All categories

2 years ago

Enrique bought a packing tube to ship a poster to his cousin. If the packing tube had a volume of 1761 cubic centimeters and

Mathematics

1 answer:

Whitepunk [10]2 years ago

4 0

Answer:

r = 7 cm

Step-by-step explanation:

Given that,

Volume of the packing tube, V = 1761 cm²

The altitude of the tube, h = 11 cm

We need to find the radius of the packing tube. The volume of the the cylindrical shaped object is given by :

$V=\pi r^2 h\\\\r^2=\dfrac{V}{\pi h}\\\\r^2=\dfrac{1761}{\pi \times 11}\\\\r=7.13\ cm$

r = 7 cm

So, the radius of the packing tube is 7 cm.

You might be interested in

Please help with the attached question. Thanks

Mademuasel [1]

Answer:

Choice A) $F(x) = 3\sqrt{x + 1}$ .

Step-by-step explanation:

What are the changes that would bring $G(x)$ to $F(x)$ ?

Translate $G(x)$ to the left by $1$ unit, and
Stretch $G(x)$ vertically (by a factor greater than $1$ .)

$G(x) = \sqrt{x}$ . The choices of $F(x)$ listed here are related to $G(x)$ :

Choice A) $F(x) = 3\;G(x+1)$ ;
Choice B) $F(x) = 3\;G(x-1)$ ;
Choice C) $F(x) = -3\;G(x+1)$ ;
Choice D) $F(x) = -3\;G(x-1)$ .

The expression in the braces (for example $x$ as in $G(x)$ ) is the independent variable.

To shift a function on a cartesian plane to the left by $a$ units, add $a$ to its independent variable. Think about how $(x-a)$ , which is to the left of $x$ , will yield the same function value.

Conversely, to shift a function on a cartesian plane to the right by $a$ units, subtract $a$ from its independent variable.

For example, $G(x+1)$ is $1$ unit to the left of $G(x)$ . Conversely, $G(x-1)$ is $1$ unit to the right of $G(x)$ . The new function is to the left of $G(x)$ . Meaning that $F(x)$ should should add $1$ to (rather than subtract $1$ from) the independent variable of $G(x)$ . That rules out choice B) and D).

Multiplying a function by a number that is greater than one will stretch its graph vertically.
Multiplying a function by a number that is between zero and one will compress its graph vertically.
Multiplying a function by a number that is between $-1$ and zero will flip its graph about the $x$ -axis. Doing so will also compress the graph vertically.
Multiplying a function by a number that is less than $-1$ will flip its graph about the $x$ -axis. Doing so will also stretch the graph vertically.

The graph of $G(x)$ is stretched vertically. However, similarly to the graph of this graph $G(x)$ , the graph of $F(x)$ increases as $x$ increases. In other words, the graph of $G(x)$ isn't flipped about the $x$ -axis. $G(x)$ should have been multiplied by a number that is greater than one. That rules out choice C) and D).

Overall, only choice A) meets the requirements.

Since the plot in the question also came with a couple of gridlines, see if the points $(x, y)$ 's that are on the graph of $F(x)$ fit into the expression $y = F(x) = 3\sqrt{x - 1}$ .

5 0

3 years ago

Read 2 more answers

A large mixing tank currently contains 350 gallons of water, into which 10 pounds of sugar have been mixed. A tap will open, pou

Marysya12 [62]

Answer

Let t be number of minutes since tap is opened

water is increased by 20 gallons of water per minute.

sugar increase rate of 3 pounds per minute

water :- W(t) = 350 + 10 t

sugar :- S(t) = 10 + 3 t

concentration

C(t) = $\dfrac{S(t)}{W(t)}$

at t = 15 minutes

C(15) = $\dfrac{S(15)}{W(15)}$

C(15) = $\dfrac{10 + 3\times 15 }{350 + 10\times 15}$

C(15) = 0.11

at beginning t = 0 minutes

C(0) = $\dfrac{S(0)}{W(0)}$

C(0) = $\dfrac{10 + 3\times 0}{350 + 10\times 0}$

C(0) = 0.0286

C(15) > C(0)

hence, concentration is increasing as time is passing.

3 0

3 years ago

Verify the identity. 4 csc 2x = 2 csc2x tan x

vlada-n [284]

Step-by-step explanation:

$4csc(2x) = 2csc^2(x) tan(x)$

We start with Left hand side

We know that csc(x) = 1/ sin(x)

So csc(2x) is replaced by 1/sin(2x)

$4 \frac{1}{sin(2x)}$

Also we use identity

sin(2x) = 2 sin(x) cos(x)

$4 \frac{1}{2sin(x)cos(x)}$

4 divide by 2 is 2

Now we multiply top and bottom by sin(x) because we need tan(x) in our answer

$2\frac{1*sin(x)}{sin(x)cos(x)*sin(x)}$

$2\frac{sin(x)}{sin^2(x)cos(x)}$

$2\frac{1}{sin^2(x)} \frac{sin(x)}{cos(x)}$

We know that sinx/ cosx = tan(x)

Also 1/ sin(x)= csc(x)

so it becomes 2csc^2(x) tan(x) , Right hand side

Hence verified

6 0

2 years ago

Victoria made some chocolate pudding. For every 2 cups of chocolate, she added 5 cups of milk. The ratio of chocolate to milk in

vampirchik [111]

Answer:

B. 2 Over 5

Step-by-step explanation:

The answer would be B because 2 cups of chocolate to 5 cups of milk the ratio would be 2:5 and you can't put 5:2 because it's asking the ratio of chocolate milk to chocolate pudding not chocolate pudding to chocolate milk.

5 0

2 years ago

Please help I’ll make you a branliest!!!!!!!

masya89 [10]

Answer:

2 answer is right

Step-by-step explanation:

I think

7 0

3 years ago