Answer:
The relation is:
cosec^2(a) - cot^2(a) = 1.
Where:
cosec(x) = 1/sin(x)
cot(x) = 1/tan(x) = cos(x)/sin(x)
Let's prove this.
Ok, we know by the Pythagorean theorem, that:
r^2 = x^2 + y^2
And we have the trigonometric relations, for an angle "a" measured from the x-axis
cos(a) = x/r
sin(a) = y/r
tan(a) = y/x
Where r is the hypotenuse, x and y are the catheti.
Now, let's divide the Pythagorean theorem by y^2 in both sides to get:
(r^2/y^2) = (x^2 + y^2)/y^2
r^2/x^2 = x^2/y^2 + y^2/y^2
r^2/y^2 = 1 + x^2/y^2
(r/y)^2 = 1 + (x/y)^2
and remember that:
y/r = sin(a)
then:
r/y = 1/sin(a) = cosec(a)
(r/y)^2 = cosec^2(a)
and:
y/x = tan(a)
then:
x/y = 1/tan(a) = cot(a)
and:
(x/y)^2 = cot^2(a)
replacing these in the equation (r/y)^2 = 1 + (x/y)^2 we get:
cosec^2(a) = 1 + cot^2(a)
cosec^2(a) - cot^2(a) = 1
Need help ASAP fine the value of x. Round to the nearest tenth x=
Answer:
x = 13.5
Step-by-step explanation:
To find x, we use the sine rule
For the sine rule,
the ratio of the sides to the sine of the angle facing the side is equal for all the sides of the triangle
Thus,
x/sin 34 = 11/ sin 27
x = 11 sin 34/sin 27
x = 13.5
A recipe for punch calls for 5 parts grape soda to 2 part seltzer. If hector has 10 cups of of grape soda, how much seltzer does he need?
Answer:
assuming 10 cups it 10 parts then the answer is 4 cups of seltzer
Alexis can buy an 12-pound- bag of dog food for $10.80 or an 8-pound bag of the same dog food for $10.20. Which is the better buy?
Answer:
The 12-pound bag of dog food.
Step-by-step explanation:
To find out which is the better buy you start by divinging 10.80 by 12 and then you divide 10.20 by 8 and you get .90 cents for the 12 pound while you get 1.275 dollars. Which means the 12 pound bag is the better by because it is less money per pound than the 8 pound bag.
The ruler below shows a 7-inch segment divided into 2 equal parts. What is the length of one of those parts?
Answer:
3.5 inches
Step-by-step explanation:
HELP SND U WILL GET BRAINLISTED
for brainliest
Answer:
h=(3v)/(pi r^2)
Step-by-step explanation:
you simply have to move everything to one side.
Answer:
h = [tex]\frac{3V}{\pi r^2}[/tex]
Step-by-step explanation:
Given
V = [tex]\frac{1}{3}[/tex]πr²h ( multiply both sides by 3 to clear the fraction )
3V = πr²h ( isolate h by dividing both sides by πr² )
[tex]\frac{3V}{\pi r^2}[/tex] = h
Help pleasee! Thank uu
Answer:
The answer is the 2nd option
Step-by-step explanation:
5+5+5+5+5+5+5+5+5+5+11111111111111111111111122222222222222222222222333333333333333333333333333334444444444444444444444444455555555555555555555555555666666666666666666666666666666677777777777777777777777777788888888888888888888888888888889999999999999999999999999999991111111111111111111111111111111100000000000000000000000000000000000
Answer:
w t f
Step-by-step explanation:
Answer: Its kinda confusing lol
Step-by-step explanation:
I would help but I dont get it sorry
Berry Delicious is a popular shop that sells chocolate-covered strawberries. Last year, the shop used 9,200 kilograms of strawberries to make its treats. This year, the shop used 7,739.4 kilograms. What is the percent of decrease in the amount of strawberries used annually?
Answer:
15.9%
Step-by-step explanation:
Percent decrease formula =
(Initial value - New value/Initial value) × 100
Initial value = 9200kg
New value = 7739.4kg
Percent decrease = (9200 - 7739.4/9200) × 100
Percent decrease = (1460.6/9200) × 100
Percent decrease = 15.8760869565%
Approximately = 15.9%
The percent of decrease in the amount of strawberries used annually is 15.9%
EXPAND:
(p-2p)^3
Plz answer.
Answer:
-p^3
Step-by-step explanation:
( p - 2 p ) ^ 3
combine p and 2p to get -p
》expand (-p)^3
》(-1)^3p^3
calculate -1 to the power of 3 and get -1
and this equals -p^3
if you got a 23/25 on a quiz, what is your grade? How do you determine that?
Answer:
well 25x4=100 so multiply 23 by 4 and that would be 92 so you would have an A or 92%
A market research survey has 15 questions and will be sent to 500 people. What is the total cost to conduct the survey if it has a $1,000 base fee plus $5 per question and $2 per person surveyed?
Answer:
Total cost to conduct survey = $2075
Step-by-step explanation:
Given that:
Number of questions on survey = 15
Number of people = 500
Base fee = $1000
Per question charge = $5
Per person surveyed = $2
Let,
q be the number of questions
p be the number of people
Total cost = Base fee + 5q + 2p
Total cost = 1000 + 5(15) + 2(500)
Total cost = 1000 + 75 + 1000
Total cost = $2075
Hence,
Total cost to conduct survey = $2075
Which is a composite number 42,29,21,37
Answer:
42 and 21 are composite numbers
The perimeter of a rectangular plot of land
is 46.4m. If the width of the plot is 7.4m.
what is its length?
A. 15.8m
B. 8.8m
C. 13.6m
D. 9.2 m
Answer:
A. 15.8
Step-by-step explanation:
First the perimeter of a rectangle = 2 (L +W)
So; 46.4 = 2(L + 7.4)
46.4 = 2L + 14.8
2L = 46.4 - 14.8
2L = 31.6
L =15.8
Rico bicycles at an average speed of 15.5 miles per hour. What distance will Rico bicycle in 4.5 hours? Rico will bicycle ________ miles in 4.5 hours.
Answer:
69.75 miles
Step-by-step explanation:
15.5 miles = 1 hour
x miles = 4.5 hours
Cross product
15.5 * 4.5 = 1 * x
69.75 = x
x = 69.75 miles
Rico will bicycle 69.75 miles in 4.5 hours
Question 6
Which is the graph of y= 2x-3?
Answer:
Graph A
Step-by-step explanation:
The line is going to pass through -3 as the y intercept then you go over 4 blocks and up 3 of x
Answer:
Graph A
Step-by-step explanation:
If you take a pair of x,y coordinates from each graph and input it into the equation (y=3/4x-3), only Graph A makes the equation true.
(3y^2 – 4y + 1) +
(- y^2 + 4y – 3)
Answer:
2y^2-4y+2
Step-by-step explanation:
3y^2-4y+1-y^2+4-3
3y^2-y^2-4y+1+4-3
2y^2-4y+1+4-3
2y^2-4y+2
This is due today please help will give brainliest
Answer:
The answer for the given expression is 23 after putting the values of a,b and c.
Step-by-step explanation:
Given expression is:
[tex](\frac{2c}{a})^2-10*\frac{(b+a)}{c}[/tex]
We have to find the value of expression, when
a = -2, b = 3 and c = 5
We will put these values in the given expression and then simplify the given expression,
[tex](\frac{2*5}{-2})^2-10*\frac{3+(-2)}{5}\\\\(\frac{10}{-2})^2-10*\frac{3-2}{5}\\\\(-5)^2-10*\frac{1}{5}\\25-2\\23[/tex]
Hence,
The answer for the given expression is 23 after putting the values of a,b and c.
Work out the equation of a line which has a gradient of 1/2 and passes through the point 4,-2? Pls answer i dont know
Answer:
y-y1=m (x- x1)…………..(1)
Here m=1/2 and (x1,y1)= (4,-2)
(1) => y-4=1/2(x+2)
=> 2y-8=x+2
=> x-2y-10=0
So, equation of line is x-2y-10=0.
PLZ HELP ME I AM TIMED HELP PLZ
Answer:
c
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
If a= 11, solve for b and c (will give Brainliest ❤️)
Answer:
a = 11
b = 11
c = 11√2
It is an equilateral triangle, because to angles are equal (45°).
[tex] |a| = |b| = 11 \\ |c^{2} | = \sqrt{ {a}^{2} + {b}^{2} } \\ c = \sqrt{ {11}^{2} + {11}^{2} } \\ c = 11 \sqrt{2} [/tex]
Let x denote the number of broken pencils in a randomly selected 50-count box from a local office supply store. The variable x has the
following probability distribution:
a)
0.82; if we were to select many boxes of pencils randomly, the number of broken pencils would typically vary about 0.82 from the
mean
b)
0.31; if we were to select many boxes of pencils randomly, we would expect about 0.31, on average, to contain broken pencils
c)
0.65; if we were to select many boxes of pencils randomly, the number of broken pencils would typically vary about 0.65 from the
mean
d)
0.52; if we were to select many boxes of pencils randomly, we would expect about 0.52 to have no broken pencils
e)0.13; if we were to select many boxes of pencils randomly, we would expect about 0.13, on average, to contain broken pencils
Answer:
0.82
Step-by-step explanation:
I literally took the test
What is 271403 rounded to the nearest thousand
Answer:
271000
Step-by-step explanation:
Answer: 300,000
Step-by-step explanation:
Evelyn has a 32 ounce flavored water. She drinks 23 ounces. Enter the percentage of ounces Evelyn has left of her flavored water. Round your answer to the nearest hundredth. 10 points Your answer
Answer:
The answer is 7.36.
Step-by-step explanation:
23% of 32 = 7.36.
HELP ME RIGHT NOW GRAND PRIZE IS 10 POINTS COME ON COME ON PLEASE SJNDINKOJDEWNIOEW
Solve the system of equations using the substitution method. Make sure to check your solution.
y = 3x + 2
-4x + 4y = 16
In the blanks below, type just the number for the x-coordinate in blank 1 and just the number for the y-coordinate in blank 2.
x-coordinate:
y-coordinate:
Answer: X = 1
Y= 5
Step-by-step explanation:
Plug in y = 3x + 2 in the Y coordinate to find X
-4x + 4(3x + 2) = 16
Now you can solve for X
X = 1
Then plug in 1 in the X coordinate to find Y
-4(1)+ 4y= 16
Now you can solve for Y
Y= 5
YOUR WELCOME
What is element b31 for the question help
Answer:
the answer is A =3 ... this is the correct answer
How much is 75% of 10 liters of milk?
Answer:
1. 75% of 10 liters of milk = 0.75 * 10 liters of milk = 7.5 liters of milk
2. To find 75% of a number, multiply the number by 0.75.
Answer by mathstudent55 give credit to him/her
Answer 7.5
Step-by-step explanation:
You can find this by dividing the number by 10, for example let’s use the number 20.
you would divide 20 by 10 which is 2 and times it by 7.
This is 14.
By finding this you have found 70% of 20.
now to find 5%, i would divide 20 by 10 once again which is 2 and then i would divide it by 2 which is 1.
then you would add the 2 numbers so 14+1 to get 15 therefore 75%of 20=15
HELP!! What is the exact value of Tangent (pi/12)
A. StartFraction 1 Over 2 + StartRoot 3 EndRoot EndFraction
B. StartFraction 1 Over StartRoot 3 EndRoot EndFraction
C. StartFraction 3 Over StartRoot 3 EndRoot EndFraction
D. StartFraction 1 Over 2 minus StartRoot 3 EndRoot EndFraction
Answer:
2 - sqrt(3)
Step-by-step explanation:
Split pi/12 into two angles where the values of the six trigonometric functions are known.
tan (pi/4 - pi/6)
Apply the difference of angles identity
[tex]\frac{tan(pi/4) - tan(pi/6)}{1 + tan(pi/4)tan(pi/6)}[/tex]
tan(pi/4) = 1 , tan(pi/6) = (sqroot3)/3
Plug in and Simplify
[tex]\frac{1-\frac{\sqrt{3} }{3} }{1+1\frac{\sqrt{3} }{3} }[/tex]
[tex]\frac{\frac{3-\sqrt{3} }{3} }{\frac{3+\sqrt{3} }{3} }[/tex]
[tex]\frac{3-\sqrt{3} }{3} *\frac{3}{3+\sqrt{3} }[/tex]
[tex]\frac{3-\sqrt{3} }{3+\sqrt{3}}[/tex] Need to multiply this by [tex]\frac{3+\sqrt{3} }{3+\sqrt{3} }[/tex]
Expand and simplify numerator: [tex]\frac{6}{(3+\sqrt{3} )^{2} }[/tex]
Expand and simplify denominator: [tex]\frac{6}{12+6\sqrt{3}}[/tex]
Cancel the common factor: [tex]\frac{1}{2+\sqrt{3}}[/tex]
Answer:
D: 1/2 - √3.
Step-by-step explanation:
The Unit Circle is a circle with radius 1 that is used to determine the value of sine and cosine of any angle.
But that table do not directly give the exact value so to solve for its exact value, express π/12 as a sum or difference of two angles where the values of the six trigonometric functions are known.
tan π/12 = tangent (π/4 - π/6)
Using the the difference of angles identity we get,
tan (π/4 - π/6) = (1 - √3 / 3) / (1 + 1 x √3 / 3)
Multiply by 3,
tan (π/4 - π/6) = (3 - √3) / (3 + √3)
Multiply by 3 - √3
tangent (π/4 - π/6) = (3 - √3)(3 - √3) / (3 - √3)(3 + √3)
FOIL and simplify.
tangent (π/4 - π/6) = 9 - 6√3 + 3 / 9 -3
tangent (π/4 - π/6) = 1/2 - √3
I WILL GIVE BRAINLEST IF YOU HELP ME PLEASE
Subtract (2x - 2y) from the sum of (10x - 2y) and (-3y)
Subtract (2x - 2y) from the sum of (10x - 2y) and (-3y) is 8x -3y.
What is subtraction?Subtraction is a mathematic operation. Which is used to remove terms or objects in an expression.
The sum of (10x - 2y) and (-3y).
(10x - 2y) + (-3y),
= 10x -2y -3y
= 10x -5y
Subtract (2x - 2y) from the sum of (10x - 2y) and (-3y),
= 10x -5y - (2x - 2y)
= 8x -3y
Therefore, the expression is 8x -3y.
To learn more about the subtraction;
https://brainly.com/question/2346316
#SPJ2
Answer:
option c
Step-by-step explanation:
Answer:
its A
Step-by-step explanation:
because in the end QP go together so it either A or B and it A because thats how the triabgle goes
what is 1/2x + 8 < -4 ?
Answer:
-1/24 < x < 0
Step-by-step explanation: