Prove the identity sin^2theta x csc^2 theta = sin^2 theta + cos^2 theta 20 points!!

Answers

Answer 1

Answer:

Step-by-step explanation:

sin² Θ csc² Θ =sin² Θ + cos² Θ

sin² Θ 1/sin² Θ = sin² Θ + cos² Θ

1 = sin² Θ + cos ² Θ (this is a trig identity)


Related Questions

If area of a rhombus is 336 cm and one of its diagonal is 14 cm, find its perimeter.

Answers

Answer:

The perimeter of the Rhombus is 100 cm

Step-by-step explanation:

First of all, we will need to find the length of the other diagonal.

let’s call the diagonals p and q

Mathematically, the area of the Rhombus is;

pq/2 = Area of Rhombus.

Let’s call the missing diagonal p

So;

(p * 14)/2 = 336

14p = 672

p = 672/14

p = 48 cm

Now, we can find the perimeter of the Rhombus using these diagonals.

Mathematically;

P = 2 √(p^2 + q^2)

Substituting these values, we have;

P = 2 √(14)^2 + (48^2)

P = 2 √(2500)

P = 2 * 50

P = 100 cm

The perimeter of the rhombus is the sum of its side lengths

The perimeter of the Rhombus is 100 cm

The length of one of its diagonal is given as:

[tex]p= 14[/tex]

And the area is given as:

[tex]A = 336[/tex]

Assume the other diagonal is q.

The area of the rhombus is represented as:

[tex]A = \frac{pq}2[/tex]

So, we have:

[tex]336 = \frac{14q}2[/tex]

This gives

[tex]336 = 7q[/tex]

Divide both sides by 7

[tex]48 = q[/tex]

Rewrite as:

[tex]q = 48[/tex]

The perimeter (P) of the rhombus is calculated as:

[tex]P =2\sqrt{p^2 + q^2[/tex]

So, we have:

[tex]P =2\sqrt{48^2 + 14^2[/tex]

Evaluate the squares

[tex]P =2\sqrt{2500[/tex]

Take positive root of 2500

[tex]P =2 \times 50[/tex]

[tex]P =100[/tex]

Hence, the perimeter of the Rhombus is 100 cm

Read more about areas and perimeters at:

https://brainly.com/question/14137384

Evaluate 2^2⋅4^3=

Your answer


Answers

Answer:

256

Step-by-step explanation:

First, handle the exponent:

2²=4 (2*2=4)     and     4³=64 (4*4=16*4=64)

Now multiply those two outcomes:

4*64=256

This equation is also known as 4⁴

What is the real part of 4 - 5i

Answers

Answer:

 5i is an imaginary number

In these questions it contains two parts

real and imaginary parts . thus answer to these questions is 5i

Explanation

Complex Number is the number which contains both real and imaginary numbers i is the specified elements.  5i is an imaginary parts number and 4 is real part number.

Thus we conclude that above statement for the question is correct.

To know more about the complex number

https://brainly.com/question/20566728

The expansion of (1 + 4x)5 is​

Answers

Answer:

5+20x

Step-by-step explanation:

multiply 5 to 1 and 4x respectively

The braking distance, D, of a car is directly proportional to the square of its speed, v. When d=5, v=10
Find d when v=70​

Answers

Answer:

         d = 245

Step-by-step explanation:

d is directly proportional to the square of a speed v

d = av²

5 = a•10²

5 = 100a

a = 0.05

d = 0.05v²

d = 0.05•70²

d = 0.05•4900

d = 245

A box has a base of 12 inches by 12 inches and a height of 30 inches. What is the length of the interior diagonal of the box? Round to the nearest hundredth.

Answers

This is a problem using the Pythagorean theorem.

The square of the length required is 122 + 122 + 302 = 1188

 

The length is the square root of this number; I will leave it to you to extract the square root.

Answer:

34.47

Step-by-step explanation:

Each lap around a park is 1 1⁄5 miles. Kellyn plans to jog at least 7 1⁄2 miles at the park without doing partial laps. How many laps must Kellyn jog to meet her goal?

Answers

Answer:

25/4 laps or (6.25 laps)

Step-by-step explanation:

1 lap = 1 1/5 miles

kellyn plans to jog 7 1/2 miles

                                                      1  lap

number of laps = 7 1/2 miles x  --------------   = 25/4 laps or (6.25 laps)

                                                    1 1/5 miles

help me with guys plzzzzz

Answers

Answer:

C

Step-by-step explanation:

So the lion weighs more than the ant right?

And we wish to figure out how much greater the lion's weight is compared to the ant's weight.

So only thing we have to do is divide.

[tex]\frac{1 * 10^5}{2*10^-3} = \frac{10^5}{2*10^-3} = \frac{10^8}{2} = 50000000 = 5 * 10^7[/tex]

Answer:

5×10^7

Step-by-step explanation:

2×10^-3    1×10^5

(1×10^5)/(2×10^-3)=

5×10^7

to scheck :(2*10^-3)(5*10^7)=(1*10^5)

an inch worm is how long in general

Answers

Answer:

A inch

Step-by-step explanation:

Pls answer this urgently

Answers

Answer:

The pic there has a step by step explanation

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[tex]\frac{(3^-2)^2 * (5^2)^-3 * ( t ^-3)^2 }{( 3^-2) ^5 ( 5^3) ^-2 ( t ^-4)^3}[/tex]

[tex]= \frac{\frac{1}{1265625^t12} }{1}[/tex]

[tex]= \frac{\frac{1}{992640625^t6} }{1}[/tex]

[tex]= \frac{992640625^t6}{1265625}[/tex]

[tex]= \frac{922640625tttttt}{1265625}[/tex]

[tex]= 729t^6[/tex]

Answer : [tex]729t^6[/tex]

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What is the slope of the line? x + 3 y = 10 x+3y=10x, plus, 3, y, equals, 10 Choose 1 answer: Choose 1 answer: (Choice A) A 1 3 3 1 ​ start fraction, 1, divided by, 3, end fraction (Choice B) B 1 10 10 1 ​ start fraction, 1, divided by, 10, end fraction (Choice C) C − 1 10 − 10 1 ​ minus, start fraction, 1, divided by, 10, end fraction (Choice D) D − 1 3 − 3 1 ​

Answers

Answer:

-1/3

Step-by-step explanation:

The standard from of equation of a line written in slope-intercept format is expressed as y = mx+c where c is the slope of the line and c is the y-intercept.

Given the equation of the line x+3y = 10, to get the slope of the line, we need write he equation in standard from first by making y the subject of the formula as shown;

[tex]x+3y = 10\\\\subtract\ x \ from \ both \ sides\\\\x+3y-x = 10 -x\\\\3y = -x+10\\\\Divide \ through\ by \ 3\\\\\frac{3y}{3} = -\frac{x}{3} +\frac{10}{3} \\\\[/tex]

[tex]y = -\frac{1}{3}(x) +\frac{10}{3} \\[/tex]

Comparing the resulting equation with y = mx+c, the slope 'm' of the equation is -1/3

The slope of the line is -1/3.

the correct option is D.

To find the slope of the line given by the equation x + 3y = 10, we need to rewrite it in slope-intercept form, which is y = mx + b, where m represents the slope.

Let's rearrange the equation to solve for y:

x + 3y = 10

3y = -x + 10

y = (-1/3)x + 10/3

Comparing this equation to the slope-intercept form, we can see that the coefficient of x (-1/3) represents the slope.

Therefore, the slope of the line is -1/3.

Learn more about Slope here:

https://brainly.com/question/17158875

#SPJ6

A train moves at a speed of 90 km/hr. How far will it travel in 36 minutes?

Answers

Answer:

(90/60)*36 = 54 km

Step-by-step explanation:

If AC = 40, find the length of JK.

Answers

Answer:

JK = 24

Step-by-step explanation:

Δ BKJ and Δ BCA are similar triangles and ratios of corresponding sides are equal, that is

[tex]\frac{JK}{AC}[/tex] = [tex]\frac{BK}{BC}[/tex] , substitute values

[tex]\frac{JK}{40}[/tex] = [tex]\frac{3}{5}[/tex] ( cross- multiply )

5JK = 120 ( divide both sides by 5 )

JK = 24

the triangles are all similar, because they have proportional sides and equal angles.

if you assume the smallest, equal part of side to be x

the biggest triangle has "5 parts" so BC=5x and BK has 3 parts so BK=3x .

since they're similar, ratio of their corresponding sides is constant or equal.

[tex] {BK\over BC}={JK \over AC}[/tex]

BK/BC=3/5

and AC=40

so JK = 40*3/5=24

Between what two consecutive integers on the number line is the graph of the sum sqrt(30) + sqrt(50)?

Answers

Answer:

sqrt(30)+sqrt(50) = 12.5482933869171364     which is between   m and n    12 and 13

A principal of $2600is invested at 6.75% interest, compounded annually. How much will the investment be worth after 14 years

Answers

Answer:

$6488.19

Step-by-step explanation:

To solve this problem we use the compounded interest formula:

[tex]amount = principal(1 + (r \n))^({n}{t})[/tex]

a = $2600(1+(0.0675/1))¹*¹⁴

a = $6488.19

the cost of cementing a wall 8 feet wide and 24 feet long at 14.40 a square yard is

will mark brainlist

Answers

Answer:

$307.20

Step-by-step explanation:

8×24=192

Convert 192 square feet to square yards, which is 21.3333

Then multiple: 21.333×14.40=307.1999

Then round to the nearest hundredths

The final answer is $307.20

HELP ME PLEASE The student's in Roberto's school are painting a mural that will be 8 feet by 15 feet. First they make a scale drawing of the mural with a scale of 2 feet:5 feet. What are the length and width of the scale drawing in feet

Answers

Answer:

Length = 3.2feets ; width = 6feets

Step-by-step explanation:

Given the following :

Actual dimension of Mural:

8feets by 15feets

Scale drawing ratio of Mural :

2feets : 5feets

This means :

2 Feets on paper equals 5 Feets of actual drawing:

Therefore, with actual dimension of Length = 8feets ;

Length of scale drawing = (2/5) * 8 = 3.2feets

Actual dimension of width 15feets ;

Width of scale drawing = (2/5) * 15 = 6 Feets

Find the solutions to $x^2 + 64 = 0.$[tex]Find the solutions to $x^2 + 64 = 0.$[/tex]

Answers

Answer:

x=8i,\:x=-8i

Step-by-step explanation:

x^2+64-64=0-64

x^2=-64

x=\sqrt{-64},\:x=-\sqrt{-64}

x=8i,\:x=-8i

Please answer this question now

Answers

Answer:

54 degrees

Step-by-step explanation:

Measure of arc DCB is 125*2 = 250.

So, measure of arc BAD is 360-250 = 110.

So, measure of arc AD is 110 - 56 = 54 degrees

0.0000458 as scientific notation

Answers

Answer:

4.58 * 10 ^ -5

Step-by-step explanation:

0.0000458

Move the decimal 5 places to the right to get a number between 1 and less than 10

00004.58

That will give us an exponent of -5 ( the negative is because we moved it to the right)

4.58 * 10 ^ -5

━━━━━━━☆☆━━━━━━━

▹ Answer

4.58 * 10⁻⁵

▹ Step-by-Step Explanation

The decimal point is moved 5 times to the left, meaning the scientific notation will be negative. Therefore, the answer is 4.58 * 10⁻⁵.

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Suppose you roll a fair six-sided die 25 times. What is the probability that you roll 5 or more 6’s on that die?

A. 0.3883

B. 0.5937

C. 0.5

D. 0.4063

Answers

Answer:

D. P(5+ 6's) = 0.4063

Step-by-step explanation:

Binomial distribution.

For the distribution to be applicable, the experiment must

1. Have a know and constant number of trials

2. Probability of success of each trial remains constant (and known if available)

3. Each trial is a Bernoulli trial, i.e. with only two outcomes, success or failure.

4. Independence between trials.

Let  

n = number of trials  = 25

p = probability of success of each trial  = 1 / 6

x = number of successes  (0 ≤ x ≤ n)  = 5

C(n,x) = number of combinations of picking x identical objects out of n

Applying binomial distribution

P(x,n) = probability of x successes in an experiment of n trials.

= C(n,x) * p^x * (1-p)^(n-x)

For n = 25 trials with probability of success (roll a 6) = 1/6

and x = 5,6,7,8,...25

It is easier to calculate the complement by

P(5+ 6's) = 1 - P(<5 6's)

= 1 - ( P(0,25) + P(1,25) + P(2,25) + P(3,25) + P(4,25) )

1- (

    P(0,25) = C(25,0) * (1/6)^0 * (5/6)^25 = 0.0104825960103961

    P(1,25) = C(25,1) * (1/6)^1 * (5/6)^24 = 0.05241298005198051

     P(2,25) = C(25,2) * (1/6)^2 * (5/6)^23 = 0.1257911521247532

    P(3,25) = C(25,3) * (1/6)^3 * (5/6)^22 = 0.1928797665912883

    P(4,25) = C(25,4) * (1/6)^4 * (5/6)^21 = 0.2121677432504171

)

= 1 - 0.59373

= 0.40626

= 0.4063 (to 4th decimal place)

Nan left her house at 1 p.m. driving at a constant speed of 40 miles perhour. If she continues at that same speed for the entire trip, she will reach
her destination at 4:45 p.m. If Nan were to drive 10 miles per hour faster,
how much quicker would she arrive?

Answers

Answer:

45 minutes faster

Step-by-step explanation:

Distance:

40 x 3.75 = 150

If travel 50 miles/h:

150/50 = 3

3.75 - 3 = 0.75 of hour

45 minutes

Hope that helped!!! k

Which of the following can be used to express the total area of a figure?

A. (5)(4x)(3x)

B. 12x^2 + 15x

C. (3x + 4x) (5)

D. 3x (4x + 5)

Answers

Answer:

The answer is option B

Step-by-step explanation:

The figure above is a rectangle

Area of a rectangle = length × width

From the question

The total length of the rectangle = 3x

The total width of the rectangle = 4x + 5

So the area of the figure is

A = 3x( 4x + 5)

Expand

We have the final answer as

A = 12x² + 15x

Hope this helps you

solve for x 13x + 7 = 5x - 20

Answers

Answer:

13x + 7 = 5x - 20

Step-by-step explanation:

SOLVE for X

13x + 7 = 5x - 20

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

-5x                   -7  

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

8x=-27

x= -3.375 or -27/8

Answer:

x = -27/8

Step-by-step explanation:

combine the x terms.  To do this, subtract 5x from both sides.  We get:

8x + 7 = -20.  

Next, subtract 7 from both sides, obtaining:

8x = -27, or x = -27/8

Write an expression to represent the product of 6 and the square of a number plus 15.

Answers

Answer:

6x^2 + 15

Step-by-step explanation:

We don't know what the square of a number is, so we represent it as x^2

The first part tells us to find the product of 6 and the square of a number, so

6x^2

The second part tells us to add 15 so,

6x^2 + 15

The expression that should be represented is [tex]6x^2 + 15[/tex]

Given that

The product of 6.The square of number + 15.

Based on the above information,

Let us assume the number should be x

So, from the above information, the expression should be [tex]6x^2 + 15[/tex]

Therefore we can conclude that The expression that should be represented is [tex]6x^2 + 15[/tex]

Learn more about the equation here:brainly.com/question/21105092?

A file that is 276 megabytes is being dowloaded . If the downloaded is 16.7% complete how many megabytes have been dowloaded? Round ur answer to the nearest tenth ( can ya please hurry and answer thank you)

Answers

46.1 megabytes
276 x .167 = 46.092

Answer: 46.1 megabytes

Step-by-step explanation:

The focus of a parabola is (3,-7) and the directrix is y = -4.
What is an equation of the parabola?

Answers

Answer:

  (a)  (x -3)^2 = -6(y +5.5)

Step-by-step explanation:

The equation of a parabola can be written as ...

  (x -h)^2 = 4p(y -k)

where (h, k) is the vertex, and p is the distance from the focus to the vertex.

The vertex is half-way between the focus and directrix, so is ...

  (h, k) = (1/2)((3, -7) +(3, -4)) = (3, -5.5)

The focus is at y=-7, and the vertex is at y=-5.5, so the distance between them is ...

  -7 -(-5.5) = -1.5

Then the equation for the parabola is ...

  (x -3)^2 = 4(-1.5)(y -(-5.5))

  (x -3)^2 = -6(y +5.5) . . . . matches the first choice

Simplify:
[tex] \frac{ {a}^{5} {b}^{8} }{ {a}^{4} {b}^{10} } [/tex]
HELP! answer if you can !​

Answers

Answer: a/(b^2)

In general, (x^n1)/(x^n2)=x^(n1-n2). So the simplified version is a*(b^-2)=a/(b^2).

Answer:

a^5b^8/a^4b^10

= a^5-4 b^8-10

= a^1 b^-2

= a/b^2

I hope this helps

if u have question let me know in comments ^_^

It takes Matt 3 minutes to read one page in a book. If he continues to read at the same pace, he can read 15 similar pages in minutes. If the book has 300 pages, it will take him minutes to read it.

Answers

Answer:

a)45min

b)900min

Step-by-step explanation:

We were told that it takes Matt 3 minutes to read one page in a book.

It implies that 3minutes = 1page of the book

Then he continues to read at the same pace, he can read 15 similar pages in minutes.

a)Then, he can read 15 similar pages in

15x3 minutes.which is 45minutes.

b)Then if the book has 300 pages, it will take him. 300×3 minutes to read it.which is 900mins

Answer: has anyone seen my dad?

help me please ;))) (yes im very rich that's why I'm giving out lots of points -_- (and brainly ;))

Answers

Answer:

(I) 17.25 miles

(ii) 1hr56mins20seconds

(III) 4hrs47mins38seconds

Step-by-step explanation:

(I) read from the lowest distance given

(ii) read from the longest time given

(III) added all times together to get total cycling time

Step-by-step explanation:

here,

shortest distance is 17.25 miles

the longest time is 1:56:20 hrs:mins:secs

total time is 4:47:38

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