Step-by-step explanation:
[tex] \tan( \frac{x}{2} ) = \frac{ \sin(x) }{1 + \cos(x) } [/tex]
[tex] \tan( \frac{x}{2} ) = \frac{ \sqrt{1 - \cos(x) } }{ \sqrt{1 + \cos(x) } } [/tex]
So we have
[tex] \frac{ \sqrt{1 - \cos(x) } }{ \sqrt{1 + \cos(x) } } = \frac{ \sin(x) }{ \sqrt{1 + \cos(x) } } [/tex]
Next, we then rationalize the numerator so we get
[tex] \frac{ \sqrt{1 - \cos(x) } }{ \sqrt{1 + \cos(x) } } \frac{ \sqrt{1 + \cos(x) } }{1 + \cos(x) } = \frac{ \sin(x) }{ {1 + \cos(x) } } [/tex]
The denominator should be square root so to let you know .
So know we ahev
[tex] \frac{ \sqrt{1 - \cos {}^{2} (x) } }{1 + \cos(x) } = \frac{ \sin(x) }{1 + \cos(x) } [/tex]
[tex] \frac{ \sqrt{ \sin {}^{2} (x) } }{1 + \cos(x) } = \frac{ \sin(x) }{ {1 + \cos(x) } } [/tex]
[tex] \frac{ \sin(x) }{1 + \cos(x) } = \frac{ \sin(x) ) }{1 + \cos(x) } [/tex]
write this verbal phrase as an algebraic expression
the quotient of g and 15
Answer:
g÷15 or g15
Step-by-step explanation:
hope it helps
PLS HELP ME, PLS THIS IS DUE FIRST CORRECT ANSWER GETS BRAINLIEST
Answer:
C
Step-by-step explanation:
160/-5 = -32
-1/2 times 64 is -32
evuate the equation r/10 = (-6)
A. r = 60
B. r = 16
C. r = -16
D. r = -60
Answer:
D
Step-by-step explanation:
r/10 = -6
So r = -6x10
= -60
A local newspaper did a survey asking people of different ages how many hours they spend using social media sites each week. The results of the survey and the least squares regression line are displayed in the graph. Use the least squares regression line to predict about how many hours a 40-year-old person spends on social media sites each week.
Answer:
Step-by-step explanation:
Answer:
5 hours
Step-by-step explanation:
I did it on Imagine Math
Please help
Worth 20 points
Show the work
Answer:
area: 60π cm² ≈ 188.5 cm²volume: 63π cm³ ≈ 197.9 cm³doubling the radiusStep-by-step explanation:
(a)The surface area of a right cylinder is given by the formula ...
SA = 2πr(r +h) . . . . . radius r, height h
Filling in the given values, we find the area to be ...
SA = 2π(3 cm)(3 +7 cm) = 60π cm² ≈ 188.5 cm²
__
(b)The volume of the cylinder is given by the formula ...
V = πr²h . . . . . radius r, height h
Filling in the given values, we find the volume to be ...
V = π(3 cm)²(7 cm) = 63π cm³ ≈ 197.9 cm³
__
(c)The volume is proportional to r², so doubling the radius will multiply the volume by 2² = 4.
The volume is proportional to the height, so multiplying the height by 3 will multiply the volume by 3.
4 > 3, so doubling the radius gives the most volume
round to the nearest tenth of a meter
Answer:
33
Step-by-step explanation:
I am not hundred percent sure this the best I got
Solve the triangle AMDM
Suppose the federal reserve increases the amount of reserbed by $100 million and the total money supply increases by $500 million. What is the money supply?
Answer: $400 million
Step-by-step explanation: $500-100= $400 million :)
Determine a possible 3rd degree polynomial function in factored form with its only zeros at (4,0) and (-1,0) and (-7,0)
if 25 ml of milk is required to make 1 cup of tea then find how many cups of tea we can make out of 25 litres of milk
Answer:
1000
Step-by-step explanation:
Well if there are 1000 ml in one L and we have 25 L of of milk and it requires 25 ml of milk per cup of tea we would first convert 25 L to ml to get 25000 ml of milk with that answer we then divide 25000 by 25 to get 1000.
Aaron drew a cone that has a volume of 90in.If Armani drew a cylinder with the same
base and height as Aaron's cone, what is the
volume of her cylinder? Explain your
reasoning.
Answer:
Step-by-step explanation:
A cone has a volume formula of [tex]\frac{1}{3} \pi r^{2} h[/tex]
A cylinder has a volume formula of [tex]\pi r^{2} h[/tex]
So if both of the shapes have the same base and height as in 'h' and 'r' are equal, than the cone has 1/3 the volume of the cylinder.
Thus:
[tex]V_{cone} =\frac{1}{3} V_{cylinder} \\90 = \frac{1}{3} V_{cylinder}\\V_{cylinder} = 270[/tex]
Thus the volume of the cylinder is 270 cubic inches.
Hope that helps!
Answer:
Vol_cylinder = 270 cubic inches
Step-by-step explanation:
Aaron's cone has the Volume
= 1/3BaseArea•height
Armani's Cylinder Volume
= BaseArea•height
The only difference here is the 1/3 in the cone formula.
So the cone volume is 1/3 of the cylinder volume. Or the cylinder volume is 3times the cone volume.
Vol_cone = 90
Vol_cyl = 3•90 = 270
90 is 1/3 of 270.
The cylinder volume is 270 cubic inches.
Simplify. Express your answer using positive exponents.
Answer:
[tex]m^9[/tex]
Step-by-step explanation:
[tex]\frac{m^0m^{-1}m^3}{m^{-7}}[/tex]
[tex]m^0m^{-1}m^3=m^2[/tex]
[tex]\frac{m^2}{m^{-7}}[/tex]
[tex]m^9[/tex]
7/12 - 4/5 i need the anwser may anyone help me
Answer:
- 13/60
Step-by-step explanation:
Have a great day!
- 13/60
Step-by-step explanation:
A suit was marked with a 10% discount.
If the discount is $18.00, what was the original price of the suit?
Answer:
$20
Step-by-step explanation:
10% = 18/9
10% = 2
2 x 10 = 20
How do you get that m
Answer:
What?
Step-by-step explanation:
Help pls
do the first one like the 2 examples but only the T-chart part\
30 points+ BRAINLIEST
Answer:
12, 9. 18, 27. 24, 36.
Step-by-step explanation:
It's a 6:9 ratio. So you multiply each by 2, 3, and 4 to find the equivilant ratios. 9 ice creams to 6 biscuits. You count the biscuits and there's 6 and you count the ice cream and there's 9. There are 6 biscuits to 9 ice creams which means... 6:9!
A certain size bottle holds exactly 4/5 pint of liquid. How many of these bottles can be filled from a 20-pint container?
Find the slope of the line
A 1
B -2
C -1
D 2
Pls help
A ship is stationary at sea. A tugboat is 28 km away at a bearing of 315°, and a yacht is 21 km from the tugboat at a bearing of 210°. Draw a scale diagram showing the positions of the three vessels. Use a scale of 1 : 350,000. Measure the distance from the ship to the yacht to the nearest km.
The distance of the yacht from the ship is found by accurately drawing
the relative location of the three vessels.
Response:
The measured distance of the yacht from the ship is approximately 30 km.Which drawing method can be used in which the distance of the yacht from the ship can be measured?The given parameters are;
Distance of the tugboat from the ship, a = 28 km
Bearing of tugboat from the ship = 315°
Distance of the yacht from the tugboat, b = 21 km
Bearing of the yacht from the = 210°
Using a scale of 1 : 350,000, we have;
[tex]The \ drawing \ of \ a = \mathbf{\dfrac{28,000}{350,000} }= 0.08[/tex]
The length of a in the drawing = 0.08 m = 8 cm
[tex]The \ drawing \ of \ b = \mathbf{\dfrac{21,000}{350,000}} = 0.06[/tex]
Which gives;
b in the drawing = 0.06 m = 6 cm
Using the above dimensions and directions, the drawing of the relative
location of the three vessels can be accurately created using MS Word.
From the application, the vector form of the distance, d, of the ship from the yacht is presented as follows;
d = 8.655·i + 0.445·jWhich gives;
d = √(8.655² + 0.445²) = 8.67
Which gives;
Distance of the yacht from the ship on the drawing is d ≈ 8.67 cm = 0.0867 mActual distance = 0.0867 m × 350,000 = 30,345 m = 30.345 km ≈ 30 km
The distance of the yacht from the ship ≈ 30 kmUsing cosine rule, where the angle formed at the tugboat = 75°, we have;
d² = 28² + 21² - 2 × 28 × 21 × cos(75°) ≈ 920.63
Which gives;
d ≈ √(920.63) ≈ 30
The distance of the yacht from the ship, d ≈ 30 km
Learn more about bearings in mathematics here:
https://brainly.com/question/10710413
If h(x) = 2x and g(x) = 3x + 1, what is h(g(x))?
O 6+1
o 6x² +2
o 12r? + 1
12x² + 2
o
Answer:
6x+2
Step-by-step explanation:
[tex]h(x) = 2x \\ g(x) = 3x + 1 \\ h(g(x)) = h(3x + 1) \\ h(3x + 1) = 2(3x + 1) \\ 6x + 2[/tex]
Solve by using subitution
Please explain your steps and explain why it's no solution thanks :)
2x-y=2. Y=2x+1
Answer:
No Solutions
Step-by-step explanation:
1. Substitute the 2x + 1 in for the y in the first equation. Rewrite it as 2x - (2x + 1) = 2.
2. Add the opposite and change the equation to 2x + -1(2x + 1) = 2.
3. Use the distributive to make the equation look like this: 2x + -2x + -1 = 2
4. Combine like terms and add 2x and -2x. They cancel each other out.
5. You will end up with -1 ≠ 2. Since -1 and 2 are not equal, there are no solutions.
x + 6 - 3 = 4x + 8
solve for x
Answer:
x= -3/5
Step-by-step explanation:
x+3=4x+8
-8 -x
-5 = 3x
-5/3 = x
Answer:
[tex]x=-\frac{5}{3}[/tex]
Step-by-step explanation:
x + 6 - 3 = 4x + 8
x + (6 - 3) = 4x + 8
x + 3 = 4x + 8
- 4x - 4x
-3x + 3 = 8
- 3 - 3
-3x = 5
/-3 /-3
[tex]x=-\frac{5}{3}[/tex]
Hope this helps!
Solve the following equation then place the correct number in the box provided 3(2x+5)> 2(x+6)
Answer:
The answer is x ≥ -3/4
Step-by-step explanation:
Eli invested $37,000 in an account paying an interest rate of 6.75% compounded quarterly. Xavier_
invested $37,000 in an account paying an interest rate of 6.25% compounded annually. After g years,
how much more money would Eli have in his account than Xavier, to the nearest dollar?
Answer: $3732
Step-by-step explanation:
Name a pair of angles of rotation with the same sine value in the same quadrant.
Answer:
Because θ' is the reference angle of θ, both sin(θ) and sin(θ') have the same value. For example, 30° is the reference angle of 210°, and if we reference the unit circle, we can see that the sine values of both have a magnitude of 1/2, albeit they have different signs.
Identify the correct solution to the problem 8 x 2/3 .
A. 5 1/3
B. 8 2/3
C. 3 1/5
D. 5 2/4
Classify the following numbers as Natural, Whole number, irrational, non real, rational
[tex] \sqrt{111} [/tex]
Answer:
sqroot(111) is irrational.
Step-by-step explanation:
Natural are 1, 2, 3, 4...
Whole are 0, 1, 2, 3...
Irrational are decimals that don't end or repeat. Sqroot(111) is 10.535653752...
Nonreal have an i, the imaginary number.
Rational are fractions (or can be written as a fraction) or decimals that end or repeat.
what does sin^2 x - cos^2 x equal
Answer:
-cos(2x)
Step-by-step explanation:
I did trig last year and tutor a trig class this year :)
Could anyone help with this whole page? My sister in 6th grade asked for help and i had no idea so help would be appreciated tysm<3
Answer:
1. Earl: $275/5 hours Mia: 376/8 hours
2. Earl raised $55 in one hour
Mia raised $47 in one hour
3. Earl made more money an hour 55 > 47
The number 100 is multiplied either by 2 or by 3, then the result is increased either by 1 or by 2, and then the new result is divided either by 3 or by 4. If the final result is a natural number, what is this final result?
Answer:
67
Step-by-step explanation:
This is the right answer
