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DanielleElmas [232]
2 years ago
11

A car and a truck are moving at the same speed. The car drives 2 hours. The truck drives 2.5 hours and goes 20 miles farther tha

n a car. What is the speed at which the car and the truck are traveling
Mathematics
1 answer:
Reptile [31]2 years ago
5 0

Answer: 40 miles an hour

Step-by-step explanation:

It goes .5 more than the car so

if .5 = 20

.5 x 2 = 1

1 = 40

So 40 miles an hour

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Find the general solution of the following ODE: y' + 1/t y = 3 cos(2t), t > 0.
Margarita [4]

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

3 0
3 years ago
The amount of interest earned every year with simple interest is constant. <br>true or false​
Charra [1.4K]

Answer:

True.

Step-by-step explanation:

If I = prt, They are all being multiplied together, therefor being constant.

4 0
2 years ago
If it costs $100,000 to put on an event for four weeks (28 consecutive nights), how much revenue per night is needed to
Arada [10]
100000+200000=300000
28x=300000
X=10714
They would need to make $10714 a night
8 0
3 years ago
Help meeeeeeeee -2+6&gt;10
joja [24]

Answer:

4 Is greater than 10. Hope this helped.

4 0
3 years ago
An 8-sided die is formed when two square pyramids are attached by their bases. The perimeter of the base shape is 6 centimeters.
Vlada [557]
This is the concept of areas of solid figures. The surface are of the solid figure formed when 2 square pyramids are attached will be given by:
SA=[number of triangular faces]*[Area of each triangle]
Number of triangular faces=8
Area of each triangle=1/2*bh
base=6/4=1.5 cm
height=2 cm
thus;
Area=1/2*2*1.5=1.5
The surface area will therefore be:
SA=1.5*8=12cm^2
3 0
3 years ago
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