Let S = number of small yogurts ($2 each).
Let M = number of medium yogurts ($3 each)
Let L = number of large yogurts ($5 each)
Total yogurts is 27, therefore
S + M + L = 27
Total revenue generated is $98, therefore
2S + 3M +5L = 98
There are five more large yogurts than small yogurts, therefore
L = S + 5, or
-S + L = 5
These three equations may be written as the matrix equation
[ 1 1 1 | |S| |27|
| 2 3 5 | |M| = |98|
| -1 0 1 | |L| | 5|
The determinant of the matrix is
D = 3 - (2+5) + 3 = -1.
Solve with Cramer's Rule to obtain
S = -[27*3) - (98-25) - 15]
= 7
M = -[(98-25) - 27(2+5) + (10+98)]
= 8
L = -[15 - (10+98) + 27(3)]
= 12
Answer: 7 small, 8 medium, 12 large yogurts.
Given data, cos(A - B) = cosAcosB + sinAsinB
<span>let, A=60' and B=30' ( here the ' sign bears degree) </span>
<span>L.H.S = cos(A - B) </span>
<span>=cos (60'-30) ( using value of A and B ) </span>
<span>=cos30' </span>
<span>= sqrt3/2 </span>
<span>R.H.S= cosAcosB + sinAsinB </span>
<span>=cos60' cos30' + sin60' sin30' </span>
<span>= 1/2* sqrt3/2+ sqrt3/2*1/2 </span>
<span>= sqrt3/4 + sqrt3/4 </span>
<span>=2 sqrt3/4 </span>
<span>= sqrt3/2 </span>
<span>so L.H.S =R.H.S or cos(A - B) = cosAcosB + sinAsinB</span>
Answer:
The distance around the lot is 4.05 miles .
Step-by-step explanation:
Formula

As given

i.e

Here


Put in the formula

L.C.M of (8,10) = 40




Perimeter of rectangle = 4.05 miles
Therefore the distance around the lot is 4.05 miles .
Answer:
The height of the building is 153.664 meter.
Step-by-step explanation:
Consider the provided function.

Here t represents the time v₀ represents the initial velocity, s₀ represents the initial height and s(t) represents the height after t seconds.
It is given that the splash is seen 5.6 seconds after the stone is dropped.
That means after 5.6 seconds height s(t) = 0, Also the initial velocity of the stone is 0.
Substitute respective values in the above function.



As height can't be a negative number so the value of s₀ is 153.664.
Hence, the height of the building is 153.664 meter.