If sin 64° = p, determine the value of the following in terms of p.
8 sin 16º.cos 16º.cos32°
We are provided that [tex]{\sf \sin (64^{\circ})=p}[/tex] and we have to find the value of [tex]{\sf 8\sin (16^{\circ})\cdot \cos (16^{\circ})\cdot \cos (32^{\circ})}[/tex] . But let's recall a identity which is gonna be very helpful to do this question i.e
[tex]{\boxed{\sf 2\sin (\theta)\cos (\theta)=\sin (2\theta)}}[/tex]Now , coming back on the question ;
[tex]{:\implies \quad \sf 8\sin (16^{\circ})\cdot \cos (16^{\circ})\cdot \cos (32^{\circ})}[/tex]
[tex]{:\implies \quad \sf 4\{ 2\sin (16^{\circ})\cos (16^{\circ})\}\cos (32^{\circ})}[/tex]
Using the above identity ;
[tex]{:\implies \quad \sf 4\sin (32^{\circ})\cos (32^{\circ})}[/tex]
[tex]{:\implies \quad \sf 2\{2\sin (32^{\circ})\cos (32^{\circ})\}}[/tex]
Again using the same identity ;
[tex]{:\implies \quad \sf 2\sin (64^{\circ})}[/tex]
Putting the given value of [tex]{\sf \sin (64^{\circ})}[/tex]
[tex]{:\implies \quad \sf 2p}[/tex]
[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{8\sin (16^{\circ})\cdot \cos (16^{\circ})\cdot \cos (32^{\circ})=2p}}}[/tex]
Proof of the above identity :-
We know that ;
[tex]{\quad \boxed{\sf \sin (A\pm B)=\sin (A)\cos (B)\pm \cos (A)\sin (B)}}[/tex]
So ;
[tex]{:\implies \quad \sf \sin (A+ B)=\sin (A)\cos (B)+\cos (A)\sin (B)}[/tex]
Putting [tex]{\sf A=B=\theta}[/tex] ,
[tex]{:\implies \quad \sf \sin (\theta+ \theta)=\sin (\theta)\cos (\theta)+\cos (\theta)\sin (\theta)}[/tex]
[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{\sin (2\theta)=2\sin (\theta)\cos (\theta)}}}[/tex]
Hence , Proved :D
helllppppp meee please
Answer:
Option B is the correct answer
Step-by-step explanation:
Hope it helps you in your learning process.
[tex]\tan 30\degree=\frac{17}{x}[/tex]
[tex]\implies\frac{1}{\sqrt 3}=\frac{17}{x}[/tex]
[tex]\implies\huge{\red{ x={17\sqrt 3}}}[/tex]
[tex]\sin 30\degree=\frac{17}{y}[/tex]
[tex]\implies\frac{1}{2}=\frac{17}{y}[/tex]
[tex]\implies\huge{\purple{ y={34}}}[/tex]
Answer:
B
Step-by-step explanation:
It would be using the law of sines.
What is the 30th term of the linear sequence
-5 -7 -9 -11 -13
Answer:
the 30th term of the given linear sequence is -63.
Step-by-step explanation:
The given sequence is in arithmetic progression whose difference is given by:
-7 - (-5) = d
d = -2
The nth term in the arithmetic progression is given by the formula:
where 'n' is the number of terms, 'a' is the first term, is the nth term, and 'd' is the difference.
Now, substitute the known terms in the above formula.
So, the 30th term of the given linear sequence is -63.
Clara surveyed 12 elementary school students in a regional spelling bee.
Is this a random sample of elementary school students?
yes
no
Answer:
No, it isn't a random sample of students because Clara surveyed students in a regional spelling bee so instead it would be a survey of the kids in the spelling bee.
In the following figure, the value of x is
20
135
с
B
Note: Round your answer to the nearest tenth.
20
y'all homeworks are easy lølllll
Joey borrowed $2,750 from
the bank at 5% simple interest
for 5 years. How much is Joey
going to pay in interest?
Answer:
Simple Interest: $3.44
Annually Compounded Interest: $3.51
Answer:
Joey is going to pay $687.5
In all Joey is going to pay $3437.5
Step-by-step explanation:
To get 687.5 you have to do $2750 x 0.05 x 5 years
That gets you 687.5
Work out the following: Share 30 in the ratio 1:9
Answer:
3
Step-by-step explanation:
share 30 in the ratio 1:9
1+9=10
30÷10 =3
3 in each part
what is 950% as a fraction
Answer:
9 1/2
Step-by-step explanation:
[tex]\frac{950}{100}=9\frac{50}{100} = 9 \frac{1}{2}[/tex]
PLEASE HELPP 8th grade
Answer:
5.83 or 6
Step-by-step explanation:
don't know for sure sorry! have a good day or night!
Answer: 5.83
Step-by-step explanation: Im a fifth grader I’m only taking an estimate
Halp me
Discuss the important features of the box-and-whiskers plot.
Answer:
As shown, a box-and-whisker plot is a way of summarizing a set of data measured on an interval scale. This type of graph is used to show the shape of the distribution, its central value, and its variability.
Explanation:
100% When I put this in
Factor: 28k^3-24k^2+49k-42
I will give Brainliest to the first person :)
Answer:
(4k^2+7)(7k+6)
Step-by-step explanation:
1. group the first two terms (28k^3-24k^2). The greatest common factor is 4k^2. If you factor that out you get 4k^2(7k-6)
2.When you group the last two terms (49k-42). you can factor out a 7.
7(7k-6).
3. There is a (7k-6) in both sections so you can combine all the terms.
4k^2(7k-6) 7(7k-6) becomes (4k^2)(7k-6)
Carl is standing the top of 35ft cliff looking down at a rock for notion in the sea. He estimates the angle of depression to the formation is 30' . What is the hozonal distance from Carl to the island?
Answer:
70 ft
Step-by-step explanation:
If you draw a diagram, a right triangle is formed from this scenario. Because Carl is directly 35 ft above the ground, this represents the opposite side length in the triangle model. The distance between Carl and island would represent the hypotenuse.
The trig function that corresponds with opposite and hypotenuse legs is Sine.
The equation is sin(30°) = [tex]\frac{35}{h}[/tex]
sin(30) is 1/2. The value of h that would make this equation true is 70. Therefore he is 70 feet away from the island
40 POINTS! Please hurry! Which equation represents a function?
A.) x=-2y^2
B.) x=y^2-9
C.) x^2+y^2=1
D.) y=3x^2+2
Answer: A. x=-2y^2
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
I just did the test
If f(x) = x-1 and g(x) = 2x, what is and g(f(x))
Answer:
[tex]f(g(x)) = 2x - 1[/tex]
Step-by-step explanation:
learn composite functions
You had an emergency at hôme and you called the police at 11:47 p.m. They
arrived at your house at 12:07 a.m. How long did it take them to get to your
house.
Answer:
20 mins
Step-by-step explanation:
The answer is 20 minutes. If you look at the times it's 11:47 and 12:07. Notice the times end in 7. You would add ten minutes until you get the time, and in the end you have 20 mins.
Hope this helps!
What should the graph of two lines look like when there are no solutions that they have in common?
Answer:
parallel
Step-by-step explanation:
if two lines are not parallel they will cross eventually at one point meaning they will have a point in common so they must be parallel
QUESTION 1 of 10: The cost of a garment was determined to be $12. 50. You have been instructed to lower the cost to $10 per garment. What
is percentage you were asked to reduce the cost by?
Answer:
20%
Step-by-step explanation:The answer is minus 2.50 so if you plug 12.50 times .2 you get your answer
The percentage reduction is 20% if the cost of a garment was determined to be $12. 50.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
The cost of a garment was determined to be $12. 50. You have been instructed to lower the cost to $10 per garment.
The difference in cost = 12.50 - 10
The difference in cost = $2.50
The percentage reduction = (2.50/12.50)100
The percentage reduce = 20%
Thus, the percentage reduction is 20% if the cost of a garment was determined to be $12. 50.
Learn more about the percentage here:
brainly.com/question/8011401
#SPJ5
The Science Club went on a two-day field trip. The first day the members paid $60 for transportation
plus $11 per ticket to the planetarium. The second day they paid $90 for transportation plus $8 per
ticket to the geology museum. Write an expression to represent the total cost for two days for the
n members of the club.
An expression that represents the total cost in dollars for two days for the n members of the club is
given by
Answer:
day 1 total $60+$15=$75
day 2 total $95+$12=$107
total 2 days = $181
Step-by-step explanation:
Answer:
Total cost for two days for the n members of the club = 155 + 27 n
Step-by-step explanation:
Total number of persons = n
The first day the members paid $60 for transportation plus $15 per ticket to the planetarium.
Day 1 cost = 60 + 15 x n = 60 + 15 n
The second day they paid $95 for transportation plus $12 per ticket to the geology museum.
Day 2 cost = 95 + 12 x n = 95 + 12 n
Total cost = Day 1 cost + Day 2 cost
Total cost = 60 + 15 n + 95 + 12 n = 155 + 27 n
Total cost for two days for the n members of the club = 155 + 27 n
Help me i posted a picture. 75 points!!!!!
Answer:
80
Step-by-step explanation:
3x8=24
7x8=56
24+56=80
For the 7x8, I'm not including x1/2 also because if we do it once without the x1/2, then it will take it for 2 triangles, and that's what we have here.
So hence, the area of the trapezoid is 80sq.units
Thanks!
Answered by: FieryAnswererGT
#learnwithbrainly
Solution:
Note that:
Area of trapezoid = (a₁ + a₂)h/2Use the formula to find the area of the trapezoid.
(a₁ + a₂)h/2=> (3 + 7 + 7 + 3) x 8/2=> (20) x 8/2=> 160/2=> 80 units²
A circular running track is 1/2 mile long. Elena runs on this track, completing each lap in 1/10 of an
hour. What is Elena's running speed?
Answer:
5 mph
Step-by-step explanation:
1/2 mile in 1/10 of an hour
1 mile in 1/5 of an hour
5 miles in 1 hour
The fourth term of a sequence is 18.
The term – to – term rule is : ‘ Subtract 3 then multiply by 3.’ What is the first term of the sequence?
Answer:
11/3
Step-by-step explanation:
let the 3rd no be x
(x-3)3 = 18
x-3 = 6
x = 9
keep solving the equation and the first term will be 11/3
If A and B are dependent events, which of these conditions must be true? A. P(A and B) = P(A) P(B) B. P(A and B) = P(B) P(A) C. P(B|A) = P(B) D. P(A|B) = P(A) E. P(B|A) P(B).
The true condition about the dependent events, P(B|A) is not equal to P(B).
What is dependent probability?Dependent events in probability mean events whose occurrence of one affect the probability of occurrence of the other.
Two events are said to be dependent if the outcome or occurrence of the first affects the outcome or occurrence of the second so that the probability is changed.
Also, Two events are said to be independent if the outcome or occurrence of the first does not affect the outcome or occurrence of the second so that the probability is not changed.
For independent events: P(A and B) = P(A) x P(B).
Recall that P(B|A) = P(A and B) / P(A) = P(A) x P(B) / P(A) = P(B).
Therefore, for dependent events, P(B|A) is not equal to P(B).
To know more about dependent probability click the link given below,
https://brainly.com/question/12283505
Answer:
Option E is correct
Step-by-step explanation:
E. P(B|A) ≠ P(B)
to make a rectangle one pair of opposite sides of a square was made 50% longer and the other pair of opposite sides was made 50% shorter. What percent of the squares area is the area of the new rectangle
Answer:
The answer to ur question is probably 100%
Can you help me solve 5(X+2)²= 4(X+3)
Answer:
5X²+16X+8=0
Step-by-step explanation:
5(X+2) (X+2)=4(X+3)
5(X²+2X+2X+4)=4(X+3)
5(X²+4X+4)=4(X+3)
5X²+20X+20=4X+12
5X²+20X-4X+20-12=0
5X²+16X+8=0
A graph of a linear function is shown on the grid. Which of these best represents 0 of the function? A 8. B 10. C 16. D 24.
answer:
C. 16
explanation:
when x is 0, the y-intercept is 8
coordinates: (0,8) and (4,6)
slope:
[tex]\sf \frac{y2-y1}{x2-x1}[/tex]
[tex]\sf \frac{6-8}{4-0}[/tex]
[tex]\sf \frac{-2}{4}[/tex]
[tex]\sf -\frac{1}{2}[/tex]
equation:
[tex]\sf y = mx +b[/tex] [ where m is slope and b is y-intercept ]
[tex]y = \sf -\frac{1}{2}x +8[/tex]
solve for x-intercept:
note: zeros of a function are the values of x when f(x) is equal to 0
[tex]y = \sf -\frac{1}{2}x +8[/tex]
[tex]0= \sf -\frac{1}{2}x +8[/tex]
[tex]-8= \sf -\frac{1}{2}x[/tex]
[tex]\sf x = -8 * -2[/tex]
[tex]\sf x = 16[/tex]
Answer:C 16.
Step-by-step explanation:
its 16
Find the range of values for which x25x + 6 < 0
I hope this helps you! God Bless and have a great day!
:)
solve and simplify 2/3 x 3/4
Answer:
6/12 ≈ 1/2
Step-by-step explanation:
Q) 2/3 × 3/4 = ?
→ a = 2/3 × 3/4
→ a = (2 × 3)/(3 × 4)
→ a = 6/12
→ [ a = 1/2 ]
1/2
Multiply the numerators and the denominators of both fractions,
2 * 3
_____
3 * 4
= 6/12
Simplify.
1/2
Some number added to 5 is equal to -11. What is the number?
Answer:-16
Step-by-step explanation:x + 5= -11
isolate x by subtracting 5 on both sides
x=-16
1. Ernest calculated the slope of the graph during the uphill climb to be 10. His work is shown below. Determine whether his calculation was correct or incorrect, and then
explain why.
(2 points: 1 for the answer, 1 for the explanation)
Points: (60, 900). (15, 450)
900-450/60-15 = 450/45 = 10
Answer:
answer is correctthe correct formula was used appropriatelyStep-by-step explanation:
The slope of a line on a graph is found using the slope formula:
m = (y2 -y1)/(x2 -x1)
Ernest used (x1, y1) = (15, 450) and (x2, y2) = (60, 900) to fill values into this formula. In doing so, he got ...
m = (900 -450)/(60 -15) = 450/45 = 10
This is an appropriate use of the formula, so gave Ernest the correct answer.
If the dot product of two nonzero vector v1 and v2 is zero, what dose this tell us
It means that the two vectors are perpendicular or orthogonal
