Tanh x = 12/13
1) Calculate cosh x:
cosh² x = 1/(1-tanh² x) →→ 1/[1-(12/13)²] = 1/(1-144/169) = 1/[(169-144)169]
cosh²x = 169/25 and cosh x = + or - 13/5
2) Calculate sinh x
sinh x/cosh x = tanh x →→sinh x = (cosh x)(tanh x)
sinh x = + or - (13/5)(12/13) →→sinh x= + or - 12/5
From here onward you can calculate easily coth x, sech x, csch x
1. (-5,-11)
2. C, reflected across x-axis then translated.
3. A’(-1,7), B’(-4,6), C’(-2,2)
4. C’(3,-4)
5. B, rotates 90 counter clockwise and then translate
(if any of these are wrong i’m sorry! :<)
The current area is 15 x 9 = 135 square feet.
He wants to increase both the length and width by X:
Set up an equation:
(15 +x) * (9 +x) = 135 * 2
Simplify :
x^2 + 24x + 135 = 270
Subtract 270 from both sides:
x^2 + 24x - 135 = 0
Use the quadratic formula to solve for x:
-24 +/- √(24^2 - 4(1*-135) / 2*1
x = 4.7 or -28.7
The answer has to be a positive value, so x = 4.7 feet.
Answer:
x^2 | y^25 |√187x
Step-by-step explanation:
First you simplify the equation then you factor 184 into its prime factors which is 184 = 23 • 23
To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent. Factors which will be extracted are: 4 = 22 Factors which will remain inside the root are: 46 = 2 • 23 To complete this part of the simplification we take the square root of the factors which are to be extracted. We do this by dividing their exponents by 2: 2 = 2 At the end of this step the partly simplified SQRT looks like this: 2 • sqrt (46x5y50) Rules for simplifing variables which may be raised to a power: (1) variables with no exponent stay inside the radical (2) variables raised to power 1 or (-1) stay inside the radical (3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples: (3.1) sqrt(x8)=x4 (3.2) sqrt(x-6)=x-3 (4) variables raised to an odd exponent which is >2 or <(-2) , examples: (4.1) sqrt(x5)=x2•sqrt(x) (4.2) sqrt(x-7)=x-3•sqrt(x-1) Applying these rules to our case we find out that SQRT(x5y50) = x2y25 • SQRT(x) sqrt (184x5y50) = 2 x2y25 • sqrt(46x)
pls brainlist
The weight of the air in the room is 172.8 lb if the dimensions of a living room are 18 ft. by 15 ft. by 8ft.
<h3>What is a rectangular prism?</h3>
It is defined as the six-faced shape, a type of hexahedron in geometry.
It is a three-dimensional shape. It is also called a cuboid.
It is given that:
The dimensions of a living room are 18 ft. by 15 ft. by 8ft.
The volume of the living room = volume of the cuboid:
V = length×width×height
V = 18×15×8
V = 2160 cubic ft
The weight of the air = 0.08 lb. per cubic foot
The weight of the air in the room = 0.08×2160
The weight of the air in the room = 172.8 lb
Thus, the weight of the air in the room is 172.8 lb if the dimensions of a living room are 18 ft. by 15 ft. by 8ft.
Learn more about the rectangular prism here:
brainly.com/question/21308574
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