Answer:
[tex](\frac{sin\ x}{1 - cos^2x})(tan\frac{x}{2}) = \frac{1}{1+cosx}[/tex]
Step-by-step explanation:
Given
[tex](\frac{sin\ x}{1 - cos^2x})(tan\frac{x}{2})[/tex]
Required
Simplify
[tex](\frac{sin\ x}{1 - cos^2x})(tan\frac{x}{2})[/tex]
---------------------------------------------------------------------------------------------------
Considering the denominator of the first bracket
[tex]1 - cos^2x[/tex]
This can be rewritten using different of two squares as follows:
[tex](1 - cosx)(1 + cosx)[/tex]
So, [tex]1 - cos^2x[/tex] can be replaced with [tex](1 - cosx)(1 + cosx)[/tex] in the given expression.
Also, from trigonometry identity
[tex]tan\frac{x}{2} = \frac{1 - cos x}{sin x}[/tex]
So, [tex]tan\frac{x}{2}[/tex] can be replaced with [tex]\frac{1 - cos x}{sin x}[/tex] in the given expression
---------------------------------------------------------------------------------------------------
[tex](\frac{sin\ x}{1 - cos^2x})(tan\frac{x}{2})[/tex] becomes
[tex](\frac{sinx}{(1-cosx)(1+cosx)}) * \frac{1 - cos x}{sin x}[/tex]
[tex](\frac{sinx * (1 - cos x)}{(1-cosx)(1+cosx) * sin x})[/tex]
Cancel out similar expressions
[tex]\frac{1}{1+cosx}[/tex]
The expression cannot be further simplified.
Hence:
[tex](\frac{sin\ x}{1 - cos^2x})(tan\frac{x}{2}) = \frac{1}{1+cosx}[/tex]
The simplified form of the expression :
[tex]\frac{sinx}{1-cos^{2} x} .tan\frac{x}{2} =\frac{1}{1+cosx}[/tex]
We have some trigonometric formula as:
[tex]sin2x=2sinx= cosx\\2cos^{2} x=1+cos2x[/tex]
We have the expression
[tex]\frac{sinx}{1-cos^{2} x} .tan\frac{x}{2} \\=\frac{sinx}{sin^{2} x} .tan\frac{x}{2} \\=\frac{1}{sin x} .tan\frac{x}{2}\\=\frac{1}{2sin \frac{x}{2} cos\frac{x}{2}} .tan\frac{x}{2}\\=\frac{1}{2sin \frac{x}{2} cos\frac{x}{2}} .\frac{sin\frac{x}{2}}{cos\frac{x}{2}} \\=\frac{1}{2cos^{2} \frac{x}{2}}\\=\frac{1}{1+cos{x} }[/tex]
Therefore, the simplified form of the expression is:
[tex]\frac{sinx}{1-cos^{2} x} .tan\frac{x}{2} =\frac{1}{1+cosx}[/tex]
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What number is between 0.3 and 7.5
Answer:
3.9?
Step-by-step explanation:
Sam deposits $1,000 in his savings account which will earn 2.5% interest. How much interest will Sam have earned after 2 years? *
Answer: $50, The account will have $50 in interest after 2 years.
Step-by-step explanation:
2.5% / 100 = 0.025
$1,000 * .025 = 25
25 * 2 = 50
Every time you have your cholesterol measured, the measurement may be slightly different due to random fluctuations and measurement error. Suppose that for you, the population of possible cholesterol measurements if you are healthy has a mean of 190 and a standard deviation of 10. Further, suppose you know you should get concerned if your measurement ever gets up to the 97th percentile. What level of cholesterol does that represent?
Complete Question
The complete question is shown on the first uploaded image
Answer:
a i
[tex]P(X < 185 ) = 0.3085 [/tex]
a ii
[tex]P(X > 195 ) = 0.3085 [/tex]
a iii
[tex]P(185 < X < 195 ) = 0.3829 [/tex]
b
[tex]x = 208.8[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 190[/tex]
The standard deviation is [tex]\sigma = 10[/tex]
Generally the probability is less than 185 is mathematically represented as
[tex]P(X < 185 ) = P(\frac{X - \mu }{\sigma } < \frac{185 - 190 }{10 } )[/tex]
Generally [tex]\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ \ of \ X)[/tex]
=> [tex]P(X < 185 ) = P(Z< -0.5)[/tex]
From the z-table the p value of (Z< -0.5) is
[tex]P(Z< -0.5) = 0.3085[/tex]
So
[tex]P(X < 185 ) = 0.3085 [/tex]
Generally the probability is less than 185 is mathematically represented as
[tex]P(X > 195 ) = P(\frac{X - \mu }{\sigma } > \frac{195 - 190 }{10 } )[/tex]
=> [tex]P(X > 195 ) = P(Z > 0.5)[/tex]
From the z-table the p value of (Z > 0.5) is
[tex]P(Z > 0.5) = 0.3085[/tex]
So
[tex]P(X > 195 ) = 0.3085 [/tex]
Generally the probability is less than 185 is mathematically represented as
[tex]P(185 < X < 195 ) = P( \frac{185 - 190 }{10 } < \frac{X - \mu }{\sigma } < \frac{195 - 190 }{10 } )[/tex]
=> [tex]P(185 < X < 195 ) = P(-0.5 < Z > 0.5)[/tex]
=> [tex]P(185 < X < 195 ) = P(Z < 0.5 ) - P(Z < -0.5) [/tex]
From the z-table the p value (Z < 0.5) and (Z < -0.5) is
[tex]P(Z < 0.5) = 0.6915 [/tex]
and
[tex]P(Z < - 0.5) = 0.3085[/tex]
So
=> [tex]P(185 < X < 195 ) = 0.6915 - 0.3085 [/tex]
=> [tex]P(185 < X < 195 ) = 0.3829 [/tex]
Generally the level of cholesterol the 97th percentile represents is mathematically evaluated as
[tex]P(X < x ) = 0.97[/tex]
=> [tex]P(X < x ) = P(\frac{X - \mu}{\sigma } < \frac{x - 190}{10 } ) = 0.97[/tex]
=> [tex]P(X < x ) = P(Z < \frac{x - 190}{10 } ) = 0.97[/tex]
From the z-table the z-score for 0.97 is
[tex]z-score = 1.88[/tex]
=>
[tex]\frac{x - 190}{10 } = 1.88[/tex]
=>[tex]x = 208.8[/tex]
There are four different sets of objects shown in the answer choices. Select all of the sets of objects that could be modeled by perpendicular lines. Two roads that meet at an intersection. The top of a desk and the floor. A tree and its shadow on the ground. Two stars seen in the sky.
Answer:
Step-by-step explanation:
Select all of the object sets that could be modelled by perpendicular lines.
A perpendicular line is one that divides a 180 degrees line (or a straight line) into two; creating 90 degrees on one hand and 90 degrees on the other.
OPTIONS:
(A) APPLICABLE
Two roads that meet at an intersection can be modelled by perpendicular lines. Use the definition above as a yardstick.
(B) APPLICABLE
The top of the desk to the floor will represent the dividing line while the floor itself will be the 180° line.
(C) NOT APPLICABLE
A tree and its shadow on the ground will only form a right-angled triangle
(D) NOT APPLICABLE
Two stars seen in the sky cannot be modelled by perpendicular lines. They can only be modelled by a straight line; a line which extends from the first star to the other.
Write the function whose graph is the graph of y=|x| , but is translated 3units to the left and 4 units upward.
y=
Answer:
y=|x+3|+4
Step-by-step explanation:
3 units left is + 3
4 units up is + 4
The graph of function y = |x+3|+4 is translated as 3 units to the left and 4 units upward.
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
Vertical shifting of a graph is done by adding any arbitrary constant to the function in shifting.
For example, If shift up by 1 unit, add 1 to the function
If shift down by 4 units, subtract 4 from the function
To determine the function whose graph is the graph of y=|x| ,
Translated is 3 units to the left and 4 units upward.
x+3 because adding 3 to the x coordinate would shift it over 3
y-4 because subtracting 4 to the y coordinate would shift it up 4
⇒ f(x) = ( x + 3, y - 4 )
⇒ y - 4 = |x+3|
⇒ y = |x+3| + 4
Therefore, the graph of function y = |x+3|+4 is translated as 3 units to the left and 4 units upward.
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Neve built the following graph to model the flight of a rocket from Earth to outer space. Which of the following domains is appropriate for the graph and the context?
A) All Positive Real Numbers and Zero
B) All Real Numbers
C) All Negative Real Numbers and Zero
D) 0 to 2
Answer:
A
Step-by-step explanation:
Because its the most reasonable answer
Answer:
wya
Step-by-step explanation:
PLEASE PLEASE help me
Answer:
I couldn't fit it all in one photo but here you go!
Can someone help me plz
Answer:
1. Vertex-M sides- LM MN
2. Vertex-D sides- ED CD
3. Vertex-R sides- SR RQ
4. Vertex-T sides- ST TU
5. angle 3 angle D angle CDE
6. angle 4 angle F angle GFE
7. angle 1 angle F angle GFE
8. angle 3 angle I angle HIJ
Write an equation, in slope-intercept form,
for a line that passes through points (-4, 1)
and (2. 4).
Answer:
y = (3/2)x + 7
Step-by-step explanation:
(−4, 1) and (−2, 4)
slope m = rise/run = (4-1)/(-2-(-4)) = 3/2
Slope intercept form is y=mx+b
where m=slope, b = y-inercept
y = (3/2)x + b
Use one of the given points for (x,y) to find b
1 = (3/2)(-4) + b
1 = -6 + b
7 = b
y = (3/2)x + 7
The ratio of boys to girls in an after school recycling club is 4:7. If there are 20 boys in the recycling club, how many girls are there?
Answer:
There are 35 girls in the recycling club
Step-by-step explanation:
4 boys : 7 girls
20 boys : x girls
In order to get to 20, you have to multiply 4 by 5, so multiply 5 to 7 for the girls.
7(5) = 35
There are 35 girls
What is 2+2-2X2 divided by 2??
Answer:
0
Step-by-step explanation:
cause 2+2 is 4 and 2x2 is four and since u put - it take it away a then divide 0 by 2 u get 0
simplify this expression 3p+2p-p
Answer:
Step-by-step explanation:
3p + 2p - p
= 3p + p
= 4p
(add the co-efficients)
-5<2-h or 6h +5<71 chapter 2 test
Answer:
-5<2-h or 6h+5<71
-7<-h or 6h<66
7>h or h<11
h<7 or h<11
Step-by-step explanation:
The inequality that represents the solution of the given set -
- 5 < 2 - h or 6h + 5 < 71 is h < 11.
What is inequality in mathematics?
In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
Given are the following inequalities -
- 5 < 2 - h or 6h + 5 < 71
We will solve the given inequalities one by one -
Inequality - 1
- 5 < 2 - h
Subtract 2 from both sides -
- 7 < - h
Multiply by -1 on both sides -
h < 7
Inequality - 2
6h + 5 < 71
Subtract 5 from both sides -
6h < 66
Divide by 6 on both sides -
h < 11
Now, h can be either -
h < 11 or h < 7
We can write it as a single inequality as -
h < 11 [this set of numbers will include all numbers less than 7]
Therefore, the inequality that represents the solution of the given set -
- 5 < 2 - h or 6h + 5 < 71 is h < 11.
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Read the problem in the box below. Make a list to help you find the correct
answer
Eudora's grandfather has decided to move to a
desert island. In his new place, he will only have
room for 2 of his 4 favorite jazz records. The 4
records are by Ben Webster, Miles Davis,
Cannonball Adderley, and Lester Young. How
many combinations of 2 records, in any order, can
he make?
O A. 12 combinations
B. 8 combinations
O C. 6 combinations
OD. 10 combinations
Find the value of x so that the function has given value
M(x)=4x+15; m(x)=7
It takes 10 pounds of potatoes to make 15 pounds of mashed potatoes. At this rate:
How many pounds of mashed potatoes can they make with 15 pounds of potatoes?
Answer:
22.5 pounds of mashed potatoes are made from 15 pounds of potatoes.
Step-by-step explanation:
According to the statement, we notice that the amount of pounds of potatoes ([tex]x[/tex]) is directly proportional to the amount of mashed potatoes ([tex]y[/tex]). That is:
[tex]y\propto x[/tex]
[tex]y = k\cdot x[/tex] (Eq. 1)
Where [tex]k[/tex] is the proportionality constant, dimensionless.
Then we eliminate such constant by building this relationship:
[tex]\frac{y_{2}}{y_{1}} = \frac{x_{2}}{x_{1}}[/tex]
[tex]y_{2} = \left(\frac{x_{2}}{x_{1}} \right)\cdot y_{1}[/tex] (Eq. 2)
If we know that [tex]x_{1} = 10[/tex], [tex]x_{2}=15[/tex], [tex]y_{1} = 15[/tex], then the amount of pounds of mashed potatoes is:
[tex]y_{2} = \left(\frac{15}{10} \right)\cdot (15)[/tex]
[tex]y_{2} = 22.5[/tex]
22.5 pounds of mashed potatoes are made from 15 pounds of potatoes.
In one full day, a kudzu vine can grow 15 inches in length. How many inches per hour is this?
Answer:
0.625
Step-by-step explanation:
15 divided by 24 which equals 0.625
Write a quadratic equation with the following transformations.
1. Reflected over the x-axis
2. Moved down 6
9 square root of 45 help me please
Answer:
60.3738353925. Rounded, this is 60.4
Step-by-step explanation: If this is the wrong answer you may delete this.
Two parallel lines are crossed by a transversal.
What is the value of b?
O b 32
O b = 118
Ob=52
o b = 128
Answer:
D. b = 128
Step-by-step explanation:
Find the diagram to the question attached.
From the diagram, line p is parallel to line q i.e p//q
You must understand that the angle at the opposite side of the transversal are equal i.e alternate angle.
From the diagram, <b = 118° (alternate angle)
Hence option D is correct
Answer:
D) o b = 128
Step-by-step explanation:
YW :)
Find f’(2) for f(x)=5e^-xln(x^2+5x)
9514 1404 393
Answer:
f'(2) ≈ −1.3508
Step-by-step explanation:
The derivative of the function is ...
f'(x) = 5(-e^-x·ln(x^2 +5x) +e^-x·(2x +5)/(x^2 +5x))
Then ...
f'(2) = 5e^(-2)(-ln(14) +9/14) ≈ -1.3508
Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 135 millimeters, and a variance of 64. If a random sample of 32 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by more than 3.6 millimeters? Round your answer to four decimal places.
Answer:
0.3264
Step-by-step explanation:
The formula for calculating a z-score is is z = (x-μ)/σ, where
x is the raw score,
μ is the population mean,
σ is the population standard deviation.
(x-μ) = 3.6 mm
σ = √variance = √64 = 8mm
z = 3.6/8
z = 0.45
Using the Probability table
P(x<Z) = 0.67364
P(x>Z) = 1 - P(x<Z)
1 - 0.67364
= 0.32636
Approximately = 0.3264
What is the final cost of an item that is priced at $22.35 with a sales tax rate of 6%?
Answer:
$23.69
Step-by-step explanation:
Multiply the price by the tax percent, then add the two numbers.
An iPhone X costs $1,000. One website is selling it for 20% off. What would the sale price be?
If the cosmic radiation to which a person is exposed while flying by jet across US is a random variable having mean 4.35 mrem and standard deviation 0.59 mrem,find the probabilities that the amount of cosmic radiation to which a person will be exposed on such a flight is:_______
(a) Between 4.00 and 5.00 mrem
(b) At least 5.50 mrem
(c) Less than 4.00 mrem
Answer:
a
[tex]P(4.00 < X < 5.00) = 0.58818 [/tex]
b
[tex]P(X \ge 5.5) = 0.02564 [/tex]
c
[tex]P(X < 4 ) = 0.27652[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 4.35[/tex]
The standard deviation is [tex]\sigma = 0.59[/tex]
Generally the probability that the amount of cosmic radiation to which a person will be exposed on such a flight is between 4.00 and 5.00 mrem is mathematically represented as
[tex]P(4.00 < X < 5.00) = P(\frac{ 4 - \mu }{\sigma} < \frac{X - \mu}{\sigma} < \frac{ 5 - \mu }{ \sigma} )[/tex]
Here [tex]\frac{X - \mu}{\sigma} = Z (The \ standardized \ value \ of \ X )[/tex]
=> [tex]P(4.00 < X < 5.00) = P(\frac{ 4 - 4.35 }{0.59} < Z < \frac{ 5 - 4.35 }{ 0.59} )[/tex]
=> [tex]P(4.00 < X < 5.00) = P(-0.59322 < Z < 1.1017 )[/tex]
=> [tex]P(4.00 < X < 5.00) = P( Z < 1.1017 ) - P(Z < -0.59322) [/tex]
From the z -table the probability of ( Z < 1.1017 ) and (Z < -0.59322) are
[tex]P( Z < 1.1017 ) =0.8647[/tex]
and
[tex]P( Z < -0.59322 ) =0.27652[/tex]
So
=> [tex]P(4.00 < X < 5.00) = 0.8647 - 0.27652 [/tex]
=> [tex]P(4.00 < X < 5.00) = 0.58818 [/tex]
Generally the probability that the amount of cosmic radiation to which a person will be exposed on such a flight is At least 5.50 mrem is mathematically represented as
[tex]P(X \ge 5.5) = 1- P(X < 5.5)[/tex]
Here
[tex]P(X < 5.5) = P(\frac{X - \mu }{\sigma} < \frac{5.5 - 4.35}{0.59} )[/tex]
[tex]P(X < 5.5) = P(Z< 1.94915) [/tex]
From the z -table the probability of (Z< 1.94915) is
[tex]P(Z< 1.94915) = 0.97436[/tex]
So
[tex]P(X \ge 5.5) = 1- 0.97436[/tex]
=> [tex]P(X \ge 5.5) = 0.02564 [/tex]
Generally the probability that the amount of cosmic radiation to which a person will be exposed on such a flight is less than 4.00 mrem is mathematically represented as
[tex]P(X < 4) = P(\frac{X - \mu }{\sigma} < \frac{4 - 4.35}{0.59} )[/tex]
[tex]P(X < 4) = P(Z< -0.59322) [/tex]
From the z -table the probability of (Z< 1.94915) is
[tex]P(Z< -0.59322) = 0.27652[/tex]
So
[tex]P(X < 4 ) = 0.27652[/tex]
An oilfield contains 6 wells that produce a total of 1,800 barrels of oil per day. For each additional well that is drilled, the average production per well decreases by 25 barrels per day.
Required:
How many additional wells should be drilled to obtain the maximum amount of oil per day?
Answer:
The additional wells for maximum amount of oil per day is 3 wells.
Step-by-step explanation:
Given;
initial number of wells, n = 6
total production, T = 1800
average production per well, = 1800/6 = 300 barrels per day
Let the additional well = y
total number of wells after optimization = 6 + y
new production per well = 300 - 25y
new total production = (6+y)(300-25y)
t = 1800 - 150y + 300y - 25y²
t = 1800 + 150y - 25y²
dt / dy = 150 -50y
for maximum value, dt/dy = 0
150 - 50y = 0
50y = 150
y = 150 / 50
y = 3
Therefore, the additional wells for maximum amount of oil per day is 3 wells.
33 additional wells should be drilled, reaching 39 wells, to obtain the maximum amount of oil per day.
Given that an oilfield contains 6 wells that produce a total of 1,800 barrels of oil per day, and for each additional well that is drilled, the average production per well decreases by 25 barrels per day, to determine how many additional wells should be drilled to to obtain the maximum amount of oil per day, the following calculation must be performed:
1800 x 6 = 10800 1200 x 30 = 36000 1000 x 38 = 38000 950 x 40 = 38000 900 x 42 = 37800 975 x 39 = 38025
Therefore, 33 additional wells should be drilled, reaching 39 wells, to obtain the maximum amount of oil per day.
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Use the scientific calculator given in this course to simplify 8^3.
Answer:
512
Step-by-step explanation:
8x8x8 is equals to 512
In what year will the two quantities be equal?
Its the second because i did this already
solve for a in the figure shown.
Answer:
40
Step-by-step explanation:
110+30=140
but a full triangle should equal 180
so 180-140=40
140+40=180
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The table below shows the location of four treasure chests relative to sea level. Which treasure chest is the farthest away from sea level?
a 0.75 foot
b 5/4 feet
c -0.5 foot
1 foot
Answer:
Step-by-step explanation:
sea level means negative so it have to be C -0.5 foot
problem solved
