If Acot theta + Bcot theta =4 and
Bcot theta + Acot theta = q, then p^2-q^2=? .
(Please Answer Quickly!!! I will mark you as Brainliest)

Answers

Answer 1

Answer is: B

Step-by-step explanation: correct answer is B

b  

2

−a  

2

 

Given, acotθ+bcscθ=p

           bcotθ+acscθ=q

⇒p  

2

−q  

2

=(p−q)(p+q)

                   =[acotθ+bcscθ−bcotθ−acscθ][acotθ+bcscθ+bcotθ+acscθ]

                   =[cotθ(a−b)−cscθ(a−b)][cotθ(a+b)+cscθ(a+b)]

                   =(a−b)(cotθ−cscθ)(a+b)(cotθ+cscθ)

                   =(a  

2

−b  

2

)(cot  

2

θ−csc  

2

θ)

                   =(−1)(a  

2

−b  

2

)[∵csc  

2

θ−cot  

2

θ=1]

                   =(b  

2

−a  

2

)


Related Questions

integers
[tex]18 \div ( - 9) = [/tex]
[tex] - 10 \div 2 = [/tex]
[tex] - 2 + ( - 6) = [/tex]
[tex] - 8 - 4 = [/tex]
[tex]( - 2 \times - 12) \div (18 \div - 9 = [/tex]
[tex](120 - 30) \div ( - 42 - 3) = [/tex]
[tex]1000 \div (125 \times - 2) = [/tex]
[tex](5 - 30) \div ( 8 - 3) = [/tex]
[tex]12 \div (4 - 8) = [/tex]


Answers

(1) 18÷(-9)= -2(2) -10÷2= -5(3) -2+(-6)= -2-6= -8(4) -8-4= -12(5) (-2×-12)÷(18÷9)= 24÷2= 12(6) (120-30)÷(-42-3)= 90÷(-45)= -2(7) 1000÷(125×-2)=1000÷(-250)= -4(8) (5-30)÷(8-3)= -25÷5= -5(9) 12÷(4-8)=12÷(-4)= -3

please mark this answer as brainlist


write x²-y² in factorize form.
write (p+p) ²in expanded form. ​

Answers

Answer:

(x-y)^2

p^2+p^2

Step-by-step explanation:

^2 means square

Answer:

see explanation

Step-by-step explanation:

x² - y² ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , then

x² - y²

= (x - y)(x + y)

------------------------------

(p + p)²

= (2p)²

= 2p × 2p

= 4p²

Please help: 6m - m = 5/6(6m - 10)

Will mark brainliest!!

Answers

Answer:

No solution.

Step-by-step explanation:

[tex]6m-m=\frac{5}{6}(6m-10)\\5m=5m-\frac{25}{3}\\0\neq -\frac{25}{3}[/tex]

Therefore, there is no solution.

convert six yard to feet

Answers

Answer:

18 feet

Step-by-step explanation:

To convert : multiply the length value by 3

=> 6 x 3

=> 18 feet

NEED some HElp please
Explain why the amount of money in the account at the end of the first year is given by the formula with n as the exponent:

P = P∨0 (1 + r/n)^n

Answers

Answer:

Is this answer correct.Does the anwer help you

If 12 out of 30 fruits are oranges, how many oranges fruits will there be per 100 fruits total?​

Answers

Answer:

40 oranges are there in 100 fruites.

Can u help solve this

Answers

Answer:

Sure:)! the answer is-487.5

Step-by-step explanation:

1.3x3xr^31.3x3=3.93.9r^3r=55x5x5=1253.9x125=487.5

As said in the problem pie=3 as determined in the problem. Hence, the answer is 487.5

Hope this helps :)!

Step-by-step explanation:

[tex]volume = \frac{4}{3} \pi \: {r}^{3} \\ = here\pi = 3 \\ then \: v = \frac{4}{3} \times 3 \times {5}^{3} \\ = 4 \times 125 \\ = 500 {in}^{3} \\ thank \: you[/tex]

The numbers 8,x,9 and 36 are in proportion.Find x​

Answers

If you can give the proportion then it would be better.

I am asuming

8:x::9:36

Then 8:x::1:4

So x = 32

Answered by Gauthmath must click thanks and mark brainliest

Answer:

x = 32

Step-by-step explanation:

[tex]\frac{8}{x}[/tex] = [tex]\frac{9}{36}[/tex] = [tex]\frac{1}{4}[/tex] ( cross- multiply )

x = 8 × 4 = 32

if you have 500 dollars and spend 20 every week then what would be the slope explain

Answers

Answer:

y=-20m+500

Step-by-step explanation:

Find the area of the shaded region. Round your answer to the nearest hundredth.

Answers

Answer:

Step-by-step explanation:

The formula for finding the area of a pentagon(regular) given 1 side is

A = [tex]\frac{1}{4}\sqrt{5(5+2\sqrt{5})}s^{2}\)[/tex]

s (the side) = 12

Area = [tex]\frac{1}{4}\sqrt{5(5+2\sqrt{5})}12^{2}\)[/tex]

Area = [tex]\frac{1}{4}\sqrt{5(5+2\sqrt{5})}144\)[/tex]

Area = sqrt(5(5 + 2*2.2361) * 36

Area = sqrt(5( 5 + 4.4721)) * 36

Area = sqrt(5*9.4721) * 36

Area = sqrt(47.3606) * 36

Area = 6.882 * 36

Area = 247.7485

The area of the circle = pi r*2 but we don't have r.

If you know any trig, the formula for the radius of the circle is

R = s/(2*sin(180)/n)     n = 5 because you are using a 5 sided figure.

R = 12/(2*sin(180/5)

R = 12/2* sin(36)

R = 6 / sin(36)

R = 10.207

So the area of the circle is pi * R^2

Area = 3.14 * 10.2078^2

Area = 327.1854

The area of the shaded part is the difference between the 2 areas we found

Answer: 327.1854 -  247.7485

Answer: 79.44

Find the value of x for which (4/5)-4 X(4/5)-7 = (4/5)2x-1

Answers

Answer:

0.8 -4*0.8-7=0.8*2x-1

0.8-3.2-7=1.6x-1

0.8-10.2+1=1.6x

1.8-10.2=x1.6

-8.4=x 1.6

x= -8.4 / 1.6

x= - 5.25

Urgently need help step by step explanation needed

Answers

Answer:

p=8

Step-by-step explanation:

-5log(p+1)+2=-8

-5log(p+1)=-10

log(p+1)=2

p+1=9, p=8

please answer algebra question I put it into a calculator and it didn’t work 4x-5=4(x-2)+3

Answers

Answer:

solving for X it would be (-infinity ♾️, +infinity ♾️) or all real numbers

Simplify the following expression: 5(3x) - 3(7x - 2)
�� 6x + 6 �� 36x + 6
�� 6 - 6x �� 6 - 36x

Answers

Answer:

The answer is in the screenshot -6x-6

Step-by-step explanation:

Simplify: squrt 18x⁷

Answers

Answer:

3x^3 ⋅ √2x

Step-by-step explanation:

m. Proportions
1) Write a proportion for the situation, then solve the
proportion to answer the question.
nation:
a. A 6 foot high fence casts a 7 foot shadow.
Standing beside the fence is a tree that casts a
31.5 foot shadow. How tall is the tree?

Answers

Answer:

height of tree is 27 ft

Step-by-step explanation:

The corresponding parts of the problem are in proportion

let h be the height of the tree , then

[tex]\frac{6}{h}[/tex] = [tex]\frac{7}{31.5}[/tex] ( cross- multiply )

7h = 189 ( divide both sides by 7 )

h = 27

Height of tree is 27 feet

Find the surface area of the composite figure

Answers

Answer: SA = 644 cm²

Step-by-step explanation:

STEP ONE: Find the surface area of the smaller rectangle (green)

There are in total 5 sides because one of the sides is not shown on the surface level.

Upper base = 3 × 3 = 9 cm²

4 sides = 3 × 8 × 4 = 96 cm²

Total = 9 + 96 = 105 cm²

STEP TWO: Find the surface area of the larger rectangle (orange)

There are in total 5 whole sides with one side covered by the base of the smaller rectangle (green) which should later be subtracted.

Front and back = 7 × 10 × 2 = 140 cm²

Left and right = 7 × 12 × 2 = 168 cm²

Lower base = 10 × 12 = 120 cm²

Upper base = 10 × 12 - 3 × 3 = 111 cm²

Total = 140 + 168 + 120 + 111 = 539 cm²

STEP THREE: Find the total surface area

SA = Green + Orange = 105 + 539 = 644 cm²

Hope this helps!! :)

Please let me know if you have any questions

The football team loses 5 yards on first down.
a. Write an integer to represent this situation.

Answers

Answer:

-5

Step-by-step explanation:

since it is a lose, it is represented by a negative sign.

Sandra is 5 years old. When she asked her father about his age, he gave her this answer. "When you are my age, I will be 67." How old is her dad?​

Answers

Step-by-step explanation:

Her father is 34 years old

solve for x on the diagram below

Answers

Answer:

20 is the answer

Step-by-step explanation:

x+3x+10=90(right angle triangle)

4x=90-10

x=80/4

x=20°

Answer:

x = 20

Step-by-step explanation:

Based on the square indication at the corner of the angle, we can assume it's a right angle, so 90°. This means that x + 3x + 10 = 90. Solve it like any algebraic equation, isolating x. add x to 3x + 10, this would net you 4x + 10 = 90. Subtract 10 on both sides of the equation to further isolate x, meaning 4x = 80. Simplify this, dividing 4 on both sides, meaning x = 20.

i need help anybody ?

Answers

Answer and Step-by-step explanation:

Simply use the Pythagorean Theorem to solve.

The Pythagorean Theorem is used to solve for a side in right triangles.

[tex]A^{2} +B^{2}= C^{2}[/tex]

Plug the sides values into the equation.

[tex]A^{2} + 13^2 = 20^2\\\\A^2 + 169 = 400\\\\A^2 = 231\\\\A = 15.1987[/tex]<- This is the answer.

#teamtrees #PAW (Plant And Water)

1. write it on a piece of paper

Answers

[tex]\\ \sf\longmapsto 1\dfrac{1}{2}+2\dfrac{3}{4}[/tex]

[tex]\\ \sf\longmapsto \dfrac{3}{2}+\dfrac{11}{4}[/tex]

[tex]\\ \sf\longmapsto \dfrac{6+11}{4}[/tex]

[tex]\\ \sf\longmapsto \dfrac{17}{4}[/tex]

2:-

[tex]\\ \sf\longmapsto 4\dfrac{3}{7}+6\dfrac{1}{5}[/tex]

[tex]\\ \sf\longmapsto \dfrac{31}{7}+\dfrac{31}{5}[/tex]

[tex]\\ \sf\longmapsto \dfrac{155+225}{35}[/tex]

[tex]\\ \sf\longmapsto \dfrac{380}{35}[/tex]

[tex]\\ \sf\longmapsto 12[/tex]

3:-

[tex]\\ \sf\longmapsto 4\dfrac{2}{5}+5\dfrac{2}{6}[/tex]

[tex]\\ \sf\longmapsto \dfrac{22}{5}+\dfrac{32}{6}[/tex]

[tex]\\ \sf\longmapsto \dfrac{132+160}{30}[/tex]

[tex]\\ \sf\longmapsto \dfrac{292}{30}[/tex]

4:-

[tex]\\ \sf\longmapsto 3\dfrac{7}{7}+3\dfrac{1}{3}[/tex]

[tex]\\ \sf\longmapsto \dfrac{28}{7}+\dfrac{10}{3}[/tex]

[tex]\\ \sf\longmapsto 4+\dfrac{10}{3}[/tex]

[tex]\\ \sf\longmapsto \dfrac{12+10}{3}[/tex]

[tex]\\ \sf\longmapsto \dfrac{22}{3}[/tex]

1.

[tex] \bf \large \longrightarrow \: \: 1 \frac{1}{2} \: + \: 2 \frac{3}{4} \: = \: \\ [/tex]

[tex] \bf \large \longrightarrow \: \: \frac{3}{2} \: + \: \frac{11}{4} \\ [/tex]

[tex] \bf \large \longrightarrow \: \: \frac{6 \: + \:11 }{4} \\ [/tex]

[tex] \bf \large \longrightarrow \: \: \frac{17}{4} \\ [/tex]

2.

[tex]\bf \large \longrightarrow \: \: 4 \frac{3}{7} \: + \: 6 \frac{1}{5} \\ [/tex]

[tex]\bf \large \longrightarrow \: \: \frac{31}{7} \: + \: \frac{31}{5} \\ [/tex]

[tex]\bf \large \longrightarrow \: \: \frac{155 \: + \: 217}{35} \\ [/tex]

[tex]\bf \large \longrightarrow \: \: \frac{372}{35} \\ [/tex]

3.

[tex]\bf \large \longrightarrow \: \: 4 \frac{2}{5} \: + \: 5 \frac{2}{6} \\ [/tex]

[tex]\bf \large \longrightarrow \: \: \frac{22}{5} \: + \: \frac{32}{6} \\ [/tex]

[tex]\bf \large \longrightarrow \: \: \frac{132 \: + \: 160}{30} \\ [/tex]

[tex]\bf \large \longrightarrow \: \: \frac{292}{30} \\ [/tex]

4.

[tex]\bf \large \longrightarrow \: \: 3 \frac{7}{7} \: + \: 3 \frac{1}{3} \\ [/tex]

[tex]\bf \large \longrightarrow \: \: \frac{28}{7} \: + \: \frac{10}{3} \\ [/tex]

[tex]\bf \large \longrightarrow \: \: \cancel\frac{28 ^{4} }{7 \: ^{1} } \: + \: \frac{10}{3} \\ [/tex]

[tex]\bf \large \longrightarrow \: \: \frac{4}{1} \: + \: \frac{10}{3} \\ [/tex]

[tex]\bf \large \longrightarrow \: \: \frac{12 \: + \: 10}{3} \\ [/tex]

[tex]\bf \large \longrightarrow \: \: \frac{22}{3} \\ [/tex]

A regular square pyramid has a slant height of 5 in and a base area of 49 in2. Find the surface area of the pyramid. ------------------------------------------------------------------------------------------- 171.5 square inches 70 square inches 119 square inches 245 square inches

Answers

Answer:

C: 119 square inches

Step-by-step explanation:

We are given;

Slant height; L = 5 in

Base area; B = 49 in²

Since it's a square pyramid, the base portion has a square shape.

Thus, area of base = x²

Where x is a side of the square.

Thus;

x² = 49

x = √49

x = 7

Perimeter of base = 7 × 4 = 28 in

Area of pyramid = ½PL + B

Plugging in the relevant values;

Area of pyramid = (½ × 28 × 5) + 49

Area of pyramid = 119 in²

In a random sample of 190 people, 151 said that they watched educational television. Find the 90% confidence interval of the true proportion of people who watched educational television. Round intermediate answers to at least five decimal places. Round your final answers to at least three decimal places.

Answers

Answer:

(0.7465 , 0.8429 )

Step-by-step explanation:

Confidence Level - "P" values  

90% 1.645

Confidence Interval - "P" values  

(0.7465 , 0.8429 )  

I will be marking brainliest please help me with these questions.

Answers

Answer/Step-by-step explanation:

1. To find the area of the shaded region, you'd find the area of the white rectangular shape, next, find the area of the whole triangular shape, then find the difference of their areas to get the area of the shaded region. Thus, the formula to use would be:

Area of shaded region = area of triangle - area of rectangle

Area of shaded region = ½*base*height - length*width

1. a. Volume of triangular prism = area of triangular base * height of prism

Volume of triangular prism = ½bh * H

Where,

b = 6 m

h = 4 m

H = 8 m

Substitute

Volume of prism = ½*6*4*8

Volume of prism = 96 m³

b. Volume of sphere = ⁴/3πr³

Where,

r = 9 cm

Substitute

Volume = ⁴/3*π*9³

Volume = ⁴/3*π*729

Volume ≈ 3,053.6 cm³ (nearest tenth)

2. Use Pythagorean theorem to find the height of the cone

radius of the cone (r) = ½(16) = 8 cm

Slant height (l) = 11 cm

height (h) = ?

Using Pythagorean theorem, we have:

h = √(l² - r²)

Substitute

h = √(11² - 8²)

h = √(57)

h ≈ 7.5 cm (nearest tenth)

b. Volume of the cone = ⅓πr²h

where,

r = 8 cm

h = 7.5 cm

Volume = ⅓*π*8²*7.5

Volume = 502.7 cm³ (nearest tenth)

When leaving a town, a car accelerates from 30 kmh-1 to 60 kmh-1 in 5 s. Assuming the
acceleration is constant, find the distance travelled in this time.
A. 6 m
B. 62.5 m
C. 41.7 m
D. 20.8 m

Answers

Answer:

B .62.5 m

Step-by-step explanation:

convert Kmh-1 in to ms-1

30 Kmh-1 = (30×1000) ÷3600 = 8.3ms-1

60 Kmh-1 = (60×1000) ÷3600 = 16.6 ms-1

acceleration = (16.6 - 8.3) ÷ 5 = 1.66 ms-2

V^2 = U^2 +2aS

(16.6)^2 = (8.3)^2 + 2×1.66 ×S

S = 62.5 m

PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!

Answers

Answer: will be A

Step-by-step explanation:

The most reasonable answer would be A

What is the expected value?

Answers

Answer:

2.1

Step-by-step explanation:

The expected value of a probability is given by the formula:

E(x) = Σxp(x)

Therefore from the table showing the winnings of a game, the expected value of the probability distribution is:

E(x) = Σxp(x) = (0 * 0.5) + (2 * 0.2) + (4 * 0.15) + (6 * 0.1) + (10 * 0.05)

E(x) = 0 + 0.4 + 0.6 + 0.6 + 0.5 = 2.1

Hence we can conclude that the expected value of the winnings of the game is 2.1.

PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
The median of the lower half of the data set is the _____________.
A. Third quartile
B. First quartile
C. Fourth quartile
D. Second quartile

Answers

Answer:

B. First quartile

Step-by-step explanation:

The first quartile is the first 25% of a line graph, and the median of the lower half of a data set would be the median of the median, which means it would split the graph at 25%

provisions for 630 men to last for 25 days. How many men must be transferred to another camp so that the food lasts for 30 days?​

Answers

Answer:

105

Step-by-step explanation:

25 days = Food for 630 men

30 days = x           (Inverse variation)

30 * x = 630 * 25

x = 630 * 25/30

  = 21 * 25

  = 525 men.

630 - 525 = 105 men.

Therefore, 105 men must be transferred to another camp so that the food lasts for 30 days.

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