Solve cos x + √2 = -cos x for x over the interval [0, 2Π)
Answers
Answer:
[tex]x=\frac{3\pi}{4}\\\\x=\frac{5\pi}{4}[/tex]
Step-by-step explanation:
Trigonometric Equations
It's required to solve:
[tex]\cos x+\sqrt{2}=-\cos x[/tex]
for [tex]x\in [0,2\pi)[/tex]
Adding cos x:
[tex]2\cos x+\sqrt{2}=0[/tex]
Subtracting [tex]\sqrt{2}[/tex]
[tex]2\cos x=-\sqrt{2}[/tex]
Dividing by 2:
[tex]\displaystyle \cos x=-\frac{\sqrt{2}}{2}[/tex]
Solving for x:
[tex]\displaystyle x=\arccos\left(-\frac{\sqrt{2}}{2}\right)[/tex]
We need to find the angles whose cosine is [tex]-\frac{\sqrt{2}}{2}[/tex] over the given interval.
These angles lie on the quadrants III and IV respectively and they are:
x=135°, x=225°
Converting to radians:
135 * π / 180 = 3π/4
225 * π / 180 = 5π/4
The two solutions are:
[tex]\mathbf{x=\frac{3\pi}{4}}[/tex]
[tex]\mathbf{x=\frac{5\pi}{4}}[/tex]
Answer:
The correct answer is option C
Step-by-step explanation:
Related Questions
For which system of equations is the graph below a solution
Answers
Answer:
what is the equation for D?
Step-by-step explanation:
Answer: A
Step-by-step explanation:
1. 2x+5(6x-9)=179
2. -40=6x-5(-4x-18)
solve for X
Answers
Answer:
1. x = 7
2. x = -5
Step-by-step explanation:
1. Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation: 2*x+5*(6*x-9)-(179)=0
Pull out like factors 6x - 9 = 3 • (2x - 3)
(2x + 15 • (2x - 3)) - 179 = 0
Pull out like factors: 32x - 224 = 32 • (x - 7)
Solve: x-7 = 0
Add 7 to both sides of the equation = 7
2. Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation: -40-(6*x-5*(-4*x-18))=0
Pull out like factors: -4x - 18 = -2 • (2x + 9)
-40 - (6x - -10 • (2x + 9)) = 0
Pull out like factors: -26x - 130 = -26 • (x + 5)
-26 • (x + 5) = 0
Solve: x+5 = 0
Subtract 5 from both sides of the equation: x = -5
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Thanks!
Find p(4) p(x) = 3x - 9
Answers
Answer:
p(4)=3
Step-by-step explanation:
p(4)=3(4)-9=12-9=3
Let x=
-
11
8
and y=
11
4
0
Which expression has a negative value?
Copyright 2017 Open Up Resources
Select one
OA. x+y
OB. xy
OC. x.y
OD. x/y
Answers
Answer:
OD. x/y
Step-by-step explanation:
NEED HELP!! what are the coordinates of point j?
Answers
Answer:
(7,4)
Step-by-step explanation:
Consider the following equation.
9x + 3y = 6
On a recent Algebra test, Brian was asked to rewrite the equation in slope-intercept form
The slope of the equation is
The y-intercept is
Answers
Answer: The slope is -3 and the y- intercept is (0,2)
Step-by-step explanation:
HELLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLP! what x-45 divided by 17 if x=98?
Answers
Answer:
98-45/17=3.11
Step-by-step explanation:
Thanks for the points
Solve -2a - 5>3
Which graph shows the solutions?
Answers
-4>3
Step-by-step explanation:
Answer:
First line
Step-by-step explanation:
Isolating 2a is the first step, so adding 5 to each side. That leaves -2a > 8. Divide both sides by -2, and because it's a negative, you flip the sign. so you get a < -4
8 4/5 ÷ 4 = ?
The principal is equally distributing 8 4/5 cakes on 4 tables for a school party. How many cakes are on each table?
Answers
Answer:
Step-by-step explanation:
8 4/5 divided by 4= 2.2
nce a year, a store offers a free frozen yogurt to its customers. Each customer can cl he flavor of frozen yogurt and one topping. There are 8 possible ways to order the fro gurt. How many flavors and toppings could the customers choose from? 4 flavors and 3 toppings 2 flavors and 4 toppings 2 flavors and 2 toppings 4 flavors and 4 toppings
Answers
What is the solution to 0.3(12x - 16) = 0.4(12 - 3x)?
Answers
Step-by-step explanation:
The solution is one-solution
.3(12x-16)=.4(12-3x) (you do the distributive property)
3.6x-4.8=4.8-.12x (you add 1.2 to both sides)
3.6x-3.6=4.8 (You add 3.6 to both sides)
3.6x=8.4 ( You divide 3.6 both numbers)
x=0.4285...
Its a one-solution
Which graph shape represents the polar curve r = 1 + 4sin(θ)?
a cardioid
a rose curve
a limaçon with an inner loop
a limaçon without an inner loop
Answers
Answer:
A cardioid
Step-by-step explanation:
A cardioid is a curve in the shape of a heart traced by a point on the circumference of a circle as it rolls around a fixed circle of the same radius.
The equation of vertical cardioid is [tex]r=a[/tex] ± [tex]a\sin \theta[/tex]
Given the polar curve is [tex]r=[/tex] [tex]1+[/tex] 4 [tex]\sin \theta[/tex]
This is an equation of vertical cardioid.
So, it represents a cardioid.
Answer:
C - a limaçon with an inner loop
Step-by-step explanation:
If you have a graphing calculator, use it to plug in the equation.
Based on what you have learned, you will recognize the graph is C
10x-3=-5x-18
I don’t know can some one help
Answers
Answer:
x=-3 (x equals negative three)
Explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Need help pleaseeee
Answers
10(x-3) = 9x
10x - 30 = 9x
-1x = -30
X = 30
Answer:
x = 30
Step-by-step explanation:
Which is the BEST estimate of the average rate of change for the function graphed, over the interval 1 sxs 3?
es)
A)
-2
B)
-3
D)
-6
Answers
Answer: -3
Step-by-step explanation: just multiply
The best estimate of the average rate of change for the function graphed over the interval 1 ≤ x ≤ 3 is 3.
What is Average Rate of Change of a Function?Average rate of change of a function is defined as the rate at which the value of the function is changing with respect to the change in the input values.
The interval given is 1 ≤ x ≤ 3.
The graph of the function is given below.
It can be clearly seen that,
The y value corresponding to x = 1 is y = f(1) = 2.
So one point on the graph is (1, 2).
The y value corresponding to x = 3 is y = f(3) = 8.
So the other point on the graph is (3, 8).
Average rate of change over 1 ≤ x ≤ 3 = [f(3) - f(1)] / [3 - 1]
= [8 - 2] / [2]
= 6/2
= 3
Hence the best estimate for the average rate of change of function over the interval 1 ≤ x ≤ 3 is 3.
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Enter the equation of the line in slope-intercept form. Enter the answer in fraction form.
The line perpendicular to y =
5
3
x + 8 that passes through (5, −1).
The equation of the line that passes through (5, −1) is y = .
Answers
Answer:
25
Step-by-step explanation: this is because you have a negative
Althea traveled 280 miles at a speed of 70 miles/hour. How much time did she take to cover this distance?
Answers
ming took a cab across town. His fare was $22, and he leaves a 18% tip. What is the total amount Ming pays to the cab driver?
Answers
Answer:
25.96
Step-by-step explanation:
18% of 22 is 3.96
3.96+22=25.96
Which expression is equivalent to (m^2-3m+7)(m-5)^-1
Answers
Answer:
a
Step-by-step explanation:
Carl Cornfield has been wondering whether he should plant white corn this year. He decides to sample 100 customers. 38% say they would purchase white corn. Carl wants to have a 95% confidence interval for this proportion.
The confidence interval is from 33% to 43% (to the nearest percent).
True
False
Answers
Answer:
true
Step-by-step explanation:
What is the y-intercept of the graph?
Answers
Answer:
4
Step-by-step explanation:
The y-intercept is 2
what is the difference between 6204 and 5735
Answers
Answer:
469
Step-by-step explanation:
Difference = subtraction6,204 - 5,735 = 469I hope this helps!
the difference is 469
Solve-1 + 8 =
10 - 3a.
Answers
Answer:
a = 1
Step-by-step explanation:
Original Equation:
-1 + 8 = 10 - 3a
Add 1 to both sides
8 = 11 - 3a
Subtract 11 from both sides
-3 = -3a
Divide both sides by -3
a = 1
Hope this helps :)
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Answer:
a = 1
Step-by-step explanation:
-1 + 8 = 10 - 3a
7 = 10 - 3a
-10 -10
-3 = -3a
---- -----
-3 -3
1 = a
A recipe for salad dressing calls for 3 tablespoons of oil for every 2 tablespoons of vinegar. The line represents the relationship between the amount of oil and the amount of vinegar needed to make salad dressing according to this recipe. The point ( 1, 1.5) is on the line.
a. Label the axes appropriately with the quantities they represent.
· b. Write an equation that represents the proportional relationship between oil and vinegar. Indicate the meaning of each variable.
Equation: ___________________________________________________________ ·c. Explain the meaning of the point (1, 1.5) in terms of the situation.
Explanation: __________________________________________________________
What's B and C?? Please help.
Answers
a.(answer):
Y represents table spoons in oil and the X represents the table spoons in vinegar.
b.(answer):
oil needed is one(1) tablespoon the amount of vinegar used is 1.5 tablespoons to make the salad dressing the correct and for it to be proportional.
linear equation
y = 3/2x
c.(answer)
For every 1 tablespoon of vinegar there is 1.5 table spoons of oil X=1,Y=1.5.
Learn more about the vinegar and oil here:
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a bag contains 10 red marbles, the ratio of red marbles to blue marbles is 5 to 1 find the numbers of blue marbles in the bag
Answers
Answer:
The Answer is 2 blue marbles.
Step-by-step explanation:
The numbers of blue marbles in the bag will be 2.
What is proportion ?
A proportion is an equation based on the equality of two ratios.
Here it is given that :
a bag contains = 10 red marbles
the ratio of red marbles to blue marbles is = 5:1
That is :
5 ratio of marbles is equals to = 10 marbles
now,
1 ratio of marbles is equals to = 2 marbles
Therefore, the numbers of blue marbles in the bag will be 2.
Read more about ratio at:
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charles has 24 marbles. he has 6 more yellow marbles then blue marbles. which equation represents this senctence
Answers
Answer: n+(n+6)=24,where n is the number of blue marbles. 3. n+6n=24,where n is the number of blue marbles.
Step-by-step explanation:
PLZ HAAAALP
One winter day, the temperature was -15°F. Later that day, the temperature rose 12°F to reach the high temperature for the day. If t represents the high temperature, what is t?
Answers
Answer:
-3°F
Step-by-step explanation:
-15 + 12 = -3
Answer:
-3
Step-by-step explanation:
On a number line what number represents the point half the distance between A and B?
Answers
Answer:
A: -4
Step-by-step explanation:
Math.
Answer:
A. -4
Step-by-step explanation:
What theorem proves that this congruent
Answers
sss
Step-by-step explanation:
side side side
all 3 or congruent
Will mark brainliest who ever answers first !!!
Please help
Answers
I believe the answer is x=-2