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3 years ago

write an expression to represent this verbal expression: the quotient of a number x and 5 less than 75.

Mathematics

1 answer:

Lera25 [3.4K]3 years ago

3 0

Answer:

x / 5 < 75

Step-by-step explanation:

A quotient is the result of the operation of division. Write a division problem between the terms x and 5. This is written as x / 5.

Next the quotient is less than the value 75.

Write this as x / 5 < 75.

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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)

<em>u' = v</em>

since <em>u' = v </em>

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

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

7 0

3 years ago

Solve for x. Round your answer to the nearest hundredth.

Zarrin [17]

Answer:

Option B is correct

Step-by-step explanation:

2x² - 6x + 3 = 0

Using Quadratic formula:

x = $\frac{-b+-\sqrt{b^{2}-4ac}}{2a}$

a = 2, b = -6, c = 3

x = $\frac-(-6)+-{\sqrt{(-6)^{2}-4(2)(3)}}{2(2)}$

x = $\frac{-(-6)+-\sqrt{(-6)^{2}-4(2)(3)}}{2(2)}\\$

$=\frac{6+-\sqrt{36-24}}{4}\\\\=\frac{6+-\sqrt{12}}{4}\\\\=\frac{6+-3.46}{4}\\\\$

$=\frac{6+3.46}{4}$

x = 2.37

$=\frac{6-3.46}{4}$

x = 0.63

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