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3 years ago

Giselle spent 7/10 of her money on a book and 10/100 of her money on food. What fraction of her money did she spend altogether?

Mathematics

2 answers:

aleksklad [387]3 years ago

8 0

Answer:

80/100 or 80%

Step-by-step explanation:

7/10 = 70/100

70/100 + 10/100 = 80/100

zysi [14]3 years ago

8 0

Answer:

She spent 80/100 or 8/10 of her money on food.

Step-by-step explanation:

You can multiply 7/10 by 10 to get 70/100, then add it with 10/100. You're finally result would be 80/100. If supposed to be simplifed, choose 8/10

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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

Help me pls I really really need help with this I'm so bad at math

MAVERICK [17]

Question 7: Answer J (7/8 - 1/2 = 3/8)

6 0

4 years ago

What is the midpoint M of that line segment?

pychu [463]

Answer:

Midpoint = ( (x1+x2)/2 , (y1+y2)/2 )

Step-by-step explanation:

Please upload the line segment otherwise, you can use the equation above to solve for it.

8 0

3 years ago

Read 2 more answers

The sum of w and 5 into algebraic expression

Alina [70]

Answer: w + 5

Step-by-step explanation: The sum of w and 5 translates into an algebraic expression form to w + 5.

7 0

4 years ago

What are possible coordinates of point F if triangle DEF is<br> congruent to triangle ABC?

Lemur [1.5K]

Answer:

(-1, 4)

Step-by-step explanation:

Point B is 5 units below point A, and point E is 5 units above point D: AB = ED. This means that BC will be equal to EF. B and C are 7 units apart, so 7 units left from E is (-1, 4).

Hope this helps!

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3 years ago