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Which statement is true of the determinant of a matrix? A. It can be either positive or zero, but never negative. B. It can have

Andre45 [30]

Answer: D

Step-by-step explanation:

A. Det can be negative.

B. Is gobbledygook

C. All components of the matrix are included.

D. The others have been eliminated, and it's true.

8 0

3 years ago

Evaluate the integral by reversing the order of integration. Integral from 0 to 1 integral from √x to 1 of 5/(y³+1) dydx

ELEN [110]

Answer:

⁵/₃ ln 2

Step-by-step explanation:

∫₀¹ ∫√ₓ¹ 5 / (y³ + 1) dy dx

We want to change the order of integration. To do this, we start by graphing the region contained by the four limits.

x = 0, x = 1

y = √x, y = 1

(Notice that y = √x is the same as x = y²).

Once we've graphed the region, we need to write the domain of x in terms of y. In this case, 0 < x < y².

Then, we find the range: 0 < y < 1.

Now we can rewrite the integral:

∫₀¹ ∫₀ʸ² 5 / (y³ + 1) dx dy

Notice that the integrand itself, 5 / (y³ + 1), does not change. Only the limits have changed.

Solve the integral.

∫₀¹ [ 5 / (y³ + 1) x |₀ʸ² ] dy

∫₀¹ [ 5y² / (y³ + 1) ] dy

⁵/₃ ∫₀¹ [ 3y² / (y³ + 1) ] dy

(⁵/₃ ln|y³ + 1|) |₀¹

⁵/₃ ln|1³ + 1| − ⁵/₃ ln|0³ + 1|

⁵/₃ ln 2

7 0

3 years ago

Describe how multiplying all the linear dimensions of a cone by one

Anton [14]

Answer: $\frac{1}{64}^{th}$

Step-by-step explanation:

Given

Suppose V is the original volume of cone having r as radius and h as height

If we multiply all the linear dimensions of ac one by $\frac{1}{4}^{th}$

the $r'=\frac{r}{4}$

$h'=\frac{h}{4}$

Therefore new volume is

$V'=\frac{1}{3}\pi r'^2h'$

$V'=\frac{1}{3}\pi (\frac{r}{4})^2(\frac{h}{4})$

$V'=\frac{1}{64}\times \frac{1}{3}\pi r^2h$

$V'=\frac{V}{64}$

So new volume becomes $\frac{1}{64}^{th}$ of the original one

6 0

3 years ago

Pleas helpppp please

vlada-n [284]

Answer:

48cm^2

Step-by-step explanation:

We are given some of the measurements of the piece of cardboard.

First, let's find the lengths of all the sides of the cardboard, as it will be easier to then find the area.

Going in clockwise order, from top to bottom, the dimensions are:

4cm, 7cm, 6cm, 2cm, 10cm, 9cm.

Now, we can easily find the area by using the formula BH=Area. Let's split the cardboard into sections that will be easier to find the area of. Say we split it in two, rather like a sneaker with the person wearing a sock showing at the ankle (I have strange explanations, I know).

To find the top part (the sock part) we can multiply 4 by 7 to get 28.

To find the shoe part, we can multiply 10 by 2 to get 20.

Finally, add these areas together to get the total area.

20 + 28 = 48

Another way to do this (if my sock and sneaker explanation was too chaotic for you) would be to imagine that the cardboard piece were an entire rectangle (ignore that chunk that has been cut out).

The area of that would be 90, from 9 by 10 as the side lengths. Then, from earlier, we know that the width and length of the chunk that has been cut out is 6 and 7, so the area that will be cut out is 42.

Subtract 42 from 90 to get 48.

8 0

3 years ago

How long does it take a snail to crawl 81 inches

quester [9]

Answer:

5 hours just measured

Step-by-step explanation:

3 0

3 years ago

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