Answer:
x < 3
Step-by-step explanation:
4x - 7 < 5
Add 7 to both sides;
4x < 12
Divide both sides by 4;
x < 3
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:
Amount each friend pays for the gift = $20
Step-by-step explanation:
Market price of a gift = $70
The store manager takes $10 off the market price.
Marked down amount = $10
New cost price = Marked price - Marked down amount 
The cost of the gift is divided among three friends.
This means that the cost of gift which is $60 is divided by three to get each one's contribution in the gift.
∴ Amount each friend pays for the gift 
Answer:
About 16 years
Step-by-step explanation:
First we need to figure out 5.25% of 12000
5.25 x 0.12000 = 0.63
Then we move the decimal
630
Then we need to figure out how many years it will take to reach $22000
Since we already owe $12000, we can just divide using $10000 because 10000 + 12000 = 22000
10000/630 = 15.87
Which is about 16 years
Answer:
19 degrees, 70 degrees, 91 degrees
Step-by-step explanation:
to make an interior angle of a triangle you need to make a 180-degree triangle and 19+70+91 make 180 degrees
