Step-by-step explanation:
arccos(sin(5π/4))
= arccos(sin(-π/4))
= arccos(-√2/2)
= 3π/4.
The value of trigonometric function arccos(sin(5π/4)), π/4
What is trigonometry?Trigonometry is a branch of mathematics, which deals with the study of right angle triangles. Trigonometry is concerned with specified functions of angles and their applications to calculations.
There are 6 commonly used functions in trigonometry with their name and abbreviations-
sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), cosecant (cosec)
First, we can use the trigonometric identity sin(θ) = cos(π/2 - θ) to rewrite this expression:
sin(5π/4) = cos(π/2 - 5π/4)
Next, we can use the fact that cos(x) is an increasing function on the interval [0, π], so cos(x) is unique on this interval for each value of x.
This means that the inverse cosine function, arccos, is also unique on the interval [0, π].
Therefore, we can conclude that:
0 ≤ π/2 - 5π/4 ≤ π
arccos(sin(5π/4)) = π/2 - 5π/4 = π/4.
So the answer is π/4 in radians.
To know more about trigonometry check:
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A new tablet was originally $180. It was on sale for 10% off the original price. The amount of the tablet after 10%
Answer:
$162
Step-by-step explanation:
10% of 180 is 18
180-18=162
On a shelf there are 60 novels and 20 poetry books. What is the probability that person A chooses a novel and walks away with it and then person B walks up shortly after and picks another novel?
Model the unknown number problem by writing in algebraic expression. Jonas shared a bag of trail mix equally with 10 of his teammates. T-11 t/11 11t t+11
Answer: its t over 11. T/11
Step-by-step explanation:
I took the assignment
Answer:
b
Step-by-step explanation:
Hello help me plsss plssss pretty pleasee!!!
Answer:6.1638 7.69 8.18.04
Step-by-step explanation:
6. 1638
7. 20
8. 9 4/12 or 9 1/3 (simplified)
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I need you guys help on dis...like I don’t even know anymore.
Explain if you can please!!
6. The diameter of a circle is 9 feet. What is the measure of its circumference? Round to the nearest tenth.
A. 28.3 ft
B. 63.6 ft
C. 4.5 ft
D. 14.1 ft
Answer:
A.
[tex]C= 28.3 \ \ feet[/tex]
Step-by-step explanation:
Formula for Circumference is
[tex]C=2\pi r[/tex]
We know radius is half of diameter
[tex]r=\frac{d}{2} \\r=\frac{9}{2}[/tex]
[tex]C=2(3.14)\frac{9}{2}[/tex]
[tex]C=(3.14)9\\C=28.3 feet[/tex]
The access code for a car's security system consists of four digits. The second digit cannot be zero and the last digit must be odd. How many different codes are available?
Answer:
4,500 different codes.
Wait whats the equation for this?
Answer:
10.5
Step-by-step explanation:
Both widths are the same in a rectangle. So both are 6.5. Then you subtract 13 from 34. Now you are left with 21. No divide that by two to get your two lengths. That is l. L=10.5
Answer:
Step-by-step explanation:
P=2L+2W
P=34 W= 6.5
34=2L+2*6.5
34=2L+13
2L=21
L=10.5
or
Given:
P = 34 [Perimeter]
W = 6.5 {let's use W and L to make it easy to read]
Also known:
P = W + L + W + L = 2(W+L)
Fill in values:
34 = 2(6.5+L) [NOTE: This is an equation to determine the length (L) of the rectangle."]
. . .
17 = 6.5 + L [NOTE: This is a simplified form of the above equation.]
. . .
10.5 = L [NOTE: This is the solution (the value of L)]
if a 60-page magazine cost $1.20 to print, find the cost per page to print.
Answer:
the answer is 2 cents per page
Please I need help!
Answer:
pls don't give up and try your best!
Step-by-step explanation:
try you best pllss
Lee read 1/6 of book on monday and another 1/3 of it on tuesday ,he took another 4 days to finish reading the book he read the same number of pages on each of the days ,what fraction of the book did he read on each of these days?
Answer:
1/8
Step-by-step explanation:
Let
The total fraction of the book read = 1
The remaining 4 days be represented as= x
Hence:
1 = Fraction of book read on Monday + Fraction of the book read on Tuesday + Fraction of the book on the remaining 4 days
1 = 1/6+ 1/3 + x
x = 1 - (1/6+ 1/3)
x = 1 - (1 + 2/6)
x = 1 - (3/6)
x = 1 - 1/2
x = 1/2
The fraction of the book read in 4 days = 1/2
To calculate the fraction of the book read on each of the days, since he read the same number of pages on each of the days we have:
1/2 ÷ 4 days
= 1/2 × 1/4
= 1/8
Therefore, the fraction of the book that was read on each of the 4 days is 1/8
Original price of a computer game: $24.50
Discount: 20%
What is the selling price
Answer:
You will pay $19.6 for a item with original price of $24.50 when discounted 20%. In this example, if you buy an item at $24.50 with 20% discount, you will pay 24.50 - 4.9 = 19.6 dollars.
Step-by-step explanation:
What is the Midpoint of segment BC with B(-9, -4) and C(-3, 5)?
Answer:
(-6,0.5)
Step-by-step explanation:
(-9 + -3)÷2= -6
(-4 + 5)÷2=0.5
(-6,0.5)
Determine whether the function is linear or nonlinear. y−1/x=11 *
Answer:
vjhghjsbzkcbjhvdhmvh
Step-by-step explanation:
determine if the following statement is true or false. if it is false, rewrite the statement so it is true. if a function has an inverse, and the function contains the point (r,q), then the inverse also contains the point (r,q).
She ran 52.16 seconds per 400 meters, how fast was she running in meters per hour?
Answer:
27607.36 meters per hour
Step-by-step explanation:
400/52.16 = 7.66871165644
7.66871165644 meters per second
7.66871165644 × 60 = 460.122699386 meters per minute
460.122699386 * 60 = 27607.3619632 meters per hour
27607.3619632 meters per hour
The number of trees in a rainforest decreases each month by 0.5%. The forest currently has 2.5 billion trees. Which expression represents how many trees will be left in 10 years.
Given:
Present number of trees = 2.5 billions
Rate of decrease = 0.5% per month
To find:
The expression that represents how many trees will be left in 10 years?
Solution:
Exponential decay model:
[tex]P(t)=a(1-r)^t[/tex] ...(i)
where, a is initial value, r is decreasing rate and t is time period.
We have,
a = 2.5 billions
r = 0.5% = 0.005 per month
t = 10 years = 120 months [1 year = 12 months]
Putting a=2.5, r=0.005 and t=120 in (i), we get
[tex]P(120)=2.5(1-0.005)^{120}[/tex]
[tex]P(120)=2.5(0.995)^{120}[/tex]
[tex]P(120)=1.3699657[/tex]
[tex]P(120)\approx 1.37[/tex]
Therefore, the required expression is [tex]2.5(1-0.005)^{120}[/tex] and the remaining trees after 10 years is about 1.37 billions.
determnine if each table shown below represents a function or not.
Answer:
Table 1 does not represent a function.
Table 2 does not represent a function.
Step-by-step explanation:
Table 1
Input (x) 1 3 5 5 9
Output (y) 7 16 19 20 28
We know that a function is a relation where each input or x-value of the X set has a unique y-value or output of the Y set.
In other words, we can not have duplicated inputs as there should be only 1 output for each input.
Table 1 indicates that x = 5 is repeated twice. In other words, the input x = 5 is duplicated and we know that we can not have duplicated inputs as there should be only 1 output for each input.
Therefore, table 1 does not represent a function.
Table 2
Input (x) 0.5 7 7 12 15
Output (y) 1 15 10 23 30
We know that a function is a relation where each input or x-value of the X set has a unique y-value or output of the Y set.
In other words, we can not have duplicated inputs as there should be only 1 output for each input.
Table 2 indicates that x = 7 is repeated twice. In other words, the input x = 7 is duplicated and we know that we can not have duplicated inputs as there should be only 1 output for each input.
Therefore, table 2 does not represent a function.
Conclusion:
We have concluded that both tables do not represent the function.
Kiran scored 223 fewer points in a computer game than Tyler. Kiran scored 409 points. Which equation would Kiran use to determine how many points, t, Tyler scored?
Answer:
[tex]t-223=409[/tex]
Step-by-step explanation:
Since Kiran scored 223 fewer points in a computer game than Tyler, Tyler's score can be represented as:
[tex]k+223=t[/tex], where [tex]t[/tex] is Tyler's score and [tex]k[/tex] is Kiran's score.
Since Kiran scored 409 points, we can set [tex]k=409[/tex]:
[tex]409+223=t[/tex].
Re-arranging this, we get:
[tex]\fbox{$t-223=409$}[/tex].
Answer:
h
Step-by-step explanation:
j
6 people are playing a game 1 person beat the high score from 746 more than 10254
the other 5 failed and had to retry then all 5 got the same score 10999
what was the score the 6th person got
Answer: Hello hope you had a good day, Answer should be 11,000
Step-by-step explanation:
if the first guy beat it by 746 more that 10254 then add the two together for 11,000
-
it also says the OTHER 5 meaning a diffrent 5 so the 6th got 11,000.
what happens to the value of the expression 80_h as h increases from a small positive number to a large positive number
Answer:
It decreases
Step-by-step explanation:
Hope you don't need an explanation, it decreases is the real answer.
help me pleasee i dont know how to do thiss
Step-by-step explanation:
Since UV bisects TW, TW also bisects UV.
=> Line segments UV and TW bisect each other.
=> 4y - 3 = 2y + 1 and 3x + 8 = 3y + 2
=> 2y = 4 and 3x = 3y - 6
=> y = 2 and x = y - 2
=> y = 2 and x = (2) - 2
=> y = 2 and x = 0.
Answer:
y= 181/7 or 25.86
i really dont know about x
HALP! WORD PROBLEM 20 points: A store has reduced the price by $20. How large must the next discount be so the new price will be half of the original price? Express your answer as a percent to the nearest tenth.
Answer:
HALP word is wrong all word is but HALP is wrong.
If "k" is a negative number, then k + 2 is a negative number.
Answer:
Not exactly, if a possitive and a negetive are added together the number that was larger will choose its symbol. Say "k" is -3, so -3 + 2 = -1, or if "k" was -1, then -1 + 2 = 1.
Step-by-step explanation:
I hope that makes sense
Ms. Lynette earns $19.50 an hour when she works overtime. She worked overtime twice this week. One day she worked 3 hours of overtime. Her total overtime pay for the week is $146.25.
Write an equation to find the number of overtime hours she worked on the second day, x.
Answer:
146.25 divided by 2
Step-by-step explanation:
Use the number line below, where RS = 6y + 3, ST = 4y + 7, and RT = 60.
Answer:
Step-by-step explanation:
RS + ST = RT
6y + 3 + 4y + 7 = 60
6y + 4y + 3 + 7 = 60
10y + 10 = 60
10y = 60 - 10
10y = 50
y = 50/10
y = 5
RS = 6*5 + 3 = 30 +3 = 33
ST = 4*5 + 7 = 20 + 7 = 27
Step-by-step explanation:
[Diagram in image attached]
RS + ST = RT
(6y +3) + (4y + 7) = 60
6y + 3 + 4y + 7 = 60
10y + 10 = 60
10y = 60 - 10
10y = 50
y = 50/10
y = 5
RS = 6y +3 = 6(5) + 3 = 30 + 3 = 33
ST = 4y +7 = 4(5) + 7 = 20 + 7 = 27
RT = 60
{RS + ST = RT
33 + 27 = 60}
HOPE THIS HELPS YOU
MARK AS BRAINLIEST
The slope formula can be used to find the slope, m, of a line with points (L1, y1) and (22, 42).
Y2 - Yi
22 - 21
m
Which is an equivalent equation?
O Y1 = -m (22 – x1) + y2
yı = -m (x2 – 21) – Y2
Oyı = m (22 – 21) + y2
Oyı = m (22 – 21) – Y2
Answer:
A. [tex] y_1 = -m(x_2 - x_1) + y_2 [/tex]
Step-by-step explanation:
Given, slope formula = [tex] m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
To find an equivalent equation, let's make [tex] y_1 [/tex] the subject of the formula.
[tex] m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Cross multiply
[tex] 1(y_2 - y_1) = m(x_2 -x_1) [/tex]
[tex] y_2 - y_1 = m(x_2 - x_1) [/tex]
Subtract [tex] y_2 [/tex] from both sides
[tex] y_2 - y_1 - y_2 = m(x_2 -x_1) - y_2 [/tex]
[tex] - y_1 = m(x_2 - x_1) - y_2 [/tex]
Divide both sides by -1
[tex] \frac{- y_1}{-1} = \frac{m(x_2 -x_1) - y_2}{-1} [/tex]
[tex] y_1 = -m(x_2 - x_1) + y_2 [/tex]
What is 2i-3=2(6-i)+7i as a fraction or decimal or whole number
Answer:
i = - 5
Step-by-step explanation:
Given
2i - 3 = 2(6 - i) + 7i ← distribute and simplify right side
2i - 3 = 12 - 2i + 7i
2i - 3 = 12 + 5i ( subtract 5i from both sides )
- 3i - 3 = 12 ( add 3 to both sides )
- 3i = 15 ( divide both sides by - 3 )
i = - 5
Emily wants to buy a new Gucci purse. She goes into the store and sees that they are running a January Blowout Sale and all purses are 60% off! She finds one that she likes and the tag reads $475.00. How much is Emily going to spend?
Answer:
Emily is going to spend $285
Step-by-step explanation:
You need to multiply 475.00 by 0.60 to get 285 spent on Emily's new purse.
At a restaurant your bill is $32. You have a coupon for 15% off. You are in Idaho and they charge you 7% tax. (Discount before tax) What is the final cost of your meal after your discount and with tax included? Round to the nearest cent.
Answer:
the answer is 25.30
Step-by-step explanation:
1. first you subtract the 15% from the bill that comes out to $27.20
2. next subtract the 7% tax from the $27.20 to get your answer