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4 years ago

A grocer stacks oranges in a four-sided pyramid that is 8 layers high. How many oranges are in the pile?

Mathematics

2 answers:

marusya05 [52]4 years ago

6 0

91 oranges is the answer.

ser-zykov [4K]4 years ago

5 0

32 4 sides*8layers=32

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What is the length of AB please don’t do it for fun just try to do it for me hurry?

Lerok [7]

Answer:

y6%cf4yergby65thrbgtrvbh

Step-by-step explanation:

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3 years ago

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Sum points lol. I'm being generous :)

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3 years ago

Let y 00 + by0 + 2y = 0 be the equation of a damped vibrating spring with mass m = 1, damping coefficient b > 0, and spring c

stira [4]

Answer:

Step-by-step explanation:

Given that:

The equation of the damped vibrating spring is y" + by' +2y = 0

(a) To convert this 2nd order equation to a system of two first-order equations;

let y₁ = y

y'₁ = y' = y₂

So;

y'₂ = y"₁ = -2y₁ -by₂

Thus; the system of the two first-order equation is:

y₁' = y₂

y₂' = -2y₁ - by₂

(b)

The eigenvalue of the system in terms of b is:

$\left|\begin{array}{cc}- \lambda &1&-2\ & -b- \lambda \end{array}\right|=0$

$-\lambda(-b - \lambda) + 2 = 0 \ \\ \\\lambda^2 +\lambda b + 2 = 0$

$\lambda = \dfrac{-b \pm \sqrt{b^2 - 8}}{2}$

$\lambda_1 = \dfrac{-b + \sqrt{b^2 -8}}{2} ; \ \lambda _2 = \dfrac{-b - \sqrt{b^2 -8}}{2}$

(c)

Suppose $b > 2\sqrt{2}$ , then λ₂ < 0 and λ₁ < 0. Thus, the node is stable at equilibrium.

(d)

From λ² + λb + 2 = 0

If b = 3; we get

$\lambda^2 + 3\lambda + 2 = 0 \\ \\ (\lambda + 1) ( \lambda + 2 ) = 0\\ \\ \lambda = -1 \ or \ \lambda = -2 \\ \\$

Now, the eigenvector relating to λ = -1 be:

$v = \left[\begin{array}{ccc}+1&1\\-2&-2\\\end{array}\right] \left[\begin{array}{c}v_1\\v_2\\\end{array}\right] = \left[\begin{array}{c}0\\0\\\end{array}\right]$

$\sim v = \left[\begin{array}{ccc}1&1\\0&0\\\end{array}\right] \left[\begin{array}{c}v_1\\v_2\\\end{array}\right] = \left[\begin{array}{c}0\\0\\\end{array}\right]$

Let v₂ = 1, v₁ = -1

$v = \left[\begin{array}{c}-1\\1\\\end{array}\right]$

Let Eigenvector relating to λ = -2 be:

$m = \left[\begin{array}{ccc}2&1\\-2&-1\\\end{array}\right] \left[\begin{array}{c}m_1\\m_2\\\end{array}\right] = \left[\begin{array}{c}0\\0\\\end{array}\right]$

$\sim v = \left[\begin{array}{ccc}2&1\\0&0\\\end{array}\right] \left[\begin{array}{c}m_1\\m_2\\\end{array}\right] = \left[\begin{array}{c}0\\0\\\end{array}\right]$

Let m₂ = 1, m₁ = -1/2

$m = \left[\begin{array}{c}-1/2 \\1\\\end{array}\right]$

∴

$\left[\begin{array}{c}y_1\\y_2\\\end{array}\right]= C_1 e^{-t} \left[\begin{array}{c}-1\\1\\\end{array}\right] + C_2e^{-2t} \left[\begin{array}{c}-1/2\\1\\\end{array}\right]$

So as t → ∞

$\mathbf{ \left[\begin{array}{c}y_1\\y_2\\\end{array}\right]= \left[\begin{array}{c}0\\0\\\end{array}\right] \ \ so \ stable \ at \ node \ \infty }$

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3 years ago

HELP I WILL MARK YOU AS A BRAINLIEST!

vfiekz [6]

$6.90 divided by 3 is $2.30 which is the unit rate and if you multiply $2.30 by 10 you get $23

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3 years ago

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How do i solve this?<br>13=x/4

Alex17521 [72]

Answer:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

13-(x/4)=0

Step by step solution :

Step 1 :

Simplify —

Equation at the end of step 1 :

13 - — = 0

Step 2 :

Rewriting the whole as an Equivalent Fraction :

2.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using 4 as the denominator :

13 13 • 4

13 = —— = ——————

1 4

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

13 • 4 - (x) 52 - x

———————————— = ——————

4 4

Equation at the end of step 2 :

52 - x

—————— = 0

Step 3 :

When a fraction equals zero :

Now, to get rid of the denominator, Tiger multiple's both sides of the equation by the denominator. 3.1 When a fraction equals zero …

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Here's how:

52-x

———— • 4 = 0 • 4

Now, on the left hand side, the 4 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

52-x = 0

Solving a Single Variable Equation :

3.2 Solve : -x+52 = 0

Subtract 52 from both sides of the equation :

-x = -52

Multiply both sides of the equation by (-1) : x = 52

7 0

3 years ago