Answer:

Step-by-step explanation:
A second order linear , homogeneous ordinary differential equation has form
.
Given: 
Let
be it's solution.
We get,

Since
, 
{ we know that for equation
, roots are of form
}
We get,

For two complex roots
, the general solution is of form 
i.e 
Applying conditions y(0)=1 on
, 
So, equation becomes 
On differentiating with respect to t, we get

Applying condition: y'(0)=0, we get 
Therefore,

(a)The ratio of the number of machine to the number of crates packed is 1:4.5
(b) crates of oranges in 90 pack per day by machine is 405.
What is Ratio?
An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)
Given that;
40 identical machines in a factory pack 180 crates of oranges per day
So,
a) The ratio of the number of machines to the number of crates packed per day is:
40/180 = 1:4.5
b) crates of oranges would 90 of these machines pack per day is
40/180 = 90/x

x = 4.5 x 90
x = 405
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Answer:
(4,-5)
Step-by-step explanation:
Y = 3-2X
8X +5(3-2X) =7
8x + 15 - 10x = 7
-2x = -8
x = 4
y = 3 - 2(4)
y = -5
Answer:
TU = LM
KM = SU
LK = TS
Step-by-step explanation:
It is given that ΔSTU ≅ ΔKLM
Since, the corresponding parts of congruence triangle are equal,
The corresponding sides TU of ΔSTU and LM of ΔKLM are equal.
The corresponding sides KM of ΔKLM and SU of ΔSTU are equal.
The corresponding sides LK of ΔKLM and TS of ΔSTU are equal.
Hence,
TU = LM
KM = SU and
LK = TS