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2 years ago

A firkin is an old British unit of volume equal to 9 gallons. How many cubic meters are there in 6.00 firkins?

Mathematics

1 answer:

Rainbow [258]2 years ago

7 0

Answer:

0.245489 cubic meters.

Step-by-step explanation:

It is given that a firkin is an old British unit of volume equal to 9 gallons.

1 firkin = 9 gallons

6 firkins = 54 gallons

We need convert 6.00 firkins to cubic meters.

We know that,

1 gallon = 0.00454609 cubic meters

54 gallon = 0.24548886 cubic meters

6 firkins = 0.245489 cubic meters.

Therefore, 6.00 firkins is equivalent to 0.245489 cubic meters.

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We would like to know the velocity of the block when it reaches some position x. Finding this requires an integration. However,

Slav-nsk [51]

Answer:

An alternative definition for the acceleration ax that can be written in terms of $v_x$ and $\frac{dv_x}{dx}$ is $a_x=v_x \frac{dv_x}{dx}$

Step-by-step explanation:

We know that :

$a_x=\frac{dv_x}{dt}$

Now we are supposed to find an alternative definition for the acceleration ax that can be written in terms of $v_x$ and $\frac{dv_x}{dx}$

So, We will use chain rule over here :

$a_x=\frac{dv_x}{dt}\\a_x=\frac{dv_x}{dt} \times \frac{dx}{dx}\\a_x=\frac{dv_x}{dx} \times \frac{dx}{dt}\\a_x=\frac{dv_x}{dx} \times \frac{dx}{dt} [\frac{dx}{dt}=v_x]\\a_x=\frac{dv_x}{dx} \times v_x\\a_x=v_x\frac{dv_x}{dx}$

Hence an alternative definition for the acceleration ax that can be written in terms of $v_x$ and $\frac{dv_x}{dx}$ is $a_x=v_x \frac{dv_x}{dx}$

4 0

2 years ago

Simplify 14.2 + 6.5(p + 3q) – 4.05q

anzhelika [568]

Answer is C
14.2+6.5(p+3q)-4.05q
14.2+6.5p+19.5q-4.05q
14.2+6.5p+15.45q→6.5p+15.45q+14.2
so the answer is C

7 0

1 year ago

A 20-inch diameter bicycle tire rotates 200 times.

fenix001 [56]

Answer: B)1,047 feet

Step-by-step explanation:

Hi, to answer this question, first, we have to calculate the circumference of the tire:

Circumference(C): π x diameter

C = π (20) = 62.83 inches.

Since 1 foot is equal to 12 inches.

62.83 ÷ 12 = 5.23 feet

Finally we have to multiply the result by 200:

5.23 x 200 = 1,047 feet

Feel free to ask for more if needed or if you did not understand something.

8 0

2 years ago

A hexagonal pyramid is cut by a plane as shown in the diagram. What is the shape of the resulting cross section? see diagram

Alenkasestr [34]

From the diagram you can see that plane cuts each lateral face of hexagonal pyramid and do not cut the base. A hexagonal pyramid has six lateral faces. The intersection of each of these lateral faces with given cutting plane is segment. The figure which consists of these segments is hexagon. This hexagon is not the same as base and even is not similar to the base because the cutting plane is not parallel to the base.

Answer: resulting cross section is a hexagon, correct choice is option 4.

9 0

2 years ago

Read 2 more answers

A university warehouse has received a shipment of 25 printers, of which 10 are laser printers and 15 are inkjet models. If 6 of

Tanya [424]

Answer:

The probability is 0.31

Step-by-step explanation:

To find the probability, we will consider the following approach. Given a particular outcome, and considering that each outcome is equally likely, we can calculate the probability by simply counting the number of ways we get the desired outcome and divide it by the total number of outcomes.

In this case, the event of interest is choosing 3 laser printers and 3 inkjets. At first, we have a total of 25 printers and we will be choosing 6 printers at random. The total number of ways in which we can choose 6 elements out of 25 is $\binom{25}{6}$ , where $\binom{n}{k} = \frac{n!}{(n-k)!k!}$ . We have that $\binom{25}{6} = 177100$

Now, we will calculate the number of ways to which we obtain the desired event. We will be choosing 3 laser printers and 3 inkjets. So the total number of ways this can happen is the multiplication of the number of ways we can choose 3 printers out of 10 (for the laser printers) times the number of ways of choosing 3 printers out of 15 (for the inkjets). So, in this case, the event can be obtained in $\binom{10}{3}\cdot \binom{15}{3} = 54600$

So the probability of having 3 laser printers and 3 inkjets is given by

$\frac{54600}{177100} = \frac{78}{253} = 0.31$

4 0

2 years ago