Answer:
[tex]cos\Theta =\frac{4}{5}[/tex]
[tex]tan\Theta =\frac{3}{4}[/tex]
Step-by-step explanation:
Given : sin θ = 3/5
To Find : value of cos θ and tan θ
Solution :
use the identity:
[tex]sin^{2}\Theta +cos^{2}\Theta =1[/tex]
putting value of sin θ
⇒ [tex](\frac{3}{5})^{2} + cos^{2}\Theta =1[/tex]
⇒[tex]\frac{9}{25} +cos^{2}\Theta =1[/tex]
⇒[tex]cos^{2}\Theta = 1-\frac{9}{25}[/tex]
⇒[tex]cos^{2}\Theta = \frac{16}{25}[/tex]
⇒[tex]cos\Theta = \sqrt{\frac{16}{25}}[/tex]
⇒[tex]cos\Theta =\frac{4}{5}[/tex]
Thus , [tex]cos\Theta =\frac{4}{5}[/tex]
Now to find value of tan θ
Since we know that
⇒ [tex]tan\Theta =\frac{sin\Theta }{cos\Theta }[/tex] (identity)
⇒[tex]tan\Theta =\frac{\frac{3}{5} }{\frac{4}{5} }[/tex]
⇒[tex]tan\Theta =\frac{3}{5}\div \frac{4}{5}[/tex]
⇒[tex]tan\Theta =\frac{3}{5}\times \frac{5}{4}[/tex]
⇒[tex]tan\Theta =\frac{3}{4}[/tex]
Thus , the value of
[tex]tan\Theta =\frac{3}{4}[/tex]
[tex]cos\Theta =\frac{4}{5}[/tex]
Final answer:
This detailed answer provides the values of cos θ and tan θ for an angle θ in the second quadrant given sin θ = 3/5. It explains the process using the Pythagorean identity and the characteristics of the second quadrant.
Explanation:
cos θ = -4/5
tan θ = -3/4
Given sin θ = 3/5 and the angle θ lies in the second quadrant, we can determine cos θ using the Pythagorean identity. Since sin θ = 3/5 is positive in the second quadrant, the x-coordinate in the triangle would be negative. Therefore, cos θ = -4/5. Similarly, tan θ can be calculated as tan θ = sin θ / cos θ = (3/5) / (-4/5) = -3/4.
45 equals the quotient of a number n and 3
The equation representing the student's question is 45 = n / 3. To find n, we multiply both sides by 3, resulting in n = 135.
Explanation:The student's question, "45 equals the quotient of a number n and 3," can be translated into a mathematical equation. The word 'quotient' indicates a division operation. We set up the equation as 45 = n / 3.
To find the value of n, we multiply both sides of the equation by 3, giving us 3 * 45 = n. Therefore, n equals 135. The solution to this problem demonstrates how to manipulate an equation to solve for an unknown variable.
In this question, 45 is equal to the quotient of a number, represented by n, and 3.
We can represent this equation as:
45 = n / 3
To find the value of n, we can multiply both sides of the equation by 3:
45 * 3 = n
Therefore, n is equal to 135.
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Prove that a triangle cannot have two right angles.
A triangle cannot have two right angles. Suppose a triangle had two right angles.
A triangle cannot have two right angles because the sum of the interior angles in any triangle is equal to two right angles. Having two right angles would necessitate that the third angle also be a right angle, forming a straight line instead of a triangle.
Proof that a Triangle Cannot Have Two Right Angles
The notion that a triangle cannot have two right angles is fundamentally rooted in the geometry axiom stating that the sum of the interior angles in any triangle is equal to two right angles (or 180 degrees). If a triangle were to have two right angles, the third angle would also have to be a right angle to satisfy the sum of 180 degrees. However, if the third angle is a right angle, this contradicts the definition of a triangle being a three-sided polygon with three angles that add up to 180 degrees; with three right angles, the figure would no longer be a triangle, as the three lines AC, CD, and BD would line up to form a straight line, eliminating the closed polygon structure of a triangle.
If we consider the work of notable mathematicians such as Legendre and Dehn, we find substantial evidence supporting the statement that the sum of the interior angles of a triangle cannot be greater than two right angles. Legendre's attempts to prove this led to understanding the consistency of triangle angle sums across all triangles; that is, if one triangle's angles added up to two right angles, it would be the same for all triangles. Furthermore, Dehn's hypothesis indicated that without parallel lines, the sum of the angles of a triangle is greater than two right angles.
Overall, every triangle must have at least two acute angles, and any attempt to form a triangle with two right angles would result in a shape that does not adhere to the fundamental properties of a triangle.
If m arc AB = 120°, then which of the following have measures of 60°? (pick as many as you want)
a)∠ADB
b)∠ACD
c)∠BCA
d)∠BAD
e) m arc BC
The correct answers are:
a)∠ADB; and c)∠BCA.
Explanation:
The measure of an intercepted arc is twice as much as the measure of its inscribed angle. AB corresponds with both ∠ADB and ∠BCA. Since the arc is 120°, each angle would be half of that, or 60°.
Find the lowest common denominator for the set of fractions: 6/a^2-7a+6 and 3/a^2-36
Answer:
(a-6)(a-1)(a+6)
Final answer:
The lowest common denominator for the fractions [tex]6/(a^2-7a+6)[/tex] and [tex]3/(a^2-36)[/tex] is (a-6)(a-1)(a+6).
Explanation:
To find the lowest common denominator for the fractions [tex]6/(a^2-7a+6)[/tex] and [tex]3/(a^2-36),[/tex] we need to determine the least common multiple of the denominators.
The denominator of the first fraction can be factored as (a-6)(a-1) and the denominator of the second fraction can be factored as (a-6)(a+6).
The common factors are (a-6) and (a-1)(a+6).
Therefore, the lowest common denominator is (a-6)(a-1)(a+6).
What is 8/25 as a percentage?
what is the distance between 0 and 7/10?
Five boxes of candles contain a total of 60 candles. each box holds the same number of candles.
Answer:
60/5=12
Step-by-step explanation:
Point E has a negative x-coordinate, and its y-coordinate is not 0
Where could point E be located on the coordinate plane?
PLEASE HELP!!!! I DON'T KNOW HOW TO DO THIS!!
Point H is the incenter of triangle ABC. Find DH.
a. 14
b. 7
c. 18
d. 21
Due to a lack of information provided, the length of segment DH in the triangle ABC, where H is the incenter, cannot be determined as provided options could all be possible or might be something entirely different.
Explanation:The question doesn't provide enough information to determine the length of segment DH. In a triangle, the incenter is the center of the inscribed circle (incircle). This is the point where all the angle bisectors of the triangle meet. Segment DH would be a line from the incenter to a point on one of the triangle's sides, in other words, a radius of the incircle. However, without more information such as the length of the sides of the triangle or its area, it isn't possible to determine the length of DH. It could be any of the provided options (14, 7, 18, 21) or something else entirely.
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The incenter of a triangle is the point where the angle bisectors of the three angles of the triangle intersect.
Explanation:The incenter of a triangle is the point where the angle bisectors of the three angles of the triangle intersect. To find the distance DH, we can use the fact that the incenter is equidistant from the three sides of the triangle.
Let AD, BE, and CF be the angle bisectors of triangle ABC, where D, E, and F are the points of intersection with the sides.The incenter H is equidistant from each side of the triangle. So, we have DH = EH = FH.Let DH = x. Then, we have AH = 2x, BH = 2x, and CH = 2x.Therefore, DH = x = (AH + BH + CH)/3 = (2x + 2x + 2x)/3 = 6x/3 = 2x.
Since DH = 2x, the distance DH will be twice the distance from the incenter to any side of the triangle. Without knowing the specific values of the sides of triangle ABC, we cannot determine the exact value of DH. Therefore, none of the given options (a, b, c, d) is the correct answer.
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An electrician charges a $50 house call fee and $65 per hour for work
What is the solution to the equation -2n -2 / 3 =12 ? n =
a student finds the slope of a line between (14,1) and (18,17). she writes 1-17/18-14 what mistake did she make?
Answer:
Mistake was in denominator.
Step-by-step explanation:
If a line passes through two points ( a, b ) & ( c, d )
Then slope of this line will be = [tex](\frac{d-b}{c-a})[/tex]
Now we come to the question.
a student finds the slope of a line passing through ( 14, 1 ) and ( 18, 17 ) as
slope = [tex](\frac{1 - 17}{18-14})[/tex]
This formula is not the form of [tex](\frac{d-b}{c-a})[/tex]
Accurate answer should be
slope = [tex](\frac{1-17}{14-18})[/tex]
So mistake was in denominator.
Given the set of numbers (3, 5, 7, 11, 23), what number must be added to the set so that the median of the 6 numbers is 9? what number must be added to the set so that the mean of the 6 numbers is 9?
Suppose
cos(π/2−x) =3/5, cos x =4/5
find sin, tan, csc, sec, cot
To find the values of sin, tan, csc, sec, and cot, we use trigonometric identities and given information. Sin x = 3/5, tan x = 3/4, csc x = 5/3, sec x = 5/4, and cot x = 4/3.
Explanation:To find the values of sin, tan, csc, sec, and cot, we can use the trigonometric identities. From the given information, we know that cos x = 4/5. Using the Pythagorean identity, sin² x = 1 - cos² x, we can find sin x as:
sin x = sqrt(1 - (4/5)²) = sqrt(1 - 16/25) = sqrt(9/25) = 3/5
Now, we can calculate the remaining trigonometric values:
tan x = sin x / cos x = (3/5) / (4/5) = 3/4
csc x = 1 / sin x = 1 / (3/5) = 5/3
sec x = 1 / cos x = 1 / (4/5) = 5/4
cot x = 1 / tan x = 1 / (3/4) = 4/3
Which of the following is a factor of 3x3 + 18x2 + 27x?
9x
x3
x + 3
x - 3
The radius,
R
, of a sphere is
5.8m
. Calculate the sphere's volume,
V
.
Use the value
3.14
for
π
, and round your answer to the nearest tenth.
If you pay for $25.00 for purchase which includes 11% sales tax. how much is the sale tax?
Sales tax is $ 2.75
Further Explanation
How to calculate
Tax = $ 25.00 x (11/100)
Tax = $ 25.00 x 0.11
Tax = $ 2.75
Initial purchase of $ 22.25 + 11% Tax ($ 2.75) = $ 25.00
Or other alternatives:
11% tax
n = sales tax value
11% = $ 25.00 / n
n = $ 25.00 x 11%
n = ($ 25.00 x 11) / 100
n = $ 275/100
n = $ 2.75
So, the sales tax is $ 2.75
Sales tax (VAT) is tax before Value Added Tax (VAT) and is charged each time a sales transaction. A VAT is charged at the manufacturer level / not to retailers (end users). A VAT is collected when delivering goods or services.
Definition of Tax Debt
Debt is an engagement as a result of a special agreement called a debt payable, which requires the debtor to pay the amount of money he has borrowed from creditors.
Sales tax / value-added debt or Sales tax payable is the company's debt to the tax office for sales tax collected by the company from customers for the sale of goods/services. Sales tax rates are deposited by the tax office multiplied by sales / net sales (net sales).
Example
$ 12 cash sale including 10% VAT
Tax Amount: 10 / ÷ 100 × 12 = $ 1.2
Sales Amount: 12 - 1.2 = $ 10.8
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Details
Class: High School
Subject: Mathematics
Keywords: VAT, Tax, Sales
How do you write 6.8 as a fraction?
The first term in a sequence is x. Each subsequent term is three less than twice thw preceding term. what is the 5th term in the sequence?
A) 8x-21
B) 8x-15
C) 16x-39
D) 16x-45
E) 32x-93 ...?
graph the function g (x)=1/3-4/3x
2-5|5m-5|=-73 absoute value
What is 0.17 in standard form?
The function f(x)=5000(0.98)^0.3x
represents the number of white-blood cells, per cubic millimeter, in a patient x days after beginning treatment for a virus.
What is the average decrease per day in white-blood cells per cubic millimeter between days 1 and 5?
a.) −29.75 mm^3/day
b.)-34.75 mm^3/day
c.)-282.47 mm^3/day
d.-)353.08 mm^3/day
Describe the graph of the function f(x) = x3 − 11x2 + 36x − 36. Include the y-intercept, x-intercepts, and the shape of the graph.
Evaluate 0!÷1!.
0
1
undefined
Answer:
it is actually not undefined because of the (!), due to this the answer is 1
Step-by-step explanation:
0! 1 5! 120
1! 1 6! 720
2! 2 7! 5,040
3! 6 8! 40,320
4! 24 9! 362,880
those are the factorial calculations
Which law would you use to simplify the expression (x^⁴)⁹ ?
A. product of powers
B. power of a product
C. power of a quotient
D. power of a power
if you see this similar format you will recognize the equation as power of a power ^^•
A flower bed is in the shape of a triangle with one side twice the length of the shortest side, and the third side is 13 feet more than the length of the shortest side. Find the dimensions if the perimeter is 125 feet
SERIOUSLY NEED HELP WITH THIS QUESTION.
The cube in the image has a volume of 1,000 cubic feet. The other solid has the same base and height as the cube, but the length of each of its slanted sides is 2 units longer than the height. What is the volume of the tilted solid?
800 cubic feet
1,000 cubic feet
1,200 cubic feet
2,000 cubic feet
Answer:
The correct option is 2.
Step-by-step explanation:
It is given that the volume of cube is 1,000 cubic feet.
The volume of cube is
[tex]V=a^3[/tex]
[tex]1000=a^3[/tex]
[tex]a=10[/tex]
The side length of cube is 10 feet.
It is given that the other solid has the same base and height as the cube, but the length of each of its slanted sides is 2 units longer than the height.
The area of tilted solid is
[tex]V=\text{Area of base}\times \text{height}[/tex]
Since height and base are same, so the area of tilted solid is
[tex]V=(10 \times 10)\times 10=1000[/tex]
The volume of the tilted solid is 1,000 cubic feet. Therefore the correct option is 2.
Philip charges $12 to rake the yard she charges $5 per hour to bag the piles of leaves for 2 hours what is the expression