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Alisiya [41]
3 years ago
12

(GIVING BRAINLIYEST) 7. what is the volume of these 2 objects

Mathematics
2 answers:
inessss [21]3 years ago
6 0
3. 140 m^3
(3 x 6 x 7) + (1 x 2 x 7) = 126 + 14 = 140

4. 216 in^3
(4 x 4 x 9) + (3 x 4 x 6) = 144 + 72 = 216
kati45 [8]3 years ago
4 0

figure #1

smaller part

4x7x2= 56m

larger part

4x3x7= 84m

84+56= 140m³

figure #2

smaller part

2x4x3= 24m

larger part

4x4x12= 192m

192+24= 216in³

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Write 243 as a product of primes.
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Answer:

243 = 3⁵

Step-by-step explanation:

Firstly we will find the factors of 243. On calculating it see that the factors of 243 are 3 x 3 x 3 x 3 x 3.

or

243 = 9 x 9 x 3

We need to write 243 as the product of primes.

The number that divides itself or 1 are prime numbers.

3 is the only prime number here such that,

243 = 3⁵

Hence, this is the required solution.

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3 years ago
A line with a slope of–2 passes through the points (q,–6) and (9,–10). What is the value of q?
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no

Step-by-step explanation:

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Find the general solution of the following ODE: y' + 1/t y = 3 cos(2t), t &gt; 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
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