What is the tan of 30 degrees
Answers
Answer:
The value of tan 30 degrees is 0.57736.
Step-by-step explanation:
Tan 30 degrees in radical form is = [tex]\frac{1}{\sqrt{3} }[/tex]
We know [tex]\sqrt{3}[/tex] = 1.732
So, tan 30 degrees = [tex]\frac{1}{1.732}[/tex]
= 0.57736
The answer is 0.57736.
Please find attached the exact value reference triangle .
The required value of tan 30 degrees is 1/[tex]\sqrt{3}[/tex].
Given the trigonometric function tan 30 degrees.
The tangent of 30 degrees, written as tan(30°), can be evaluated without a calculator by using the trigonometric properties of special angles.
In a right triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
For a 30°- 60°- 90° right triangle, the side opposite the 30-degree angle is half the length of the hypotenuse, and the side adjacent to the 30-degree angle is equal to the length of the hypotenuse multiplied by
[tex]\sqrt{3}[/tex]/2.
In a 30°-60°-90° triangle, the tangent of 30 degrees is given by:
tan(30°) = (opposite side) / (adjacent side)
tan(30°) = (1/2) / ([tex]\sqrt{3}[/tex]/2)
tan(30°) = 1/[tex]\sqrt{3}[/tex] = [tex]\sqrt{3}[/tex]/3.
tan (30°) = [tex]\sqrt{3}[/tex]/3
Multiply both numerator and denominator by [tex]\sqrt{3}[/tex] gives,
tan(30°) = 3/3[tex]\sqrt{3}[/tex].
Divide both numerator and denominator by 3 gives,
tan(30°) = 1/[tex]\sqrt{3}[/tex].
Therefore, the tangent of 30 degrees is 1/[tex]\sqrt{3}[/tex].
Hence, the required value of tan 30 degrees is 1/[tex]\sqrt{3}[/tex].
Learn more about trigonometric functions and special angles here:
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Related Questions
If i drove 34 times over a 7 mile bridge. how many miles in all did i drive?
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Miles times amount =
238 miles in total.
Hope this helped!
What unit of measurement would Guatemalans typically use to measure the weight of flour?
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A heart beats 8 times in 3 seconds.About how many times will a cats heart beat in 2 minutes
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Consider the equation v + 4 + v = 8. What is the resulting equation after the first step in the solution?
a. v +4 = 8 – v
b. v +4 = 8
c. 4 + v = 8 – v
d. 2v + 4 = 8
Answers
d. 2v + 4 = 8.
Answer:
The resulting equation after the first step is 2v+4=8
d is the correct option
Step-by-step explanation:
We have been given the equation v + 4 + v = 8. In order to solve it for v, we'' perform the below mentioned steps.
Add the like terms in the left hand sideSubtract 4 to both sides of the equationFinally divide both sides by 2Hence, in the first step, we can group the like terms and combine. In the left hand side v and v are like terms and hence, we can add them
On adding v and v we get 2v
Thus, we have
[tex]v+v+4=8\\2v+4=8[/tex]
Thus, the resulting equation after the first step is 2v+4=8
My math homwork is asking me for the word form and the expanded form for 3.4 and 2.51,and i don't understand this. we just started it today and she my teacher gave us 3 pages of the math.
Answers
the word form would be three and four tenths
the expanded form would be :
3.0 = 3
0.4 = .4
2.51:
the word form would be two and fifty one hundredths
the expanded form would be 2.00 + 0.50 + 0.01
hope this helps you
What is the product? enter your answer as a fraction, in simplified form, in the box. −1/4⋅(−6/11)?
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yeah it would be 3/11 i just did the test
Find the discriminant of the following equation.
4x2 + 16x + 16 = 0 ...?
Answers
Discriminant = b^2 - 4ac
a = 4
b = 16
c = 16
16^2 - 4(4 x 16)
256 - (4x64)
256 - 256 = 0
Therefore it only has one root
The measures of each exterior angle in a regular hexagon is (4x + 15)°. Find the value of x. Show equations and all work that leads to your answer.
...?
Answers
A regular hexagon has 6 equal exterior angles.
6(4x + 15) = 360
4x + 15 = 360/6 = 60
4x = 60 - 15 = 45
x = 45/4 = 11.25
x = 11.25
a rectangeler field is twice as long as it is wide a golf cart travrling at 12 miles per hour takes 7.5 minutes to travel the perimeter of the field what is the length (in miles) of the field
Answers
can someone explain how to find two positive numbers such that their product is 192 and the sum of the first plus three times the second is a minimum?
Answers
xy = 192
y = 192/x
dy/dx = -192/x^-2 . . . (1)
Sum (S) = y + 3x
If the sum is minimum, then
dS/dx = dy/dx + 3 = 0
dy/dx = -3
From (1), -192/x^2 = -3
3x^2 = 192
x^2 = 192/3 = 64
x = sqrt(64) = 8
y = 192/8 = 24
The two positive numbers are 8 and 24.
in the decimal number .98703, the 0 holds what place value
Answers
Answer:
it is in the 10 thousansth place.
Step-by-step explanation:
.98703
9=10nth place
8=100th place
7=thousandth place
0=ten thousandth place
3=hundred thousandth place
I hope this helps.
Write the equation of a line in slope-intercept form from the graph below.
Write the equation of a line in slope-intercept form from the graph below.
Answers
Slope of 1, y-intercept of (0,0)
y=1x+0...same as the initial answer
Answer: Y=x or y=1x
Step-by-step explanation:
Slope of 1 y-intercept of (0,0)
What is the length of segment LM?
Answers
Answer:
Step-by-step explanation:
From the given figure, we have
[tex]KN=NM[/tex]
⇒[tex]14x-3=25[/tex]
⇒[tex]14x=28[/tex]
⇒[tex]x=2[/tex]
Also, a is the angle bisector of ∠KNM and also it bisects the side KM such that KL=LM, thus
[tex]KL=LM[/tex]
Also, [tex]KL=9x+5[/tex]
Substituting the value of x in the above equation, we get
[tex]KL=9(2)+5[/tex]
[tex]KL=18+5[/tex]
[tex]KL=23[/tex]
Therefore, [tex]KL=LM[/tex]
[tex]LM=23[/tex]
Thus, the value of the segment LM is 23.
if you drive your car constant speed of 45 miles per hour, how long will it take to travel 378 miles
Answers
distance/speed=time
given
distance=378
sped=45mph
d/s=t
378/45=t
8.4=t
8.4 hours or 8 hours and 24 minutes
125, 0.12, 0.1 listed to least to greatest
Answers
hope this helps you
2 1/7 into a improper fraction
Answers
as an improper fraction it would be 15/7
hope this helps you
2x7=14
14+1=15
The. Put that over the original denominator
sin^2(75)-cos^2(75)=?
Answers
1: puting numbers in calculator and get answer
2: try to simplify this and than calculate.
We will do second way.
there is trigonometric formula: cos2α = cos^2(α) - sin^2(α)
if we take "-" in front of our expression:
-(cos^2(75) - sin^2(75)) = -cos(2*75) = -cos(150) = -√3/2
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in DEF DE=17 m angle =32 Find DF nearest tenth
Answers
let x be the length of side DF.
sin(32)= 17/x
x= 17 / sin(32)
x= 32.08
approximately 32.1
Answer:
(A) 32.1
Step-by-step explanation:
It is given that in ΔDEF, DE=17 and m∠F=32, thus
Using the trigonometry, we have
[tex]sinx=\frac{Perpendicular}{Hypotenuse}=\frac{DE}{DF}[/tex]
⇒[tex]sin32^{\circ}=\frac{17}{DF}[/tex]
⇒[tex]DF=\frac{17}{sin32^{\circ}}[/tex]
⇒[tex]DF=\frac{17}{0.529}[/tex]
⇒[tex]DF=32.1[/tex]
Therefore, the value of DF is 32.1.
Hence option A is correct.
How are rigid transformations used to justify the SAS congruence theorem?
Answers
In this diagram there is defined two Sides and an Angle in between (SAS).
Notice how there are two loose endpoints in the diagram. A single line segment can be drawn connecting the endpoints, forming a unique triangle.
If the original diagram is transformed, the dimensions and angles formed by the third line segment remains the same relative to the first two.
Therefore, if two triangles have the same SAS configuration, then they are congruent.
The method in which rigid transformations used to justify the SAS congruence theorem is given.
What is rigid transformation?A rigid transformation (also called an isometry) is a transformation of the plane that preserves length. In a rigid transformation the pre-image and image are congruent (have the same shape and sizes).
We are given that;
Theorem is SAS
Now,
The SAS congruence theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. To prove this theorem using rigid transformations, we can start with two distinct triangles that have a pair of corresponding congruent sides and a corresponding congruent included angle23. Then we can use a translation to move one triangle so that its congruent side matches the other triangle’s congruent side. Next, we can use a rotation to align the congruent angles of both triangles. Finally, we can use another translation to move the second congruent side of one triangle to match the second congruent side of the other triangle. By doing these rigid transformations, we have shown that one triangle can be mapped onto the other triangle exactly, which means they are congruent
Therefore, by the transformations the answer will be given above.
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alice leaves her house and walks to school she walks 45 meters south and 336 meters east. how far is Alice from her house?
Answers
so 336squared+45squared=Csquared
112896+2025=114921
C=114921
the square root of C=339
so diagonally from her house to the point of 45south and 336east is 339meters
Alice's distance from her home is 339 meters.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Alice leaves her house and walks to school she walks 45 meters south and 336 meters east.
We can write the Alice's distance from her home as -
{x} = √(45)² + (336)²
{x} = √(2025 + 112896)
{x} = 339 meters
Therefore, Alice's distance from her home is 339 meters.
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Solve the problem. Susan purchased some municipal bonds yielding 7% annually and some certificates of deposit yielding 9% annually. If Susan's investment amounts to $19,000 and the annual income is $1590, how much money is invested in bonds and how much is invested in certificates of deposit? a. $13,500 in bonds; $5500 in certificates of deposit b. $5500 in bonds; $13,500 in certificates of deposit c. $13,000 in bonds; $6000 in certificates of deposit d. $6000 in bonds; $13,000 in certificates of deposit
...?
Answers
Susan invested $6,000 in municipal bonds and $13,000 in certificates of deposit. For the bond investment scenario, given the increase in market interest rate to 9%, you would pay less than $10,000 for the bond. The calculation shows you would be willing to pay approximately $9,724.77.
Explanation:To solve Susan's investment problem, we can set up a system of equations using the information provided in the problem. Let x be the amount invested in municipal bonds and y be the amount invested in certificates of deposit (CDs). We can then set up the following equations:
x + y = $19,000 (Total investment amount)
0.07x + 0.09y = $1,590 (Total annual income from investments)
Now, we solve the system of equations. Multiplying the second equation by 100 to get rid of decimals:
7x + 9y = 159,000
Next, we can multiply the first equation by 7 to help us eliminate one variable:
7x + 7y = 133,000
Subtracting the modified first equation from the second equation:
9y - 7y = 159,000 - 133,000
2y = 26,000
y = $13,000
Using y = $13,000 in the first equation:
x + 13,000 = 19,000
x = $6,000
Therefore, Susan invested $6,000 in municipal bonds and $13,000 in certificates of deposit.
Regarding the bond investment scenario:
a. Since the market interest rate has risen to 9%, higher than the bond's 6% interest rate, you would expect to pay less than $10,000 for the bond.
b. To calculate the price you would be willing to pay, you need to find the present value of the expected payment from the bond one year from now:
The expected payment is $10,000 (the face value) plus $600 (the final interest payment), which totals $10,600.
Using the market interest rate of 9%, the present value (PV) formula is:
PV = Payment / (1 + market interest rate)
PV = $10,600 / (1 + 0.09)
PV = $10,600 / 1.09
PV ≈ $9,724.77
Therefore, you would be willing to pay approximately $9,724.77 for the bond.
f(x)=2x*e^2x. find lim of f(x) as x--> - infinity and +infinity ...?
Answers
2x times e raised to the 2x power, and not 2 times e raised to the 2x**
as it approaches infinity, your f(x) --> infinity
we can see by inspection, as 2x will approach inf, and e^(2x) will approach infinity even faster.
inf x inf = inf
as it approaches neg infinity, your f(x) --> 0
we can see by inspection, as 2x will approach neg inf, and e^(2x) will approach zero.
- inf x 0 = - 0
The minimum(or maximum) is given when the derivative = 0
Using the product rule,
f ' (x) = 2e^(2x) + 4x e(2x)
f ' (x) = 2e^(2x) ( 1 + 2x )
We find the roots
2e^(2x) will never equal 0
1 + 2x = 0, x = -1/2
The minimum value will be when x = -0.5
The end of a hose was resting on the ground, pointing up an angle. Sal measured the path of the water coming out of the hose and found that it could be modeled using the equation f(x) = –0.3x2 + 2x, where f(x) is the height of the path of the water above the ground, in feet, and x is the horizontal distance of the path of the water from the end of the hose, in feet.
When the water was 4 feet from the end of the hose, what was its height above the ground?
Answers
f(4)=-0.3(4^2)+2(4)
f(4)=-0.3(16)+8
f(4)=-4.8+8
f(4)=3.2
3.2ft above the ground
Answer:
3.2 feet
Step-by-step explanation:
The equation [tex]f(x)=-0.3x^{2}+2x[/tex] shows the height of water [[tex]f(x)[/tex]] and horizontal distance [[tex]x[/tex]].
Given the horizontal distance is 4 feet, they want to know the height.
Simply put 4 in [tex]x[/tex] of the equation and solve for [tex]f(x)[/tex]. So,
[tex]f(x)=-0.3(4)^{2}+2(4)\\f(x)=3.2[/tex]
So, the height of the water was 3.2 feet above the ground.
1000 millimeters equals what =
Answers
1000 millimeters equals:
0.001 kilometers
1 meter
100 centimeters
1e+6 Micrometers
1e+9 Nanometers
0.000621371 Miles
1.09361 Yard
3.28084 Feet
39.3701 Inches
0.0005399570950324 Nautical Miles
heeeelp!
Line segments with the same length are said to be __________.
Answers
Harry’s team has won 13 less than 6 times as many games as it has lost. The team lost n games. What expression could you use to find the number of games the team has won?
Answers
For spring break this year your family decided to visit Michigan, but it snows the first weekend you are there. You decide to make a snowman. If the bottom ball is 3 feet across, the middle ball is 2 feet across, and the top is 1 foot across, how much snow is needed to build the whole snowman? Round your answer to the nearest cubic foot.
A)
19 cubic feet of snow
B)
31 cubic feet of snow
C)
511 cubic feet of snow
D)
1022 cubic feet of snow ...?
Answers
Answer:
A
Step-by-step explanation:
Final answer:
To find the amount of snow needed to build the snowman, we need to calculate the volume of each ball and then add them together. The total volume is 18.84 cubic feet, rounded to 19 cubic feet.So,Option A.19 cubic feet of snow is correct.
Explanation:
To find how much snow is needed to build the whole snowman, we need to calculate the volume of each ball and then add them together. The volume of a sphere can be found using the formula V = (4/3) * pi * r³, where r is the radius of the sphere.
The bottom ball has a diameter of 3 feet, so the radius is 3/2 = 1.5 feet. The volume of the bottom ball is (4/3) * 3.14 * (1.5³) = 14.13 cubic feet.
The middle ball has a diameter of 2 feet, so the radius is 2/2 = 1 foot. The volume of the middle ball is (4/3) * 3.14 * (1³) = 4.19 cubic feet.
The top ball has a diameter of 1 foot, so the radius is 1/2 = 0.5 feet. The volume of the top ball is (4/3) * 3.14 * (0.5³) = 0.52 cubic feet.
The total volume of the snowman is 14.13 + 4.19 + 0.52 = 18.84 cubic feet. Therefore, the answer is 19 cubic feet of snow.
How is the graph of Y=√X) -5 translated from the graph of √X ?
shifted 5 units right
shifted 5 units down
shifted 5 units left
shifted 5 units up
Answers
i need work shown write .569 as a percent
Answers
therefore the answer is .568 * 100 =56.9%
.569as a percent equals 56.9%
In the triangle below, determine the value of a.