Answers
Answer:
option D
Step-by-step explanation:
[tex]sin^2 ( \frac{3\pi}{2}) + cos^2(\frac{3\pi}{2}) = 1\\\\( -1)^2 + 0^2 = 1[/tex]
Explanation:
[tex]sin x = cos( \frac{\pi}{2} - x)\\\\sin(\frac{3\pi}{2}) = cos ( \frac{\pi}{2} - \frac{3\pi}{2})\\[/tex]
[tex]=cos(\frac{\pi - 3\pi}{2})\\\\ =cos(\frac{2\pi}{2})\\\\=cos \ \pi\\\\= - 1[/tex]
Therefore ,
[tex]sin^2( \frac{3\pi}{2}) = ( - 1)^2[/tex]
Related Questions
How do you complete the square of x2+8x+26?
Answers
Answer:
see below
Step-by-step explanation:
x^2+8x+26
Take the coefficient of the x term
8
Divide by 2
8/2 = 4
square it
4^2 =16
we need to add 16 to 26 = 16+10
x^2 + 8x+16 +10
(x+4)^2 +10
The answer you are looking for is (x+4)²+10.
Solution/Explanation:
Selecting the "x" term's coefficient,
It would be 8.
Now, dividing it by 2,
8/2=4.
Squaring 4,
4²=16.
So, now, since (x+4)²=x²+8x+16, you must solve for 26-16, which equals 10, which you would supplement into the equation.
So, therefore, (x+4)²+10.
I hope this has helped you. Enjoy your day.
Primo car rental agency charges $21 per day plus $0.20 por milo. Ultimo car rental agency charges $24 per day plus $1.00 per milo. Find the daily mileage for which the Ultimo charge is four times the Primo charge.
The mileage is
Answers
Answer:
300 miles
Step-by-step explanation:
Let us consider the miles they travelled is 'm'
Mileage for Primo= 21 + (m × 0.20) = 21+0.2m
Mileage for Ultimo= 24+ ( m× 1.00) = 24 + m
Question says The mileage is equal when Ultimo's charge is 4× Primo
Thus,
4 × (21+0.2m) = 24+ m
84 + 0.8m = 24 + m
60 = 0.2m
m = 300
A bicyclist is at point A on a paved road and must ride to point C on another paved road. The two roads meet at
an angle of 38° at point B. The distance from A to B is 18 mi, and the distance from B to C is 12 mi (see
the figure). If the bicyclist can ride 22 mph on the paved roads and 6.8 mph off-road, would it be faster for the bicyclist to ride from A to C on the paved roads or to ride a direct line from A to C off-road? Explain.
Answers
Answer:
Step-by-step explanation:
The diagrammatic expression to understand this question very well is attached in the image below.
By applying the law of cosine rule; we have:
a² = b² + c² - 2bc Cos A --- (1)b² = a² + c² - 2ac Cos B --- (2)c² = a² + b² - 2ab Cos C --- (3)From the diagram attached below, we need to determine the side "b" by using equation (2) from above:
b² = a² + c² - 2ac Cos B
From the information given:
a = 12 miles; c = 18 miles; ∠B = 38°
∴
replacing the values into the above equation:
b² = 12² + 18² - 2(12)(18) Cos (38°)
b² = 144 + 324 - 432 × (0.7880)
b² = 468 - 340.416
b² = 127.584
[tex]b = \sqrt{127.584}[/tex]
b = 11.30 miles
However, we are also being told that the speed from A → C = 6.8 mph
Thus, the time required to go from A → C can be determined by using the relation:
[tex]\mathbf{speed = \dfrac{distance}{time}}[/tex]
making time the subject of the formula, we have:
[tex]\mathbf{time= \dfrac{distance}{speed }}[/tex]
[tex]\mathbf{time= \dfrac{11.30}{6.8}}[/tex]
time = 1.66 hours
By using the paved roads, the speed is given as = 22 mph
thus, the total distance covered = |AB| + |BC|
= (18+12) miles
= 30 miles
∴
[tex]\mathbf{time= \dfrac{distance}{speed }}[/tex]
[tex]\mathbf{time= \dfrac{30}{22}}[/tex]
time = 1.36 hours
Therefore, the time used off-road = 1.661 hours while the time used on the paved road is 1.36 hours.
Since we are considering the shortest time possible;
We can conclude that it would be faster for the bicyclist to ride from A to C on the paved roads since it takes a shorter time to reach its destination compared to the time used off-road.
Learn more about Law of cosine here:
https://brainly.com/question/24077856?referrer=searchResults
It would be faster for the bicyclist to ride from A to C on the paved roads since the time to go from A to C on the paved roads is 1.4 h and the time to go from A to C off-road is 1.7 h.
To calculate which way would be faster we need to find the distance from point A to C with the law of cosines:
[tex] \overline{AC}^{2} = \overline{AB}^{2} + \overline{BC}^{2} - 2\overline{AB}\overline{BC}cos(38) [/tex]
Where:
[tex]\overline{AB}[/tex]: is the distance between the point A and B = 18 mi
[tex]\overline{BC}[/tex]: is the distance between the point B and C = 12 mi
[tex] \overline{AC} = \sqrt{(18 mi)^{2} + (12 mi)^{2} - 2*18 mi*12 mi*cos(38)} = 11.3 mi [/tex]
Now, let's find the time for the two following cases.
1. From point A to C on the paved roads (t₁)
[tex] t_{1} = t_{AB} + t_{BC} [/tex]
The time can be calculated with the following equation:
[tex] t = \frac{d}{v} [/tex] (1)
Where:
d: is the distance
v: is the velocity
Then, the total time that it takes the bicyclist to go from point A to C on the paved roads is:
[tex] t_{1} = t_{AB} + t_{BC} = \frac{18 mi}{22 mph} + \frac{12 mi}{22 mph} = 1.4 h = 84 min [/tex]
2. From point A to C off-road (t₂)
With equation (1) we can calculate the time to go from point A to C off-road:
[tex] t_{2} = \frac{\overline{AC}}{v_{2}} = \frac{11.3 mi}{6.8 mph} = 1.7 h = 102 min [/tex]
Therefore, it would be faster for the bicyclist to ride from A to C on the paved roads.
To find more about the law of cosines, go here: https://brainly.com/question/15740431?referrer=searchResults
I hope it helps you!
9sin(Θ)-7=0. Solve the trigonometric equation
Answers
Step-by-step explanation:
here's the answer to your question
½ sejam berapa minit?
Answers
Answer:
1/2 jam 30 menit mungkin?
1/2 jam adalah 30 minit
1/2 × 60 = 30 mins
English translation
1/2 an hour is 30 minutes
1/2 × 60 = 30 mins
Answered by Gauthmath must click thanks and mark brainliest
the guys is wrong i checked
Answers
Step-by-step explanation:
the guys is wrong i checked
look at the image below
Answers
Answer:
201.1 km²
Step-by-step explanation:
Surface area of the figure,
4πr²
= 4×π×4²
= 64π
= 201.1 km² (rounded to the nearest tenth)
Length of a line segment with endpoints (3,-2) and (-3,4).
Answers
Answer:
6squareroot2
Step-by-step explanation:
that's the answer I think
Which statement is sufficient to prove that quadrilateral ABCD is a parallelogram?
A) m∠A ≅ m∠C, m∠B ≅ m∠D
B) AB ≅ CD
C) AC ≅ BD
D) BC // AD
Answers
Answer:
A) m∠A ≅ m∠C, m∠B ≅ m∠D
Step-by-step explanation:
If both pairs of opposite angles are congruent, then the figure is a parallelogram.
Salaries of entry-level computer engineers have Normal distribution with unknown mean and variance. Three randomly selected computer engineers have following salaries (in $1000s): 70, 80, 90. The average and the standard deviation of the data in the sample are 80 and 10. Using hypothesis testing, determine if this sample provides a sufficient evidence, at a 10% level of significance, that the average salary of all entry-level computer engineers is different from $60,000.
a. Null hypothesis.
b. alternative hypothesis.
c. test statistic.
d. acceptance region.
Answers
Answer:
H0 : μ = 60000
H1 : μ ≠ 60000
Test statistic = 3.464
Step-by-step explanation:
Given :
Sample mean salary, xbar = 80000
Sample standard deviation, s = 10000
Population mean salary , μ = 60000
Sample size, n = 3
Hypothesis :
H0 : μ = 60000
H1 : μ ≠ 60000
The test statistic :
T = (xbar - μ) ÷ (s/√(n))
T = (80000 - 60000) ÷ (10000/√(3))
T = 20000 / 5773.5026
T = 3.464
The Decison region :
If Tstatistic >Tcritical
Tcritical at 10%, df = 2 ; two - tailed = 2.9199
Tstatistic > Tcritical ; He
what is the aswer to 5 is 2 more than?
Answers
Answer:
Cuz 5 is greater than 2
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
Mariah owed her grandfather 52.25 but was recently able to pay him back $1.50. How much does Mariah currently
owe her grandfather?
Answers
The answer is 50.75.
Answer:
52.25 - 1.50 = 50.75
Step-by-step explanation:
I'd recommend using a calculator or pencil and paper
53.25
- 1.50
--------
50.75
HELPPPP PLZ
Witch statement is true about the value of |6|?
Answers
Answer:
The third choice is the correct one.
Step-by-step explanation:
The absolute value of six means that it's the distance from 0 to six, and that distance will be positive regardless of the number being negative or not.
Answer: The third answer is correct
Step-by-step explanation:
Since |6| is the absolute value of positive six, the value of an absolute value of any number is always positive.
Let f(x)=−5x+18 and g(x)=x2+15.
Find f(−2)−g(−2).
Answers
Answer:
21
Step-by-step explanation:
-5(-2)-(-2)²+15
10-(4)+15
10-4+15
21
Answer:
9
Step-by-step explanation:
f(x)=−5x+18
f(-2) = -5(-2)+18 = 10+18 = 28
g(x)=x^2+15
g(-2) = (-2)^2 +15 = 4+15 = 19
f(02) - g(-2) = 28 - 19 = 9
 evaluate P(6,2) or 6p2
Answers
Answer:
30
Step-by-step explanation:
Permutation equation: [tex]\frac{n!}{(n-r)!}[/tex]
n = Total number of objects, r = Number of objects selected
[tex]_6P_2=\frac{6!}{(6-2)!}=30[/tex]
AABC is reflected across the x-axis and then translated 4 units up to create AA'BC. What are the coordinates of the vertices of AABC?
Answers
However the Triangle is then translated 4 units up, so the New and Final coordinates for Triangle ABC is A(-3,3) B(-1,0) and C(-2,4)
Hope this helps
PLEASE ANSWER
Triangle ABC is similar to triangle DEF. find the length of median CP
A. 12
B. 16
C. 24
D.48
Answers
12/16 = (3x-12)/(2x+8)
16(3x-12)=12(2x+8)
48x-192=24x+96
48x-24x=192+96
24x=288
X=288/24
X=12
3x-12
=(12x3)-12
=36-12
=24
C is the answer
Hope this helps!
Answer:
48
Step-by-step explanation:
2x+8=3x-12(ABCP ~FDQE)
2x-3x= -8-12
-x= -20
x=20
now,
CP=3x-12
3*20-12
48
if the value of a any quadratic function f (x)=ax^2 + BX + C is -8, the function will
Answers
Answer:
The parabola will open downward
Step-by-step explanation:
f (x)=ax^2 + BX + C
Since a = -8
The parabola will open downward
When a< 0 the graph opens downwards
a>0 the graph opens upwards
find the area of the shaded region
Answers
Answer:
22 cm²Step-by-step explanation:
Shaded area is the difference of the bigger circle and two smaller ones:
A = π(3²) - 2π(1²) = 7π = 7*3.14 ≈ 22 cm²730 million, 5
how to write it in digits
Answers
Answer:
730 million in numbers = 730,000,000
730M in short form.
What is the slope of a line perpendicular to line A?
Answers
Hope your day is going well
The slope equation is y2- y1/ x2-x1
Y2 = 5
Y1 = 0
X2= 3
X1= -7
5-0/ 3 - -7
5/10 5 divided by 10 is 2
Your slope is 2
Hope this helps *smiles*
Please help out explanation need it
Answers
Answer:
[tex] \sin(θ) = \frac{19}{41} \\ θ = 27.6 \\ θ = 28[/tex]
2. Solve the following system of equations. y = 5 + x 2x + 2y = 30
Answers
since we know y= 5 + x , plug this into y in the second equation.
2x + 2 (5 + x) = 30
distribute 2 into the 5 and x
2x + 10 + 2x = 30
combine like terms
4x + 10 = 30
subtract 10 from both sides
4x = 20
divide four by both sides to isolate the variable
x = 5
the area of a rectangular park is 7/8 sqaure mile. the length of the park is 3/4 mile. what is the width of the park?
Answers
Answer:
7/6
Step-by-step explanation:
since the formula of area is length times width,you have to divide the area by the length to find the width
area=length×width
the width will be
width=area÷length
=7/8÷3/4
7/8×4/3
7/2×1/3
7/6
that's the width you can prove it by multiplying the length times the width to see if you will get 7/8..
I hope this helps
What's the distance between the points (7,3) and (7,–8)?
Answers
Answer:
11
Step-by-step explanation:
The distance is found by
d =sqrt ( (x2-x1)^2 + (y2-y1)^2)
= sqrt( ( 7-7)^2 +(3 - -8)^2)
= sqrt(0 +(3+8)^2)
= sqrt( 11^2)
= 11
The distance between (7, 3) & (7, -8) is 11
Step-by-step explanation:
I used distance formula for the following explanation attached with an image.
Hope this explanation helps!
Sydney has finished all his work on time, but many of his teammates are still struggling to complete their assignments. What should he do? a) Not distract them; they may get farther behind. O b) Listen to them complain about their workloads O c) Help them complete their work d) Share his thoughts on how they could get their work done faster
Answers
Answer:
I think the correct option is c
Answer:
I think the correct answer is (d)
Step-by-step explanation:
if he shares his thoughts on how they could get their work done faster like using an app like this, then it would be of great help to them
In an experiment, the initial temperature of a solution is -5 °C. The solution is heated up at 3 °C per minute for 19 minutes and then it is cooled at 4 °C per minute for 6 minutes. Calculate the final temperature, in °C, of the solution.
Answers
Answer:
28°C
Step-by-step explanation:
First you do 3*19=57°C
-5+57= 52°C
then you do 4*6=24 °C
as its being cooled you takeaway
52-24=28°C
You have $90 in your bank account. Each work you plan to deposit $3 from your allowance and $25 from your paycheck. The equation b: 90+ (25+5)w gives the amount b in your account after w woeks. How rary works from
now will you have $220 in your bank account?
There will be 5220 in the account after works
(Type a whole number
Answers
33w=220-90
33w=130 /33
W = 3.94
simplify by using the distributive property and then combine like terms:
4 (3x – 9)
ANSWER PLS
Answers
Answer:
12x - 36
Step-by-step explanation:
4 (3x – 9)
Distribute
4 *3x - 4*9
12x - 36
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{4(3x - 9)}[/tex]
[tex]\huge\text{= 4(3x) + 4(-9)}[/tex]
[tex]\huge\text{= 12x - 36}[/tex]
[tex]\huge\boxed{\textsf{Answer: 12x - 36}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment \& enjoy your assignment!}[/tex]
~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]
For the partially complete factorization, find the other binomial which will complete the factorization n^2-8n-20=(n+2)(_____)
Answers
Answer:
(n-10)
Step-by-step explanation:
Jdjdjdhbejdudjkdff
