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3 years ago

Simplify the expression √100/49

Mathematics

1 answer:

Mekhanik [1.2K]3 years ago

4 0

Answer: 10/7

Step-by-step explanation:

The square root of 100 is 10 and the square root of 49 is 7 so the answer will be 10/7

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Let the matrix below act on C². Find the eigenvalues and a basis for each eigenspace in C².

forsale [732]

Hello, let's note A the matrix, we need to find $\lambda$ such that A $\lambda$ = $\lambda$ I, where I is the identity matrix, so the determinant is 0, giving us the characteristic equation as

$\left|\begin{array}{cc}1-\lambda&3\\-3&1-\lambda\end{array}\right|\\\\=(1-\lambda)^2+9\\\\=\lambda^2-2\lambda+10\\\\=0$

We just need to solve this equation using the discriminant.

$\Delta=b^2-4ac=2^2-40=-36=(6i)^2$

And then the eigenvalues are.

$\lambda_1=\dfrac{2-6i}{2}=\boxed{1-3i}\\\\\lambda_2=\boxed{1+3i}$

To find the basis, we have to solve the system of equations.

$A\lambda_1-\lambda_1 I=\left[\begin{array}{cc}3i&3\\-3&3i\end{array}\right] \\\\=3\left[\begin{array}{cc}i&1\\-1&i\end{array}\right] \\\\\text{For a vector (a,b), we need to find a and b such that.}\\\\\begin{cases}ai+b=0\\-a+bi=0\end{cases}\\\\\text{(1,-i) is a base of this space, as i-i=0 and -1-}i^2\text{=-1+1=0.}$

$A\lambda_2-\lambda_2 I=\left[\begin{array}{cc}-3i&3\\-3&-3i\end{array}\right] \\\\=3\left[\begin{array}{cc}-i&1\\-1&-i\end{array}\right]\\\\\text{For a vector (a,b), we need to find a and b such that.}\\\\\begin{cases}-ai+b=0\\-a-bi=0\end{cases}\\\\\text{(1,i) is a base of this space as -i+i=0 and -1-i*i=0.}$

Thank you

4 0

3 years ago

The graph below shows the relationship between the amount of peanuts and the amount of chocolate in different packages of snack

Tomtit [17]

Answer:

Option (B)

Step-by-step explanation:

Since the linear graph is passing through the origin, there is a proportional relationship between the amount of chocolate (C) and amount of peanuts (P) used in the package of snacks mix,

P ∝ C

P = kC

k = $\frac{P}{C}$

Here k = proportionality constant

Since, the given line passes through a point (3, 2),

k = $\frac{2}{3}$

Therefore, ratio of chocolate and peanuts mixed is $\frac{2}{3}$ .

Option (B) is the correct option.

5 0

3 years ago

The temperature of pot of water fell from 72 degrees to 36 degrees in 4 minutes. Find the average change in temperature per minu

Sedaia [141]

I believe the change in temperature by minute is 9

8 0

3 years ago

In rhombus ABCD below, AC=30 cm and BD=18 cm. Find the area of the rhombus .I will give brainliest for the best and correct answ

barxatty [35]

Area of rhombus = 0.5 x D1 x D2

Thus,
Area = 0.5 x 30 x 18
= 270 units ^2

7 0

2 years ago

Which polynomial is equivalent to (y+10)^2?

notka56 [123]

Answer:

Step-by-step explanation:

(a + b)² = a² + 2ab +b²

a = y & b = 10

(y + 10)² = y² + 2 *y*10 + (10)²

= y² + 20y + 100

3 0

3 years ago