Answer: The value of (1 + sin 8)(1-sin 8) (1 + cos 0) (1 - cos8) =0.2086
and [tex]cot^{1}[/tex]θ=7/8
Step-by-step explanation:
Let base and height of a triangle be 7k and 8k
By applying Pythagoras theorem in Δ ABC, we get
[tex]AC^{2} = AB^{2} +BC^{2}[/tex]
= (7k)2 + (8k)2
= 49k2 + 64k2
= 113k2
AC = √113k2
= √113k
so hypotenuse =[tex]\sqrt{133}k[/tex];
now ;
=(1 + sin θ) (1 - sin θ)(1 + cos θ) (1 - cos θ)[since : (a + b)(a - b) = (a2 - b2)]
=(1 - [tex]sin^{2}[/tex]θ)(1 - [tex]cos^{2}[/tex]θ)
=[1 - (8/√113)2] [1 - (7/√113)2]
= (1 - 64/113) (1 - 49/113)
= (49/113) (64/113)
= 0.2086
hence;
The value of (1 + sin 8)(1-sin 8) (1 + cos 0) (1 - cos8) =0.2086
and [tex]cot^{1}[/tex]θ=7/8
Learn more about trignometry here https://brainly.com/question/28493506
#SPJ9
Answer:
Step-by-step explanation:We will use the basic concepts of trigonometric ratios to solve the problem.
Consider ΔABC as shown below where angle B is a right angle.
If cot θ = 7/8, evaluate: (i) (1 + sin θ)(1 - sin θ) / (1 + cos θ)(1- cos θ), (ii) cot²θ
cot θ = side adjacent to θ / side opposite to θ = AB/BC = 7/8
Let AB = 7k and BC = 8k, where k is a positive integer.
By applying Pythagoras theorem in Δ ABC, we get
AC2 = AB2 + BC2
= (7k)2 + (8k)2
= 49k2 + 64k2
= 113k2
AC = √113k2
= √113k
Therefore, sin θ = side opposite to θ / hypotenuse = BC/AC = 8k/√113k = 8/√113
cos θ = side adjacent to θ / hypotenuse = AB/AC = 7k/√113k = 7/√113
(i) (1 + sin θ) (1 - sin θ) / (1 + cos θ) (1 - cos θ) = 1 - sin2θ / 1 - cos2θ [Since, (a + b)(a - b) = (a2 - b2)]
= [1 - (8/√113)2] / [1 - (7/√113)2]
= (1 - 64/113) / (1 - 49/113)
= (49/113) / (64/113)
(ii) cotФ≈
= 49/64
Which expression represents the product of a³ + 2x - 1 and 4 - x³ + 3?
Option C) is correct that is the product of (x³ + 2x – 1) * ( x⁴ – x³ + 3) is
x⁷ – x⁶ + 2x⁵ – 3x⁴ + 4x³ + 6x – 3
The two terms that we have been given are x³ + 2x – 1 and x⁴ – x³ + 3
To find the product of these two terms we will multiply term by term that is
(x³ + 2x – 1) * ( x⁴ – x³ + 3) = x³( x⁴ – x³ + 3) + 2x( x⁴ – x³ + 3) - 1( x⁴ – x³ + 3)
=x⁷ – x⁶ + 3x³ + 2x⁵ – 2x⁴ + 6x - x⁴ + x³ – 3
(x³ + 2x – 1) * ( x⁴ – x³ + 3) = x⁷ – x⁶ + 2x⁵ – 3x⁴ + 4x³ + 6x – 3
Hence the product of (x³ + 2x – 1) * ( x⁴ – x³ + 3) is
x⁷ – x⁶ + 2x⁵ – 3x⁴ + 4x³ + 6x – 3
That is option C) is correct
Learn more about product here : https://brainly.com/question/13934852
#SPJ9
Which is the correct way to write 602,200,000,000,000,000,000,000 in scientific notation? 6022 times. 1019 6022 times. 1020 6.022 times. 1022 6.022 times. 1023
The correct way to write 602,200,000,000,000,000,000,000 in scientific notation is 6.022 [tex]*[/tex] [tex]$$10^{23[/tex].
What is meant by scientific notation?Scientific notation is a method of expressing numbers that are either too large or too small to be written in decimal form. In the United Kingdom, it is known as scientific form, standard index form, or standard form.
The proper scientific notation format is [tex]a*10^b[/tex], where an is a number or decimal number with an absolute value greater than or equal to one and less than ten, or 1 |a| 10. b is the power of ten required for scientific notation to be mathematically equivalent to the original number.
In the scientific notation, the number is written as a multiplication of a number from 1 to 9 and 10 raised to the adequate power.
602,200,000,000,000,000,000,000
= 6.202 [tex]*[/tex] 100,000,000,000,000,000,000,000.
Since 10 = [tex]10^1[/tex]; 100 = [tex]$$10^2[/tex]; 1,000 = [tex]$$10^3[/tex], etc. then
100,000,000,000,000,000,000,000 = [tex]$$10^{23[/tex].
602,200,000,000,000,000,000,000
= 6.202 [tex]*[/tex] 100,000,000,000,000,000,000,000 = 6.022 [tex]*[/tex] [tex]$$10^{23[/tex].
The correct way to write 602,200,000,000,000,000,000,000 in scientific notation is 6.022 [tex]*[/tex] [tex]$$10^{23[/tex].
Therefore, the correct answer is option d) 6.022 [tex]*[/tex] [tex]$$10^{23[/tex].
The complete question is:
Which is the correct way to write 602,200,000,000,000,000,000,000 in scientific notation?
a) 6022 [tex]*[/tex] [tex]$$10^{19[/tex]
b) 6022 [tex]*[/tex] [tex]$$10^{20[/tex]
c) 6.022 [tex]*[/tex] [tex]$$10^{22[/tex]
d) 6.022 [tex]*[/tex] [tex]$$10^{23[/tex]
To learn more about scientific notation, refer to:
https://brainly.com/question/1199149
#SPJ4
Answer: D
Explanation: 6.022 x 10^23
Please help :(
Use PEMDAS to find the surface area.
81 + 72(4) =
157 km²
369 km²
612 km²
(4y - 15) 7y + x = 180
2(6-9)-31 helpppppppppppppppp
Answer: -37
Step-by-step explanation:
Use order of operations
2(6-9)-31
2(-3)-31
-6-31
= -37
can someone help me with this question
Answer:
50 69 600 5.2 2
Step-by-step explanation:
this is because this is simple interest i=pxrxt
WILL MARK BRAINLIST !!
Find the value of xº from the given figure applying the activity.
Answer:
total inner angle of quadrilateral is 360 so
66 is remaining angle.
Please mark me as brainlist answer.
You has promised. Don't broke promise that you will give brainlist answer.
Answer:
The sum of the interior angle of a quadrilateral is given by the formula
(n-2)×180°
n represent the number of sides
(4-2)×180°
2×180°
=360°
then equate the angle to 360°
Match the angle with its classification
Answer:angels
Step-by-step explanation:bea
2r+1+(−4r)+72 please solve
Answer:
[tex] \sf \large \: −2r+73[/tex]
Step-by-step explanation:
Let's simplify step-by-step.
2r+1−4r+72
=2r+1+−4r+72
Combine Like Terms:
=2r+1+−4r+72
=(2r+−4r)+(1+72)
=−2r+73
x+8=-(2x +1) Can you help
Please and thank you
HEEYYY PLEASE ANSWER THIS I GOT COVID SO I DONT UNDERSTAND IT SINCE I CANT BE IN CLASS
You can just try out all the answers but I'll give you a solution.
We will expand out the middle term to 5x^2 - 30x - 6x + 36, then we group the first 2 terms together, and the last 2 terms together.
= 5x (x - 6) - 6(x - 6)
And we put x-6 out : (x-6)(5x-6) = 0
Now, we can just set the value of one bracket to 0 and find out the value of x, and do the same for the other one
x - 6 = 0 -> x = 6
5x - 6 = 0 -> x = 6/5
Because 6 is not a possible option, the answer is x = 1.2
which property is shown by 2 + 0 = 2
A. Associative Property of Addition
B. Commutative Property of Addition
C. Distributive Property
D. Identify Property of Addition
The property shown in 2 + 0 = 2 is the Identify Property of Addition
How to name the property shown?The expression is given as:
2 + 0 = 0
The Identify Property of Addition property states that
a * 0 = a
This means that the property shown is the Identify Property of Addition
Hence, the property shown in 2 + 0 = 2 is the Identify Property of Addition
Read more about algebraic property at
brainly.com/question/12956307
#SPJ1
I am a number greater than $4,000 less than $6,000 by ones digit and 10 digit are the same my 10,000
digit is a one less than three times the sum of my ones digit and 10 digit in my thousand digit is half my hundred digit and the sum of those two digit is a 9
Answer:
the number is 53611
Step-by-step explanation:
mark me brainliest hope this answer helps
Q.4 - Simplify: 7y + 8 = 9 + 3y + 2y. Show your work.
Answer:
y = 1/2
Step-by-step explanation:
7y + 8 = 9 + 3y + 2y
7y + 8 = 9 + 5y
7y - 5y + 8 = 9 + 5y - 5y (subtract 5y from both sides)
2y + 8 - 8 = 9 - 8 ( subtract 8 from both sides)
2y = 1
(2/2)y = (1/2) divide by 2 on both sides
y = 1/2
If two events, event a with probability p(a) and event b with probability p(b) are complementary events then __________.
If two events, event A with probability P(A) and event b with probability P(B) are complementary events then the sum of the probability of events A and B will be one.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
When one event happens if and only if the other one doesn't, two occurrences are said to be complimentary. The odds of two complementary events equal one.
P(A) + P'(A) = 1
The chance of events A and B added together will equal one if events A with probability P(A) and event B with probability P(B) are complementary occurrences.
More about the probability link is given below.
https://brainly.com/question/795909
#SPJ4
- x≤-2 or x > 1 needs to be put on a number line pls help
Answer:
Step-by-step explanation:
Answer: closed circle on -2 with the arrow to the left
open circle on 1 with the arrow to the right
2 1/7 + 3/7(3x-5)=-4
Answer:
Answer 2 1/7 +3/7(3x-5)= -4
2 1/7 + 9/7x-15/7= -4
0+ 9/7x = -4
x= -28/9
Step-by-step explanation:
If a person with an hourly pay of $9.50 per hour gets a 20% raise, what is the hourly pay?
-8(1-a)=-8(a-7) solve the equation
Answer:
a=4
Step-by-step explanation:
Solve the systems of equation 4x + y = 10 3x - 2y = 13
The solution to the system of equation is (7/5, 22/5)
System of equationGiven the system of equation as shown below;
4x + y = 10 * 2
3x - 2y = 13 * 1
_____________
8x + 2y = 20
3x - 2y = 13
Subtract
8x - 3x = 20 - 13
5x = 7
x = 7/5
Substitute the value of x into any of the equation
4x + y = 10
4(7/5) + y = 10
28/5 + y = 10
y = 10 - 28/5
y = 22/5
Hence the solution to the system of equation is (7/5, 22/5)
Learn more on system of equation here: https://brainly.com/question/25976025
#SPJ1
the desert temperature, h, oscillates daily between 40°f at 5am and 80°f at 5pm. write a possible formula for h, measured in hours from 5am, using the form h
The form of a periodic function is H(t) = 20cos(π/12(t+12))+ 60.
What do periodic functions mean?
A function that periodically returns to the same value. Despite the similarity in sound between periodic motion and oscillatory motion, not all periodic motions are oscillatory motion.
Since the values of H oscillates between two values, then the choices of the function are either sine or cosine. However, since the variable measures the time from 4 AM, and 4 AM represents the trough of the oscillation, then cosine is the more appropriate choice. Recall the form of a periodic function
y =A cos(B(x +C))+D
It is given that the peak of desert temperature is at 80F, and the lowest is 40F. Note that the distance between the two temperatures is
80F − 40F =40F
Since the amplitude is the distance from the middle line to either peak or trough, then it is half the distance from the trough to the peak. Hence
A = 40/2= 20
Notice that one full oscillation occurs after one day or 24 hours. Hence the period is
B =2π/24 = π/12
The graph of the cosine function begins at the peak, whereas the function needs to begin at the trough, since the variable t represents the number of hours after 4 AM. Thus, the graph must be shifted horizontally to the left one half-cycle, which is
C = 12
Since the original cosine function has the centerline at x= 0 the centerline of the function must be shifted by the number of units corresponding to the midway point of the peak and the trough. Hence
D= 80 + 40/2 = 120/2 = 60
ubstituting
A =20, B = π/12. C= 12 , and D= 60 into
The form of a periodic function
H(t) = 20cos(π/12(t+12))+ 60
Learn more about periodic function
brainly.com/question/28223229
#SPJ4
A) ((7.4), (6, 3). (5, 2)}
Function?
Explain:
Answer:
Yes
Step-by-step explanation:
This function is called a discrete function since the function isn't continuous like a line but consists of individual points.
Also, the points in the function don't share the same x-coordinate, so the function passes the vertical line test.
1. (-32) (-3) =? 2. (79) (-2) =?
Answer:
1. = 96
2. = -158
Step-by-step explanation:
When you multiply two negatives the answer is positive, and when you multiply one negative and one positive the answer is negative
Which of the following numbers is divisible by 3?
a) 539
b) 85
c) 9,285
d) 640
Answer:
C
Step-by-step explanation:
539/3 = 179.666
85/3 =28.3333
9285/ 3 = 3095
640/3=213.3333
Answer:
C
Hope this helps :)
Step-by-step explanation:
All the others numbers equal a decimal when divided by 3. However, C equals a whole number so it's C.
9,285 ÷ 3 = 3,095
BIG IDEAS MATH
#14 i
MODELING REAL LIFE You deposit $2000 in an account that earns simple interest at an annual rate of 4%. How long must
you leave the money in the account to earn $500 in interest?
(answer is in years)
Answer:
6.25years
Step-by-step explanation:
2000*4% = 80
500/80 = 6.25
6 years and 3 months
Two points on the y axis that are 25 units from (-24,3)
The two points on the y axis that are 25 units from (-24,3) will be (0, 10) and (0, - 4).
We are given a point:
( - 24 , 3 )
We need to find a point on the y - axis, that is 25 units away from the axis.
The coordinate of the point will be:
(0, y)
So, by using the distance formula, we get that:
D = √ ( y₂ - y₁)² + ( x₂ - x₁)²
25 = √ ( y + 3)² + (0 + 24)²
625 = y² + 9 - 6 y + 576
625 = y² - 6 y + 585
y² - 6 y - 40 = 0
y² - 10 y + 4 y - 40 = 0
y ( y - 10 ) + 4 ( y - 10 ) = 0
(y - 10)(y + 4) = 0
y = - 4 or y = 10.
So, the two points will be:
(0, 10) and (0, - 4)
Therefore, we get that, the two points on the y axis that are 25 units from (-24,3) will be (0, 10) and (0, - 4).
Learn more about points here:
https://brainly.com/question/25870256
#SPJ9
Johnny wants to buy a box of
donuts. The donuts normally cost
$12 dollars but they are on sale for
10% off. What is the sale price for
the donuts? Please I need help
Answer:
$1.20
Step-by-step explanation:
if the donuts normally cost 12 dollars, but they are on on sale for 10% off, then all you have to do is divide 12 by 10.
12 ÷ 10 = 1.2
since we are working with money, we need to add a 0 at the end to make it 1.20, since you need 100 cents to make a dollar.
another way you could write the equation is,
10% × 12 = 1.2
1.2 = 1.20
hence, the sale price for the donuts is $1.20
Step-by-step explanation:
Hope it helps!
Helppppppppooppppppp please
What percentage of the data values are greater than 80?
64.71% percent of the data values are greater than 80.
What is the percentage?
In Ancient Rome, long before the actuality of the decimal system, computations were constantly made in fractions in the multiples of '/ 100', For illustration, Augustus levied a duty of1/ 100 on goods sold at sale known as centesimal Rerum valium. Computation with these fractions was original to calculating chances. They named it as a percentage.As nomenclatures of capitalism grew in the Middle ages, computations with a denominator of 100 came increasingly standard, analogous that from the late 15th century to the early 16th century, it came common for calculation-handbooks to include analogous computations known as percentage.Multitudinous of these handbooks applied these styles to profit and loss, interest rates, and the Rule of Three. By the 17th(seventeenth) century, it was standard to quote interest rates in hundredthsMin. value = 30
Max. value = 85
Percentage (%) of data values greater than 30(thirty) = [tex]\frac{55}{85} X 100[/tex]
= 64.71%
Learn more about percentages here: https://brainly.com/question/24304697
#SPJ9
A sqaure garden has an area of 144 square feet. how many yards of fence will it take to enclose the garden?
The number of yards of fence it will take to enclose the square garden is 48 feet.
It is given in the question that a square garden has an area of 144 square feet.
We have to find the number of yards of fence it will take to enclose the garden.
Let the length of side of the square garden be x feet.
We know that,
Area of a square = [tex]side^2[/tex]
Hence,
According to the data given in the question, we can write,
144 = [tex]side^{2}[/tex]
We know that,
144 = [tex]12^2[/tex]
Hence,
[tex]12^2=side^2[/tex]
Hence,
Side = 12 feet
We know that,
Number of yards of fence it will take to enclose the square garden = perimeter of the square garden.
Hence,
Number of yards of fence it will take to enclose the square garden = 4* side of the square garden = 4*12 = 48 feet.
To learn more area of square, here:-
https://brainly.com/question/1658516
#SPJ4