FInd the value of x, between -π and π, satisfying the following inequality.
tan x < cos x
Answers
Answer:
(-1.570796, 0.666239) ∪ (1.570796, 2.475353)
Step-by-step explanation:
A graphing calculator can give you the numerical values that limit the intervals of the solution. The attachment shows this solution.
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algebraic solutionWe can multiply by cos(x) and solve the resulting quadratic inequalities. Two cases arise:
tan(x) -cos(x) < 0 . . . . . . subtract cos(x)
sin(x) -cos(x)² < 0 . . . . . . . for cos(x) > 0
sin(x) -cos(x)² > 0 . . . . . . . for cos(x) < 0 (inequality is reversed)
Replacing cos(x)² with (1 -sin(x)²) gives quadratic equations in sin(x). (We're using <> to mean "could be greater than; could be less than, depending on cos(x)".)
sin(x) -(1 -sin(x)²) <> 0
sin(x)² +sin(x) -1 <> 0 . . . . put in standard form
(sin(x)² +sin(x) +1/4) -1 -1/4 <> 0 . . . . complete the square
(sin(x) +1/2)² -5/4 <> 0 . . . . . write as a square
((sin(x) +1/2)-√(5/4))·((sin(x) +1/2) +√(5/4)) <> 0 . . . . factor
Note that the second factor is always positive, so it has no impact on the intervals of solution.
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The zeros of the first factor are located at ...
sin(x) = 1/2(-1 +√5)
x ≈ 0.666239 radians, and π - 0.666239 radians ≈ 2.475353 radians
The sine function will be positive between these angle values.
__
However, the intervals of solution to the inequality depend on the cosine function. Effectively, the solution space is where (sin(x) +(1-√5)/2) and cos(x) have opposite signs.
cosine positiveThe cosine function is positive for -π/2 < x < π/2, so one of the intervals of solution will be ...
-π/2 < x < arcsin((√5 -1)/2), approximately (-1.570796, 0.666239)
cosine negativeThe cosine function is negative for -π < x < -π/2 and for π/2 < x < π. The other interval of solution will be ...
π/2 < x < (π -arcsin((√5 -1)/2)), approximately (1.570796, 2.475353)
_____
Additional comment
In the above, we have used α=arcsin( ) to mean the values of angle in the principal branch: -π/2 ≤ α ≤ π/2. That is why we have to subtract it from π to find the other end of the interval of interest.
Related Questions
HELP PLS WILL GIVE BRAINLIEST
Answers
Answer:
The answer is B and D :)
Step-by-step explanation:
It is b because the x value is getting bigger while the y value is getting smaller. :)
Have an amazing day!!
Please rate and mark brainliest!!
Answer:
Options B and D
Step-by-step explanation:
Step 1: Determine what negative association is
Negative association basically means that the best-fit line for the scatter plot would be in a downwards slope which means that it has a negative association.
In the given examples, Option A wouldn't work because we can see that the best-fit line would be going up which is a positive association. Option B would work because we see the downward slope. Option C wond't work for the same reason as Option A. And finally Option D would work since we have a downward slope.
Answer: Options B and D
A square is circumscribed about a circle with a diameter of 10 cm. What is the correct set up to find the area of the shaded region?
Answers
Answer:
21.5 cm² (nearest tenth)
Step-by-step explanation:
FormulaeArea of a square = x² (where x is the side length)Area of a circle = πr² (where r is the radius)Radius = 1/2 diameterSolutionTo find the shaded region, subtract the area of the circle from the area of the square.
Square
Area of the square = 10² = 100 cm²
Circle
Given diameter of circle = 10 cm
⇒ radius = 10 ÷ 2 = 5 cm
⇒ Area of the circle = π · 5² = 25π cm²
Area of shaded region
= area of square - area of circle
= 100 - 25π
= 21.46018366...
= 21.5 cm² (nearest tenth)
The expression (8+8+8+8+8)−(6+6+6+6+6) is equal to 10 .
Use any of the operations below to create another expression that is equal to 10 , but only uses the numbers 6 and 8 .
Addition (+)
Subtraction (−)
Multiplication (⋅)
Division (÷)
Squaring ( )2
Square Root ( )−−√
Answers
6²-(8+8)
Solution:There are plenty of expressions with numbers 6 and 8 that are equivalent to 10.Here is one of them:6²-(8+8)→36-16=10Hope it helps.
Do comment if you have any query.
What is the equation of the line x–3y=18in slope-intercept form?
Drag and drop the appropriate number, symbol, or variable to each box.
Response areaResponse areaResponse areaResponse areaResponse areaResponse area
Answers
A circular fountain has 132 feet of railing around it. What is the area of the fountain, Use 3.14 for π.
Answers
Answer:
1387.2 ft² (nearest tenth)
Step-by-step explanation:
Formulae
Circumference of a circle = [tex]2 \pi r[/tex]Area of a circle = [tex]\pi r^2[/tex](where r is the radius of the circle)
The railing of the circular fountain is the circumference of a circle.
The area of the fountain is the area of a circle.
First, find the radius by using the circumference formula:
Given:
circumference = 132 ft[tex]\implies 132=2 \pi r[/tex]
[tex]\implies r=\dfrac{132}{2 \pi}=\dfrac{66}{\pi}[/tex]
Now input the found value of r into the formula for the area of a circle:
[tex]\begin{aligned}\implies \textsf{Area} & =\pi \left(\dfrac{66}{\pi}\right)^2\\\\ & = \dfrac{4356}{\pi}\\\\ & = \dfrac{4356}{3.14}\\\\ & = 1387.261146...\\\\ & = 1387.3 \: \sf ft^2\:(nearest\:tenth)\end{aligned}[/tex]
46/154 to a percentage
Answers
Answer:
29.87%
Step-by-step explanation:
46/154 = 0.2987013
29.87 (move the decimal 2 places to the right. :)
Hope this helped!
What is the perimeter of a shape?
Answers
Perimeter is the combined ammount of all the sides added together.
For example, if a square has sides of 4, it would be 16 because 4+4+4+4 = 16 units.
Answer:
Perimeter is the total distance around the outside of a shape.
Step-by-step explanation:
A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications. A calculated perimeter is the length of fence required to surround a yard or garden. The perimeter of a wheel/circle (its circumference) describes how far it will roll in one revolution. Similarly, the amount of string wound around a spool is related to the spool's perimeter; if the length of the string was exact, it would equal the perimeter.
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Hope it helps you :)
pls mark brainleist :P
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Tori
The dimensions of a
Blue
rectangular pyramid are shown in
the diagram. What is the volume
of the pyramid in cubic meters?
Answers
Answer:
8 cubic meters
Step-by-step explanation:
Formula for the volume of a rectangular pyramid:
[tex]V=\frac{lwh}{3}[/tex]
Take note
[tex]l=[/tex] base length
[tex]w=[/tex] base width
[tex]h=[/tex] pyramid height
We are given [tex]l[/tex], [tex]w[/tex], and [tex]h[/tex].
Lets solve for [tex]V[/tex]
[tex]l=3[/tex]
[tex]w=2[/tex]
[tex]h=4[/tex]
Now plug in our numbers into the formula:
[tex]V=\frac{3*2*4}{3}[/tex]
Evaluate the numerator
[tex]3*2*4=24[/tex]
Then we have
[tex]V=\frac{24}{3}[/tex]
Simplify and we get:
[tex]V=8[/tex]
Find the area of a circle with a diameter of 16.
Either enter an exact answer in terms of piπpi or use 3.14 for piπpi and enter your answer as a decimal.
Answers
Answer:
64π or 200.96
Step-by-step explanation:
The area of a circle is [tex]\pi r^2[/tex]. The radius of the circle is half the diameter, which is 16/2 = 8. The area of the circle is 64π.
Answer:
64π = area
200.96 = area
Step-by-step explanation:
Diameter = radius * 2
16 = 2r
radius = 8
Radius^2 * π = area
8^2 * π = area
64π = area
64*3.14 = area
200.96 = area
Hope this helped!!
If you invest $200 at an interest rate of 10%, how much money will you have after three years?
Answers
If it’s an annual interest rate (yearly interest rate), then you would have $266.20
1st year: $200 x 1.10 = $220
2nd year: $220 x 1.10 = $242
3rd year: $242 x 1.10 = $266.20
PLS HELP!!! No links pls and Ty <333
Sid is making a pizza. The diameter of the pizza is 15 inches.
What is the area of the pizza (use 3.14 for pi and round to the nearest
tenth)?
Answers
Answer:
176.6 inches.
Step-by-step explanation:
15 is the diameter, so 15/2 is 7.5 which is the radius
A of a circle is 3.14 x r^2
7.5^2=56.25
56.25 x 3.14=176.625
rounded makes it 176.6
Amy is standing 70 meters from the base of the Washington Monument in Washington, DC. She estimates that the angle of
elevation to the top of the building is 60°. One of her friends is at the top of the building. What is the distance between Amy and
her friend? (Assume the monument meets the ground at a right angle.)
Answers
Answer:
140m
Step-by-step explanation:
use the forMula SOHCAHTOA cos x=adjacent/hypotenuse. cos 60=70/hypotenuse. hyp=70/cos 60. =140m away
What is the range of the data set? 32, 21, 88, 64, 88, 107, 101 enter your answer in the box.
Answers
. What is the area of this polygon?
6 cm
8 cm
4 cm
18 cm?
40 cm?
16 cm
24 cm2
Answers
Answer:
B) 40cm²
Step-by-step explanation:
4*8=32/2=16
8*6=48/2=24
16+24=40
(A= b*h/2)
Hope this helped
Car insurance companies want to keep track of the average cost per claim. The current data in use for Auto Insurance R Us is an average of $2,200 for each claim with a standard deviation of $500. With this average, the company can stay competitive with rates but not lose money. However, the statistician for the company believes that the cost of the average claim has increased. He pulled 40 recent claims and found the average to be $2,350. Which most restrictive level of significance would suggest that the company should raise rates
Answers
Answer:
The answer is 5% because its correct lol
Step-by-step explanation:
The most restrictive level of significance that would suggest the company should raise rates is a p-value less than or equal to 0.01.
What is hypothesis testing?Hypothesis testing is a statistical method that is used to make decisions about a population based on a sample of data.
It involves testing a null hypothesis (H0) against an alternative hypothesis (Ha) using statistical techniques.
We have,
To determine if the increase in the average cost per claim is statistically significant, we can perform a hypothesis test.
Let's use a one-sample t-test, where:
Null hypothesis (H0): The average cost per claim is still $2,200.
Alternative hypothesis (Ha): The average cost per claim is greater than $2,200.
We can use a t-test because we have a sample mean, sample size, and population standard deviation.
The test statistic is calculated as:
t = (sample mean - hypothesized mean) / (standard deviation/√ (sample size))
Plugging in the values given, we get:
t = (2350 - 2200) / (500 / √(40))
t = 4.38
Using a t-table with degrees of freedom (df) = 39 (sample size - 1), we can find the p-value associated with this test statistic.
At the 0.01 level of significance (most restrictive level), the critical t-value is 2.704.
Since our calculated t-value is greater than the critical t-value, we reject the null hypothesis and conclude that there is evidence to suggest that the average cost per claim has increased.
Therefore,
The most restrictive level of significance that would suggest the company should raise rates is a p-value less than or equal to 0.01.
Learn more about hypothesis testing here:
https://brainly.com/question/30588452
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What is the slope of the line that passes through the points (7, -6) and (6, -6)? Write your answer in simplest form.
Answers
Undefined
Solution:Notice that the x-coordinates of the points that the line intersects are the same.If the x-coordinates are the same, then the slope is undefined.If the slope is undefined, then the line's run is equal to 0 units.Remember the slope formula: Rise/RunRise - how many units we move up or downRun - how many units we move left or rightIf the run is zero, then we basically divide by zero, which we can't do.Hope it helps.
Do comment if you have any query.
maths equation i need help with
Answers
Answer:
2^11 * 3^3 * 5^6.
Step-by-step explanation:
c = 2^10 * 3 * 5^6
18c = 2^10 * 3 * 5^6 * 18
= 2^10 * 5*6 * 54
= 2^10 * 5^6 * 2 * 27
= 2^10 * 5^6 * 2* 3^3
= 2^10 * 2 * 3^3 * 5^6
= 2^11 * 3^3 * 5^6
Can you help finish my trigonometry maze?? And show me the equation for each I know some of them are finding angles and I’m stuck please help.
Answers
Using the trigonometric ratios of sine, cosine and tangents will help solve navigate the maze.
What is trigonometry?Trigonometry is the study of the relationships between side lengths and angles of triangles.
The three main trigonometry functions are sine, cosine and tangent.
For right-angled triangles, the ratios of the three trigonometric functions are:
Sine = opposite/hypotenuseCosine = adjacent/hypotenuse Tangent = opposite/adjacentFor the given maze, the missing measures are found using the angles and the side given.
For example:
tan 52 = 40/x
x = 40/tan 52 = 31.3
Therefor, using the trigonometric ratios will help solve navigate the maze.
Learn more about trigonometry at: https://brainly.com/question/24236629
i need help (please help me)
Amelie spins the following spinner, which has 10 equally sized spaces numbered 1 through 10. The numbers 1 and 7 are colored blue; the numbers 2, 4, and 6 are red; and the numbers 3, 5, 8, 9, and 10 are green.
A spinner as described in the text.
What is the probability that Amelie spins either an odd number or a red number?
Enter your answer as a reduced fraction, like this: 3/14
Answers
Step-by-step explanation:
It's 4/5 as a reduced fraction.
What shape is created by the rotation and what is the approximate circumference of the base? circumference of a circle: c = 2πr a cylinder with a circumference of about 63 mm a cylinder with a circumference of about 126 mm a cone with a base circumference of about 63 mm a cone with a base circumference of about 126 mm
Answers
The triangle is rotated about an axis then it creates a cone and the approximate circumference of the base is 63 mm. Then the correct option is C.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
The equilateral triangle shown is rotated about line a.
Each side of the triangle measures 20 mm.
If the triangle is rotated about an axis then it creates a cone.
Then the radius of the cone will be
[tex]\rm r = \dfrac{20}{2} = 10 \ mm[/tex]
Then the height of the cone will be
[tex]\rm h = 20 \sin 60^o\\\\h = 17.32 \ mm[/tex]
Then the circumference of the base circle will be given as
[tex]\rm Circumference = 2 \pi r\\\\Circumference = 2 \pi \times 10\\\\Circumference = 62.8318 \approx 63 \ mm[/tex]
More about the geometry link is given below.
https://brainly.com/question/7558603
Answer:
C. A cone with a base circumference of about 63 mm !!!
Step-by-step explanation:
Correct on Edge2022 <3
What type of polygon is needed to use the Pythagorean theorem?
A. Acute triangle
B. Right triangle
C. Rectangle
D. Isosceles triangle
Answers
Ahh, yes, the Pythagorean Theorem!
The Pythagorean Theorem is applied to right triangles. Only right triangles. So our answer would be B.
I hope this makes sense. I can continue to expand on this if you like.
-Toremi
The correct answer is option (B) Right triangle.
What is a right triangle?A triangle with one of its angles measuring 90° is known as a right triangle.
The Pythagorean theorem is applicable only to a right triangle.
The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the legs of the triangle.
Hence, the correct answer is option (B) Right triangle.
Learn more about right triangles here:
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Please answer asap. The question is how many is tablets is given in 24hrs
Answers
Answer:
So first, we figure out the maximum the patient could be taking each day: 2 tabs every 4 hours = 12 tabs per day at the most.
A student said that the sum of the measures of a pair of adjacent angles must equal 180°. Is the student correct?
Choose the correct answer and explanation
OA) The student is correct; adjacent angles must share a common vertex and sum to 180°
OB) The student is not correct; two adjacent angles form a right angle, so the sum is always equal to 90°
OC) The student is correct; any pair of adjacent angles forms a straight line, and the angle measure of a straight line is 180°
D) The student is not correct; a pair of adjacent angles must share a common vertex, share a common side, and not overlap. They
may equal 180° but do not have to
Answers
Answer:
Step-by-step explanation:
D) The student is not correct; a pair of adjacent angles must share a common vertex, share a side, and not overlap have to
I promised to do my gfs homework but I'm mostly clueless someone help pls
Answers
Answer:
Read Step by step
Step-by-step explanation:
For number 5. This is the Transitive property because they mirror each other.
for 3, this is the symmetric property as they are split by a single shared line and they are both of equal properties.
Please help me with this question.
Answers
Answer:
12/60 (1/5)
Step-by-step explanation:
9+15+24+12= 60 total
There are 12 purple.
12/60
12 / 12 = 1
60 / 12 = 5
please let me know if my math is correct, which it should be but just to make sure
A truck driver drives 245 miles and needs to drive m miles in all. Write an equation for the number of miles d the driver has left to drive
Answers
Answer:
245 + d = m :)
Step-by-step explanation:
We have how many miles they have already driven, 245. We need to find how many miles until he reaches m :)
Have an amazing day!!
Please rate and mark brainliest!!
Please help, select all that apply
Answers
Answer:
Answer is
B. (Related with F)
C. (Related to the number of cars)
D. (Related with F)
F.
Hope it helps
BYE
(x + 4) (x - 4) - x² + 16
Answers
Answer:
infinite solutions
Step-by-step explanation:
Hey there!
In order to solve this problem, we need to first distribute the [tex](x+4)(x-4)[/tex]
This is equal to [tex]x^2-16[/tex]
Now we can combine like terms
[tex]x^2[/tex] and [tex]-x^2[/tex] cancel out
also
[tex]16[/tex] and [tex]-16[/tex] cancel out
The equation ends up as 0 = 0
So the answer to this answer is infinite solutions
What is 1+2_#_+#+#+#+3?
Answers
Answer:
Noice
Step-by-step explanation:
what is the distance between the points (-7, -8) & (2, -8)
Answers
Answer:
5 units cause that ordinates are same abssisae is different