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3 years ago

What is 45% of 900kg

Mathematics

1 answer:

alina1380 [7]3 years ago

3 0

45% of 900 kg is 405 kilograms

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-x/8<-1/2 solve each inqequality

Sindrei [870]

-x/8<-1/2. Use the reverse order of operations to solve this. So, as both sides are negative, multiply them by -1 to get you to x/8>1/2, as multiplying by a negative flips the symbol. Solve that by multiplying 1/2 to 8/1. Multiply the numerators and denominators, to give you 8/2. Simplified, x>4

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3 years ago

Simplify: 4x + 6(3x - 2)

gavmur [86]

Answer:

2 • (2x - 3) • (3x - 2)

Step-by-step explanation:

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2 years ago

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Solve the following ODE's: c) y* - 9y' + 18y = t^2

Nastasia [14]

Answer:

y = $C_1e^{3t}+C_2e^{6t}$ + $\dfrac{1}{18}(t^2+\frac{2t}{6} + \frac{2}{36}+\frac{2t}{3}+\frac{2}{18}+\frac{2}{9})$

Step-by-step explanation:

y''- 9 y' + 18 y = t²

solution of ordinary differential equation

using characteristics equation

m² - 9 m + 18 = 0

m² - 3 m - 6 m+ 18 = 0

(m-3)(m-6) = 0

m = 3,6

C.F. = $C_1e^{3t}+C_2e^{6t}$

now calculating P.I.

$P.I. = \frac{t^2}{D^2 - 9D +18}$

$P.I. = \dfrac{t^2}{(D-3)(D-6)}\\P.I. =\dfrac{1}{18}(1-\frac{D}{3})^{-1}(1-\frac{D}{6})^{-1}(t^2)\\P.I. =\dfrac{1}{18}(1-\frac{D}{3})^{-1}(1+\frac{D}{6}+\frac{D^2}{36}+....)(t^2)\\P.I. =\dfrac{1}{18}(1-\frac{D}{3})^{-1}(t^2+\frac{2t}{6} + \frac{2}{36})\\P.I. =\dfrac{1}{18}(1+\frac{D}{3}+\frac{D^2}{9}+....)(t^2+\frac{2t}{6} + \frac{2}{36})\\P.I. =\dfrac{1}{18}(t^2+\frac{2t}{6} + \frac{2}{36}+\frac{2t}{3}+\frac{2}{18}+\frac{2}{9})$

hence the complete solution

y = C.F. + P.I.

y = $C_1e^{3t}+C_2e^{6t}$ + $\dfrac{1}{18}(t^2+\frac{2t}{6} + \frac{2}{36}+\frac{2t}{3}+\frac{2}{18}+\frac{2}{9})$

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2 years ago

Find the vertex of the graph of the function. f(x) = 2x^2 - 8x + 9

Rashid [163]

$\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{2}x^2\stackrel{\stackrel{b}{\downarrow }}{-8}x\stackrel{\stackrel{c}{\downarrow }}{+9} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{-8}{2(2)}~~,~~9-\cfrac{(-8)^2}{4(2)} \right)\implies \left( \cfrac{8}{4}~~,~~9-\cfrac{64}{8} \right) \\\\\\ (2~~,~~9-8)\implies (2~~,~~1)$

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3 years ago

Jason draws a line in the sand at the beach the line is 7/8 feet long he wants to divide the line into sections that are 1 8 fee

abruzzese [7]

The answer is 7 sections
In this type of question, you just need to divide the total length of the line that drawn by Jason with the length of sections that Jason want.

So, the calculation would be:

(7/8) / (1/8)

= 7/8 x 8/1

= 7 amount of sections

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3 years ago

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