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3 years ago

Evaluate the determinant for the following matrix: [- 5 1 1 4] A. –21 B. 19 C. –17 D. –24

Mathematics

2 answers:

mariarad [96]3 years ago

6 0

Answer:

-21

Step-by-step explanation:

I assume this is a 2 by 2 matrix.

$\begin{bmatrix} -5 & 1\\1 & 4 \end{bmatrix}$

determinant = -5 * 4 - 1 * 1 = -20 - 1 = -21

lara [203]3 years ago

6 0

Answer:

Option A.

Step-by-step explanation:

If a matrix is defined as

$A=\begin{bmatrix}a\:&\:b\:\\ c\:&\:d\:\end{bmatrix}\:$

then its determinant is

$|A|=\:ad-bc$

Let the given matrix is

$B=\begin{bmatrix}-5&1\\ \:1&4\end{bmatrix}$

We need to find the determinant for the given matrix.

Using the above formula we get

$|B|=\left(-5\right)\cdot \:4-1\cdot \:1$

$|B|=-21$

The determinant of given matrix is -21. Therefore, the correct option is A.

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Jlenok [28]

Answer:

3 centimeters per minute so solving the equation 15 divided by 4 for the y value equal to 30

Step-by-step explanation:

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3 years ago

The second of two number is 5 times first. Their sum is 42 . Find both numbers

Harman [31]

Hey there!

To start, first let the variable, x, represent your first unknown number. Now, because the second number is 5 times the first, this will be represented as 5x (you simply multiply 5 to your variable of the first number, x).

Now, since the sum of the two numbers are 42, you can represent this by setting up this equation:
5x+x=42

Combine your like terms (terms of the same variable and are raised to the same power):
5x+x=42
6x=42

Divide both sides by 6 to solve for x:
6x/6=42/6
x=7

Because x represents the first number, your first number would be 7.

Now, since the second number is 5 times the first, you can find the second number by multiplying x by 5:
x=7
7*5=35

Your second number is 35.

To check if both numbers are correct, you can add your first number, 7 to your second number, 35, to see if you get 42 since you know their sum must be 42:
7+35=42

Therefore, your final answer would be that the first number is 7, and the second number is 35.

Hope this helps, and have a marvelous day! :)

7 0

3 years ago

Read 2 more answers

Need help with radical expression!!! It’s asking for a set of all x where the expression is defined in interval form!

gayaneshka [121]

Answer: (0, 25) ∪ (25, ∞)

Step-by-step explanation:

The expression is undefined when the denominator is equal to zero and when the radicand (expression inside the radical) is less than zero.

Let's deal with the denominator first by finding the x-values that would make the denominator equal to zero (these are the values that will NOT be included in the interval notation)

x - 5√x = 0

x = 5√x added 5√x to both sides

x² = 25x squared both sides

x² - 25x = 0 subtracted 25x from both sides

x(x - 25) = 0 factored the quadratic equation

x = 0 and x - 25 = 0 applied the Zero Product Property

x = 0 and x = 25 solved for x

So, x ≠ 0 and x ≠ 25

Next, let's deal with the radicand by setting the expressions inside the radicals to "greater than or equal to zero".

2√x and 5√x both have a radicand of x

x ≥ 0

Now, let's put it all together

x ≥ 0 and x ≠ 0 and x ≠ 25

so, x is between 0 and ∞ but not including 0 or 25.

Interval Notation: (0, 25) ∪ (25, ∞)

Reminder that interval notation uses a bracket [ ] when the value is included and a parenthesis ( ) when the value is not included. Infinity always uses a parenthesis since it is not an actual number.

6 0

3 years ago

Integrate sin²2x cos²2xdx

Masteriza [31]

$\sin^2x=\dfrac{1-\cos2x}2$
$\cos^2x=\dfrac{1+\cos2x}2$

From the identities above, you have

$\sin^22x\cos^22x=\dfrac{(1-\cos4x)(1+\cos4x)}4=\dfrac{1-\cos^24x}4$

Applying once more, you have

$\dfrac{1-\cos^24x}4=\dfrac{1-\dfrac{1+\cos8x}2}4=\dfrac{1-\cos8x}8$

So,

$\displaystyle\int\sin^22x\cos^22x\,\mathrm dx=\frac18\int(1-\cos8x)\,\mathrm dx=\frac x8-\frac1{64}\sin8x+C$

3 0

3 years ago

Consider the parametric curve x = 2t^(3)-3t^(2)+2 and y = t^(3)-12t,-pi leq t leq pi . (a) Find the values of t (if any) where t

bagirrra123 [75]

Answer:

(a) t = ±2

(b) t ∈ {0, 1}

Step-by-step explanation:

(a) dy/dx = 0 when dy/dt = 0

dy/dt = 3t^2 -12 = 0 = 3(t -2)(t +2)

The slope is zero at t = ±2.

(b) dy/dx = (dy/dt)/(dx/dt) = undefined when dx/dt = 0

dx/dt = 6t^2 -6t = 6(t)(t -1) = 0

The slope is undefined for t ∈ {0, 1}.

(c) At t=3, dy/dx = (dy/dt)/(dx/dt) = 3(3-2)(3+2)/(6(3)(3-1)) = 15/36 = 5/12

The general direction of movement is away from the origin along a line with a slope of 5/12, about 22.6° CCW from the +x direction.

_____

The first attachment shows the derivative and its zeros and asymptotes. It also shows some of the detail of the parametric curve near the origin.

The second attachment shows the parametric curve over the domain for which it is defined, along with the point where t=3.

5 0

3 years ago