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FinnZ [79.3K]
2 years ago
8

Which expression is equivalent to 6 Superscript 4 times 6 cubed? (6 times 6 times 6 times 6) (6 times 6 times 6) (6 6 6 6) times

(6 6 6) (6 times 6 times 6 times 6) times (6 times 6 times 6) (6 times 6 times 6 times 6 times 6) times (6 times 6 times 6 times 6).
Mathematics
1 answer:
malfutka [58]2 years ago
5 0

The expression which is equivalent to 6 Superscript 4 times 6 cubed and posses same value as this expression is,

6\times6\times6\times6)\times6

<h3>What is the equivalent expression?</h3>

Equivalent expressions are the expression whose result is equal to the original expression, but the way of representation is different.

The given statement for the expression is 6 Superscript 4 times 6 cubed. This expression cab be written as,

6^4\times6

Suppose the equivalent expression of this equation is n. Thus,

n=6^4\times6

The 4 power of number 6 means that the number 6 should be multiplied 4 times.

n=(6\times6\times6\times6)\times6

Hence, the expression which is equivalent to 6 Superscript 4 times 6 cubed and posses same value as this expression is,

6\times6\times6\times6)\times6

Learn more about the equivalent expression here;

brainly.com/question/2972832

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A particle moving in a planar force field has a position vector x that satisfies x'=Ax. The 2×2 matrix A has eigenvalues 4 and 2
andrey2020 [161]

Answer:

The required position of the particle at time t is: x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}

Step-by-step explanation:

Consider the provided matrix.

v_1=\begin{bmatrix}-3\\1 \end{bmatrix}

v_2=\begin{bmatrix}-1\\1 \end{bmatrix}

\lambda_1=4, \lambda_2=2

The general solution of the equation x'=Ax

x(t)=c_1v_1e^{\lambda_1t}+c_2v_2e^{\lambda_2t}

Substitute the respective values we get:

x(t)=c_1\begin{bmatrix}-3\\1 \end{bmatrix}e^{4t}+c_2\begin{bmatrix}-1\\1 \end{bmatrix}e^{2t}

x(t)=\begin{bmatrix}-3c_1e^{4t}-c_2e^{2t}\\c_1e^{4t}+c_2e^{2t} \end{bmatrix}

Substitute initial condition x(0)=\begin{bmatrix}-6\\1 \end{bmatrix}

\begin{bmatrix}-3c_1-c_2\\c_1+c_2 \end{bmatrix}=\begin{bmatrix}-6\\1 \end{bmatrix}

Reduce matrix to reduced row echelon form.

\begin{bmatrix} 1& 0 & \frac{5}{2}\\ 0& 1 & \frac{-3}{2}\end{bmatrix}

Therefore, c_1=2.5,c_2=1.5

Thus, the general solution of the equation x'=Ax

x(t)=2.5\begin{bmatrix}-3\\1\end{bmatrix}e^{4t}-1.5\begin{bmatrix}-1\\1 \end{bmatrix}e^{2t}

x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}

The required position of the particle at time t is: x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}

6 0
3 years ago
A pack of 9 toilet rolls costs £4.23
OleMash [197]
 a)  9 toilet rolls cost $ 4.23
       1 toilet roll costs  $ x

          9x = 4.23 * 1
           x= 4.23 / 9
            x = 0.47
So in first case one toilet roll costs $ 0.47.

b) 4 toilet rolls cost $1.96
    1 toilet roll costs  $ x
     
    4x = 1.96 * 1
     x = 1.96 / 4
     x = 0.49
So in second case one toilet roll costs $ 0.49.

0.47 < 0.49
The toilet roll in first case is cheaper than the toilet roll in second case.

Hope this heps!


8 0
3 years ago
What is the value of the expression (2)^6?
Mumz [18]
The value of the expression (2)^6 is 64.
6 0
3 years ago
Read 2 more answers
Quadrilateral LMNO is similar to quadrilateral PQRS. Find the measure of side QR.
dalvyx [7]

Answer:

The measure of the side QR is 8.8.

Step-by-step explanation:

Since LMNO \sim PQRS, then SP \propto OL, RS \propto ON, RQ \propto MN and QP \propto LM. From figure we have the following relationship:

k = \frac{OL}{SP} = \frac{ON}{RS} = \frac{MN}{QR} = \frac{ML}{QP} (1)

Where k is the proportionality ratio.

If we know that SP = 13, OL = 55, MN = 37, then the measure of side QR is:

k = \frac{OL}{SP} (1b)

k = \frac{55}{13}

k = \frac{MN}{QR}

QR = \frac{MN}{k} (1c)

QR = \frac{37}{\frac{55}{13} }

QR = 8.745

The measure of the side QR is 8.8.

4 0
3 years ago
I WILL GIVE BRAINIEST Which statement is correct about the product of 9/10 ​​and ​ 7/8 ​
Wewaii [24]

Answer:

7/10 and 7/8 are both less than 1.

Step-by-step explanation:

The product must be less than either factor because when you multiply a number by less than 1, the number gets smaller.

3 0
3 years ago
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