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2 years ago

Find the Surface Area of the cone.

Mathematics

1 answer:

STatiana [176]2 years ago

6 0

Cone surface area:

πr(r + s)

= 3,14 × 3 × (3 + 7)

= 3,14 × 3 × 10

= 9,42 × 10

= 94,2 m²

Nt: I from IDN

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Read 2 more answers

Write the given second order equation as its equivalent system of first order equations. u′′−5u′−4u=1.5sin(3t),u(1)=1,u′(1)=2.5

lakkis [162]

Answer:

hi your question options is not available but attached to the answer is a complete question with the question options that you seek answer to

Answer: v = 5v + 4u + 1.5sin(3t),

1.5sin(3t)

Step-by-step explanation:

u" - 5u' - 4u = 1.5sin(3t) where u'(1) = 2.5 u(1) = 1

v represents the "velocity function" i.e v = u'(t)

As v = u'(t)

u' = v

since u' = v

v' = u"

v' = 5u' + 4u + 1.5sin(3t) ( given that u" - 5u' - 4u = 1.5sin(3t) )

= 5v + 4u + 1.5sin(3t) ( noting that v = u' )

so v' = 5v + 4u + 1.5sin(3t)

d/dt $\left[\begin{array}{ccc}u&\\v&\\\end{array}\right]$ = $\left[\begin{array}{ccc}0&1&\\4&5&\\\end{array}\right]$ $\left[\begin{array}{ccc}u&\\v&\\\end{array}\right]$ + $\left[\begin{array}{ccc}0&\\1.5sin(3t)&\\\end{array}\right]$

Given that u(1) = 1 and u'(1) = 2.5

since v = u'

v(1) = 2.5

note: the initial value for the vector valued function is given as

$\left[\begin{array}{ccc}u(1)&\\v(1)\\\end{array}\right]$ = $\left[\begin{array}{ccc}1\\2.5\\\end{array}\right]$

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3 years ago