Deduce the minimum value of sinx+cosx and give the corresponding values of x, for x E [-360;360]
The minimum value of both sine and cosine is -1. However the angles that produce the minimum values are different, [tex]-\pi/2, \pi[/tex] for sine and cosine respectively.
The question is, can we find an angle for which the sum of sine and cosine of such angle is less than the sum of values at any other angle.
Here is a procedure, first take a derivative
[tex]\frac{d}{dx}(\sin x+\cos x)=\cos x -\sin x[/tex]
Then compute critical points of a derivative
[tex]\cos x-\sin x=0\implies x_1=\frac{\pi}{4},x_2=\frac{5\pi}{4}[/tex].
Then evaluate [tex]\sin x +\cos x[/tex] at [tex]x_1,x_2[/tex].
You will obtain global maxima and global minima [tex]\sqrt{2}, -\sqrt{2}[/tex] respectively.
The answer is [tex]-\sqrt{2}[/tex].
Hope this helps.
Given sin^2 x = (1 - cos(2x))/2 Prove: sin(x/2) = plus/minus sqrt((1 - cos(x))/2) Prove Complete the steps of the proof
Answer:
1. half angle
2. x
Step-by-step explanation:
The missing parts of the proof is the variable x.
What are Trigonometric Functions?Trigonometric functions are those functions which are the ratio of the sides of a right angled triangle.
Given,
sin² (x) = [1 - cos (2x)] / 2
We have to prove sin ([tex]\frac{x}{2}[/tex]) = ± [tex]\sqrt{\frac{1-cos (x)}{2} }[/tex]
First, we have
sin² (x) = [1 - cos (2x)] / 2
Substituting x/2 in place of x, we get,
sin² (x/2) = [1 - cos (2x/2)] / 2
sin² (x/2) = [1 - cos (x)] / 2
sin² ([tex]\frac{x}{2}[/tex]) = [tex]{\frac{1-cos (x)}{2} }[/tex]
Taking square root on both sides,
sin ([tex]\frac{x}{2}[/tex]) = ± [tex]\sqrt{\frac{1-cos (x)}{2} }[/tex]
Hence it is proved.
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I NEED HELP FAST! Which of the following sets of numbers could not represent the three sides of a triangle?
Answer:
(8, 23, 31)
Step-by-step explanation:
The sum of the lengths of the two shorter legs must be greater than the length of the longer leg
(not equal to either)
A restaurant chef has designed a new set of dishes for his menu. His set of dishes contains 10 10 main courses, and he will select a subset of them to place on the menu each night. To ensure variety of main courses for his patrons, he wants to guarantee that a night's menu is neither completely contained in nor completely contains another night's menu. What is the largest number of menus he can plan using his 10 10 main courses subject to this requirement
Answer:
252 menu
Step-by-step explanation:
Total number courses, n = 10
The largest number of menu the chef can plan using his 10 main courses.
There are various combinations of menu obtainable from the available courses :
Ranging from :
nC0 to nCn
The largest number of menu he can plan is the highest output obtainable between :
10C0 to 10C10
10C0 = 1
10C1 = 10
10C2 = 45
10C3 = 120
10C4 = 210
10C5 = 252
10C6 = 210
10C7 = 120
10C8 = 45
10C9 = 10
10C10 = 1
Hence, the largest number of menu he can plan using his 10 main courses is 252
What is the inverse operation needed to isolate the variable 4 = p - 8
Answer:
To do this you need to add both sides by 8. yw
Step-by-step explanation:
my points is going lower and lower and lower and lower until its zero
But i dont care.
Just answer my question in the picture above.
Answer:
c, a, b
...................
A quarter falls off a building that is 144
feet tall. If the equation for height as a
function of time is
h(t) = -16t2 + initial height where t is
time in seconds and h(t) is height in
feet, how many seconds will it take for
the quarter to hit the ground?
Answer:
3 seconds
Step-by-step explanation:
Initial height = 144 feet
t = Time taken
The equation of the height from the ground is
[tex]h(t)=-16t^2+\text{Initial height}[/tex]
The time taken to reach the ground is needed. Here the ground is taken as reference so [tex]h(t)=0[/tex]
[tex]0=-16t^2+144\\\Rightarrow -144=-16t^2\\\Rightarrow t=\sqrt{\dfrac{144}{16}}\\\Rightarrow t=3\ \text{s}[/tex]
So, time taken by the quarter to reach the ground is 3 seconds.
Find the value of x and y. This has to do with geometry
Answer:
x = 30°
y = 30°
Step-by-step explanation:
By inscribed angle theorem:
[tex]x = y = \frac{1}{2} \times 60 \degree \\ \\ x = y = 30 \degree[/tex]
Declan's goal is to score 90% on the upcoming science test. If there are 50 questions on the test, how many does he need to answer correctly?
Answer:
45
Step-by-step explanation:
Alice sells bracelets 10 for $5. How much does 1 bracelet cost?
Answer:
FOR ALL MY POINTS write an argumentative essay on why dog parks are "helpful or harmful"
READ PROMPT
Step-by-step explanation:
Answer:
$2
Step-by-step explanation:
Because Alice sells 10 bracelets for 5 dollars, you have to do 10/5 which is equal to 2. Therefore, 1 bracelet cost $2.
Item 8
Select the cone(s) that are similar to a cone with a height of 9 meters and a radius of 3 meters.
cone with a height of 15 meters and a radius of 6 meters
cone with a height of 12 meters and a radius of 4 meters
cone with a height of 6 meters and a radius of 3 meters
cone with a height of 3 meters and a radius of 1 meter
OMG?!?!?!!?! HELP!!!?!?!?! PLEASE !?!?!? Thanks to those who do :D <3
A pump can fill 1800KL tank in one hour. How long would it take to fill a 90 KL tank?
HELP ASAP
The radius of a quarter circle is 1.4 millimeters. What is the quarter circle's area?
Answer:
A = 1.5386
Step-by-step explanation:
Quarter circle area formula:
A = (πr²)/4
A= (π1.4²)/4
A = (3.14*1.96)/4
A = (6.1544)/4
A = 1.5386
(2+5x)9= combine like terms
Answer:
18+45x
Step-by-step explanation:
A baseball player throws a ball from second base to home plate. How far does the player throw the ball? Include a diagram showing how you got your answer. Decide how many decimal points of accuracy are reasonable. Explain your reasoning.
Answer:
Distance=123.28. Two decimal places is reasonable, because it gives a close approximate to the exact answer, while remaining short and easy to use.
Step-by-step explanation:
Use Pythagorean theorem.
90^2+90^2=c^2
8100+8100=16200
The square root of 16200 is 127.279220614
127.279220614~127.28
What is the probability that a six sided dice rolls on the four and the card is a heart
Answer:
4/6
Step-by-step explanation:
the total time the dice roll over four.. which is also 4/6
A rocket is fired directly upwards with a velocity of 80 ft/sec. The equation for its height, H, as a function of time, t, is
given by the function
H (t) = -1612 + 80+
Find the time at which the rocket reaches its maximum height, and its maximum height.
5
a) O time =
22
sec, max height = 200 ft
b) O time = 80 sec, max height = 100 ft
5
c) O time =
2
sec, max height = 100 ft
d) O time = 5 sec, max height = 200 ft
5
e) Otime = sec, max height = 400 ft
23
Revie
Answer:
(c).
Step-by-step explanation:
h(t) = - 16 t² + 80 t
Coordinates of the vertex are:
t = - [tex]\frac{80}{2(-16)}[/tex] = [tex]\frac{5}{2}[/tex] = 2.5 sec.
h = - 16(2.5)² + 80(2.5) = - 100 + 200 = 100 ft.
HELP PLEASE DUE IN 4 MINUTES
Christina built a small hot air balloon and recorded the distance it traveler (v) during the first 4 seconds after starting (s)
Which of the following equations representd the relationship between the distance traveled and the elpsed time?
A: v=1.2s
B: s=1.2v
C:v=1.2+s
D:s=1.2+v
Table is attatched
Answer "v = 1.2s"
Step-by-step explanation: because 1.2 is 1*1.2, 2.4 is 2*1.2 and so on..
What is the range of the shoe sizes?
Answer:
The answer will be 9 and the frequency will be 18
which is equivalents to 9/8
Answer:
12
Step-by-step explanation:
Answer: 9/8 , 18/16 , 27/24 , 36/32 , 45/40 , 54/48 , 63/56
what is the equation to 3x+2x+-x
Answer:
the answer qould be 4x if you are just simplifying
if a state issued license plates using the scheme of one letter followed by five digits, how many plates could it use
Answer:
786240 different license plates.
Step-by-step explanation:
The required number of plates that can be used is 2,599,974.
Given that,
State-issued license plates use the scheme of one letter followed by five digits, how many plates could it used is to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Maxium five-digit number = 99999
Total letters = 26
Number of plates = 26 × 99999 = 2,599,974
Thus, the required number of plates that can be used is 2,599,974.
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Which is the solution to the inequality? 2 3/5 <b - 8/15
A. b<2 1/15
B. b>2 1/15
C. b<3 2/15
D. b>3 2/15
PLS NO CHEATING. I RLY NEED THIS. IF U DONT CHEAT I WILL MARK BRAINLIEST
Step-by-step explanation:
i think it's a b and answer my new question it's 100 point question I really need the answer pls help me
the u.s. landfill contained a total of 200 million tons of trash how many more million tons of trash has been paper than Rubber and leather?
Answer:
9,160,000 tons
a map that created using a scale of 1 inch equals 3 miles shows a lake with an area of 18 square inches was a actual area of the lake
Answer:
Step-by-step explanation:
18in^2(3mi/in)^2
18in^2(9mi^2/in^2)
162 mi^2
What is the area of the part that is not shaded.
Answer: 48
Step-by-step explanation:
big square is 64, shaded square is 16
64-16= the unshaded region
PLEASEEEEE SOMEBODY CAN YOU LOOK AT THE ATTACHMENTS ITS MATH IM OFFERING A 69 POINTS
I don't know sorry but I recommend using quizlet
In ΔDEF, the measure of ∠F=90°, the measure of ∠D=69°, and FD = 64 feet. Find the length of DE to the nearest tenth of a foot.
Answer:
Step-by-step explanation:
ASAP I WILL GIVE BRAINIEST IF ANSWERED ASAP!! PLEASE PLEASE HELP
Answer:
2x + 3 =84
Step-by-step explanation:
Answer:
2x + 3 = 84
Step-by-step explanation: