Given cot A = 5/6 and that angle A is in Quadrant I, find the exact value of csc A in
simplest radical form using a rational denominator.
The trigonometric function gives the ratio of different sides of a right-angle triangle. The value of Cosec A is (√61)/(6).
What are Trigonometric functions?The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
The Cot is the ratio of the base of the triangle to the perpendicular side of the triangle, therefore, we can write,
Cot A = Base/Perpendicular = 5/6
Thus, the base of the triangle is 5 units, while the length of the perpendicular of the triangle is 6 units. Now the length of the hypotenuse side of the triangle is,
H² = 5² + 6²
H² = 25 + 36
H = √61
Now, the value of Cosec A can be written as,
Cosec A = Hypotenuse/Perpendicular = (√61) / (6)
Hence, the value of Cosec A is (√61)/(6).
Learn more about Trigonometric functions:
https://brainly.com/question/6904750
#SPJ1
What is the solution of 3x + y = 9 and 3x - 5y = 15?
Answer:
(10/3, -1)
Step-by-step explanation:
So there are two different ways.
First you could address for y and fitting it into the number cruncher. one condition for y1 and another for y2. At that point go second follow and press 5 and afterward press enter multiple times to discover the convergence.
the subsequent path is to tackle by hand. I would recommend address the primary condition for y and attachment the condition tackled for y into the other condition. so y = - 3x + 9 and 3x-5y=15. At that point you could do 3x - 5(- 3x+9) = 15. At long last address for x and plug in x into the two conditions to check whether you get a similar y esteem.
The appropriate response ought to be (10/3, - 1)
Answer:
x = 3 1/3, x = -1.
Step-by-step explanation:
3x + y = 9
3x - 5y = 15
Subtract second equation from the first to eliminate the 3x :
3x - 3x + y - (-5y) = 9 - 15
6y = -6
y = -1.
Plug y = -1 in first equation:
3x + -1 = 9
3x = 10
x = 10/3 = 3 1/3.
I NEED HELPP PLS!!!!!!!!!!!!!!!!!!!
Answer:
270
Step-by-step explanation:
The formula for finding the area of a triangle is base · height ÷ 2, or [tex]\frac{bh}{2}[/tex]
After plugging in the numbers given to the formula, we find that the area of the triangle is 27.
Then to account for the length, we multiply the area of the triangle by 10.
This gets us to 270.
Please help me I really need help
Answer:
im not sure but i think its 0.25
Step-by-step explanation:
A candy store makes chocolate bars in large quantities. To make this large amount, a chocolate
maker weighs 6 identical bricks of chocolate plus a 3 pound brick for a recipe that calls for 27
pounds of chocolate.
Aubree invested $27,000 in an account paying an interest rate of 0.0825% compounded monthly. Addison invested $27,000 in an account paying an interest rate of 0.08625 % compounded continuously. After 20 years, how much more money would Addison have in her account than Aubree, to the nearest dollar?
Answer:
A = $27,445.50
Step-by-step explanation:
Equation:
A = P(1 + rt)
Calculation:
First, converting R percent to r a decimal
r = R/100 = 0.0825%/100 = 0.000825 per year.
Solving our equation:
A = 27000(1 + (0.000825 × 20)) = 27445.5
A = $27,445.50
The total amount accrued, principal plus interest, from simple interest on a principal of $27,000.00 at a rate of 0.0825% per year for 20 years is $27,445.50.
Answer: $11741
Step-by-step explanation:Rate 1: 8
4
1
%=8+1/4=
\,\,8.25\%\rightarrow 0.0825
8.25%→0.0825
\text{Rate 2: }8\tfrac{5}{8}\%=8+5/8=
Rate 2: 8
8
5
%=8+5/8=
\,\,8.625\%\rightarrow 0.08625
8.625%→0.08625
\text{Calculate Final Amount for Aubree}
Calculate Final Amount for Aubree
\overline{\phantom{\text{Calculate Final Amount for Aubree}}}
Calculate Final Amount for Aubree
\text{Compounded Monthly:}
Compounded Monthly:
A=P\left(1+\frac{r}{n}\right)^{nt}
A=P(1+
n
r
)
nt
P=27000\hspace{35px}r=0.0825\hspace{35px}t=20\hspace{35px}n=12
P=27000r=0.0825t=20n=12
A=27000\left(1+\frac{0.0825}{12}\right)^{12(20)}
A=27000(1+
12
0.0825
)
12(20)
A=27000(1.006875)^{240}
A=27000(1.006875)
240
A=139796.9278
A=139796.9278
\text{Calculate Final Amount for Addison}
Calculate Final Amount for Addison
\overline{\phantom{\text{Calculate Final Amount for Addison}}}
Calculate Final Amount for Addison
\text{Compounded Continuously:}
Compounded Continuously:
A=Pe^{rt}
A=Pe
rt
P=27000\hspace{35px}r=0.08625\hspace{35px}t=20
P=27000r=0.08625t=20
A=27000e^{0.08625(20)}
A=27000e
0.08625(20)
A=27000e^{1.725}
A=27000e
1.725
A=151538.0678
A=151538.0678
\text{How much more money Addison has:}
How much more money Addison has:
151538.0678-139796.9278
151538.0678−139796.9278
a(3x - 8) = b - 18x
Find the value of a
find the value of b
Explain how the value of a and b you got makes the equation true
Step-by-step explanation:
a(3x-8)=b-18x
TRANSPOSE
a(3x +18x)=b+8
a(21x)=b+8
help please
Marcie heated a beaker of water in science class. The scatter plot shows the temperature (y), in degrees Celsius, of the water based on the number of minutes (x) she heated the water.
Part A: The line of best fit for this data is
y = 5.3x + 23. Use this equation to make a conjecture about the temperature of the water in the beaker if heated for 6 minutes.
A.
The water will be about 71⁰C.
B.
The water will be about 55⁰C.
C.
The water will be about 32⁰C.
D.
The water will be about 50⁰C.
Part B: What is the y-intercept in the line of best fit? What does the y-intercept represent in the scatter plot?
A.
5.3; the amount the temperature increases each minute
B.
5.3; the temperature of the water before it is heated
C.
23; the amount the temperature increases each minute
D.
23; the temperature of the water before it is heated
Answer:
Part AGiven function
y = 5.3x + 23The value of y at x = 6:
y = 5.3*6 + 23 = 54.8° CThe closest choice is :
B. The water will be about 55⁰CPart BThe y-intercept is the value of y when x = 0
y = 5.3*0 + 23 = 23° CThis is the initial temperature at zero minute time, before heating is applied.
Correct choice is:
D. 23; the temperature of the water before it is heatedIf x = 4, y = 3, z = -5, then evaluate: z - z + x - y
1/2x+45 what is the answer to the problem
a little helps? frvvrfew3
Answer:
Step-by-step explanation:
x ≤ 165
Hope that helps!
Sara's mother has bought 90 lollipops and 105 pencils for goody bags for Sara's birthday. What is the largest number of goody bags that Sara's mother can make so that each goody bag has the same number of lollipops and the same number of pencils?
All lollipops and pencils should be used for the goody bags.
Answer:
90 because you have one lollipop in each bag and then your will have 15 dollars left
Step-by-step explanation:
what is the value of y in the triangle
Answer:
y ≈ 6.7
Step-by-step explanation:
Using the sine ratio in the right triangle
sin26.5° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{15}[/tex] ( multiply both sides by 15 )
15 × sin26.5° = y , then
y ≈ 6.7 ( to 1 dec. place )
PLEASEE HELP MEEE I DONT UNDERSTAND IT
which expression is equivalent to 189 1/5 -(-22 2/5)-(-40 1/5),
Answer:
[tex]251 \frac{4}{5}[/tex] or [tex]\frac{1259}{5}[/tex]
Draw BC that divides ABD
into two smaller angles.
Measure each angle. Solve
this problem any way you
choose.
Answer:
Attached below is the missing figure
answer : ∠ABD = ∠AbC + ∠ CbD
Step-by-step explanation:
when Line BC is drawn to divide ∠ABD equally
solving each angle :
∠ABD > ∠AbC also angle
∠ABD > ∠ CbD
∴ ∠ABD = ∠AbC + ∠ CbD
assuming ∠B = 60°
therefore ∠b = 60 / 30 = 30°
Each day Gianna practices penalty kicks with her older brother as the goalie. Yesterday she made 18/24 of her penalty kicks. Today she plans on shooting 36 penalty kicks. How many penalty kicks would Gianna have to make to successfully shoot an equivalent fraction as yesterday?
Answer: 27
Step-by-step explanation:
Since we are informed that Gianna practices penalty kicks and that she made 18/24 of her penalty kicks yesterday, this will be converted to its simplest form which will be:
= 18/24 = 3/4 .
If she plans on shooting 36 penalty kicks, the number of penalty kicks that Gianna would have to make to successfully shoot an equivalent fraction as yesterday will be:
= 3/4 × 36
= 3 × 9
= 27 penalty kicks.
Find the volume of this composite figure.
[?] cubic centimeters
2 cm
2 cm
2 cm
2 cm
5 cm
5 cm
11 cm
Answer:291
Step-by-step explanation:
Whereas the basic formula for the area of a rectangular shape is length × width, the basic formula for volume is length × width × height.
hoped this helped.
A toy train set has a circular track piece. The inner radius of the piece is 6 cm. One sector of the track has an arc length of 33 cm on the inside and 55 cm on the outside. What is the width of the track?
Answer:7cm difference
Step-by-step explanation:when the circumference is 55 the diameter is 17 when the circumference is 33 the diameter is 10
17-10=7
Answer:4
Step-by-step explanation:
-6x^2-5x-5=
−6x
2
−5x−5=
\,\,-4x^2
−4x
2
Answer:
what is the question? it's not clear
whats the area of this square help me, please
Answer:
The area is 36m^2
Step-by-step explanation:
6×6=36
Answer:
6 x 6 = 12
Step-by-step explanation:
area is length x width and all sides on a square are congruent ( so all of the sides are 6)
. Write an equation in slope-intercept form that shows the cost y for flowers for x number
of arrangements.
ok
Answer:
He placed his most loyal subjects in government jobs. He developed civil service exams to reduce corruption. He enforced strict rules for workers to ensure job effectiveness.
Answer:
ahh
Step-by-step explanation:
Explain relationship between x # 2 and the factor x - 2.
Answer:
x#2 and x-2 is the same
Step-by-step explanation:
Here is a triangular prism.
A triangular prism, the triangle has base 6 centimeters, sides 5 centimeters each, and height 4 centimeters perpendicular to the 6 centimeter base. The prism has height 10 centimeters.
What is the volume of the prism, in cubic centimeters?
Which data set has a variation, or mean absolute deviation, similar to the data
set in the given dot plot?
Answer:
d
Step-by-step explanation:
I took the test .......................
In figure find the value of x triangle PQR
20 POINTSSSS
Answer:
Divide
Step-by-step explanation:
AB is a diameter in a circle whose centre is the origin where A =(2,0) then B=
Answer:
(-2,0)
Step-by-step explanation:
Solve for x. Round your answer to the nearest tenth (0.1)
Answer:
[tex]x\approx 7.0[/tex]
Step-by-step explanation:
Since we are given a right triangle, we can use right trigonometric ratios.
x is the opposite side to our angle. 10 is the adjacent side to it. Thus, we can use the tangent ratio:
[tex]\displaystyle \tan(\theta^\circ)=\frac{\text{opposite}}{\text{adjacent}}[/tex]
Substitute:
[tex]\displaystyle \tan(35^\circ)=\frac{x}{10}[/tex]
Solve for x:
[tex]x=10\tan(35^\circ)[/tex]
Use a calculator:
[tex]x=7.0020...\approx 7.0[/tex]
x=7 yards
Answer:
Solution Given:
Opposite = x
base=10yards
and angle is 35°
we know that
relationship between opposite and base is given by Tan angle
so
Tan 35°= opposite/base
Tan 35°*10=x
x= 7.002
x≈7 yards
Write the sentence as an equation.
35 is equal to 92 less than c
Find the gradient for y= 1/4x-2
Answer:
1/4
Step-by-step explanation:
comparing with y=mx+c