for how many months is d's capital invested?Please quote me !
84x , 8yx , 72x , 5zx
let total profit be = 267
84x + 72x = 156
=> x = 1
84 , 8y , 72 , 5z
8y + 5z = 111
6 12
only solution , when y = 7 and z = 11
so , required answer will be = 11 months
let total profit be = 267
84x + 72x = 156
=> x = 1
84 , 8y , 72 , 5z
8y + 5z = 111
6 12
only solution , when y = 7 and z = 11
so , required answer will be = 11 months
@Asfakul said:I am not sure bhai .. Can you post your approach ??
their profit share represented by
a : b : c : d
7*12:8*(6+x):6*12:5*(6+y)
=84:8*(6+x):72:5*(6+y)
profit share of b&d;=8*(6+x)+5*(6+y)/84+8*(6+x)+72+5*(6+y) =111/267(given)
from here ,8*(6+x)+5*(6+y)=111
78+8x+5y=111
=>8x+5y=33
only x=1 and y=5 satisfies (as,1hence no. of months upto which d's capital invested=6+y=6+5=11
a : b : c : d
7*12:8*(6+x):6*12:5*(6+y)
=84:8*(6+x):72:5*(6+y)
profit share of b&d;=8*(6+x)+5*(6+y)/84+8*(6+x)+72+5*(6+y) =111/267(given)
from here ,8*(6+x)+5*(6+y)=111
78+8x+5y=111
=>8x+5y=33
only x=1 and y=5 satisfies (as,1hence no. of months upto which d's capital invested=6+y=6+5=11
@Torque024 said:Good Morning question.GivenAB=12, BC=18, AC=10Both incircles touch at a common point E.Can AD be determined? If yes, what's the length of it?
sqrt(356/9) 
A Simple Question but I have a doubt,
Q) Sheela completes 25% of a painting on the first day. The next day, she completes twice the percentage as on the previous day. How many days does she take to complete the painting?
a)2 b)3 c)5 d)6 e)CBD
@ron123 said:A Simple Question but I have a doubt, Q) Sheela completes 25% of a painting on the first day. The next day, she completes twice the percentage as on the previous day. How many days does she take to complete the painting?a)2 b)3 c)5 d)6 e)CBD
Let the area of painting be A
First Day - A/4
Second Day - 3A/8 [50% of the remaining painting, so total completed = 5A/8, left = 3A/8]
Third Day = 3A/8 [100% of the remaining painting]
-> It takes him 3 days
Find the value of tanx+cotx if tanx^4+cotx^4=194
@soham2208 said:Let the area of painting be AFirst Day - A/4Second Day - 3A/8 [50% of the remaining painting, so total completed = 5A/8, left = 3A/8]Third Day = 3A/8 [100% of the remaining painting]-> It takes him 3 days
My doubt is, its given in the question how much work sheela does on day 1 and 2 but its not given how work she does on day 3 ....
@jain4444 said:Find the value of tanx+cotx if tanx^4+cotx^4=194
tan(x) = a
a^4 + (1/a)^4 + 2 = 14^2 => (a^2) + (1/a)^2 = 14
=> (a + 1/a)^2 = 4^2 => a + 1/a = 4 or -4
=> tan(x) + cot(x) = 4 or -4 ?
@ron123 said:My doubt is, its given in the question how much work sheela does on day 1 and 2 but its not given how work she does on day 3 ....
No, the relation between the present day's work and the previous day's work is given. Applicable to any day starting from 2nd
@jain4444 said:Find the value of tanx+cotx if tanx^4+cotx^4=194
(tanx+cotx)^4
=tanx^4+4*tanx^2+6+4cotx^2+cotx^4
=200+4[(tanx+cox)^2-2]
tanx+cotx=z
=>z^4=200+4z^2-8
=>z^4-4z^2-192=0
=>z=4
tanx+cotx=4
=tanx^4+4*tanx^2+6+4cotx^2+cotx^4
=200+4[(tanx+cox)^2-2]
tanx+cotx=z
=>z^4=200+4z^2-8
=>z^4-4z^2-192=0
=>z=4
tanx+cotx=4