Find the exact value, without a
calculator.
710
6
sin
2
tan
12
6
2
7Tt/6
COS
Answers
Answer:
[tex]-2 -\sqrt{3}[/tex]
Step-by-step explanation:
First consider numerator
[tex]sin \frac{\frac{7\pi}{6}}{2} = sin \frac{7\pi}{12}= sin (\frac{\pi}{4} + \frac{\pi}{3})[/tex]
Using the formula : sin (A + B) = sin A cos B + cos A sin B
[tex]sin \frac{\pi}{4} = \frac{\sqrt{2} }{2}, \ cos \frac{\pi}{4} = \frac{\sqrt{2} }{2}\\\\sin \frac{\pi}{3} = \frac{\sqrt{2} }{2}, \ cos \frac{\pi}{3} = \frac{1}{2}[/tex]
[tex]sin(\frac{\pi}{4} + \frac{\pi}{3}) = sin \frac{\pi}{4} \cdot cos \frac{\pi}{3} + cos \frac{\pi}{4} \cdot sin \frac{\pi}{3}[/tex]
[tex]=\frac{\sqrt{2} }{2} \cdot \frac{1}{2} + \frac{\sqrt{2} }{2} \cdot \frac{\sqrt{3} }{2} \\\\= \frac{\sqrt{2} }{4} + \frac{\sqrt{6} }{4}\\\\=\frac{\sqrt{2} +\sqrt{6} }{4}[/tex]
Second consider denominator
[tex]cos \frac{\frac{7\pi}{6}}{2} = cos \frac{7\pi}{12}= cos (\frac{\pi}{4} + \frac{\pi}{3})[/tex]
Using the formula : cos (A + B) = cos A cos B - sin A sin B
[tex]sin \frac{\pi}{4} = \frac{\sqrt{2} }{2}, \ cos \frac{\pi}{4} = \frac{\sqrt{2} }{2}\\\\sin \frac{\pi}{3} = \frac{\sqrt{2} }{2}, \ cos \frac{\pi}{3} = \frac{1}{2}[/tex]
[tex]cos(\frac{\pi}{4} + \frac{\pi}{3}) = cos \frac{\pi}{4} \cdot cos \frac{\pi}{3} -sin \frac{\pi}{4} \cdot sin \frac{\pi}{3}[/tex]
[tex]=\frac{\sqrt{2} }{2} \cdot \frac{1}{2} - \frac{\sqrt{2} }{2} \cdot \frac{\sqrt{3} }{2}\\\\=\frac{\sqrt{2}}{4} - \frac{\sqrt{6}}{4}\\\\= \frac{\sqrt{2} -\sqrt{6} }{4}[/tex]
Therefore,
[tex]tan \frac{7\pi}{12} = \frac{sin \frac{7\pi}{12}}{cos\frac{7\pi}{12}}[/tex]
[tex]= \frac{\frac{\sqrt{2} +\sqrt{6} }{4}} {\frac{\sqrt{2} -\sqrt{6} }{4} }\\\\=\frac{\sqrt{2} +\sqrt{6} }{4} \times \frac{4 }{\sqrt{2} -\sqrt{6}}\\\\=\frac{\sqrt{2} +\sqrt{6} }{\sqrt{2} -\sqrt{6}}[/tex]
Either we can stop here or Rationalize the denominator:
[tex]\frac{\sqrt{2} +\sqrt{6} }{\sqrt{2} -\sqrt{6}} \times \frac{\sqrt{2} +\sqrt{6} }{\sqrt{2} +\sqrt{6}} = \frac{(\sqrt{2} +\sqrt{6})^{2} }{(\sqrt{2})^2 -(\sqrt{6})^2} = \frac{2 + 6 +2\sqrt{12} }{2-6} = \frac{8+2\sqrt{12} }{-4} = \frac{8+ 4\sqrt{3} }{-4} = -2-\sqrt{3}[/tex]
Related Questions
how to represent -23/6 on number line
Answers
So -23/6 = -3 5/6
Make a number line with (on the left) -4, -3, -2 -1 , 0 , 1, 2, 3, 4
Then put a dot very close to -4 BUT not on -4
i need help with this
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Answer:
7x^2 + 8x-7
7×4^2 + 8×4-7
7×16+32-7
112+25
137
The Martz family pays a rate of 37.5 mills the property tax versus value of the home is 68,000 what is the property tax
Answers
If the property tax versus value of the home is 68,000 the property tax is $2,550.
Property taxUsing this formula
Property tax=Mills rate× Property value /1000
Where:
Mills rate=37.5
Property value=$68,000
Let plug in the formula
Property tax=37.5×68,000/1000
Property tax=$2,550,000/1000
Property tax=$2,550
Or
Convert the mills rates to dollar rate amounts by dividing the mill rate by 1,000 and then multiply it by the property value.
Property tax=37.5/1000×$68,000
Property tax=$2,550
Inconclusion the property tax is $2,550.
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A ladder is placed 10 feet away from a tree. The length of the ladder is 25 feet. Find the height of the tree?
STEP BY STEP PLS I WILL MARK BRAINLIEST PYTHAGORUS THEOREM
Answers
C= 25^2 + 10^2
C= (25)(25)+ (10)(10)
= 625 + 100
= 725
square root of 725 is 26.9 ; you can round to the nearest tenth which will be 27 feet ! hope i helped(:
Find the volume of the cone using 3.14 for pi. Please help asap i need it!
Answers
Answer:
29.32
Step-by-step explanation:
We are given the diameter on the bottom, so we can find the radius. Since a radius is half the diameter, the radius is 2mi. The formula for the volume of a cone is:
1/3 * pi * r^2 * h
We can substitute:
1/3 * pi * 2^2 * 7
29.32153
This rounds to about 29.32
Answer:
V = 117.23
Step-by-step explanation:
V = (1/3) pi x r^2 x h
Input.
V = (1/3) 3.14 x 4^2 x 7
V = (1/3) 3.14 x 16 x 7
V = (1/3) 3.14 x 112
V = (1/3) 351.68
V = 117.23
Note: Please disregard my answer as I used the incorrect radius. I needed to find the correct radius instead of using the diameter as it was.
Please help!!! Will give brainliest!
Answers
Answer:hhhhhhhhhbbbbb
Step-by-step explanation:
44444444
This prism has a right triangle for a base. What is the volume of the prism?
Answers
length = 6 x 1/3 = 2 inches
width = 4 x 1/3 = 4/3 inches
height = 8 x 1/3 = 8/3 inches
volume = lwh = 2 x 4/3 x 8/3 = 64/9 cubic inches
Another approach is the following:
There are 6 x 4 x 8 = 192 cubes inside the prism,.
Each cube has a volume of 1/27 cubic inches.
Therefore total volume = 192 x 1/27 = 192/27 = 64/9
ayuda resta de fracciones
(+4/7) - (3/7)
Answers
Answer:
Step-by-step explanation:
=4/7-3/7
=4-3/7
=1/7
Answer:
Step-by-step explanation:
así que lo primero que harías es ... alinearlos así ...(el primer archivo)
Entonces para solucionarlo ...(El segundo archivo).
¡Espero que esto sea correcto y ayude!
Figure D is the result of a transformation on figure C. which transformation would accomplish this?
PLEASE HURRY
Answers
Answer:
A translation 1 unit left and 2 units up
Step-by-step explanation:
1) look at the point at the very bottom-we can call that point A
2) that point on figure C would be at (3,-5)
3) if you move it to the left one and up two, you get that same point but on figure D
So, the answer is the second option
3x −3 y −4 ⋅ 3x 3 y 3
Answers
-
1
2
3
3
+
3
−
3
Is 5.585786438 rational or irrational
Answers
From what I have learnt:
The number has an ending so it is rational
Irrational numbers don't end, e.g. π (3.1415926...)
Express tan W as a fraction in simplest terms.
U
W
24
6
Answers
Answer:
The simplest terms is, tan W=4.
Explanation:
Definition of trigonometry:Trigonometry is a discipline of mathematics that deals with certain angle functions and how to use them in computations. In trigonometry, there are six functions of an angle that are often utilised. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their names and acronyms (csc).
Step by step:
Simplest term of tan W are calculated as:
We know that, [tex]tan[/tex]θ [tex]=\frac{opposite}{adjacent}[/tex]
According to the question:
[tex]tan W=\frac{VU}{VW} \\\\tan W=\frac{24}{6} \\\\tan W =4[/tex]
Hence, The simplest form of tan W is 4.
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A rectangular room is 9 m long and 6 m broad. Find the number of
pieces of carpet each of 4 m long and 1.5 m wide to cover the floor of
the room. If the rate of cost of carpet is Rs 110 per metre, find the cost
of carpeting the floor.
Answers
Answer:
880
Step-by-step explanation:
Answer:
Rs. 3,960 is the cost of carpeting.
Violet buys a premium sound system that is on sale for 40% off the original price. The original price is $224 more than the sale price
Answers
Answer:
The original price was of $560, while the sales price was of 560 - 224 = $336.
Step-by-step explanation:
Original price:
x
Sales price:
224 less than the sales price, that is:
x - 224.
On sale fo 40% of the original price:
So the sales price is 100 - 40 = 60% = 0.6 of the original price. That means that:
[tex]x - 224 = 0.6x[/tex]
[tex]0.4x = 224[/tex]
[tex]x = \frac{224}{0.4}[/tex]
[tex]x = 560[/tex]
The original price was of $560, while the sales price was of 560 - 224 = $336.
Can someone help its math :)
Answers
Answer:
m<F = 53
Step-by-step explanation:
Exterior angles thm:
5x - 10 + 3x + 14 = 100
8x + 4 = 100
8x = 104
x = 13
m<F:
3x + 14
3(13) + 14
39 + 14
53
4) 9i(5) + 5i(3)– 10i
Answers
Answer:
50i
Step-by-step explanation:
Pls help anyone plsss
Answers
3 times flipped, two sides fo a coin heads and tails, 2/3 meaning most likely
NEED HELP ASAP!!!!!The perimeter of a ractangle is 176 ft. If the ratio of the length to the width is 9 : 2, what is the length of each side?
(P = 2l + 2w)
Answers
P=2l+2w
l+w equals half of the perimeter
220/2=110
the ratio of the length to the width is 7:3
7x+3x=110
10x=110
x=11
7*11=77 for the length
3*11=33 for the width
A=l*w
A=77*33
A=2541 square inches for the area
maybe you are getting the formula mixed up ?!?!
make m the subject in the relation
[tex]2m - x + 3y \h = 2y \p[/tex]
Answers
Answer:
[tex]m = \frac{-y+x}{2}[/tex]
Step-by-step explanation:
[tex]2m - x + 3y = 2y[/tex]
Take [tex]-x[/tex] and [tex]+3y[/tex] on the other side of the equal to sign:
[tex]2m = 2y +x-3y[/tex]
Now solve for y:
[tex]2m = -y +x[/tex]
Take 2 one the other side of the equation:
[tex]m = \frac{-y +x}{2}[/tex]
Hope this helps :)
write the number into 3 significant figures 7.00956
Answers
=================================================
Explanation:
Use a marker to highlight the first three digits on the left. That would be the 7, 0 and 0.
The digit just to the right of that second "0" is the digit "9". Since this 9 is larger than 5, we'll bump the 7.00 up to 7.01
The 0 in 7.01 is significant because it's between two nonzero values. So we have three sig figs here.
A company makes fish tanks in the shape of right rectangular prisms. The company has an order for a fish tank that must be exactly 4 feet long and hold at least 35 cubic feet of water. The company wants to save money on materials and will make the tank with the smallest surface area possible. The dimensions of the tank must be in whole foot increments and a top is included in the construction What dimensions for the width and height of the fish tank will satisfy the requirements
Answers
The dimensions for the width and height of the fish tank will be 4 feet and 2 feet .
What is dimension?Dimension is the measurable extent of a particular kind, such as length, breadth, depth, or height.
According to the given problem,
let , b = is the width of the fish tank
h = is the height of the fish tank given that , hold at least 35 cubic feet of water .
so ,
4×b×h ≥ 35
⇒ h ≥ 35/4b
now , surface area of the fish tank
⇒ 4b + 2× 4h + 2× bh
now substitute the value of h
here
⇒ ≥ 4b +70/b + 35/2
⇒ ≥ 40(70)^1/2 + 35/2 (if and only if b= (70)^1/2 / 2 , the equal sign holds )
therefore ,
= (70)^1/2 / 2 b ≈ 4.18 so b is 4 . when b = 4 ,
h = 35 / 4 × 4 = 2.1875 round off h = 2
so , the minimum surface area of fish tank is
⇒ 4×4+ 2× 4×2 + 2× 4×2⇒ 48
hence , the height and the width of the fish tank is 2 and 4 .
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Liz records her pet hamster's weight once every month for one year. How many observations does she make?
Answers
Answer: 12 observations
Step-by-step explanation:
1 year = 12 months
Number of observations = 1 per month
Therefore number of observations
for a year = 1 × 12
= 12 observations.
what is the slope of the line through the points (0,2) and (3,-6)
Answers
Answer:
-8/3
Step-by-step explanation:
You can find the slope when given two points
m = (y2-y1)/(x2-x1)
= ( -6-2)/ (3 -0)
= -8/3
Tom has some marbles in two bags. In one bag he has 3 yellow, 2 green and 1 red marble. In the other bag he has 3 yellow, 3 green and 3 red marbles. If Tom takes one marble out of each bag, how probable is it that neither one is yellow?
Answers
Answer:
1 /3
Step-by-step explanation:
Bag 1 :
Yellow = 3 ; green = 2 ; red = 1
Total = 6
P(not yellow) = (2 +1) / 6 = 3/6 = 1/2
Bag 2 :
Yellow = 3 ; green = 3 ; red = 3
Total = 9
P(not yellow) = (2 +3) / 9 = 6/9 = 2/3
P(neither yellow from the two bags) = 1/2 * 2/3 = 2 /6 = 1/3
What is the measure of arc GH?
Answers
Answer:
62 degrees
Step-by-step explanation:
The angle is an inscribed angle, so its measure is half the measure of the intercepted arc.
Said another way, the intercepted arc is twice the measure of the inscribed angle.
2 x 31 = 62
Set up the equations to determine s and t.
Answers
Answer:
t° = 11° s°= 71°
Step-by-step explanation:
79° + t° =90° (Given)
t°= 90° - 79°
t°= 11°
s°+79°+11°+19° =180° (angles on an str line)
s° = 180° - 109°
s° = 71°
PLEASE HELP ASAP WILL GIVE POINTS AND BRAINLIEST! TY BESTIES! Factor using GCF 20x^2+10x please show work
Answers
Answer:
10x(2x+1)
Step-by-step explanation:
20x^2+10x
2*10*x*x + 10 *x
Factor out the common terms
10x(2x+1)
Will mark the correct answer brainliest
Answers
2x+15=33 solve for x
Answers
Answer:
x = 9
Step-by-step explanation:
2x + 15 = 33
2x = 33 - 15
2x = 18
x = 18/2 = 9
Answer:
x=9
Step-by-step explanation:
2x+15=33
Subtract 15 from each side
2x+15-15=33-15
2x=18
Divide by 2
2x/2 = 18/2
x = 9
helppppppppppp no links or you'll get reported
Answers
Answer:
1.95
Step-by-step explanation:
area = (1/2 ×1 ×1 )×3 = 1.5 ( for sides)
area = ( 1/2 ×1 ×0.9) = 0.45 for base
area =1.5+0.45 = 1.95