Answers
Answer:
Given expression is [tex]\frac{1}{\text{cosec}A-1}-\frac{1}{\text{cosecA+1}}[/tex] = 2tan²A
We have to prove this identity.
[tex]\frac{1}{\text{cosec}A-1}-\frac{1}{\text{cosecA+1}}=\frac{(\text{cosecA+1})-(\text{cosecA-1})}{(\text{cosecA-1})(\text{cosecA+1})}[/tex]
= [tex]\frac{(\text{cosecA}-\text{cosecA})+(1+1)}{cosec^2A-1}[/tex]
= [tex]\frac{2}{cosec^{2}A-1}[/tex]
= [tex]\frac{2}{cot^{2}A}[/tex] [From the identity, (cosec²A - 1) = cot²A]
= 2tan²A [From the identity, cotA = [tex]\frac{1}{\text{tan}A}[/tex]]
Hence the given equation is proved.
Related Questions
7x + 2 = -19 (b) 3x - 1/3 = 5 (c) 5x - 4 = 21 (d) -7x = 21 (e) 18 - 7x = -3 (f) 3(x + 4) = 21 (g) 3x - 9 = 5x - 3 (h) 4x + 6 - 7x + 9 = 18 (i) - 4/9 x = - 36 (j) -7/8x - 6 = 8 can any please elp me find the variables in the question
Answers
Answer:
Step-by-step explanation:
a)7x + 2 = -19 {subtract 2 from both sides}
7x + 2 - 2 = -19 - 2
7x = -21 {Divide both sides by 7}
7x/7 = -21/7
x = -3
b) 3x - 1/3 = 5
3x - 1/3 +1/3 = 5 + 1/3 {Add 1/3 to both sides}
3x =15/3 + 1/3
3x =16/3
3x/3 = 16/3*3 {Divide both sides by 3}
x =16/9
x =1 7/9
c) 5x - 4 = 21
5x -4 + 4 = 21 +4 {Add 4 to both sides}
5x = 25
5x/5 = 25/5 {Divide both sides by 5}
x = 5
d) -7x = 21 {Divide both sides by -7}
-7x/-7 = 21/-7
x = -3
e) 18 - 7x = -3
18 - 7x - 18 = -3 - 18 {Subtract 18 from both sides}
-7x = -21 {Divide both sides by -7}
-7x/-7 = -21/-7
x = 3
f) 3(x+4) = 21 {use distributive property}
3x + 3*4 = 21
3x + 12 = 21
3x + 12 - 12 = 21 - 12 {Subtract 12 from both sides}
3x = 9 {Divide both sides by 3}
3x/3 = 9/3
x = 3
g) 3x - 9 = 5x - 3 {add 9 to both sides}
3x - 9 + 9 = 5x - 3 + 9
3x = 5x + 6
3x - 5x = 5x + 6 - 5x { subtract 5x form both sides}
-2x = 6 {Divide both sides by -2}
-2x/-2 = 6/-2
x = -3
h) 4x + 6 - 7x + 9 = 18 {Add the like terms}
-3x + 15 = 18 {Subtract 15 from both sides}
-3x + 15 -15 = 18 - 15
-3x = 3 {Divide both sides by -3}
-3x/-3 = 3/-3
x = -1
[tex]i) \frac{-4}{9}x = -36[/tex]
Multiply both sides by 9
[tex]9*\frac{-4}{9}x =9*-36[/tex]
-4x = -324 {Divide both sides by -4}
-4x/-4 = -324/-4
x = -81
[tex]j)\frac{-7}{8}x - 6 = 8[/tex] {Add 6 to both sides}
[tex]\frac{-7}{8}x-6+6=8+6\\\\\frac{-7}{8}x=14\\[/tex] {Multiply both sides by 8}
[tex]\frac{-7}{8}x*8=14*8\\\\-7x=14*8\\[/tex] {Divide both sides by -7}
[tex]\frac{-7}{-7}x=\frac{14*8}{-7}[/tex]
x =-2*8
x = -16
Sin (7 pi/6) = ____?? Help
Answers
Answer:
-0.5 or -1/2 or A
Step-by-step explanation:
180 degrees is Pi radians. To find out what the measure is in the paranthesees, divide 180 by 6 and get 30. Now multiply it by 7 to get 210. The question is asking for the sin(210). The sin of 210 is -0.5
You are driving to visit a friend in another state who lives 440 miles away. You are driving 55 miles per hour and have already driven 275 miles. Write and solve an equation to find how much longer in hours you must drive to reach your destination. A. 55h + 275 = 440 ; h=3 B.55h - 275 = 440 ; h= 13 C.440h -275 = 55 ; h =0.75 D. 55h +275h = 440 ; h=1.3
Answers
Answer:
A. 55h + 275 = 440; h=3
Step-by-step explanation:
Since all answer choices have a different H= , finding how many hours you have left to drive will give you the right answer.
You've already driven 275 miles in your 440 mile trio so you can subtract the 275 to find out how much you will still need to drive.
440 - 275 = 165
You already know that you are driving at 55 mph so divide 165 by 55 and the answer is three.
Option A was the only answer choice which listed h=3 so that is the correct answer.
Suppose that for some function g,
g(x+4)= 7x + 2. Find g(-3).
Help i don’t understand
Answers
-21
-21 + 2
-19
What is the value of the expression i To the power of 1 times I to the power of 2 times I to the power of 3 times I to the power of 4
Answers
Answer:
-1
Step-by-step explanation:
[tex]i^1\cdot i^2\cdot i^3\cdot i^4= \\\\i^{1+2+3+4}= \\\\i^{10}= \\\\-1[/tex]
Hope this helps!
Find the area of the compound shapes below !Please help
Answers
Answer:
86cm
Step-by-step explanation:
Answer:
Step-by-step explanation:
the first figure is rectangle , so
length = 15cm, breadth = 6cm
therefore area = l * b = 15*6 = 90cm^2
second figure is also a rectangle so,
length = 12+6 =18 cm ( or 9+9) , breadth = 9cm
therefore area = l*b =18*9 = 162cm^2
third figure is a semicircle , so
d = 11+9 = 20 cm , r = d/2 =20/2 =10cm
area of semicircle = [tex]1/2[/tex] * [tex]\pi * r^2\\[/tex]
=1/2*22/7 *10*10
=1100/7 = 157 1/7 cm^2
if you add all the areas then you will get the requires area
hope it helps you
Ricky Major
3:05 AM (0 minutes ago)
to me
Fred is planning a fundraiser where he will collect $4.50 for every mile he runs. He will be running on a typical track, that has two straight lengths of 300 feet each, and two curved parts that are in the shape of semicircles with 200 foot diameters
He runs around the track exactly 15 times. To the nearest cent, how much money did he collect?
Answers
Answer:
Step-by-step explanation:
The diameter of each curved path is 200 feet. Since the two curved semi circular paths are equal, they would form a circle. It means that the distance around the two semi circular paths would be the circumference of the circle. Formula for determining the circumference of the circle is π × diameter. It becomes
200 × 3.14 = 628 feet
Total distance around the track would be
300 + 300 + 628 = 1228 feet
5280 feet = 1 mile
1228 feet = 1228/5280 = 0.23 mile
If he runs around the track exactly 15 times, it means that the number of miles covered is
0.23 × 15 = 3.45 miles
Since he will collect $4.50 for every mile he runs, the amount of money that he collected is
4.5 × 3.45 = $15.5
What is x? Im having trouble
Answers
Answer:
These are two secant lines meaning we can use theorem 6-17 to find the value of x: 6x + 8x times 8x = 16 times 7
14x times 8x = 112
112x^2 = 112
x^2 = 1
x = 1
Answer:
x=1
Step-by-step explanation:
(whole secant) x (external part) = (whole secant) x (external part)
(9+7) *7 = (6x+8x)*8x
16*7 = 14x*8x
112 =112 x^2
Divide by 112
112/112 = 112x^2/112
1 = x^2
Take the square root
1 =x
Maths * Henry is mixing concrete. To make concrete he needs to mix cement, sand and gravel in the ratio 4 : 3 : 1 by weight. Henry needs to make 120kg of concrete. He has 55kg of cement, 45kg of sand and 15kg of gravel. Which ingredient is Henry short of?
Answers
Answer:
His 55 kg of cement is 5 kg short of the 60 kg he needs.
Step-by-step explanation:
Let r be a ratio useful in determining how much of each ingredient Henry needs:
4/8 of the mix is cement, 3/8 is sand and 1/8 is gravel.
4/8 of the total 120 kg must then be 60 kg made up of cement;
3/8 must then be 45 kg made up of sand; and
1/8 must then be 15 kg made up of gravel
His 55 kg of cement is 5 kg short of the 60 kg he needs.
Move values into the boxes to create an equation that represents "8 times h 24."
h
8
16
24
32
Answers
Answer:
0+8
Step-by-step explanation:
add 8 each time
it is 0 because in times table if you have 8, 16 and 24 then you don't need to add it on or take away from it, so it will be 0.
I hope that helped.
The graph below shows the relationship between population density and pollution per person for 36 Japanese cities.
What is the best description of this relationship?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Positive linear association
(Choice B)
B
Negative linear association
(Choice C)
C
Nonlinear association
(Choice D)
D
No association
Graph:
Answers
Answer: D . No association
Step-by-step explanation:
The relationship between two variable is called correlation.
When two variables has positive correlation ( When one variable increases by increasing the other) then it reprsesents Positive linear association .When two variables has negative correlation ( When one variable decreases by increasing the other) then it reprsesents Negative linear association .When two variables in which change in one variable does not correspond with constant change in the other variable, then it represents Nonlinear association.If two variables are not interdependent such that if one increasing then there is no proportional change in the other variable, then we say there is no correlation.Hence, the correct option is D. No association.
Hi There. (Choice D) Is The Right Answer.
Step-by-step explanation:
Here’s a graph of a linear function. Write the equation that describes that function. Express it in slope-intercept form.
Answers
Answer:
y=1/3x-3
Step-by-step explanation:
slope = (y2-y1)/(x2-x1)
Use the two points: (0,-3) (3,-2)
slope = (-3+2)/(0-3)
slope = -1/-3 = 1/3
y intercept = -3
Equation: y=1/3x-3
Solve for x
6(x - 1) = 9(x + 2)
O x= -8
O x= -3
0 x = 3
0 x = 8
Answers
Answer:
[tex]A.x=-8[/tex]
Step-by-step explanation:
6x-9x=18+6
-3x=24
x=-8
Kelly invested her savings of $4800. she invested part in mutual funds, at 9% per year, and the rest in GIC's, at 10% per year. at the end of the year, the interest from both investments is $457. how much did she invest at each rate?
Answers
Answer:
For the 9% she invested $2,300
For the 10% she invested $2,500
Step-by-step explanation:
Let the amount invested be $x and $y in both cases respectively
Since the total invested is $4,800
This means that;
x + y = 4800 ••••••••••••(i)
Now let’s have a look at the interests.
For the 9%
Interest would be 9/100 * amount invested
= 9/100 * x = 9x/100
For the 10%, interest would be
10/100 * y = 10y/100
Adding both will give a total of 457
9x/100 + 10y/100 = 457
multiply through by 100
9x + 10y = 45700 •••••••• (ii)
From equation i, we can write x = 4800 - y
we can substitute this into the second equation
9(4800-y) + 10y = 45700
43200 -9y + 10y = 45,700
43200 + y = 45,700
y = 45,700-43,200 = $2,500
Recall
x = 4800 -y
so x = 4800 -2500 = 2300
what do the following two equations represent? 4x+2y=10 and 4x-2y=-10
Answers
they represent linear equations
The two equations, 4x + 2y = 10 and 4x - 2y = -10, represent a system of linear equations.
Why is this so?The equations are written in standard form, where x and y are variables, and the coefficients 4, 2, -10, and -2 are constants. Each equation represents a linear relationship between x and y.
The coefficients in front of x and y determine the slope of the line, and the constants on the right side of the equations determine the y-intercept.
Solving this system of equations simultaneously can determine the values of x and y that satisfy both equations, representing the point(s) where the two lines intersect, if they intersect at all.
Learn more about linear equations. at:
https://brainly.com/question/2030026
#SPJ2
The school board has approved the addition of a new sports team at your school.
The district ordered 30 team uniforms and received a bill for $2,992.50. The total included a 5% discount.
a. The school needs to place another order for two more uniforms. The company said the discount will not
apply because the discount only applies to orders of $1,000 or more. How much will the two uniforms
cost?
Answers
Answer:
210
Step-by-step explanation:
1: Part/whole=%/100
2: 100-5=95
3: 3150/30=$105 uniforms.
Answer: $210
Hope this helps.
If f(x)= 3x^2-2x+4.and g(x)= 5x^2 +6x -8find(f-g)(x)
Answers
Answer:
-2x^2-8x+12
Step-by-step explanation:
f(x)= 3x^2-2x+4
g(x)= 5x^2 +6x -8
(f-g)(x) = 3x^2-2x+4-(5x^2 +6x -8)
Distribute the minus sign
(f-g)(x) = 3x^2-2x+4-5x^2 -6x +8
Combine like terms
-2x^2-8x+12
What expression has a positive value
Answers
The proceeds of a $7,500.00, 10 percent simple discounted note for 85 days is
Answers
Answer:
7325.34
Step-by-step explanation:
PLZ HELP ME W DIS!!!
Answers
Answer:
6^8
Step-by-step explanation:
When the equation looks like this, you can multiply the exponents to give you 6^8. I think that's the kind of answer you're looking for :)
Hope this helps you!
1 3/4 x 4 1/6 whats answer
Answers
Answer:
7 7/24
Step-by-step explanation:
first put the wholes inside the fraction:
[tex]1 \frac34 = \frac44 + \frac34 = \frac74[/tex]
[tex]4 \frac16 = \frac{24}{6} + \frac16 = \frac{25}{6}[/tex]
Then multiply numerator times numerator, denominator times denominator and take out wholes again:
[tex]\frac74 \times \frac{25}{6} = \frac{7 \times 25}{4 \times 6} = \frac{175}{24} = 7 \frac{7}{24}[/tex]
I need help and I need explanation plz
Answers
Answer:
20 counters.
Step-by-step explanation:
50/200 or 1/4 of the counters have white paint on them.
That means you can expect 1/4 of the 80 counters pulled out to have white paint on them or 20 counters.
asssssapppp please need it now
Answers
Solution,
Volume of the prism= l*b*h
=1 1/2*8*2 1/2
= 3/2*8*5/2
= 30 cubic units
Hope it helps
Good luck on your assignment
Solve: [4x + 2] + 6 =0
Select one
a. no solution
b. -1 or 2
O c. 1 or-2
o d. all real numbers
Answers
Answer:
Given
Step-by-step explanation:
4x+2+6=0
4x+2=-6
4x= -6-2
4x= -8
x = -8/4
= -2
Answer:
x = -2
Step-by-step explanation:
[4x + 2] + 6 =0
Combine like terms
4x+ 8 =0
Subtract 8 from each side
4x+8-8 = 0-8
4x = -8
Divide each side by 4
4x/4 = -8/4
x = -2
Even the measure ofAngle six is 62 what is the measure of angle five
Answers
∠5 = 118
Step-by-step explanation:
If you look closely at this image, you can see that ∠6 and ∠5 together will be equal to line c.
A straight line is equal to 180 so if we do...
[tex]180-62[/tex]
= 118.
∠5 will be equal to 118.
If we go even further, because vertical angles are congruent...
∠7 = 62
∠8 = 118
Answer:
[tex] m \angle \: 6 = 118 \degree[/tex]
Step-by-step explanation:
[tex]m \angle \: 5 + m \angle \: 6 = 180 \degree.. (straight \: line \: \angle s) \\ \because \: m \angle \: 5 = 62 \degree \\ \therefore \: 62 \degree+ m \angle \: 6 = 180 \degree \\ \therefore \: m \angle \: 6 = 180 \degree - 62 \degree \\ \huge \red{ \boxed{\therefore \: m \angle \: 6 = 118 \degree}}[/tex]
Convert 11.7 cm3 into ml
Answers
Answer:
11.7
Step-by-step explanation:
1 Cubic centimeter (cm3) is equal to 1 milliliter (mL). 1 Liter is equal to 1 cubic decimeter and there are 1000 cubic centimeters in a cubic decimeter, that makes 1 cubic centimeter equals to 1 milliliter.
Внешний диаметр полого шара равен 16 см. Толщина стенок 2 см Найти
объем материала, из которого изготовлен шар.
Answers
Answer:
Внешний радиус
Тогда внутренний радиус
Объем материала равен разности объемов внешнего и внутреннего шаров, то есть
Answer:
1239.25 cm³
Step-by-step explanation:
Outer diameter 16 cm
⇒ R= 8 cm
Inner radius
⇒ r= R- 2= 6 cm
The volume of the wall of 2 cm thickness:
⇒ 4/3πR³- 4/3πr³= 4/3*3.14*(8³-6³)= 1239.25 cm³
sheena is shocking a shelf with bags of flour that weigh 5 1/4 pounds each if sheena stocks the shelf with 13 bags of flour find the combined weight of 13 bags
Answers
Answer:
[tex]68\frac{1}{4}[/tex] pounds
Step-by-step explanation:
The combined weight of 13 bags is 13 multiplied by the weight of each bag.
The weight of each bag is [tex]5\frac{1}{4}[/tex] pounds. Therefore, the weight of 13 bags is:
[tex]5\frac{1}{4} * 13\\ \\= \frac{21}{4} * 13\\[/tex]
[tex]= 68\frac{1}{4}[/tex] pounds
A gym’s membership in 2010 was 8,700. Now, it is 6,400. Which expression equals the percent of change?
Answers
Thank me later lol
is 262015 divisible between 4?
Answers
Answer:
No
Step-by-step explanation:
