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3 years ago

PLEASE HELP ME FOR EXTRA POINTS AND BRAINLIEST ANWSER

Mathematics

1 answer:

NNADVOKAT [17]3 years ago

3 0

Recall that tanA = sinA / cosA.

Therefore, tanA = (3/5) / (4/5) = 3/4.

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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 gross domestic product (GDP) of a certain country, which measures the overall size of the economy in billions of dollars, ca

DiKsa [7]

Answer:

The estimated GDP in 2007 is 12782 billion dollars.

The estimated GDP in 2011 is 15010 billion dollars.

The estimated GDP in 2012 is 15567 billion dollars.

Step-by-step explanation:

Consider the provided function.

$g(y) = 557y +8883$

Where y = 10 corresponds to the year 2010.

Part (b) Estimate the GDP (to the nearest billion dollars) in 2007.

If y = 10 corresponds to the year 2010 then y = 7 corresponds to the year 2007.

Substitute the value of y = 7 in the provided function.

$g(y) = 557(7) +8883$

$g(y) = 3899+8883$

$g(y) = 12782$

Hence, the estimated GDP in 2007 is 12782 billion dollars.

Part (b) Estimate the GDP (to the nearest billion dollars) in 2011.

If y = 10 corresponds to the year 2010 then y = 11 corresponds to the year 2011.

Substitute the value of y = 11 in the provided function.

$g(y) = 557(11) +8883$

$g(y) = 6127+8883$

$g(y) = 15010$

Hence, the estimated GDP in 2011 is 15010 billion dollars.

Part (C) Estimate the GDP (to the nearest billion dollars) in 2012.

If y = 10 corresponds to the year 2010 then y = 12 corresponds to the year 2012.

Substitute the value of y = 12 in the provided function.

$g(y) = 557(12) +8883$

$g(y) = 6684+8883$

$g(y) = 15567$

Hence, the estimated GDP in 2012 is 15567 billion dollars.

4 0

3 years ago

Sophia has $91,000 in a savings account that earns 7% annually. The interest is not compounded. To the nearest cent, how much wi

USPshnik [31]

Answer:

$95777.5

Step-by-step explanation:

change 7% to decimal = .07

91,000 * .07 = 5370 (annual interest)

5370 / 12 = 530.83 (monthly interest)

530.83 * 9 = 4777.5 (9 months interest)

91,000 + 4777.5 = 95777.5 (initial + 9 months interest)

6 0

3 years ago

Given that ∠S ≅ ∠A, and AB ≅ ST , what is the third congruence needed to prove that ΔABC ≅ ΔSTU by ASA?

Olenka [21]

Answer:

angle-side-angle. that's my answer

7 0

2 years ago

What is the answer of the above question in the diagram

natulia [17]

Answer: 1

Order of operations:
add first (2 + 2)
Multiply ( 2 x (4))
Divide ( 8/(8))
= 1

6 0

2 years ago