Given Sin x= 0.5, what is cos x?
Enter your answer as a decimal, round only your final answer to the nearest hundredth.
Answers
sin x = 1/2
sin x = opp/hyp
therefore the ratio of opp/hyp = 1/2, (opp = 1, hyp = 2)
Find the opp side
1² + x² = 2²
1 + x² = 4
x² = 4 -1
x² = 3
x =√3
The opp side is √3
cos x = opp/hyp = √3/2 = 0.87 (round to the nearest hundredths)
If sin x = 0.5, cos x is approximately 0.87.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = Perpendicular / Hypotenuse
Cosec = Hypotenuse / Perpendicular
Cos x = Base / Hypotenuse
Sec x = Hypotenuse / Base
Tan x = Perpendicular / Base
Cot x = Base / Perpendicular
We have,
To find cos x, we can use the identity: cos² x + sin² x = 1
We are given that sin x = 0.5.
We can substitute this into the identity to solve for cos x:
cos² x + sin² x = 1
cos² x + (0.5)² = 1
cos² x + 0.25 = 1
cos² x = 0.75
cos x = ±√0.75
We take the positive square root since cosine is positive in the first and fourth quadrants.
Evaluating the square root gives:
cos x ≈ 0.87 (rounded to two decimal places)
Therefore,
cos x is approximately 0.87.
Learn more about trigonometric identities here:
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Related Questions
If AB is a tangent then point b must be the point of tangency true or false
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Two 6-sided dice are rolled. what is the probability that the sum of the two numbers on the dice will be greater than 9?
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It can be:
• First die is 6 , second die is 3
• First die is 3 , second die is 6
• First die is 4 , second die is 5
• First die is 5 , second die is 4
How many possible combinations are made? Yep, 4 possible combinations.
Recall the formula for probability
[tex]Probability = \frac{Number of desired outcomes}{Number of all possible outcomes} [/tex]
There are 4 desired number of outcomes.
How about the total possible outcomes?
• How many numbers are possible to appear when the first die is rolled?
Answer: 6
• What about the second die?
Answer: Also 6
• Therefore, total possible outcomes = 6 * 6 = 36 outcomes
You can now solve for the probability.
[tex]Probability = \frac{4}{36} = \frac{1}{9} [/tex] or approximately 11.11%
x/10=2/4?
or x over 10
equals to 2 over 4
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_______________________________________________
Note the following:
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2/4 = 1/2 ;
1/2 = (1*5) / (2*5) = 5/10 ;
2/4 = 1/2 = 5 / 10 .
or: 2/4 = 1/2 = 0.5 = 5/ 10 .
The answer: " x = 5 " .
___________________
Or: x/ 10 = 2/4 ;
Cross-multiply:
4x = (2)(10) ;
4x = 20 ;
Divide each side by "4" ;
4x / 4 = 20/4 ;
" x = 5 " ;
_____________________
Or: x/10 = 2/4 ;
Note: "2/4 = 1/2" ; so rewrite as:
x/10 = 1/2 ; and cross-multiply:
2x = (10)(1) ;
2x = 10 ;
Divide each side of the equation by "2" ;
2x / 2 = 10 / 2 ;
" x = 5 " .
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1. Add or subtract.
a. (x^2 - 4 x + 5) + (7x^2 + 2x + 3)
b. (7x^2 + 4x - 6) - (2x^2 - 3x + 1)
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1a.
Answer is 8x² - 2x + 8
(x² - 4x + 5) + (7x² + 2x + 3)
The parentheses can go away since this is all addition (associative property of addition)
x² - 4 x + 5 + 7x² + 2x + 3
Combine like terms.
(x^2 + 7x²) + (-4x + 2x) + (5 + 3) = 8x² - 2x + 8
======
1b.
Answer is 5x^2 + 7x - 7
(7x² + 4x - 6) - (2x² - 3x + 1)
Distribute the negative into the right parentheses.
(7x² + 4x - 6) - (2x² - 3x + 1)
= 7x² + 4x - 6 - 2x² + 3x - 1
= (7x² - 2x²) + (4x + 3x) + (-6 - 1)
= 5x^2 + 7x - 7
Solve the inequality
-40 > -10k
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-40>-10k
Divide both sides by -10, and flip the inequality sign since we are dividing by a negative.
4<k
Have a nice day!
If a family has three children draw a tree diagram representing the possible outcomes for the genders of the children and then list the sample space
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HELP PLEASE
Find the value of x, if you know the hypotenuse is 10 and 1 of the sides is 5. X is the other side.
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[tex]a^2+b^2=c^2[/tex]
Solve for b (c is the hypotenuse and it doesn't matter which side is a or b):
[tex]b = \sqrt{c^2-a^2} = \sqrt{10^2-5^2} = \sqrt{100-25} = \sqrt{75} [/tex]
We can simplify this:
[tex] \sqrt{75} = \sqrt{25*3} = 5 \sqrt{3} [/tex]
So, your answer is, b = [tex]5 \sqrt{3} [/tex]
For questions like these, where you are given the hypotenuse & one side of a triangle, then we can very simply use the Pythagorean Theorem to find x.
Pythagorean Theorem : a² + b² = c²
Where :
a = side length
b = another side length
c = hypotenuse
Since we are given 10 as the hypotenuse and 5 as a side length, we can very simply plug these into the Pythagorean theorem.
a² + b² = c²
We'll plug 10 into 'c' and 5 into 'a.'
(5²) + b² = (10²)
Simplify.
25 + b² = 100
Now, subtract 25 from both sides.
b² = 100 - 25
Simplify.
b² = 75
Now, find the square root of b² and 75.
[tex] \sqrt{b^2} = \sqrt{75} [/tex]
Simplify.
[tex]b = 5 \sqrt{3} [/tex]
Therefore, our final side length is : [tex]5 \sqrt{3} [/tex]
~Hope I helped!~
want 100p and brainiest answer first, ((((please))))
what is 2 1
1__ - 2__ = ?
3 3
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help please
integral of sqrt (x^2+6x) dx
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Because this is not an integration with specific bounds, you must include a constant at the end. In general, to integrate, add 1 to the exponent of x and then whatever number is the exponent of x, divided the number in front of x by that.
In july in seattle, the grass grows 1/2 inch a day on a sunny day and 1/4 inch a day on a cloudy day. in seattle, in july, 75% of the days are sunny and 25% of the days are cloudy.
a.find the expected value of grass growth for the day
b.find the expected value of grass growth for the month of july ( 31 days ) -- round both to 2 decimal placees
Answers
a.
1/2×75％＋1/4×25％=0.4375
the expected value of grass growth for the day is 0.4375
b.
0.4375×31=13.5625
the expected value of grass growth for the month of july is 13.5625
Final answer:
Calculate the expected grass growth in Seattle based on the daily growth rates for sunny and cloudy days, then find the expected growth for the month of July.
Explanation:
a. Expected value of grass growth for the day:
Expected growth = (0.75 x 0.5) + (0.25 x 0.25) = 0.4375 inches
b. Expected value of grass growth for the month of July:
Expected growth for July = 31 days x Expected growth per day = 31 x 0.4375 = 13.56 inches
If ED = 10 and DB = 3x-8, what is the length of EB
1. 32
2. 22
3. 10
4. 20
Answers
2 times ED=EB
2(10)=20
EB is 20
EB = 20 units
Explanation:
This question can be solved using two methods:
Method #1:
From the image, we can note that D is the midpoint of EB, therefore, ED = DB
This means that:
EB = 2*10 = 20 units
Method #2:
From the image, we know that ED = DB
We are given that ED = 10 units
Therefore:
DB = 3x - 8 = 10
3x = 18
x = 6
DB = 3(6) - 8 = 18 - 8 = 10 units
EB = EB + DB = 10 + 10 = 20 units
Hope this helps :)
The difference of two numbers is 44 1/2 . If the smaller of the two numbers increases 7 times then the difference will be 10 3/14 . Find the numbers.
The numbers are: ___ ,___ or ____,___
Answers
To find these answer you have to write the following two equations.
x - y = 44 and 1/2
7y - x = 10 and 3/14
Then, you can use the substitution method to solve them. Change the first equation to: x = 44 + y. Substitute that into the second equation and solve for y. Once you have that, plug it back into the first equation and solve for x.
The smaller number is 11 and the larger number is [tex]55 \frac{1}{2}[/tex].
Let's denote the two numbers as x and y, where x is the smaller number. We're given that [tex]y - x = 44 \frac{1}{2}[/tex] and [tex]7x - y = 10 \frac{3}{14}[/tex].
To solve this system of equations, we can use substitution or elimination. Let's use elimination:
1. Multiply the second equation by 2 to clear fractions: [tex]14x - 2y = 20 \frac{6}{14}[/tex].
2. Add the modified second equation to the first equation:
[tex](y - x) + (14x - 2y) = 44 \frac{1}{2} + 20 \frac{6}{14}[/tex]
[tex]13x - y = 64 \frac{11}{14}[/tex]
Now, we have a simpler equation: [tex]13x - y = 64 \frac{11}{14}[/tex].
3. Add this equation to the original second equation to find x:
[tex]7x - y + 13x - y = 10 \frac{3}{14} + 64 \frac{11}{14}[/tex]
[tex]20x - 2y = 75[/tex]
4. Now, we can solve this equation along with the first equation to find x and y.
After solving, we get x = 11 and [tex]y = 55 \frac{1}{2}[/tex].
The smaller number is 11 and the larger number is [tex]55 \frac{1}{2}[/tex].
Thus, the numbers are [tex]{11 \text{ and } 55 \frac{1}{2}}[/tex].
Correct Question:
The difference of two numbers is 44 1/2 . If the smaller of the two numbers increases 7 times then the difference will be 10 3/14 . Find the numbers.
jack lease a car for $159\month for 39 months. the amount due when he signed the lease was 2399. how much did jack pay during the first year of the lease.
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The area of a rectangular classroom is given by the trinomial 10x^2 + 3x - 4 What are the possible dimensions of the classroom? Use Factoring.
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In a rectangle the area is L x W. So if we know the area is 10x^2 + 3x - 4, then all we have to do is factor it to find possible values for the L and W.
If you factor the expression by grouping, you will get (2x - 1) and (5x + 4).
Your questions asks for possible dimensions, you could give the two expressions as dimensions.
If you wanted to select a value for x, you could plug it in and get values that could be dimensions.
For example if you let x = 10, you would have a rectangle that has a width of 19 and a length of 54.
Answer:
(5x + 4) and (2x – 1)
Step-by-step explanation:
PLEASE HELP ASAP! BRAINLIEST TO BEST/RIGHT ANSWER
Answers
first term, you substitute 1 into n
-3 * 2^(1-1)
-3 * 2^0
-3 * 1= -3
fourth term, you substitute 4 into n
-3 * 2^(4-1)
-3 * 2^3
-3 * 8 = -24
eighth term, you substitute 8 into n
-3 * 2^(8-1)
-3 * 2^7
-3 * 128 = -384
20 POINTS! What is the slope of the line through the points (2, 5) and (6, 13)?
Answers
[tex] \frac{13-5}{6-2} [/tex]
[tex] \frac{8}{4} [/tex]
Slope = 2
So the slope of the line that passes through that point is 2.
Hope this helps :)
Find the measure of each angle please?
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The measure of angle x is 60 degrees so the measure of angles 2x is 120 degrees.
Since both interior angles are supplementary to congruent angles, they are congruent.
Let z be the measure of each upper interior angle.
2x + z = 180
z = 180 - 2x
Each upper interior angle measures 180 - 2x.
The sum of the measures of the interior angles of a triangle is 180.
180 - 2x + 180 - 2x + x = 180
-3x + 360 = 180
-3x = -180
x = 60
One interior angle measures x, so it measures 60 deg.
The other two interior angles measure 180 - 2x = 180 - 2(60) = 180 - 120 = 60
Answer: all interior angle measure 60 deg.
The exterior angles shown measure 120 deg each.
John rolls a number cube twice. What is the probability that the sum of the 2 rolls is less than 7, given that the first roll is a 1?
one over six
one over three
one over two
five over six
Answers
There are 6 ways we can roll two dice and have the first number be a 1:
1, 1
1, 2
1, 3
1, 4
1, 5
1, 6
Out of these, 5 possibilities give us a sum less than 7:
1, 1
1, 2
1, 3
1, 4
1, 5
Thus we have 5/6.
Answer: The correct option is (d) five over six.
Step-by-step explanation: Given that John rolls a number cube twice. We are to find the probability that the sum of the 2 rolls is less than 8 given that he first roll is a 1.
The sample space of an event of rolling a cube is
S = {1, 2, 3, 4, 5, 6}.
That is, n(S) = 6.
Now, let 'A' be the event that the sum of the two rolls is less than 7, then
A = {1, 2, 3, 4, 5}.
That is, n(A) = 5.
So, the probability of happening of event A is given by
[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{5}{6}.[/tex]
Thus, the required probability is five over six.
Option (d) is correct.
What is another way to write this number 300+70+5/10+8/100
Answers
Your answer is 370 [tex] \frac{29}{50} [/tex]
I hope this helped! :-)
HELP:
Whic reformer was not a journalist who investigated corruption in business or government?
(Points : 3)
Ray Stannard Baker
Upton Sinclair
Lincoln Steffens
William Booth
i wend with D
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Find m∠A given ΔABC where a=4, b=6, c=3.
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The law of cosines is the following equation:
[tex]a^2=b^2+c^2-2(b)(c) \cos(A)[/tex]
We know the values of a, b, and c. We want to find the measure of angle A.
[tex]a=4[/tex]
[tex]b=6[/tex]
[tex]c=3[/tex]
Now, plug in these values into the equation.
[tex]4^2=6^2+3^2-2(3)(6) \cos(A)[/tex]
[tex]16=45-36 \cos(A)[/tex]
Add both sides by [tex]36 \cos(A)[/tex] and subtract both sides by 16
[tex]36 \cos(A)=29[/tex]
Divide both sides by 36
[tex]\cos(A)= \dfrac{29}{36}[/tex]
Take the inverse cosine, or arc cosine, of both sides.
Using a calculator, you'll get the following result.
[tex]A \approx 36.3^O[/tex]
The measure of angle A should be 36.3 degrees. Hope this helps! :)
Will give brainliest answer!!
Answers
5:8
Explanation:
First, we will compute the ratio between the two volumes as follows:
1000 / 4096 = 125 / 512
which is equivalent to 125 : 512
Then, we will get the cubic root of the ratio. This is because volume of cube is computed by cubing its side length.
Therefore, similarity ratio iR³ will be:
125 : 512
(5)³ : (8)³
5 : 8
Hope this helps :)
a(t) = (t - k)(t - 3)(t - 6)(t + 3) is a polynomial function of t, where k is a constant. Given that a(2) = 0, what is the absolute value of the product of the zeros of a?
Answers
(2)*(3)*(6)*(-3) = -108
The absolute value of the product of zeros of a(t) is 108.
t-k=0, t=k
t-3=0, t=3
t-6=0, t=6
t+3=0, t=-3
abs value of the product= abs value of (t*3*6*-3)=54t
A population has size 25 at time t = 0, with t measured in years. (a) if the population decreases by 4 people per year, find a function for the population size, p, at time t. enter your answer as an equation with p on the left side, and an expression involving t on the right
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p = population
t: time in years
The equation that best fits this problem is a linear equation of the form:
p = -4t + 25
Note that for t = 0 the value of p is 25, which represents the initial population.
Answer:
a function for the population size, p, at time t is:
p = -4t + 25
Please help!!! Thank you!!!
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First, we will find the area of the rectangle, using the formula A = lw, where l is the length of the rectangle and w is the width of the rectangle.
The length of the rectangle is 13 cm and the width is 9 cm. If we substitute in these values into our equation, we get:
A = (13cm)(9cm)
A= 117 cm^2
Next, let’s find the area of the triangle, using the formula A=(1/2)bh, where b is the base of the triangle and h is the height.
The base of the triangle is 11 cm and the height of the triangle is 5 cm (found by subtracting 13-8 as seen in the figure). If we substitute in these values and simplify, we get:
A=1/2(11cm)(5cm)
A=1/2(55cm^2)
A=27.5 cm^2.
When we add together the area of the rectangle with the area of the triangle, we will get the total area of the figure.
117 cm^2 + 27.5 cm^2 = 144.5 cm^2
Your answer is 144.5 cm^2 or the first option.
Hope this helps!
why is 5 a rational number?
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5 is a rational number because it can be expressed as the quotient of two integers: 5÷ 1
Hope this helps!! ;))
Have a grat day!! <3
Find the inverse function for the function f(x) = mx + b?
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The inverse is created by interchanging x and y like this.
x = my + b and solving for y
(x - b) = my Now divide by m
(1/m) * (x - b) = y
Write the equation, in slope-intercept form, of the line passing through the origin and the point $(-4,3)$.
Answers
From our two points we can infer that [tex]x_{1}=0[/tex], [tex]y_{1}=0[/tex], [tex]x_{2}=-4[/tex], [tex]y_{2}=3[/tex]. Lets replace those values in the slope formula:
[tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]
[tex]m= \frac{3-0}{-4-0} [/tex]
[tex]m= \frac{3}{-4} [/tex]
[tex]m=- \frac{3}{4} [/tex]
Now that we have our slope, we can use the slope-intercept formula:
[tex]y-y_{1}=m(x-x_{1})[/tex]
[tex]y-0=- \frac{3}{4} (x-0)[/tex]
[tex]y=- \frac{3}{4} x[/tex]
We can conclude that the equation of the line passing trough the points (0,0) and (-4,3) is [tex]y=- \frac{3}{4} x[/tex].
Each blade on a windmill is in the shape of a triangle with a base of 7 feet and a height of 4 feet. If there are four blades on the windmill, what is the total area of the blades 1.56 ft2 2.14 ft2 3.28 ft2 or 4.96 ft2 im unsure of this one but im going with 2.,
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90% * x = 50 pounds of money
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x = £55.56