The answer should be C
54*30/100= 16.2
54-16.2 = 37.80
Answer:
104
Step-by-step explanation:
15 x 14= 210 divide by 2
105
180 - 105 = 75
15 + 14 + 75 = 104
Answer:
y = 3sin2t/2 - 3cos2t/4t + C/t
Step-by-step explanation:
The differential equation y' + 1/t y = 3 cos(2t) is a first order differential equation in the form y'+p(t)y = q(t) with integrating factor I = e^∫p(t)dt
Comparing the standard form with the given differential equation.
p(t) = 1/t and q(t) = 3cos(2t)
I = e^∫1/tdt
I = e^ln(t)
I = t
The general solution for first a first order DE is expressed as;
y×I = ∫q(t)Idt + C where I is the integrating factor and C is the constant of integration.
yt = ∫t(3cos2t)dt
yt = 3∫t(cos2t)dt ...... 1
Integrating ∫t(cos2t)dt using integration by part.
Let u = t, dv = cos2tdt
du/dt = 1; du = dt
v = ∫(cos2t)dt
v = sin2t/2
∫t(cos2t)dt = t(sin2t/2) + ∫(sin2t)/2dt
= tsin2t/2 - cos2t/4 ..... 2
Substituting equation 2 into 1
yt = 3(tsin2t/2 - cos2t/4) + C
Divide through by t
y = 3sin2t/2 - 3cos2t/4t + C/t
Hence the general solution to the ODE is y = 3sin2t/2 - 3cos2t/4t + C/t
Answer:


Find the multiplicative inverse of the following
(i) -13 (ii) -13/19 (iii) 1/5 (iv) -5/8 × -3/7 (v) -1 × -2/5
(vi) -1
Solution:
The reciprocal of a given rational number is known as its multiplicative inverse. The product of a rational number and its multiplicative inverse is 1.
(i) The Multiplicative inverse of -13 is -1/13
∵ -13 × (-1/13) = 1
(ii) The Multiplicative inverse of -13/19 is -19/13
∵ -13/19 × (-19/13) = 1
(iii) The Multiplicative inverse of 1/5 is 5
∵ 1/5 × 5 = 1
(iv) The Multiplicative inverse of -5/8 × -3/7 is 56/15
∵ -5/8 × (-3/7) = 15/56 and 15/56 × 56/15 = 1
(v) The Multiplicative inverse of -1 × -2/5 is 5/2
∵ -1 × (-2/5) = 2/5 and 2/5 × 5/2 = 1
(vi) The Multiplicative inverse of -1 is -1
∵ -1 × (-1) = 1
