Problem: 90 x 83
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In distributive property: 90 x (80 + 3) </span>
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Solution: 80 + 3 = 83.
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Solution: 83 x 90 = 7470
Happy studying ^-^
Step-by-step explanation:
here as base are same
-x= 6x-9
=> -7x= -9
=> x = 9/7
If we make them all quarters then 4/8, 2/8 and 4/8 which is 10/8 so 1 and 2/8 or 1 and a quarter
David would have 2/8, 3/8 and 4/8 which would be 9/8 which is 1 and 1/8 so Angela eats the most
Graph of f(x-3) is compressed by a factor of 
horizontally of f(x).
<u>Step-by-step explanation:</u>
We have, the graph of f(x)= 
, on replacing f(x) by f(x-3) we get:
= 
.Below shown are the images for graph of f(x) and f(x-3). Both are functions are exponential , and so having exponential graph but f(x-3) is compressed by a factor of horizontally . Domain and range of both functions are same i.e. F(x) & f(x-3) domain & range are same , just difference in graph : 
.
Hello,
Here is the demonstration in the book Person Guide to Mathematic by Khattar Dinesh.
Let's assume
P=cos(a)*cos(2a)*cos(3a)*....*cos(998a)*cos(999a)
Q=sin(a)*sin(2a)*sin(3a)*....*sin(998a)*sin(999a)
As sin x *cos x=sin (2x) /2
P*Q=1/2*sin(2a)*1/2sin(4a)*1/2*sin(6a)*....
*1/2* sin(2*998a)*1/2*sin(2*999a) (there are 999 factors)
= 1/(2^999) * sin(2a)*sin(4a)*...
*sin(998a)*sin(1000a)*sin(1002a)*....*sin(1996a)*sin(1998a)
as sin(x)=-sin(2pi-x) and 2pi=1999a
sin(1000a)=-sin(2pi-1000a)=-sin(1999a-1000a)=-sin(999a)
sin(1002a)=-sin(2pi-1002a)=-sin(1999a-1002a)=-sin(997a)
...
sin(1996a)=-sin(2pi-1996a)=-sin(1999a-1996a)=-sin(3a)
sin(1998a)=-sin(2pi-1998a)=-sin(1999a-1998a)=-sin(a)
So sin(2a)*sin(4a)*...
*sin(998a)*sin(1000a)*sin(1002a)*....*sin(1996a)*sin(1998a)
= sin(a)*sin(2a)*sin(3a)*....*sin(998)*sin(999) since there are 500 sign "-".
Thus
P*Q=1/2^999*Q or Q!=0 then
P=1/(2^999)
