Proof that :
[tex] {sin}^{2} \theta + {cos}^{2} \:\theta= 1[/tex]
Thx.
Answers
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.](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/OZ1iz0U16D5JyVgrze2iYM5q3NQrXnIZ.jpeg)
Related Questions
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
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?
what is the length of PR?
Answers
Answer:
nhgfdsazxcvb
Step-by-step explanation:
hfdcvbn
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%.
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
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:
. 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
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:
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)
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.
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:
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].
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
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
Multiply the two fractions together: 1/3*2/5= 2/15
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.
This question right here is worth 10 points the first one get it right will earn 10 points;)
Answers
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 circleThe given parameters are:
Circle A
Diameter = 7 inchesCircumference = 21.98 inchesCircle B
Diameter = 6 inchesCircumference = 18.84 inchesThe 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 circleThe given parameters are:
Circle A
Diameter = 7 inchesArea = 38.465 square inches.Circle B
Diameter = 6 inchesArea = 28.26 square inchesThe 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 piThe 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
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
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]
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]
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°
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
plzzz helpppp dont ignoreeee
Answers
Answer:
X= 40
Step-by-step explanation:
2(110 + 4x) = 220 + 8x = 540
8X = 320
X= 40
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
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
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
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
8. Is the 1st picture
9.is the second picture
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
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
