We can imagine the given equation cos2 x + sin2 x = 1 to be in the form of the hypotenuse equation.
Where cos x and sin x is the base and height of the triangle and 1 is the hypotenuse.
Since 1 is the hypotenuse, it also indicates to the radius of the circle. Supposing that the center of the circle is at the origin, then at all values of x (at all values of the angle), the radius of the circle will always be the same which is equal to 1.
Therefore the equation cos2 x + sin2 x = 1 holds to be true for all values of x for a unit circle.
The range of a projectile fired at an angle θ with the horizontal and with an initial velocity of v 0 feet per second is r = 1 v 20 sin 2θ where r is measured in feet. a golfer strikes a golf ball at 120 feet per second. 32 ignoring the effects of air resistance, at what angle must the golfer hit the ball so that it travels 140 feet? (round answer to nearest angle.)
What is the square root of pi?
The distance from earth to the moon is about 22^4 miles. the distance from earth to neptune is22^7 miles. which distance is the greatest and by how much
Use the given graph to determine the limit, if it exists.
limf(x)
x-->2
Answer:
Step-by-step explanation:
4
The limit as x tends to 2 is -1
How to find the limit
The limit is sought by investigating the graph. More attention is directed to when the domain or the x-value is at 2.
It can be observed that at this point we have 2 open dots and one closed dot.
The closed dot implies there is a value for x = 2, hence we trace the y coordinate at this point.
Tracing the y coordinate shows that the value is -1
Where do the following graphs intersect? Show how you can find the intersection point algebraically.
1) y-2x=3
2) y-3= x^2
What is the factored form of the expression
How you know when there is only one solution triangle possible from a side-side-angle?
Answer:
There will be only on solution if either of these conditions is met:
the given angle is opposite the longest sidethe triangle is a right triangle (the ratio of the side opposite the angle to the other given side is equal to the sine of the angle)Step-by-step explanation:
Consider the SSA geometry with the angle placed in standard position at the origin and its adjacent given side (the second side of SSA) extending along the +x axis. Draw a circle having a radius equal to the length of the first side of SSA, centered on the vertex between the two segments on the +x axis.
There are three possibilities for the way this circle intersects the other ray of the angle (the ray that is not the x-axis):
the first side is as long or longer than the second side, so there is one point of intersection (one solution to the triangle, purple in the attachment)the first side is just long enough to be tangent to the other ray, so there is one point of intersection (one solution to the triangle, green in the attachment)the first side is between these lengths, so intersects the other ray in two places, giving two solutions to the triangle, red in the attachment.What is something that multipys to 72 and adds -27?
Find the equation of the line perpendicular to -9x+4y=8 that contains the point (9,7)
Answer:
[tex]\[y=-\frac{4}{9}x+11\][/tex]
Step-by-step explanation:
Equation of the given line is [tex]\[-9x+4y=8\][/tex]
Slope of the line = [tex]\[\frac{9}{4}\][/tex]
Slope of the perpendicular line = [tex]\[-\frac{4}{9}\][/tex]
Equation of the line perpendicular to the given line is [tex]\[y=mx+c\][/tex]
[tex]\[y=-\frac{4}{9}x+c\][/tex]
But this line passes through (9,7)
Substituting the values in the equation:
[tex]\[7=-4+c\][/tex]
=> [tex]\[c=7+4=11\][/tex]
So the overall equation of the parallel line is given by [tex]\[y=-\frac{4}{9}x+11\][/tex]
What polynomial identity should be used to prove that 20 = 36 − 16
Diffrence of squares is the correct answer just score pract q
A parabola has a focus of F(2, -0.5) and a directrix of y=-1.5 P(x,y) represents any point on the parabola, while D(x, -1.5) represents any point on the directrix.
What are the steps required to find the equation of the parabola?
A rectangular flower garden has area 32 square feet. if the width of the garden is 4 feet less than the length, what is the perimeter, in feet, of the garden?
The perimeter of the garden is 24 feet.
What is a Rectangle?A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees.
How to solve it?We have, an area is 32 and width is 4,
so, the length will be 32/4 = 8 feet.
The perimeter will be 2(8+4) = 2(12)= 24 feet.
Learn more about Rectangle:
https://brainly.com/question/20968176
#SPJ2
Candida bought 334 yards of fabric. If she uses 23 of the fabric to make a dress, how much fabric will she have left?
A point on an ellipse is 11 units from one focus and 7 units from the other. What is the length of the major axis?
The sum of six consecutive odd numbers is 204. What is the fourth number in the sequence
The sum of two real numbers is 18 and the product is 70. what are the two numbers?
Shawn wants to buy a cd player that costs $48.00. If he has already saved $30.00, what percent of the price of the cd player has he saved?
Raquel and Van live in two different cities. As part of a project, they each record the lowest prices for a gallon of gas at gas stations around their cities on the same day. Raquel’s data reflect a mean price of $3.42 with a standard deviation of 0.07. Van’s data reflect a mean price of $3.78 with a standard deviation of 0.23. Which statement is true about their gas-price data? Raquel’s data are most likely closer to $3.42 than Van’s data are to $3.78. Van’s data are most likely closer to $3.42 than Raquel’s data are to $3.78. Raquel’s data are most likely closer to $3.78 than Van’s data are to $3.42. Van’s data are most likely closer to $3.78 than Raquel’s data are to $3.42.
Answer:
Raquel’s data are most likely closer to $3.42 than Van’s data are to $3.78.
Step-by-step explanation:
We know that a standard deviation is a measure that is used to find the amount of dispersion or variation of the data set.If standard deviation is low this means that the data points tends close to the mean of the data set.while a higher standard deviation means that the data values are spread to a greater range.Hence, form the given information we may imply that:
Raquel’s data are most likely closer to $3.42 than Van’s data are to $3.78.
( Since, the standard deviation of Raquel's data is low which is 0.07 as compared to Van's data ( which is 0.23).
Hence, the Raquel's data will tend close to the mean which is $ 3.42. )
The trigonometric form of a complex number is unique - True or false?
Answer with explanation:
let, Z= a + i b,be a complex number.
Where, a = r cos A
b= r sin A
[tex]a^2 + b^2=(r cos A)^2 +(r sin A)^2\\\\ a^2 + b^2=r^2(cos^2 A+sin^2 A)\\\\ a^2 + b^2=r^2\\\\r=\sqrt{a^2 + b^2}[/tex]
[tex]Z=r cos A + i r sin A\\\\Z=r(cos A + i sin A)\\\\ Z=re^{iA},\text{Where}, e^{i\alpha }=cos \alpha +i sin\alpha[/tex]
Now, if we replace A, by, 2 kπ + A,in the above equation,where k is any positive integer,beginning from ,0.k=0,1,2,3,4,....
[tex]Z=r cos (2k\pi +A) + i r sin(2k\pi + A)\\\\Z=r[cos (2k\pi +A) + i sin(2k\pi + A)]\\\\ Z=re^{i(2k\pi +A)}[/tex]
So, for different value of , k ,there will be Different Complex number.
→So,the Statement: The trigonometric form of a complex number is unique = False
The trigonometric form of a complex number is unique is a false statement. Check the reason why it is false below.
Why is the trigonometric form of a complex number not special?The trigonometric form of a complex number is commonly seen as the polar form of that number.
This is due to the fact that there are lots of infinite choices are often made for θ and as such the trigonometric form of a complex number is said to be not unique in any way.
Learn more about complex number from
https://brainly.com/question/10662770
Which of the following ordered pairs is a solution to the equation 2x+7y=8
Select one:
a. (3, -2)
b. (2, -3)
c. (-3, 2)
d. (0, 4)
Find the circumference of a circle with radius of 18 in. Leave your answer in terms of π
if M and N are midpoints in a diagram below, determine values for x and y
Don is 6 feet tall. at a given time of day, he measures his shadow to be 13 feet long. at the same time, he measures the shadow length of a nearby tree to be 51 feet. how tall is the tree
The height of the tree maintaining the given ratio is 23.54 feet.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given that,
Don height = 6 feet
His shadow = 13 feet
The ratio of height to shadow = 6/13
Tree height = x (let's say)
Tree shadow = 51 feet
Ratio = x/51
Both ratios must be the same, therefore,
x/51=6/13
x=23.54 feet
Hence "The height of the tree maintaining the given ratio is 23.54 feet".
For more information about ratios and proportions,
brainly.com/question/26974513
#SPJ2
Solve m=10x−x for x
help
Solving for x in terms of m will give [tex]\frac{m}{9}[/tex]
The given expression:
m = 10x - x
To find:
x in terms of mTo find x in terms of m, we use the following simple approach;
[tex]m = 10x - x \ \ \ (you \ can \ subtract \ 'x" \ from \ "10x" \ since \ they \ are \ similar)\\\\m = 9x\\\\divide \ both \ side s\ by \ 9\\\\\frac{m}{9} = \frac{9x}{9} \\\\\frac{m}{9} = x[/tex]
Thus, solving for x in terms of m will give [tex]\frac{m}{9}[/tex]
Learn more here: https://brainly.com/question/15469690
In the diagram below, an and bc are tangent to o. What is the measure of adc
Answer:
mADC = 220°
Step-by-step explanation:
In the given diagram AB and BC are tangents to the given circle O. We have to find the measure of arc ADC.
By theorem of tangents and arcs.
m∠ABC = [tex]\frac{1}{2}[/tex] [m ADC- m AC ]
Since it is given in the question
∠ABC = 40 & AC = 140°
Therefore, 40 = [tex]\frac{1}{2}[/tex] [ m ADC - 140 ]
40 × 2 = m ADC - 140
80 + 140 = m ADC
mADC = 220°
1. In how many different ways can 5 people be seated at a round table?
2. Each block on the grid is 1 unit by 1 unit. We wish to walk from A to B via 7 unit path but we have to stay on the grid. How many different paths can we take?
3. How many different "words" can be made from the given word by re-arranging the letters?
a) VECTOR
B) TRUST
In which section of the number line is √55?
Answer:
A. Section A
Step-by-step explanation:
imagine said it was correct
Are 60 meters equal to, greater than, or less than 6 km?
Final answer:
60 meters is significantly less than 6 kilometers, as 6 kilometers is equal to 6,000 meters.
Explanation:
To answer this, we need to compare the two measurements in the same unit. We know that 1 kilometer is equivalent to 1,000 meters, so to convert 6 kilometers to meters, we multiply by 1,000:
6 km imes 1,000 = 6,000 m
Now we can compare the two measurements:
60 m
6,000 m
Since 60 is less than 6,000, we can conclude that 60 meters is less than 6 kilometers.
In a certain? country, the true probability of a baby being a boy is 0.534. among the next six randomly selected births in the? country, what is the probability that at least one of them is a girl??
The probability that at least one of them is a girl is about 0.977
Further explanationThe probability of an event is defined as the possibility of an event occurring against sample space.
[tex]\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }[/tex]
Permutation ( Arrangement )Permutation is the number of ways to arrange objects.
[tex]\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }[/tex]
Combination ( Selection )Combination is the number of ways to select objects.
[tex]\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }[/tex]
Let us tackle the problem.
This problem is about Probability.
Given:
The true probability of a baby being a boy P(B) = 0.534
The true probability that all of six randomly selected births in the country are boys is :
[tex]P(6B) = P(B) \times P(B) \times P(B) \times P(B) \times P(B) \times P(B)[/tex]
[tex]P(6B) = \boxed {(P(B))^6}[/tex]
The true probability that at least one of them is a girl is:
[tex]P(G\geq 1) = 1 - P(6B)[/tex]
[tex]P(G\geq 1) = 1 - (P(B))^6[/tex]
[tex]P(G\geq 1) = 1 - (0.534)^6[/tex]
[tex]P(G\geq 1) \approx \boxed {0.977}[/tex]
Learn moreDifferent Birthdays : https://brainly.com/question/7567074Dependent or Independent Events : https://brainly.com/question/12029535Mutually exclusive : https://brainly.com/question/3464581Answer detailsGrade: High School
Subject: Mathematics
Chapter: Probability
Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation
The probability that out of the next six randomly selected births, at least one of them is a girl is 0.98.
What is Probability in Mathematics?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur. Mathematically -
P (Event A) = n(A)/n(S)
where -
n(A) → Number of outcomes favorable to event A.
n(B) → Total number of possible outcomes.
Given is the true probability of a baby being a boy. Its value is -
P(A) = 0.534
Assume that for the next six randomely selected births, the probability that it will be a baby boy is P(B). In one of the six randomely selected births, the probability that it will be a boy is 0.534. Therefore, the probability of being a boy in all the six cases will be -
P(B) = [P(A)]⁶
P(B) = 0.023
Now, for at least one of them to be girl, the probability of the event will be -
P(C) = P(B)' = 1 - 0.023 = 0.98
Therefore, the probability that out of the next six randomly selected births, at least one of them is a girl is 0.98.
To solve more questions on Probability, visit the link below-
https://brainly.com/question/17239706
#SPJ2
Conjecture for interior angles of complex polygons
Final answer:
The conjecture for interior angles of complex polygons involves using the formula (n-2)×180 degrees for regular polygons and more complex considerations for 3D shapes like pentagonal bipyramids or square antiprisms. As the number of sides increases, calculations become more intricate and the interior angles can approach 180 degrees in very large polygons.
Explanation:
The question involves making a conjecture for the interior angles of complex polygons. A commonly used theorem related to this is that the sum of the interior angles of a polygon can be found using the formula (n-2)×180 degrees, where n is the number of sides in the polygon. For instance, to find the sum of the interior angles of a pentagon (a polygon with five sides), we calculate (5-2)×180 degrees = 540 degrees. As the number of sides increases, our calculations can become more complex, especially when dealing with non-regular polygons (where the sides and angles don't all have the same length/measure).
When considering the interior angles of complex geometries like a pentagonal bipyramid or a square antiprism, it's essential to recognize that their interior angles may involve multiple planes and hence cannot be calculated using the simple 2D polygon interior angle sum formula. These shapes involve three-dimensional calculations and often require advanced geometry or trigonometry to dissect into understandable components.
Considering large numbers of sides and complex figures, the interior angle measures can approach different limits. For example, as the number of sides I becomes very large, the interior angle measures can become very close to 180 degrees, which is suggested by the idea that for a polygon with infinitely many sides (approaching a circle), each interior angle would be 180 degrees.