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Temka [501]
3 years ago
12

What is the following product? 3sqrt4 times sqrt3​

Mathematics
1 answer:
Harman [31]3 years ago
3 0

Answer:

\sqrt[6]{432}

Step-by-step explanation:

\sqrt[3]{4}\cdot\sqrt{3}=4^{\frac{1}{3}}\cdot3^\frac{1}{2}=(2^2)^\frac{1}{3}\cdot3^\frac{1}{2}=(2^\frac{4}{3})^\frac{1}{2}\cdot3^\frac{1}{2}=(2^\frac{4}{3}\cdot3)^\frac{1}{2}=(2^4\cdot27)^\frac{1}{6}=432^\frac{1}{6}=\sqrt[6]{432}

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Martine’s town is building a volleyball court based on a scale drawing that is 40cm to 80cm and uses the scale 1cm:22.5cm write
never [62]

Answer:

y=22.5x

Step-by-step explanation:

we have that

The scale drawing is

\frac{1}{22.5}\frac{cm}{cm}

we know that

Using proportion find out the actual dimensions of the volleyball court

Let

x -----> drawing court lengths in cm

y ----> court lengths in cm

For x=40 cm

\frac{1}{22.5}\frac{cm}{cm}=\frac{40}{y}\frac{cm}{cm}\\\\y=40*22.5\\\\y=900\ cm

For x=80 cm

\frac{1}{22.5}\frac{cm}{cm}=\frac{80}{y}\frac{cm}{cm}\\\\y=80*22.5\\\\y=1,800\ cm

Find the equation for the proportional relation ship between drawing court lengths x in centimeters and court lengths in y centimeters

 A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y/x=k or y=kx

For x=40 cm, y=900

substitute

k=y/x -----> k=900/40=22.5

The equation is

y=22.5x

5 0
3 years ago
How to convert 655.575 to word form?
Leni [432]
Six hundred fifty five thousand five hundred seventy five

6 0
3 years ago
If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple ar
Oksana_A [137]

Answer:

n + 4 {n \choose 2} + 6 {n \choose 3} + 4 {n \choose 4} + {n \choose 5}

Step-by-step explanation:

Lets divide it in cases, then sum everything

Case (1): All 5 numbers are different

 In this case, the problem is reduced to count the number of subsets of cardinality 5 from a set of cardinality n. The order doesnt matter because once we have two different sets, we can order them descendently, and we obtain two different 5-tuples in decreasing order.

The total cardinality of this case therefore is the Combinatorial number of n with 5, in other words, the total amount of possibilities to pick 5 elements from a set of n.

{n \choose 5 } = \frac{n!}{5!(n-5)!}

Case (2): 4 numbers are different

We start this case similarly to the previous one, we count how many subsets of 4 elements we can form from a set of n elements. The answer is the combinatorial number of n with 4 {n \choose 4} .

We still have to localize the other element, that forcibly, is one of the four chosen. Therefore, the total amount of possibilities for this case is multiplied by those 4 options.

The total cardinality of this case is 4 * {n \choose 4} .

Case (3): 3 numbers are different

As we did before, we pick 3 elements from a set of n. The amount of possibilities is {n \choose 3} .

Then, we need to define the other 2 numbers. They can be the same number, in which case we have 3 possibilities, or they can be 2 different ones, in which case we have {3 \choose 2 } = 3  possibilities. Therefore, we have a total of 6 possibilities to define the other 2 numbers. That multiplies by 6 the total of cases for this part, giving a total of 6 * {n \choose 3}

Case (4): 2 numbers are different

We pick 2 numbers from a set of n, with a total of {n \choose 2}  possibilities. We have 4 options to define the other 3 numbers, they can all three of them be equal to the biggest number, there can be 2 equal to the biggest number and 1 to the smallest one, there can be 1 equal to the biggest number and 2 to the smallest one, and they can all three of them be equal to the smallest number.

The total amount of possibilities for this case is

4 * {n \choose 2}

Case (5): All numbers are the same

This is easy, he have as many possibilities as numbers the set has. In other words, n

Conclussion

By summing over all 5 cases, the total amount of possibilities to form 5-tuples of integers from 1 through n is

n + 4 {n \choose 2} + 6 {n \choose 3} + 4 {n \choose 4} + {n \choose 5}

I hope that works for you!

4 0
3 years ago
What is the y value in this equation ?X(0)=(-1/3y)+6
snow_lady [41]

Answer:

18

Step-by-step explanation:

8 0
3 years ago
Simplify the expression given below.<br><br> x+2/ 4x^{2} +5x+1 *4x+1/2x-4[/tex]
VashaNatasha [74]

Answer:

pls write understandably

7 0
3 years ago
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