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2 years ago

Simplify. Divide the radicals. √80 √20

1 answer:

6 0

$\cfrac{\sqrt{80}}{\sqrt{20}} ~~ \begin{cases} 80=2\cdot 2\cdot 2\cdot 2\cdot 5\\ \qquad 4\cdot 4\cdot 5\\ \qquad 4^2\cdot 5\\ 20=2\cdot 2\cdot 5\\ \qquad 2^2\cdot 5 \end{cases}\implies \cfrac{\sqrt{4^2\cdot 5}}{\sqrt{2^2\cdot 5}}\implies \cfrac{4\sqrt{5}}{2\sqrt{5}}\implies \cfrac{4}{2}\cdot \cfrac{\sqrt{5}}{\sqrt{5}}\implies 2$

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Sum of n terms 1x2+2x3+3x4+4x5+...

lozanna [386]

Answer:

1/3(n+1)³

Step-by-step explanation:

1x2+2x3+3x4+4x5+...= 1²+1+2²+2+3²+3+...+n²+n+1=

=(1²+2²+3²+...+n²)+(1+2+3+...+n+1)=

=1/6n(n+1)(2n+1)+1/2(n+1)(1+n+1)=

=1/6(n+1)(n(2n+1)+3(n+2))=

=1/6(n+1)(2n²+4n+2)=

=1/6(n+1)*2(n+1)²=

=1/3(n+1)³

6 0

3 years ago

Tomas drew a rectangle with an area of 6 square centimeters. What is the greatest possible perimeter for this rectangle?

Naily [24]

In order for the rectangle to have an area of 6 cm^2, Tomas could have drawn it with one of two side length possibilities. He could either have drawn a rectangle with a length of 6 and a width of 1, or a rectangle with a length of 3 and a width of 2.

To find perimeter, you just add up all side lengths together, so let's compare the two options to find out which one has a greater perimeter.

Let's try the first option first.

That would be 6 + 6 + 1 + 1, which is 14.

Let's try the other one.

3 + 3 + 2 + 2 = 10

The first option (width 1, length 6) would yield the greatest perimeter.
Hope that helped! =)

6 0

3 years ago

The sum of 11 and the product of 2 and a number r

andrew-mc [135]

Algebraically that would be expressed as 2r + 11

The product of 2 and r is 2r.

The sum of 2r and 11 is 2r + 11

5 0

3 years ago

Read 2 more answers

HELP PLS A=45 help and how

MA_775_DIABLO [31]

Answer:

Step-by-step explanation:

the value of c angle is 35°

according to the question

$\frac{a}{ \sin( {45}^{o} ) } = \frac{15}{ \sin(35°) }$

$a = \frac{15 \times \frac{ \sqrt{2} }{2} }{ \sin({35}^{o} )}$

$a= 18.5$

7 0

3 years ago

Show that the set of functions from the positive integers to the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} is uncountable. [Hint: First

Sedbober [7]

Answer:

since the set of functions expressed are uncountable and they are a subset of real numbers starting from N therefore the set {0,1,2,3,4,5,6,7,8,9} is uncountable as well as its off functions

Step-by-step explanation:

set = {0,1,2,3,4,5,6,7,8,9}

setting up a one-to-one correspondence between the set of real numbers between 0 and 1

The function : F(n)= {0,1} is equivalent to the subset (sf) of (n) , this condition is met if n belongs to the subset (sf) when f(n) = 1

hence The power set of (n) is uncountable and is equivalent to the set of real numbers given

since the set of functions expressed are uncountable and they are a subset of real numbers starting from N therefore the set {0,1,2,3,4,5,6,7,8,9} is uncountable as well as its offfunctions

3 0

3 years ago