Answer:
3/16
Step-by-step explanation:
Prove that sin 20 ×sin40 × sin60 × sin80 = 3/16.
We have to prove sin 20 × sin40 × sin60 × sin80 = 3/16.
Consider LHS
sin 20 × sin 40 × sin60 × sin80
Sin Values
In trigonometry, the sine function can be defined as the ratio of the length of the opposite side to that of the hypotenuse in a right-angled triangle. The sine function is used to find the unknown angle or sides of a right triangle.
We know the trigonometric values of sin function
Proof
Consider LHS
sin 20 × sin 40 × sin60 × sin80
= sin60 [sin20 × sin40 × sin80]
= √3/2[sin20 × sin(60 – 20) × sin(60 + 20)]
= √3/2[sin 3(20)/4]
= √3/2[sin 60/4]
= √3/2[√3/2 × 4]
= √3/2 × √3/8 = 3/16
∴ LHS = RHS
Hence proved
27 + x = 42 what is the value of x
Answer: x = 15
Step-by-step explanation:
Given:
27 + x = 42
Subtract 27 from both sides of the equation:
x = 15
27 + x = 42
Subtract 27 from both sides:
X = 15
) Find the value of b for which 50y +150 is a factor of y3 – by2 +by+3b.
[tex]f(y) = y^3-by^2+by+3b\\\\\text{Since 50y+150 is a factor of f(y), }\\\\~~~~~f\left ( -\dfrac{150}{50}\right) = 0 \\\\\implies f(-3)=0 \\\\\implies (-3)^3 -b(-3)^2+b(-3)+3b =0\\\\\implies -27-9b-3b+3b=0\\\\\implies -27-9b =0\\\\\implies 9b = -27\\\\\implies b = -\dfrac{27}9\\\\\implies b = -3[/tex]
A cylinder has a highet of 20cm and a volume of 1004.8cm. Calculate the radius of the base of the cylinder
Answer:
radius = 4 cm
Step-by-step explanation:
r≈4cm
Using the formula
V=πr2h
Solving forr
r=V
πh=1004.8
π·20≈3.99899cm
If x²+ y²= 80 and xy = 12, find the value of (x - y)².
[tex](x-y)^2\\\\=x^2+y^2 -2xy\\\\=80-2(12)\\\\=80-24\\\\=56[/tex]
angle 1- what degree
Answer:
22 degrees
Step-by-step explanation:
The two bottom sides have the same angle which is 79 and all the angles must add up to 180, so 79 plus 79 is 158 and 180 minus 158 is 22.
Hope this helps.
BTW it's my birthday
Answer:
25°
Step-by-step explanation:
Exterior angle property of triangle:
Exterior angle of a triangle equals the sum of oppositer interior angles.
∠1 + 79 = 104
Subtract 79 from both sides
∠1 = 104 - 79
∠1 = 25°
help me find Find m< G .
Answer:
∠G=110°
Step-by-step explanation:
The 4 interior angles of a kite add up to 360. 100+40=140. 360-140=220. E and G are the only angles left so we know together they must equal 220. And ∠E and ∠G are congruent angles beceause of kite rules. So, we divide by 2 to get how much angle E and G are individually.
20 points. A certain event may occur, but it is unlikely to occur.
Which statement about the probability of the event is true?
A. The probability is close to 0.
B. The probability is 0.
C. The probability is 1.
D. The probability is less than 0.
Answer:
A
Step-by-step explanation:
Close to 0 means there isn't a certain number, and there also isn't a certain answer for what the probability. While all of the others are alreaady stated, this is the only one that is not.
Can y’all figure out the answer for me please
Answer:
Step-by-step explanation:
true
if angle BCA is 90° and angle EFD is 90°
and if C to A is 14, half of that is 7 which is what F to D is
A polynomial function has – 5+ 3t as a root. Which of the following must also be a root of the function?
a
Radical roots occur as conjugate pairs
Given - 5 + t is a root , then
- 5 - t is also a root → a
14,15,3,15,14,14,18,15,8 mean ,mode,median determine which measure of center best represenrs the data
Answer:
Mean: 12.9
Mode: 14,15
Median: 14
Step-by-step explanation:
Allowing 20% discount on the marked price if a watch, the value of the watch will be Rs. 2376. If the VAT of 10% is added, find its marked price.
Ans: Rs. 2700
original price be x
x-0.2x=23760.8x=2376x=2970VAT 10%
So new price is 10% less
2970-0.10(2970)2970-297Rs 2673≈2700Help picture below problem 13
Answer:
it's obtuse angle...
mark me brainliest
= Obtuse triangle
Explanation:(a triangle in which one of the interior angles measures more than 90° degrees.)
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
‼️GET BRANLIEST HERE‼️
PLS AND TY IT IS DUE SOON :))
Answer:
b = 0.62
Step-by-step explanation:
Hello!
We can look at the y-values of the function to find our multiplier. A multiplier will determine if the graph decays or grows in an exponential function, and by how much.
When x is 0, we can see the y-value is around 3, but as x approaches 1, the y-value comes to around 2.
We can find the multiplier by dividing the current term by the previous term.
2 ÷ 32/30.6666...This number is closest to 0.62, so the approximation is 0.62.
2/3
0.6666..
Approximation is 0.62 (b)
Hope this helped! Stay healthy!♡
MAX POINTS PLEASE HELP Will make Brainliest
What is the period and frequency of the function graphed and how would the equation be written
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
The required equation is :
[tex]\qquad \sf \dashrightarrow \:a \cos(bx) + k[/tex]
Now, let's find the required values :
period (p) = 6[distance between any successive Crest or trough]
a = - 4 (flipped)b = 2π/p = 2π/6 = π/3k = -2Distance of starting position from origin = k
Now, plug in the values ~
[tex]\qquad \sf \dashrightarrow \: - 4 \cos( \frac{ \pi}{3}x ) - 2[/tex]
how would the equation be written with an amplitude of 3 maximum of 4 minimum of -2 period of 4 and midline of 1 (Will report scams)
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Here we go ~
The required equation is :
[tex] \qquad \sf \dashrightarrow\: y = asin(bx) +k [/tex]
Now, let's find the required values :
period (p) = 4
[distance between any successive Crest or trough]
a = - 3 (flipped)
b = 2π/p = 2π/4 = π/2
k = 1
Distance of starting position from origin = k
Now, plug in the values ~
[tex] \qquad\dashrightarrow \sf\: y = -3sin(\frac{\pi}{2}x)+1 [/tex]
Which shapes show equivalent fractions?
A.shapes A and B
B.shapes A and D
C.shapes B and C
D.shapes A, B, and D
Answer:
B.shapes A and D
Step-by-step explanation:
Cuz if u see very carefully u will see they are cubes (except b) and A and D had one of its side's covered so the answer is simply A and D
Write an equation of the line in slope-intercept form.
y=
Answer:
The equation of the line in slope intercept form is y=1/3x+2
Step-by-step explanation:
The points (4,7) and (r. – 5) lie on a line with slope – 3. Find the missing coordinate r
Answer:
[tex]r=\frac{14}{3}[/tex]
Step-by-step explanation:
Set up an equation and solve for r using the formula for slope:
[tex]\frac{5-7}{r-4}=-3\\ \\-2=-3(r-4)\\\\-2=-3r+12\\\\-14=-3r\\\\\frac{14}{3}=r[/tex]
which has a greater magnitude 17 ft above sea level or 11 ft
Answer:
1 - 52= 52 33= 33 52 > 33, so -52 dollars has the greater magnitude. 1 - 141 = 14 [23] = 23 14 < 23, so 23 feet has the greater magnitude.
Step-by-step explanation:
Hope This Helps
Find nth term of the sequence: 11, 15, 19, 23
The term
tn=a+(n−1)d
Where a= first term and d= common difference
hope it helps...!!!
Help picture below problem 16
Answer:
Regular Hexagon
Step-by-step explanation:
There are six sides and all sides are equal
A haircut cost $16 which included tax. Joan tipped 20% and paid with a $50 bill. What was her change?
Answer:
32
Step-by-step explanation:
Answer: 30.8
Explanation: 20% of 16 is 3.2
16 + 3.2 = 19.2
50 - 19.2 = 30.8
I might be wrong but that's the answer I got
Find the area of the right triangle
Answer:
Formula for area of a triangle;
A = BH x 1/2
B = The base
H = The height
1/2 = Half of the product of (base x height)
We first need to figure out the base of this triangle, so count the units across from the base of this triangle.
The base is 4 units.
Now we need to find out the height, so count the units above starting from the base of this triangle and to the end of this triangle.
The height is 7 units.
Now plug these values into our equation:-
A = BH x 1/2
A = 4(7) x 1/2
A = 28 x 1/2
A = 28/2
A = 14, the area of this right triangle is 14 square units.
f(x) = - 0.05(x ^ 2 - 26x - 120)
What do the zeros of this function represent? Remember the zeros are where f(x) =0.
We are given function for the path coming out of the cannon.
We also given x is the horizontal distance from the cannon.
We need to explain, what f(x) represents there.
f(x) represents y-axis.
And y-axis also represents height.
Height represents a vertical distance.
Therefore, we could say f(x) represents vertical distance (height) from the cannon for x horizontal distance from the cannon.
22 mice were introduced to a new environment. Their population triples every year. Using m(t) as the function name and t for time, write this equation.
Answer:
when were they introduced?
Step-by-step explanation:
How many minutes are in 3 hours?
There are 60 minutes in one hour.
Complete the table.
Answer:
180
Step-by-step explanation:
because there are 60 minutes in an hour and you need 3 you need to add 60 + 60 + 60 or your can do 60 x 3 which equals 180
Answer:
180 minutes
Step-by-step explanation:
1 hour - 60 minutes
2 hours - 120 minutes
3 hours - 180 minutes
Because there is 60 minutes in an hour, you can do 60 x 3 = 180. This will directly tell us how many minutes are in 3 hours. Or, you can add 60 minutes 3 times for 3 hours.
So, 60 x 3 = 180. There are 180 minutes in 3 hours.
A ball is thrown from an initial height of 3 feet with an initial upward velocity of 44 ft/s. The ball's height h (in feet) after seconds is given by the following.
h = 3+44t-16t^2
Find all values of t which the balls height is 23 feet.
Answer:
See below ↓↓
Step-by-step explanation:
Given function
h = 3 + 44t - 16t²We need to calculate the possible values of t at h = 23 feet.
Subsituting h = 23,
23 = 3 + 44t - 16t²16t² - 44t + 20 = 0Divide throughout by 4 as it is a common factor4t² - 11t + 5 = 0Solving for 't' using quadratic formula
t = 11 ± √121 - 4(4)(5) / 8t = 11 ± √41 / 8Solutions
t = 11 + 6.4 / 8 = 17.4/8 = 2.175 secondst = 11 - 6.4 / 8 = 4.6/8 = 0.575 secondsAnswer:
t = 2.175 s (3 dp)
t = 0.575 s (3 dp)
Step-by-step explanation:
Given equation: [tex]h=3+44t-16t^2[/tex]
To find all values of t for which the ball's height is 23 ft, substitute h = 20 into the equation and solve for t:
[tex]\implies h=23[/tex]
[tex]\implies 3+44t-16t^2=23[/tex]
[tex]\implies 16t^2-44t-3+23=0[/tex]
[tex]\implies 16t^2-44t+20=0[/tex]
Factor out common term 4:
[tex]\implies 4(4t^2-11t+5)=0[/tex]
Divide both sides by 4:
[tex]\implies 4t^2-11t+5=0[/tex]
Quadratic formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0[/tex]
Use the quadratic formula to solve for t:
[tex]\implies t=\dfrac{-(-11) \pm \sqrt{(-11)^2-4(4)(5)} }{2(4)}[/tex]
[tex]\implies t=\dfrac{11 \pm \sqrt{41}}{8}[/tex]
Therefore,
t = 2.175 s (3 dp)t = 0.575 s (3 dp)Giving brainliest! need this question rlly soon thank you so much :)
Question 1 – A two-mass (pulley) system begins in the initial configuration shown in the figure. Once this system is allowed to
move, the cart will move to the right and the suspended mass will fall with the same (magnitude of) acceleration. Determine this
acceleration, A, of this system, and the force in the cable, F, accurate to 3 sig. dig.
Assume the pulley and cable has no mass.
Answer:
the suspended mass will fall with the same (magnitude of) acceleration. Determine this
accelerat
Step-by-step explanation: