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3 years ago

9

Given that 10 cm is approximately equal to 4 inches, which of the following expressions models a way to find out approximately h

ow many inches are equivalent to 350 cm?
A
350×(104)
B
350×(410)
C
(10−4)×350
D
(350−10)×4

1 answer:

Hatshy [7]3 years ago

4 0

Answer: I don't Know

Step-by-step explanation: Thanks for the point tho :)

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The matrix A = −14 −6 6 28 12 −4 0 0 4 has characteristic polynomial

rosijanka [135]

Answer:

Characteristic equation:

$p(\lambda) = -\lambda^3 + 2\lambda^2 + 8\lambda$

Eigen values:

$\lambda_1 = 0, \lambda_2 = -2, \lambda_3= 4$

Step-by-step explanation:

We are given the matrix:

$\displaystyle\left[\begin{array}{ccc}-14&-6&6\\28&12&-4\\0&0&4\end{array}\right]$

The characteristic equation can be calculated as:

$det(A-\lambda I) = 0\\|A-\lambda I| = 0$

We follow the following steps to calculate characteristic equation:

$=det\Bigg(\displaystyle\left[\begin{array}{ccc}-14&-6&6\\28&12&-4\\0&0&4\end{array}\right]-\lambda\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]\Bigg)\\\\= det\Bigg(\displaystyle\left[\begin{array}{ccc}-14-\lambda&-6&6\\28&12-\lambda&-4\\0&0&4-\lambda\end{array}\right]\Bigg)\\\\=(-14-\lambda)[(12-\lambda)(4-\lambda)]+6[28(4-\lambda)]-6[(28)(0)-(12-\lambda)(0)]\\\\= -\lambda^3 + 2\lambda^2 + 8\lambda$

$p(\lambda)= -\lambda^3 + 2\lambda^2 + 8\lambda$

To obtain the eigen values, we equate the characteristic equation to 0:

$p(\lambda) = -\lambda^3 + 2\lambda^2 + 8\lambda = 0\\-\lambda(\lambda^2-2\lambda-8) = 0\\-\lambda(\lambda^2-4\lambda+2\lambda-8) = 0\\-\lambda[(\lambda(\lambda-4)+2(\lambda-4)] = 0\\-\lambda(\lambda+2)(\lambda-4) = 0 \\\lambda_1 = 0, \lambda_2 = -2, \lambda_3= 4$

We can arrange the eigen values as:

$\lambda_1 = 0, \lambda_2 = -2, \lambda_3= 4\\-2 < 0 < 4\\\lambda_2 < \lambda_1 < \lambda_3$

3 0

3 years ago

How long will it take for an investment to triple, if interest is compounded continuously at 8%?

maw [93]

Answer:

<em>It will take 14 years before the investment triples</em>

Step-by-step explanation:

<u>Continuous Compounding</u>

Is the mathematical limit that compound interest can reach if it was calculated and reinvested into an account's balance over a theoretically infinite number of periods.

The formula for continuous compounding is derived from the formula for the future value of a compound interest investment:

$FV = PV\cdot e^{i.t}$

Where:

FV = Future value of the investment

PV = Present value of the investment

i = Interest rate

t = Time

It's required to find the time for an investment to triple, that is, FV = 3 PV, knowing the interest rate is i=8%=0.08.

Substituting the known values:

$3PV = PV\cdot e^{i.t}$

Dividing by PV:

$3 = e^{i.t}$

Taking logarithms:

$\ln 3=i.t$

Solving for t:

$\displaystyle t=\frac{\ln 3}{i}$

$\displaystyle t=\frac{\ln 3}{0.08}$

t = 13.7 years

Rounding up:

It will take 14 years before the investment triples

6 0

3 years ago

What is the vertex form of y=-2x^2-8x+10? Give the coordinates of the vertex, state if there is a minimum or maximum, and find t

mamaluj [8]

First off, let's notice that the squared variable is the "x", that means is a vertically opening parabola.

notice the leading term's coefficient, is -2, is negative, that means the parabola is opening downwards, is facing down, so it goes up up up, reaches the U-turn and then down down down, is a "hump" or a maximum point.

$\bf \textit{vertex of a vertical parabola, using coefficients}
\\\\
\begin{array}{lcccl}
y = & -2x^2& -8x& +10\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}
\qquad 
\left(-\cfrac{ b}{2 a}\quad ,\quad c-\cfrac{ b^2}{4 a}\right)
\\\\\\
\left( -\cfrac{-8}{2(-2)}~~,~~10-\cfrac{(-8)^2}{4(-2)} \right)\implies \left( \cfrac{8}{-4}~~,~~10-\cfrac{64}{-8} \right)
\\\\\\
\left( -2~~,~~10+8 \right)\implies (-2~~,~~18)$

and the line of symmetry, well is a vertical parabola, mirroring itself at the line x = -2, which is the x-coordinate of the vertex.

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3 years ago

What's 7 divided by 3

NeX [460]

7 divided by 3 is 21

Hope I helped! ( Smiles )

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3 years ago

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What is a multiplication equation that has a solution of 12

juin [17]

Answer:

4 x 3 = 12

Step-by-step explanation:

12 x 1 = 12

6 x 2 = 12

7 0

3 years ago

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