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valina [46]
3 years ago
12

The value of\[\left( 1-{1\over3} \right)\left( 1-{1\over4} \right)\left( 1-{1\over5} \right)....\left( 1-{1\over n} \right)\]is

equal to??
Mathematics
1 answer:
Oliga [24]3 years ago
6 0
Example 1<span>

<span><span>verbose explicit high3 <span>plus </span>4 <span>cross </span>2 <span>minus </span><span>minus </span>2 <span>equals </span>3 <span>plus </span>8 <span>plus </span>2 <span>equals </span>1 3</span><span>verbose explicit high semantics3 <span>plus </span>4 <span>times </span>2 <span>minus </span><span>negative </span>2 <span>equals </span>3 <span>plus </span>8 <span>plus </span>2 <span>equals </span>13</span><span>verbose explicit high semantics high3 <span>plus </span>4 <span>times </span>2 <span>minus </span><span>negative </span>2 <span>equals </span>3 <span>plus </span>8 <span>plus </span>2 <span>equals </span>13</span></span>
</span>

For most fractions, the beginning is indicated with "start fraction", the horizontal line is indicated with "over", and the end of the fraction is indicated by "end fraction". For the semantic interpretation, most numeric fractions are spoken as they are in natural speech. Also if a number is followed by a numeric fraction, the word "and" is spoken in between.

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Find the percent of change from the first value to the second. 72: 81 -
nordsb [41]

Answer:

+12.5%

Step-by-step explanation:

This is rather simple. Subtract 72 from 81, then put the difference over 72. Then, multiply that by 100.

(81 - 72)/72 * 100

<em>Subtract 72 from 81 to get 9</em>

9/72 * 100

<em>Multiply 9 by 100 to get 900</em>

900/72

<em>Simplify the above fraction by cancelling out 9.</em>

100/8

<em>Divide 100 by 8 to get 12.5%</em>

The percent of change is +12.5%

5 0
3 years ago
2. Given a quadrilateral with vertices (−1, 3), (1, 5), (5, 1), and (3,−1):
zlopas [31]
<h2>Explanation:</h2>

In every rectangle, the two diagonals have the same length. If a quadrilateral's diagonals have the same length, that doesn't mean it has to be a rectangle, but if a parallelogram's diagonals have the same length, then it's definitely a rectangle.

So first of all, let's prove this is a parallelogram. The basic definition of a parallelogram is that it is a quadrilateral where both pairs of opposite sides are parallel.

So let's name the vertices as:

A(-1,3) \\ \\ B(1,5) \\ \\ C(5,1) \\ \\ D(3,-1)

First pair of opposite sides:

<u>Slope:</u>

\text{For AB}: \\ \\ m=\frac{5-3}{1-(-1)}=1 \\ \\ \\ \text{For CD}: \\ \\ m=\frac{1-(-1)}{5-3}=1 \\ \\ \\ \text{So AB and CD are parallel}

Second pair of opposite sides:

<u>Slope:</u>

\text{For BC}: \\ \\ m=\frac{1-5}{5-1}=-1 \\ \\ \\ \text{For AD}: \\ \\ m=\frac{-1-3}{3-(-1)}=-1 \\ \\ \\ \text{So BC and AD are parallel}

So in fact this is a parallelogram. The other thing we need to prove is that the diagonals measure the same. Using distance formula:

d=\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2} \\ \\ \\ Diagonal \ BD: \\ \\ d=\sqrt{(5-(-1))^2+(1-3)^2}=2\sqrt{10} \\ \\ \\ Diagonal \ AC: \\ \\ d=\sqrt{(3-1)^2+(-5-1)^2}=2\sqrt{10} \\ \\ \\

So the diagonals measure the same, therefore this is a rectangle.

5 0
3 years ago
A sphere of radius 3 is inscribed in a cylinder. What is the volume inside the cylinder but not inside the sphere?
Fed [463]

Answer:

18pi units³ or 56.5 units³ (3 sf)

Step-by-step explanation:

pi×r²×h - (4/3)(pi×r³)

r = 3 h = 2r = 6

pi(3²×6 - (4/3)(3³))

18pi units³

8 0
3 years ago
Does each set of side lengths form a right triangle 10 m, 11 m, 15 m or 15 m, 8 m, 17 m,
IrinaVladis [17]
Can you be a little more specific please
6 0
3 years ago
Read 2 more answers
Someone please help!
igomit [66]

Answer:

-11/12 make sure you press the negative

8 0
3 years ago
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