Answers
Answer:
Solution given:
Sin[tex]\theta_{1}=\frac{1}{4}[/tex]
[tex]\frac{opposite}{hypotenuse}=\frac{1}{4}[/tex]
equating corresponding value
opposite=1
hypotenuse=4
adjacent=x
By using Pythagoras law
hypotenuse²=opposite²+adjacent²
4²=1²+x²
16=1+x²
x²=16-1
x=[tex]\sqrt{15}[/tex]
In II quadrant
Cos angle is negative
Cos[tex]\theta_{1}=\frac{-adjacent}{hypotenuse}[/tex]
Cos[tex]\theta_{1}=\frac{-\sqrt{15}}{4}[/tex]Answer:
[tex]\displaystyle \cos ( \theta _{1} ) = - \frac{ \sqrt{15}}{ 4 }[/tex]
Step-by-step explanation:
on a unit circle there're 4 Quadrant. on Q:I sin and cos both are positive,on Q:II cos is negative and sin positive, on Q:III both sin and cos are negative and on Q:IV cos is positive and sin negative.
actually a unit circle is a coordinate plane but
there's (cos,sin) instead of (x,y)it'll be required later
well to solve the problem we can consider Pythagorean theorem which states that the square of sin and cos is equal to 1. therefore,
[tex] \displaystyle \sin ^{2} ( \theta) + \cos ^{2} ( \theta) = 1[/tex]
[tex] \rm \displaystyle \implies \boxed{\cos ^{} ( \theta) = \sqrt{1 - \sin ^{2} ( \theta) }}[/tex]
in this case,
[tex] \rm \theta \: \: is \: \: \theta_{1}[/tex]sin[tex]\theta[/tex] is ¼Thus substitute:
[tex]\displaystyle \cos ( \theta _{1} ) = \sqrt{1 - \left( \frac{1}{4} \right) ^{2} }[/tex]
simplify square:
[tex]\displaystyle \cos ( \theta _{1} ) = \sqrt{1 - \frac{1}{16} }[/tex]
simplify substraction:
[tex]\displaystyle \cos ( \theta _{1} ) = \sqrt{ \frac{16 - 1}{16} }[/tex]
simplify numerator:
[tex]\displaystyle \cos ( \theta _{1} ) = \sqrt{ \frac{15}{16} }[/tex]
recall redical rule:
[tex]\displaystyle \cos ( \theta _{1} ) = \frac{ \sqrt{15}}{ \sqrt {16} }[/tex]
simplify square root:
[tex]\displaystyle \cos ( \theta _{1} ) = \frac{ \sqrt{15}}{ 4 }[/tex]
since cos is negative on Q:II hence,
[tex]\displaystyle \cos ( \theta _{1} ) = \boxed{- \frac{ \sqrt{15}}{ 4 }}[/tex]
and we're done!
Related Questions
How to solve y=4x+1 y=- x=-2
Answers
If someone can ride a skateboard 2 miles in 10 minutes how many miles can still ride the skateboard and 1.5 miles
Answers
Answer:
7 and a half minutes. have a good one.
Q.
10² + 20² - 5! = ?
note : ! it's a factorial sign
Goodluck
Answers
[tex] = 10 {}^{2} + 20 {}^{2} - 5! \\ = 100 + 400 - \\ (5 \times 4 \times 3 \times 2 \times 1) \\ = 100 + 400 - 120 \\ = 500 - 120 \\ = 380[/tex]
10² + 20² - 5! = ？
Answer:-380
Explanation:-=> 10² + 20² - 5!
=> 100 + 400 - (5 × 4 × 3 × 2 × 1)
=> 100 + 400 - 120
=> 500 - 120
=> 380
a recipe requires the following ingredients to make 16 gingerbread men
140g of flour
250g of sugar
80g of ginger
110g of butter
how much of each ingredient would you need to make 40 gingerbread men?
How do I work this out?
Answers
Answer:
5,600 g of flour
10,000g of sugar
3,200g of ginger
4,400g of butter
Just have to multiply each ingredient by 40
What does pie mean?
I forgot ; )
Answers
Answer:
pie means 3.142
Step-by-step explanation:
Answer:
In decimal form, the value of pi is approximately 3.14. It looks like this π.
Hope that helps. x
4. Identify the zeros and the graph of the function y = x(x − 2)(x + 5).
Answers
The zeros of
y = x(x + 2)(x + 5)y=x(x+2)(x+5)
are
x=0,x=-2,x=-5x=0,x=−2,x=−5
EXPLANATION
The given function is
y = x(x + 2)(x + 5)y=x(x+2)(x+5)
To find the zeros of the above function, we just have to equate the function to zero and solve for x.
x(x + 2)(x + 5) = 0x(x+2)(x+5)=0
This implies that,
x = 0 \: \: or \: x + 2 = 0 \:or \: x + 5 = 0x=0orx+2=0orx+5=0
x = 0 \: \: or \: x = - 2\:or \: x = - 5x=0orx=−2orx=−5
To graph the above function, we need to consider the multiplicity.
We can see that the multiplicity of the roots are odd. This means that, the graph crosses the x-axis at each x-intercept.
We also need to consider the position of the graph on the following intervals,
x < - 5x<−5
When
x = - 10x=−10
y = - 10( - 8)( - 5) \: < \: 0y=−10(−8)(−5)<0
The graph is below the x-axis.
- 5 \: < \: x \: < \: - 2−5<x<−2
When
x = - 3x=−3
y = - 3(2)( - 1) \: > 0y=−3(2)(−1)>0
The graph is above the x-axis.
- 2 \: < \: x < \: 0−2<x<0
when
x = - 1x=−1
y = -1(1)(4) \: < \: 0y=−1(1)(4)<0
The graph is below the x-axis.
Finally the interval,
x \: > \: 0x>0
when
x = 1x=1
y = 1(3)(6) \: > \: 0y=1(3)(6)>0
The graph is above the x-axis.
We can now use the above information to sketch graph as shown in the diagram above
"The square root of two times a number subtract five is equal to ten."
Answers
I think this is √2n-5 = 10.
100 POINTS PLEASE HELP ME 100 POINTS (make fullscreen)
Answers
Answer:
1) 64, 2) 6, 3) 26, 4) 33Step-by-step explanation:
#1Sum of interior angles is 180
70 + 46 + x = 180116 + x = 180x = 64#2Sum of interior angles is 180
84 + 7x + 1 + 9x - 1 = 8416x + 84 = 18016x = 96x = 6#3Vertical angles are same, the sum of remaining angles is same for both triangles:
35 + 25 = 34 + x60 = 34 + xx = 60 - 34x = 26#4Exterior angle is same as the sum of non-adjacent interior angles:
5x - 7 + 6x + 3 = 8411x - 4 = 8411x = 88x = 8m∠G = 5x - 7 = 5*8 - 7 = 40 - 7 = 33identicalAnswer:
1) 64, 2) 6, 3) 26, 4) 33
Step-by-step explanation:
#1
Sum of interior angles is 180
70 + 46 + x = 180
116 + x = 180
x = 64
#2
Sum of interior angles is 180
84 + 7x + 1 + 9x - 1 = 84
16x + 84 = 180
16x = 96
x = 6
#3
Vertical angles are identical, the sum of remaining angles is the same for both triangles:
35 + 25 = 34 + x
60 = 34 + x
x = 60 - 34
x = 26
#4
The exterior angle is the same as the sum of non-adjacent interior angles:
5x - 7 + 6x + 3 = 84
11x - 4 = 84
11x = 88
x = 8
m∠G = 5x - 7 = 5*8 - 7 = 40 - 7 = 33
Help help help math nath
Answers
Answer:
12
Step-by-step explanation:
plug in -7 where x is
5 - (-7) = 12
Answer:
12
Step-by-step explanation:
plug in -7 where x is
5 - (-7) = 12
It's pretty simple!
I hope this helps you
calculate average or arthmetic mean
Answers
Answer:
mean/average is calculated by adding all of the values and dividing by the number of values
ur welcome queen besitie slay
You have 125% of the tickets required for a souvenir. What fraction of the required tickets do you have? Do you need more tickets for the souvenir? Explain. Write your answer in simplest form.
Answers
Answer:
one and one fourth
Step-by-step explanation:
Part G Compare this activity tracker & with the calorie calculator you used in part A. Imagine that a company hires you to make an online tool that uses the best features of each calculator to give users an accurate sense of their physical activity and energy expenditure. What features would you use from each calculator? How would your calculator work?
Answers
Answer:
The physical activity calculator helps calculate minutes of activity and breaks down the types of activities performed every week. The calorie calculator doesn’t keep track of all activities. However, it calculates calorie expenditure. A new calculator might be a combination of the two calculators. It’d be a two-step process. People would be able to enter their age, gender, weight, height, and any medical factors so that they can ensure that their calorie calculations are accurate. Then, they’d be able to track the calories expended each day for a week by adding their activities for the whole day, from sitting to exercising. This information would give them an accurate portrayal of calorie expenditure and estimated caloric requirement.
exact answer
Step-by-step explanation:
Answer:
by seeing how the things they are doing and effecting them and then calulating them to add them up so i can see the amount of thier activity caused them to decrease or increase themselfs
Step-by-step explanation:
own explaination just incase teacher does suspect the answer
to be copied :)
A virus attacked 175,245 people in city A and 1,486,964 people in city B. How many people in all were affected? Thank you in advance:)
Answers
1,662,209 is the answer. You just have to add them all up
Answer:
It's 1662209.
Step-by-step explanation:
just add them
I desperately need help !
Answers
Answer:
t = 9.57
Step-by-step explanation:
We can use trig functions to solve for the t
Recall the 3 main trig ratios
Sin = opposite / hypotenuse
Cos = adjacent / hypotenuse
Tan = opposite / adjacent.
( note hypotenuse = longest side , opposite = side opposite of angle and adjacent = other side )
We are given an angle as well as its opposite side length ( which has a measure of 18 ) and we need to find its adjacent "t"
When dealing with the opposite and adjacent we use trig ratio tan.
Tan = opp / adj
angle measure = 62 , opposite side length = 18 and adjacent = t
Tan(62) = 18/t
we now solve for t
Tan(62) = 18/t
multiply both sides by t
Tan(62)t = 18
divide both sides by tan(62)
t = 18/tan(62)
t = 9.57
And we are done!
write y= - 4x on a graph
Answers
what do you do to multiplay 100
x 300
Answers
Answer: 30000
Step-by-step explanation:
[tex]100 \times 300\\\\=100 \times 100 \times 3\\\\= 10000\times 3\\\\=30000[/tex]
my Christmas present to you
Answers
Answer:
Step-by-step explanation:
if you need help let me know
Answer:
Thanks I guess…
Step-by-step explanation:
I don't know how to solve this please help.
Answers
Answer:
56 miles
Step-by-step explanation:
Let x is the total distance Sam will travel today
Sam has already biked 12 + x/4 miles
He needs to bike 3x/8 (x.3/8) + 9 miles
12 + x/4 + 3x/8 + 9 = x
21 + x/4 + 3x/8 = x
21 + 2x/8 + 3x/8 = x
21 + 5x/8 = x
21 = x - 5x/8
21 = 3x/8
21.8 = 3x
168 = 3x
x = 168/3
x = 56 (miles)
Answer:
Step-by-step explanation:
Bambino's Pizza is offering $56 per shift and $20.50 in commission for each pizza delivery write a linear equation with a greater Y- intercept and slope in Bambino's Pizza
Answers
Answer:
Y = 56X + 20.50
Step-by-step explanation:
y=mx+c
Assuming that the y intercept is an additional numeral constantly given in a linear function. and the slope represented by the main wage of the job while concluding that it's the slope since it implies rate of change.
hope it's correct
Can someone help me with this please
Answers
Answer:
r = 59
Step-by-step explanation:
59 + r = 118
59 + r - 59 = 118 - 59
r = 59
Since 59 is being added to r, and you want r alone, you must subtract 59 from the left side of the equation. The rule is that you must do the same operation to both sides of the equation. Therefore, to solve for r, subtract 59 from both sides of the equation.
What is the sum of the following
(k – 4) and (k + 3)
Please fast needed
Answers
Answer:
2k-1
Step-by-step explanation:
(k-4)+(k+3)
k+k=2k
-4+3=-1
Answer:
2k-1
Step-by-step explanation:
hope this helps! :D
have a miraculous day!! <3
y=4x−9y, equals, 4, x, minus, 9
Complete the missing value in the solution to the equation
Answers
Answer:
(3,3)
Step-by-step explanation:
To find the y - value that corresponds to x=3 , substitute the x - value in the equation.
y=4x-9
y=4*3-9
y=12-9
y=3
Therefore, (3/3) is the solution to the equation.
I hope it helps.
Answer:3,3
Step-by-step explanation: bc khan
the sum of -8 and a number is at least 9 write an inequality and solve each problem
Answers
-8 + x >= 9
Solve for x by adding 8 to both sides:
X >= 17
Alexander purchased a computer on sale the original price was 1200 the sale price was 5/6 of the original price how much did Alexander pay for the computer
Answers
Answer:
1000
Step-by-step explanation:
Answer:$1000
Step-by-step explanation:
Divide 1200 by 6 then multiply that number by 5
In Circle P, m EA=58, m BC=42, m CD=90, find:
1. m∠EDA
2. m∠BDC
3. m∠BEC
4. m arc AB
5. m∠AEB
6. m∠ECA
7. m∠BAC
8. m arc ED
9. m∠ECD
10. m∠ACB
11. m∠EBD
12. m∠ADB
13. m∠CAD
14. m∠EAB
15. m∠EBC
PLEASE HELP AHHHHH
Answers
Applying the inscribed angle theorem, the missing measures are:
1. m∠EDA = 29°
2. m∠BDC = 21°
3. m∠BDC = 21°
4. measure of arc AB = 80°
5. m∠AEB = 40°
6. m∠AEB = 29°
7. m∠BAC = 21°
8. measure of arc ED = 90°
9. m∠ECD = 45°
10. m∠ACB = 40°
11. m∠EBD = 45°
12. m∠ADB = 40°
13. m∠CAD = 45°
14. m∠EAB = 111°
15. m∠EBC = 90°
What is the Inscribed Angle Theorem?The inscribed angle theorem states that, if ∠a is an inscribed angle, that intercepts arc AB, therefore: m∠a = ½(measure of arc AB).
The diagram showing circle P is attached below. We are given the following:
measure of arc EA = 58°
measure of arc BC = 42°
measure of arc CD = 90°
Thus:
1. m∠EDA = ½(measure of arc EA)
m∠EDA = ½(58)
m∠EDA = 29°
2. m∠BDC = ½(measure of arc EA)
m∠BDC = ½(42)
m∠BDC = 21°
3. m∠BEC = ½(measure of arc BC)
m∠BDC = ½(42)
m∠BDC = 21°
4. measure of arc AB = 180 - 58 - 42
measure of arc AB = 80°
5. m∠AEB = ½(measure of arc AB)
m∠AEB = ½(80)
m∠AEB = 40°
6. m∠ECA = ½(measure of arc EA)
m∠AEB = ½(58)
m∠AEB = 29°
7. m∠BAC = ½(measure of arc BC)
m∠BAC = ½(42)
m∠BAC = 21°
8. measure of arc ED = 180 - 90
measure of arc ED = 90°
9. m∠ECD = ½(measure of arc ED)
m∠ECD = ½(90)
m∠ECD = 45°
10. m∠ACB = ½(measure of arc AB)
m∠ACB = ½(80)
m∠ACB = 40°
11. m∠EBD = ½(measure of arc ED)
m∠EBD = ½(90)
m∠EBD = 45°
12. m∠ADB = ½(measure of arc AB)
m∠ADB = ½(80)
m∠ADB = 40°
13. m∠CAD = ½(measure of arc CD)
m∠CAD = ½(90)
m∠CAD = 45°
14. m∠EAB = ½(180 + 42)
m∠EAB = ½(222)
m∠EAB = 111°
15. m∠EBC = ½(measure of arc EDC)
m∠EBC = ½(180)
m∠EBC = 90°
Learn more about the inscribed angle theorem on:
https://brainly.com/question/14267250
solve one step equation
-8 + x = 10
Answers
Answer:
x=18
Step-by-step explanation:
10-(-8)=18
Tire King is having a sale where customers can buy 4 new tires for $ 319.96 . What is the unit price of the tires?
Answers
Answer:
each tire is 79.99
Step-by-step explanation:
Answer:
$79.99
Step-by-step explanation:
a hiking trail at a state park is 8.4 miles long a park ranger wants to place signs at the beginning and end of the trail and along the trail so that the signs are 1.4 miles apart how many signs will the ranger need?
Answers
Answer:
the ranger will need 6 signs
Step-by-step explanation:
Solve with elimination:
-2x - 4y = 8
-6x +24 = 12y
Answers
Ohh, Elimination Im doing that XD So its
Anwser - No Solution
Jason and Krystal are selling pecan pies and strawberry cheesecakes for a school fundraiserJason sold 9 pecan pies and 8 strawberry cheesecakes for a total of $153. Krystal sold 2 pecan pies and 6 strawberry cheesecakes for a total of $72. If it is possible to find them, what is the cost of each pecan pie and strawberry cheesecake ? If not possible , explain why
Answers
From the equation that was gotten, the value of the pecan pies and the cheesecake will be $9 each.
Based on the information given, the equations to solve the question will be:
9p + 8s = 153 ..... i
2p + 6s = 72 ..... ii
Multiply equation i by 2
Multiply equation ii by 9.
18p + 16s = 306
18p + 54s = 648
Subtract the equations
38s = 342
s = 9
Since 2p + 6s = 72
2p + 6(9) = 72
2p + 54 = 72
2p = 72 - 54.
2p = 18
p = 18/2 = 9
They're both $9 each
Learn more about equations on:
https://brainly.com/question/25678139
