Proof that :
[tex] {sin}^{2} \theta + {cos}^{2} \:\theta= 1[/tex]
Thx.

Answers

Answer 1

Answer:

Solution given:

Right angled triangle ABC is drawn where <C=[tex]\theta[/tex]

we know that

[tex]\displaystyle Sin\theta=\frac{opposite}{hypotenuse} =\frac{AB}{AC}[/tex]

[tex]\displaystyle Cos\theta=\frac{adjacent}{hypotenuse}=\frac{BC}{AC} [/tex]

Now

left hand side

[tex] \displaystyle {sin}^{2} \theta + {cos}^{2} \:\theta[/tex]

Substituting value

[tex](\frac{AB}{AC})²+(\frac{BC}{AC})²[/tex]

distributing power

[tex]\frac{AB²}{AC²}+\frac{BC²}{AC²}[/tex]

Taking L.C.M

[tex]\displaystyle \frac{AB²+BC²}{AC²}[/tex]....[I]

In ∆ABC By using Pythagoras law we get

[tex]\boxed{\green{\bold{Opposite²+adjacent²=hypotenuse²}}}[/tex]

AB²+BC²=AC²

Substituting value of AB²+BC² in equation [I]

we get

[tex]\displaystyle \frac{AC²}{AC²}[/tex]

=1

Right hand side

proved
Proof That :[tex] {sin}^{2} \theta + {cos}^{2} \:\theta= 1[/tex]Thx.

Related Questions

Which of the following is a geometric sequence with a common ratio of 2?

A: 14, 28, 56, 112
B: 64, 32, 16, 8
C: 87, 85, 83, 81
D: 14, 16, 18, 20

Answers

Answer:

D. 14, 16, 18, 20

Step-by-step explanation:

it's adding by 2 each time

Answer:

the answer is d my guy :)

Step-by-step explanation:

Can some one help me solve these 3 questions?

Answers

7. A
8. Is the 1st picture
9.is the second picture

3 of 9
Express the ratio below in its simplest form.
2:4:2

Answers

Answer:

1 : 2 : 1

Step-by-step explanation:

2:4:2

Divide each  term by 2

2/2:4/2:2/2

1 : 2 : 1

Find the lengths of x

I tried everything I still got it wrong

Answers

if the degrees in this triangle are truly 90-45-45, then the two unknown lengths are the same

and the pythagorean theorem holds anyways: a² + b² = c², where c is the longest side in a right triangle.

c is 16, so 16² is 256

2* a² = 256

I wrote 2 times s because a and b are of same length

devide each side by 2

a² = 128

take the root

a and b are:

[tex] \sqrt{128} = 11.31378499[/tex]

. If f(x+8)=f(x)+f(8) then prove that: f(0)=0 and f(-8)=-f(8). ​

Answers

Step-by-step explanation:

Given

The equation is [tex]f(x+8)=f(x)+f(8)[/tex]

Substitute 0 for x

[tex]\Rightarrow f(0+8)=f(0)+f(8)\\\Rightarrow f(0)=f(8)-f(8)\\\Rightarrow f(0)=0[/tex]

Now, substitute [tex]-8[/tex] for [tex]x[/tex]

[tex]\Rightarrow f(-8+8)=f(-8)+f(8)\\\Rightarrow f(0)=f(-8)+f(8)\\\Rightarrow 0=f(-8)+f(8)\\\Rightarrow f(-8)=-f(8)[/tex]

Hence proved

Instructions: Find the measure of the indicated angle to the nearest
degree.
26
?
32
? =

Answers

Answer:

36

Step-by-step explanation:

Since this is a right triangle we can use trig functions

cos theta = adj side / hyp

cos ? = 26/32

Taking the inverse cos of each side

cos^-1(cos ?) = cos^-1( 26/32)

? = 35.65908

To the nearest degree

? = 36

look at photo! please help needed! 1.

Answers

Answer:

5/12

Step-by-step explanation:

it says in the question that 1/4 +1/3 is used so in order to make it simple we have to find the common denominator that is 12. so converting 1/4 is 3/12 and 1/3 is 4/12.so u add the numerator and u get 7 over 12 .so now the whole container of peanuts is 12/12 but 7/12 is used so 12-7= 5. so ur ans is 5/12

I doubt anyone can get this but...

We choose a positive divisor of $20^{20}$ at random (with all divisors equally likely to be chosen). What is the probability that we chose a multiple of $10^{10}$?

Answers

Notice that the prime factorization of [tex]20^{20}[/tex] and [tex]10^{10}[/tex] are [tex]2^{40}\cdot5^{20}[/tex] and [tex]2^{10}\cdot5^{10}[/tex], respectively. also, notice that both of their prime factorizations contain only 2 and 5.

Let the divisor of 20^20 that is a multiple of 10^10 be:

[tex]2^y\cdot5^x\cdot2^{10}\cdot5^{10}\\=2^{10+y}\cdot5^{10+x}[/tex]

where y and x are positive integers.

We can have y equal to 0, 1, 2, ... 30 before the exponent of 2 exceeds 40, and we can have x equal to 0, 1, 2, ... 10 before the exponent of 5 exceeds 20.

That is 11*31= 341 numbers in total.

There are (40+1)(20+1)=861 factors in 20^20, which means that the final answer is:

[tex]\boxed{\frac{341}{861}}[/tex]

also are you, by any chance, the same guest who posted the same question in web2.0?

Abc is bisected by bd for what value of x will dx= day be true?

Answers

Answer:

[tex]x=3\\[/tex]

Step-by-step explanation:

Note that because BD is an angle bisector, then angle XBD and angle DXY are equal. Also note that BYD and BXD are equal because they are both right angles. Also, by the transaitive property, BD = BD. Therefore, it can be concluded that BXD is congruent to BYD.

Therefore, we must solve [tex]5x+4=19 \Longrightarrow 5x = 15 \Longrightarrow x=3[/tex].

At pleasant view school, 1/3 9f the grade 8 students play in the band. Of those in the band, 2/5 play woodwind instruments. What fraction of the grade 8 students play woodwinds?​

Answers

Answer: 2/15 of the grade 8 students play woodwind instruments
Multiply the two fractions together: 1/3*2/5= 2/15

simplify.
[tex]( { - 2})^{ - 3} [/tex]
options:

8

1/8

-8

-1/8​

Answers

Answer:

-1/8

Step-by-step explanation:

Apply exponent rule ^a^-b = 1/a^B

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\large\textsf{2}\mathsf{^{-3}}\\\\\\\mathsf{= \dfrac{1}{-2\times-2\times-2}}\\\\\\\mathsf{-2\times-2\times-2 =\bf (-2)^{3}}\\\\\mathsf{(-2)^3}\\\mathsf{= -2\times-2\times-2}\\\mathsf{= 4\times-2}\\\mathsf{\mathsf{= \bf -8}}\\\\\\\mathsf{= -2^{-3} \rightarrow\boxed{\bf -\dfrac{1}{8}}}\large\checkmark[/tex]

[tex]\boxed{\boxed{\large\textsf{Answer: Option D. }\mathsf{\bf - \dfrac{1}{8}}}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The rectangle is 200 feet long 85 feet wide.Ignoring the corner rounding what is the distance around a hockey rink?

Answers

Answer:

570 feet

2*200 + 2*85

400 + 170

570

Step-by-step explanation:

A side of the triangle below has been extended to form an exterior angle of 72°. find the value of x.​

Answers

Answer:

108°

Step-by-step explanation:

The sum of angles on a straight line is 180°

Therefore:

x + 72° = 180°

x = 180° - 72°

x = 108°

Therefore, the value of x is 108°

Can someone help me with this math homework please!

Answers

Answer:

B

Step-by-step explanation:

In fact

for 5 pounds the cost will be 7.50

for 6 pounds 9

for 7 pounds 10.50

for 8 pounds 12

2z^8- 32z^8
Help plz

Answers

Answer:

-30z^8

Step-by-step explanation:

[tex]2 {z}^{8} - 32 {z }^{8} \\ = - 30 {z}^{8} [/tex]

Answer:

-30z^8

Step-by-step explanation:

2z^8- 32z^8

-30z^8

Answer quickly plz
Circle A has a diameter of 7 inches, a circumference of 21.98 inches, and an area of 38.465 square inches. The diameter of circle B is 6 inches, the circumference is 18.84 inches, and the area is 28.26 square inches.

Part A: Using the formula for circumference, solve for the value of pi for each circle. (4 points)

Part B: Use the formula for area and solve for the value of pi for each circle. (4 points)

Part C: What observation can you make about the value of pi for circles A and B? (2 points)

Answers

Answer:

The observation I can make for the values of pi for circles A and B is that the value of pi remains the same whether we find pi using the circumference of the circle or the Area of the circle, the value of pi remains the same for both circles.

Pi = π = 3.14

Step-by-step explanation:

Part A: Using the formula for circumference, solve for the value of pi for each circle. (4 points)

The formula for the circumference of circle when Diameter is given = πD

π = Circumference / Diameter

For Circle A :

Circle A has a diameter of 7 inches, a circumference of 21.98 inches.

π = 21.98 inches/7 inches

π = 3.14

For Circle B

The diameter of circle B is 6 inches, the circumference is 18.84 inches

π = 18.84 inches/6 inches

π = 3.14

Part B: Use the formula for area and solve for the value of pi for each circle. (4 points)

The formula for the area of the circle = πr²

Circle A has a diameter of 7 inches, an area of 38.465 square inches.

r = Radius = 7 inches ÷ 2

= 3.5 inches

π = Area / Radius²

π = 38.465 in²/(3.5 inches)²

π = 3.14

For Circle B

The diameter of circle B is 6 inches, and the area is 28.26 square inches.

r = Radius = 6 inches ÷ 2

= 3 inches

π = Area / Radius²

π = 28.26 in²/(3 inches)²

π = 3.14

Part C: What observation can you make about the value of pi for circles A and B? (2 points)

The observation I can make for the values of pi for circles A and B is that the value of pi remains the same whether we find pi using the circumference of the circle or the Area of the circle, the value of pi remains the same for both circles.

The observation is that the values of [tex]\pi[/tex] remain 3.14 when [tex]\pi[/tex] is calculated from the areas and circumferences of both circles

The circumference of a circle

The given parameters are:

Circle A

Diameter = 7 inchesCircumference = 21.98 inches

Circle B

Diameter = 6 inchesCircumference = 18.84 inches

The circumference of a circle is:

[tex]C= \pi d[/tex]

Make [tex]\pi[/tex] the subject

[tex]\pi = \frac{C}{d}[/tex]

For circle A, we have:

[tex]\pi_A = \frac{21.98}{7}[/tex]

[tex]\pi_A = 3.14[/tex]

For circle B, we have:

[tex]\pi_B = \frac{18.84}{6}[/tex]

[tex]\pi_B = 3.14[/tex]

Hence, the value of [tex]\pi[/tex] in both circles is 3.14

The area of a circle

The given parameters are:

Circle A

Diameter = 7 inchesArea = 38.465 square inches.

Circle B

Diameter = 6 inchesArea = 28.26 square inches

The area of a circle is:

[tex]A= \pi \frac{d^2}{4}[/tex]

Make [tex]\pi[/tex] the subject

[tex]\pi = \frac{4A}{d^2}[/tex]

For circle A, we have:

[tex]\pi_A = \frac{4 * 38.465 }{7^2}[/tex]

[tex]\pi_A = 3.14[/tex]

For circle B, we have:

[tex]\pi_B = \frac{4 * 28.26 }{6^2}[/tex]

[tex]\pi_B = 3.14[/tex]

Hence, the value of [tex]\pi[/tex] in both circles is 3.14

The value of pi

The observation is that the values of [tex]\pi[/tex] in both circles when area and circumference are used is 3.14

Read more about area and circumference at:

https://brainly.com/question/15673093

ASAPPPPPPPPPpppppppppppppp

Answers

Answer:

8 1/2

Step-by-step explanation:

Take the decimal portion

.5

This is 5 tenths

write 5/10

Simplify

1/2

Bring the whole number back

8 1/2

Answer:

8 1/2

Step-by-step explanation:

How would I answer this: How many minutes are in a 30-day month.... use vertical multiplication to get the right answer

Answers

Answer:

There are 43200 minutes in a 30-day month.

Step-by-step explanation:

We know that:

60 minutes = 1 hour

24 hours = 1 day

Thus to determine the minutes in a 30-day month, let us first determine the number of hours in the month.

   30

x  24

_______

  120

 60

_______

 720 hours

The 30-day month has a total of 720 hours.

So that the number of minutes that make up 720 hours can be determined by;

    720

 x   60

_______

   000

4320

_______

43200

Therefore, there are 43200 minutes in a 30-day month.

what is the length of PR?

Answers

Answer:

nhgfdsazxcvb

Step-by-step explanation:

hfdcvbn

The cost, c(x), for a taxi ride
is given by c(x) = 3x + 2.00, where xis the
number of minutes.
On a piece of paper, graph c(x) = 3x + 2.00. Then determine which answer
matches the graph you drew, including the correct axis labels.

Answers

Answer:

The answer is A.

Go to desmos and type your equation in

This question right here is worth 10 points the first one get it right will earn 10 points;)

Answers

LFE angles and GFE angles

Emily is entering a bicycle race for charity. Her mother pledges $0.30 for every 0.5 mile she
bikes. If Emily bikes 10 miles, how much will her mother donate?
Her mother will donate $

Answers

Answer:

The mother will donate $5

We know that her mother will donate 0.30 for every 0.5 miles she bikes. We can convert this to one mile, which is 0.60 cents per mile. We can now multiply by ten. This will gives us $6.

Another way to solve this is divide 10 by 0.5. This gives us 20, and if we multiply 20 by 0.30 we get $6.

the polygons in each pair are similar. find the scale factor of the smaller figure to the larger figure.​

Answers

Answer:

smaller figure/larger figure = 3/12 = ¼

Step-by-step explanation:

Scale factor = Smaller figure side length / corresponding side length of the larger figure.

Length of a side of the smaller figure = 3

Corresponding Length of a side of the larger figure = 12

Scale factor = smaller figure/larger figure = 3/12 = 1/4

What number cube has faces numbered 1 to 6.

Answers

Answer:

I don`t see the attachment

Step-by-step explanation:

help Find the value of x and the value of y.

Answers

Answer:

x = 2sqrt(2)

y = 2sqrt(6)

Step-by-step explanation:

The ratio of the lengths of the sides of a 30-60-90 triangle is

1 : sqrt(3) : 2

x = 0.5 * 4 sqrt(2) = 2sqrt(2)

y = x * sqrt(3) = 2sqrt(6)

Mr. Sun borrowed $15,600 for 54 months at simple interest to pay for a new swimming pool. If Mr. Sun paid the bank a total of $21,567.00, what was the simple interest rate of the loan?

Answers

Given:

Mr. Sun borrowed $15,600 for 54 months at simple interest.

Mr. Sun paid the bank a total of $21,567.00.

To find:

The rate of simple interest.

Solution:

We know that,

12 months = 1 year

1 month = [tex]\dfrac{1}{12}[/tex] year

54 months = [tex]\dfrac{54}{12}[/tex] year

54 months = 4.5 years

Simple interest is:

[tex]S.I.=Amount-Principal[/tex]

[tex]S.I.=21567-15600[/tex]

[tex]S.I.=5967[/tex]

Formula for simple interest is:

[tex]S.I.=\dfrac{P\times r\times t}{100}[/tex]

Where, P is principal, r is the rate of interest in percent and t is the number of years.

Putting [tex]S.I=5967,P=15600,t=4.5[/tex], we get

[tex]5967=\dfrac{15600\times r\times 4.5}{100}[/tex]

[tex]596700=70200r[/tex]

[tex]\dfrac{596700}{70200}=r[/tex]

[tex]8.5=r[/tex]

Therefore, the rate of simple interest is 8.5%.

SECTION B
A matatu and Nissan left town A for town B 240km away at 8.00 a.m travelling at 90km/hr
and 120km/hr respectively. After 20 minutes the Nissan had a puncture which took 30
minutes to mend.
(5mks
a) How far from town A did the Nissan catch up with the matatu?

Answers

9514 1404 393

Answer:

  180 km

Step-by-step explanation:

The Nissan had traveled (120 km/h)(1/3 h) = 40 km when it had the puncture. It started from that location when the puncture was repaired at t = (1/3+1/2) = 5/6, where t is in hours. Then the two vehicles met (again) when ...

  Matatu distance = Nissan distance

  90t = 40+120(t -5/6)

  0 = 40 +30t -100 . . . . . . subtract 90t, eliminate parentheses

  60 = 30t . . . . . . . . . . . add 60

  2 = t . . . . . . . . . . . . . 2 hours after leaving, the cars meet again

That distance from town A is ...

  y = 90t = 90(2) = 180 . . . . km

What is the value of x in this figure?

Enter your answer in the box.
x =

Answers

Answer: X = 114

Step-by-step explanation: this is because vertical angles are equal to each other.

plzzz helpppp dont ignoreeee

Answers

Answer:

X= 40

Step-by-step explanation:

2(110 + 4x) = 220 + 8x = 540

8X = 320

X= 40

Answer:

x = 17.5

Step-by-step explanation:

Since there’s a dashed line between the shape, the new total = 180* (degrees)

110* + 3x + x = 180*

Subtract 110 from 180

3x + x = 70

x = 17.5

Ross walked 3 m east and 6 m north. How far is he from the starting point

Answers

Answer:

3 sqrt(5) meters

Step-by-step explanation:

This is a right triangle so we can use the Pythagorean theorem.

a^2 +b^2 = c^2 where a and b are the legs and c is the hypotenuse

3^2+6^2 = c^2

9+36 = c^2

45 = c^2

Taking the square root

sqrt(45) = sqrt(c^2)

sqrt(9*5) = c

sqrt(9) sqrt(5) =c

3sqrt(5) = c

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

Given:-Ross walked 3 m east and 6 m north.

Find:-How far is she from the starting point?solution:-

Ross walked 3 m east and 6 m north.

so her path is a right angle triangle path.

we know that,

in a right angle triangle, According to the Pythagorean theorom,

[tex]\boxed{\sf{l^2+b^2=h^2 }}[/tex]

where

l= legs b=baseh=hypotenuse

According to the question, [tex]\sf{3^2+6^2=f^2 }[/tex]

[tex]\sf{9+36=f^2 }[/tex]

[tex]\sf{ f^2=45 }[/tex]

[tex]\sf{f=\sqrt{45} }[/tex]

[tex]\sf{f=3\sqrt{5} }[/tex]

Therefore:-

he is [tex]\sf{3\sqrt{5} }[/tex] far from the starting point

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