Answer:
<em>A = 48.81°</em>
Step-by-step explanation:
<u>Angles in a Right Triangle</u>
When the side lengths of a right triangle are known and an angle must be determined, we can use the trigonometric ratios that relate angles and sides.
The tangent ratio is defined as:
Opposite leg to angle A is 8 and adjacent leg is 7, thus:
Using the inverse tangent funcion:
Calculating:
A = 48.81°
Answer:
length of a rectangle is 5 more than twice the length. I believe
you mean the length of a rectangle is 5 more than twice the
width.
From the information given we can make two equations,
thus forming a system to solve. We know the perimeter
of a rectangle is 2(length + width) and area = length*width.
length of a rectangle is 5 more then twice the width:
L = 2w + 5
The perimeter is 130:
2(L+w) = 130
L+w = 65
Since we know L=2w+5 we can substitute that into 2nd equation
to solve for w
2w + 5 + w = 65
3w = 60
w = 20
L = 2w+5 = 45
The area is length*width = 20(45) = 900 square units
Answer:
5050
Step-by-step explanation:
Gauss has derived a formula to solve addition of arithmatic series to find the sum of the numbers from 1 to 100 as follows:
1 + 2 + 3 + 4 + … + 98 + 99 + 100
First he has splitted the numbers into two groups (1 to 50 and 51 to 100), then add these together vertically to get a sum of 101.
1 + 2 + 3 + 4 + 5 + … + 48 + 49 + 50
100 + 99 + 98 + 97 + 96 + … + 53 + 52 + 51
1 + 100 = 101
2 + 99 = 101
3 + 98 = 101
:
:
:
:
48 + 53 = 101
49 + 52 = 101
50 + 51 = 101
It was realized by him that final total will be fifty times of 101 means:
50(101) = 5050.
Based on this, Gauss has derived formula as:
The sequence of numbers (1, 2, 3, … , 100) is arithmetic and we are looking for the sum of this series of sequence. As per Gauss, the special formula derived by him can be used to find the sum of this series:
S is the sum of the series and n is the number of terms in the series, in present case, from 1 to 100, Hence
As per the Gauss formula, the sum of numbers from 1 to 100 will be 5050.
Answer : 5050
