Sin is negative where as cos is positive in the 4th quadrant.
Step-by-step explanation:
Sin, cos and tan are all positive in the 1st quadrant. Sin is only positive in the 2nd quadrant. Tan is only positive in the 3rd quadrant.Cos is only positive in the 4th quadrant.
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Graphs of sin and cos : https://brainly.com/question/9554579
Keywords: graphs, sin, cos, quadrant
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The graphs of sin and cos, while similar in shape and period, are shifted horizontally due to their phase difference. This directly affects their signs in different quadrants, revealing their interconnected nature and dependence on the unit circle representation.
Similarities in Graphs:
Shape: Both sine and cosine graphs share the same sinusoidal wave pattern, meaning they oscillate up and down between their maximum and minimum values.
Period: Both functions have the same period of 2π radians or 360 degrees, meaning they complete one full cycle within this interval.
Amplitude: Both have an amplitude of 1, meaning they oscillate between -1 and 1 on the y-axis.
Shift and Relationship between Signs:
Phase Shift: The cosine graph is essentially the sine graph shifted to the left by π/2 radians (or 90 degrees). This explains why their peaks and troughs don't coincide perfectly.
Signs in Quadrants: This phase shift plays a crucial role in determining the signs of sin and cos in different quadrants:
Quadrant I (0° to 90°): Both sin and cos are positive as they increase in value.
Quadrant II (90° to 180°): Sin remains positive as it continues increasing, but cos becomes negative as it decreases.
Quadrant III (180° to 270°): Both sin and cos are negative as they decrease in value.
Quadrant IV (270° to 360°): Sin becomes positive as it increases, but cos remains negative as it continues decreasing.
Underlying Connection:
These relationships can be further explained by their definitions based on the unit circle:
Sine: sin(θ) represents the y-coordinate of a point on the unit circle when the angle θ is measured from the positive x-axis counterclockwise.
Cosine: cos(θ) represents the x-coordinate of the same point.
Therefore, as θ moves around the circle, the signs of sin and cos change based on their positions relative to the axes.
If [tex]sin\theta = \frac{1}{3}[/tex] , [tex]\frac{\pi }{2} \ \textless \ \theta \ \textless \ \pi[/tex]. Find the exact value of
[tex]sin (\theta + \frac{\pi }{6})[/tex]
Answer:
- 0.183
Step-by-step explanation:
Given that [tex]\sin \theta = \frac{1}{3}[/tex]
and [tex]\frac{\pi }{2} < \theta < \pi[/tex]
We have to find the exact value of [tex]\sin (\theta + \frac{\pi }{6} )[/tex].
Now, [tex]\sin \theta = \frac{1}{3}[/tex]
⇒ [tex]\theta = \sin ^{-1} (\frac{1}{3} ) = 19.47[/tex]
Now, since [tex]\frac{\pi }{2} < \theta < \pi[/tex],
So, [tex]\theta = 180 - 19.47 = 160.53[/tex]
{Since [tex]\sin \theta = \sin (180 - \theta)[/tex]
Now, [tex]\theta + \frac{\pi }{6} = 160.53 + 30 = 190.52[/tex]
Hence, [tex]\sin (\theta + \frac{\pi }{6} )[/tex].
= [tex]\sin 190.52[/tex]
= - 0.183 (Approximate) (Answer)
the ratio of blueberries to strawberries is 1:7if there are 210 strawberries how many berries are there
Answer: 30
Step-by-step explanation:
1:7
x:210
find x
210 is 30 times bigger than 7 so 30 is 30 times bigger than 1
30 is the answer
Answer:
30 blueberries
Step-by-step explanation:
divide the total by the 7, it's a lot simpler since it's a 1:7 but yeah so it's 30:210 blueberries to strawberries
15 - 4x = 6 - 3x
whats the answer.
Answer:9
Step-by-step explanation: First you add the 3x to both sides(the -4x and the -3x) and then you get 15-1x=6. Next you subtract 15 from 15 and 6, so you get -1x=-9. So then you divide both sides by -1 (do -1x over -1 equals -9 over -1). Last you do the dividing and you get x=9.
Isolate the variable x by moving terms involving x to one side and constants to the other side. Simplify the equation step-by-step to find that x = 9.
To solve the equation 15 - 4x = 6 - 3x, we need to isolate the variable x. Follow these steps:
Start by getting all the terms involving x on one side of the equation. We can do this by adding 3x to both sides:Therefore, the solution to the equation 15 - 4x = 6 - 3x is x = 9.
)) Find the slope of the line that passes through (10, 1) and (1, 3).
Answer:
Slope (m)
-0.2222
m = 2 / -9 = -0.222
Step-by-step explanation:
PLEASE HELP!!! I WILL AWARD BRAINLIEST!!!
Given: BD = BF
DE ⊥ BC ,
FK ⊥ AB
Prove: ED ≅ FK
△BDE≅△________, By rule_________
Answer:
ΔB D E = ΔB F K, By rule A A S similarity
Step-by-step explanation:
a right angle is congruent to a right angle, so < B D E is congruent to
< B F K
< D B F is equal to < D B F
Side B D = B F is given
Thus, creating A A S similarity
One positive integer is 3 less than twice another. The sum of their squares is 698. Find the integers.
Answer:
The value of positive integers are 21.22 and 12.11
Step-by-step explanation:
Given as :
The sum of squares of two integer = 698
Let The one positive integer be x
And The other positive integer be y
According to question
one positive integer = 3 less than twice the other positive integer
So, x = 2 × y - 3
I.e x = 2 y - 3
And x² + y² = 698
So, Put the value of x
I.e ( 2 y - 3 )² + y² = 698
or, 4 y² + 9 - 12 y + y² = 698
Or, 5 y² - 3 y - 698 = 0
Now solving this quadratic equation
y = [tex]\frac{-b\pm \sqrt{b^{2}-4\times a\times c}}{2\times a}[/tex]
Or, y = [tex]\frac{3\pm \sqrt{-3^{2}-4\times 5\times -698}}{2\times 5}[/tex]
Or, y = [tex]\frac{3\pm \sqrt{13969}}{10}[/tex]
Or, y = [tex]\frac{3\pm 118.19}{10}[/tex]
∴ y = 12.11 , - 11.51
So , The value of y = 12.11
And the value of x = 2 × 12.11 - 3
I.e x = 21.22
Hence The value of positive integers are 21.22 and 12.11 Answer
To find the two integers, we can set up two equations based on the given information. By substituting the value of x from the first equation into the second equation, we can solve for y. Then, substituting the value of y back into the first equation, we can find the value of x.
Explanation:To solve this problem, we can set up two equations based on the given information. Let's say the first integer is x and the second integer is y. We are given that x is 3 less than twice y, so we can write the equation: x = 2y - 3. We also know that the sum of their squares is 698, so the equation becomes x^2 + y^2 = 698. Now we can substitute the value of x from the first equation into the second equation and solve for y.
Substituting x = 2y - 3 into the equation x^2 + y^2 = 698, we get (2y - 3)^2 + y^2 = 698. Expanding this equation, we get 4y^2 - 12y + 9 + y^2 = 698. Combining like terms, we have 5y^2 - 12y + 9 = 698. Rearranging this equation and simplifying, we get 5y^2 - 12y - 689 = 0. Now we can solve this quadratic equation to find the value of y.
Using the quadratic formula, y = (-(-12) ± sqrt((-12)^2 - 4(5)(-689))) / (2(5)). Simplifying the equation further, we have y = (12 ± sqrt(144 + 13780)) / 10. Taking the positive value, y = (12 + sqrt(13924)) / 10. Evaluating this expression, we find y ≈ 9.7394. Now we can substitute this value back into the first equation to find x.
Using x = 2y - 3, we have x = 2(9.7394) - 3. Simplifying this equation, we get x ≈ 16.4788. Therefore, the two integers are approximately 16.4788 and 9.7394.
9. A stock's price has been continuously declining at a rate of 5% per week. If the stock started at a price of
$62.50 per share, algebraically determine the number of weeks it will take for the price to reach $20.00 per
share. Round your answer to the nearest tenth of a week
Final answer:
It will take approximately 13.6 weeks for the stock's price to reach $20.00 per share.
Explanation:
To determine the number of weeks it will take for the stock's price to reach $20.00 per share, we need to find the number of weeks it will take for the price to decrease from $62.50 to $20.00. Since the price is declining at a rate of 5% per week, we can set up an equation:
$62.50 - ($62.50 imes 0.05 imes ext{number of weeks}) = $20.00
Simplifying the equation, we have:
$62.50 - (0.05 imes 62.50 imes ext{number of weeks}) = $20.00
$42.50 = (0.05 imes 62.50 imes ext{number of weeks})
Dividing both sides by 0.05 and 62.50, we get:
ext{number of weeks} = rac{42.50}{0.05 imes 62.50}
Calculating this, we find that it will take approximately 13.6 weeks for the stock's price to reach $20.00 per share.
Question 74 pts.
Calculate the harvesting capacity of a combine that travels 4.8 miles per hour and has a header for eight
30-inch-wide rows. The efficiency is .85. The expected yield is 120 bushels/acre.
1,187 bu/hr
1,255 bu/hr
1,522 bu/hr
1,178 bu/hr
Answer:
1,187 bu/hr
Step-by-step explanation:
4.8 mi/hr
240 inches
Efficiency: 85% (0.85)
120 bushels/acre
1 acre = 6 272 640
1 mile = 63 360 inches
4.8 miles = 304 128 inches
120/6 272 640 x 240 = 5/1089 (bushels/inch)
5/1089 x 304 128 x 85% = 1 186.9 = 1187 bu/hr
Wow, that's hard for me :) Hope it's helpful
- 8x - 16y = -166
8x + 7y - 76
Answer:
x=-1189/36, y=242/9. (-1189/36, 242/9).
Step-by-step explanation:
-8x-16y=-166
8x+7y=-76
----------------
-9y=-242
9y=242
y=242/9
8x+7(242/9)=-76
8x=-76-1694/9
8x=-2378/9
x=(-2378/9)/8
x=-1189/36
Classify the equation 6(x + 2) = 5(x + 7) as having one solution,
no solution, or infinitely many solutions.
The equation 6(x + 2) = 5(x + 7) simplifies to x = 23, indicating it has one unique solution. Substituting back into the original equation verifies the solution.
To classify the equation 6(x + 2) = 5(x + 7) as having one solution, no solution, or infinitely many solutions, we first simplify the equation:
Distribute the 6 and the 5 to the terms inside the parentheses: 6x + 12 = 5x + 35.Subtract 5x from both sides to get: x + 12 = 35.Subtract 12 from both sides to find the value of x: x = 23.This provides us with one solution for the equation, which means the equation has a single unique solution. When we substitute x = 23 back into the original equation, we get an identity, confirming that our solution is correct.
Equations with a single solution, no solution, or an infinite number of solutions are encountered often in algebra. For example, 1+x+x² = 0 may have real or complex solutions and can demonstrate the principle that an nth degree polynomial has n solutions, which can include repeated or complex roots. The equation 205+111x +4x² - 31x³ - 10x4 +5x5=0 is a higher-degree polynomial that may require numerous iterations to find a solution, emphasizing the complexity of finding solutions for polynomial equations.
The graph below shows the distance, y, in miles, of a bird from its nest for a certain amount of time, x, in minutes:
Graph titled Distance Vs Time is shown with Time in minutes along the x-axis and Distance from Nest in miles along the y-axis. The scale on the x-axis shows the numbers 0 to 25 at increments of 5, and the scale on the y-axis shows the numbers 1 to 8 at increments of 1. A straight line joins the ordered pairs 0, 3 and 5, 4 and 10, 5 and 15, 6 and 20, 7.
Based on the graph, what is the initial value of the graph and what does it represent?
3 miles per minute; it represents the speed of the bird
0.2 mile per minute; it represents the speed of the bird
0.2 mile; it represents the original distance of the bird from its nest
3 miles; it represents the original distance of the bird from its nest
Answer:
[tex]0.2[/tex] miles per minute represents the speed of the bird and 3 miles represents the original distance of the bird from its nest.
Step-by-step explanation:
As there is no graph mentioned here but the information are quite sufficient to answer the question.
We have points [tex](0,3), (5,4),(10,5)...[/tex]
From these points we can find the slope of the line .
From point slope formula [tex]y-y_1=m(x-x_1)[/tex]
And assigning [tex](x,y) (0,3)[/tex] and [tex](x_1,y_1) (5,4)[/tex]
[tex]m=\frac{y_1-y}{x_1-x} =\frac{4-3}{5-0} =\frac{1}{5}=0.2[/tex]
This slope is also the speed of the bird which is [tex]0.2\ miles\ per\ minute.[/tex]
As by plugging the values of any coordinate point we can confirm this.
Lets put [tex](10,5)[/tex], y-axis is the distance so in [tex]10[/tex] minutes the the distance covered by the bird must be equal to to y-axis value which is [tex]5[/tex] miles.
[tex]y=0.2(x),y=0.2(10)=5\ miles[/tex]
Now as in [tex]t=0[/tex] the bird has started from y-intercept value [tex]3[/tex] so we can say that,the original distance of the bird from its nest is [tex]3\ miles[/tex].
So the correct choices are:[tex]B[/tex] and [tex]D[/tex]
The birds speed is [tex]0.2\ miles[/tex] per minute and is [tex]3\ miles[/tex] away from its nest.
Answer:
(d).
Step-by-step explanation:
The y-intercept (0, 3) is initial value of graph ⇒ (d). 3 miles; it represents the original distance of the bird from its nest
find the solution of w(-15-w)=0
Answer:
w(-15-w)= 0
w= 0 or (-15-w) = 0
Now,
-15-w =0
w= -15
So,The solution of w(-15-w) = 0
w= 0, -15
Answer:
w=-15,0
Step-by-step explanation:
w(-15-w)=0
-15w-w^2=0
-(w^2+15w)=0
w(w+15)=0
w=-15,0
Two buses depart two cities moving in the same direction. The speed of the first bus is 54 mph which is 60% of the speed of the second bus. The faster bus caught up to the other bus one hour and thirty minutes after the departure. will give brainliest
Answer:
The second city is 54 miles behind the first city
Step-by-step explanation:
The first bus is assumed to go ahead of the second bus and is moving at 54 mph. The second bus is moving at a speed such as 54 mph is 60% (0.6) of its speed.
The speed of the second bus is then 54/0.6 = 90 mph
When 1 and a half hour has passed, the first bus has moved a distance of
[tex]X_1=54\times 1.5[/tex] = 81 miles
The second bus (behind the first bus) has moved
[tex]X_2=90\times 1.5[/tex] = 135 miles
The problem states they both meet in that time, it can only be possible if the second bus departed a distance 135 - 81 = 54 miles behind the first city
So, the second city is 54 miles behind the first city
Write the equation of the line that parallel to x = -3 and passes through the point (4, -7).
The equation of the line that parallel to x = -3 and passes through the point (4, -7) is y = -3x + 5
Solution:
The two forms of writing a point and slope in equation are point slope form and standard form.
The standard form of a line is in the form Ax + By = C where A is a positive integer, and B, and C are integers. The standard form of a line is just another way of writing the equation of a line.
The given point is (4,-7) and the slope is -3.
The slopes of parallel lines are always equal.
To write in standard form we will first write it in point slope form and then rearrange it into a standard from.
The equation of line in point slope form is given as:
[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]
[tex]\begin{array}{l}{y-(-7)=-3(x-4)} \\\\ {y+7=-3(x-4)} \\\\ {y+7=-3 x+12}\end{array}[/tex]
y = -3x + 5
Now, let us convert this equation to standard form
3x + y = 5
Thus the equation of line in point slope and standard form is found out
F) As a truck driver, Roland averages 400 miles every 6 hours of driving. How long will it take him to drive
2100 miles if he has to take a 2-hour break after every 6 hours of driving? It may help to make a chart.
Answer:
31.5 hours
Step-by-step explanation:
time * speed = distance
speed=400/6=66.67 miles per hour
2100/(400/6)=31.5 hours
Please answer all parts.
1: In what line is her mistake
2:Describe her mistake. [For example: "She _________________ when she was supposed to __________________."]
3.What is the CORRECT solution for x?
Thank you:)
Answer: Line C
Step-by-step explanation: She added 12 to one side and subtracted 12 from another side when she should've added 12 to both sides.
The correct answer and work would be:
8x-3(2x+4)=10
8x-6x-12=10
2x-12=10
2x=22
x=11
Solve for x 4x+8=7.8+5x
4x+8=7.8+5x
Subtract 4x from both sides:
8 = 7.8 +x
Subtract 7.8 from both sides:
x = 0.2
given that -4 is a zero of the function f(x)=x3+3x2-16x-48f(x)=x3+3x2-16x48, find the other zeros and write f(x)f(x) in factored form
Answer:
f(x) = (x + 4)(x - 4)(x + 3)
The other zeros of the function are at 4 and -3.
Step-by-step explanation:
Given function is f(x) = x³ + 3x² - 16x - 48.
Now, given that - 4 is a zero of the given function.
So, the function has a factor equals to (x + 4).
Now, f(x) = x³ + 3x² - 16x - 48
⇒ f(x) = x³ + 4x² - x² - 4x - 12x - 48
⇒ f(x) = x²(x + 4) - x(x + 4) - 12(x + 4)
⇒ f(x) = (x + 4)(x² - x - 12)
⇒ f(x) = (x + 4)(x - 4)(x + 3)
Therefore, the other zeros of the function are at 4 and -3. (Answer)
Answer:
f(x) = (x + 4)(x - 4)(x + 3)
Step-by-step explanation:
if m<1=125*, determine the measure of <3
A 85
B 125
C 55
D 105
angle = 125 degree because it is Vertically Opposite to the angle 1.
A)400
B)500
C)550
D)560
500
Step-by-step explanation:
The median is always the middle line in the box of the data set even if the data set is uneven.
What is the inequality?
PLEASE HELP ME ITS ALREADY LATE AND ITS BRINGIN MY GRADE WAY DOWN PLEASE HEPL ME!!!!
The following graph is of an exponential function of the form y=a*bx.
What values of a and b would make this equation work?
a=
b=
Answer:
[tex]a=15[/tex]
[tex]b=\frac{1}{3}[/tex]
Step-by-step explanation:
we have an exponential function of the form
[tex]y=a(b^x)[/tex]
where
a is the initial value or y-intercept
b is the base
Looking at the graph
we can see the ordered pairs (0,15) and (1,5)
(0,15) ---> y-intercept
so
The value of a is equal to
[tex]a=15[/tex]
substitute
[tex]y=15(b^x)[/tex]
with the point (1,5) find the value of b
For x=1, y=5
substitute in the exponential function
[tex]5=15(b^1)[/tex]
solve for b
[tex]5=15(b)[/tex]
[tex]b=\frac{1}{3}[/tex]
therefore
The exponential function is
[tex]y=15(\frac{1}{3}^x)[/tex]
Which lines is a parallel to the line y=1/2x+5 and passes through the point (-2,1)?
Answer:
The answer is: y = 1/2x + 2
Step-by-step explanation:
Given equation: y = 1/2x + 5
Given point: (-2, 1)
The slope of the given line is 1/2. Parallel lines have the same slope.
Use the point slope form and solve for y:
y - y1 = m(x - x1)
y - 1 = 1/2(x - (-2))
y - 1 = 1/2(x + 2)
y - 1 = 1/2x + 1/2 * 2
y - 1 = 1/2x + 1
y = 1/2x + 2
Proof:
f(-2) = 1/2(-2) + 2
= -1 + 2
= 1, giving point (-2, 1)
Hope this helps!! Have an Awesome Day!! :-)
In March, Delphine's house had 40\%40%40, percent more snowfall than in February. Delphine's house had fff centimeters of snowfall in February.
Which of the following expressions could represent how much snowfall Delphine had at her house in March?
Choose 2 answers:
Choose 2 answers:
Answer:
1.40f .
Step-by-step explanation:
One answer could be:
In March the house had f + 40% of f
= f + 0.40f
= 1.40f
Answer:
If the February snowfall is valued as fs, the snowfall in March with an additional 40% could be expressed as:
March snowfall = 1.4fsStep-by-step explanation:
In the exercise it is mentioned that the snowfall in March was 40% higher than in February, if you wanted to express it in a mathematical function it could be mentioned that:
March snowfall = February snowfall (fs) + 40% of February snowfall.What could be represented as:
March snowfall = fs + 0.4fsWhen calculating we would obtain:
March snowfall = 1.4fsHow can I factor 130x - 13
Answer:
Divide by 13, you will get 10x - 1
To factor the expression 130x - 13, find the greatest common factor, which is 13, and factor it out. The factored form is 13(10x - 1).
To factor the expression 130x - 13, you need to look for a common factor in both terms. In this case, both terms can be divided by 13, which is the greatest common factor of the two numbers. By factoring out 13, you get:
13(10x - 1)
This process is known as factoring by common factor or GCF factoring. It simplifies the expression to a product of a constant (13) and a binomial (10x - 1). This method is very useful in solving equations, simplifying expressions, and can be a first step in more complex factoring processes.
What is 1/3 x 20/9 simplified to the lowest term
Answer: 20/27
Step-by-step explanation:
multiply numerators and denominators
1/3 x 20/9 = 20/27
you can not simplify further
A cross country runner ran 2 miles in 1/4
hour. What is the average speed of the
cross country runner in miles per hour?
Need help ASP plssss
If y=2 2/3 when x=1/4, find y when x=1 1/8
Answer:
x = 1/4 when y = 8/3
Step-by-step explanation:
Divide both by 1/4
x = 1 when y = 32/3
When x = 1 1/8 = 9/8
y = 32/3 x 9/8
y = 12
44. What percent of 75 is 30?
Answer:
40%
Step-by-step explanation:
30/75 = 0.4
Move decimal point back 2 places to convert to percent.
0.4 = 40%
Answer: 40%
Step-by-step explanation:
let x equal the percent
75x=30
x=2/5=40%
Find the diagonal of a square whose sides are of the given measure.
Given = 3v3
Answer:
The measure of the diagonal is [tex]3\sqrt{6}\ units[/tex]
Step-by-step explanation:
Let
c -----> the diagonal of a square in units
a ----> the length side of a square
Remember that a square can be divided into two congruent right triangles
see the attached figure to better understand the problem
Applying the Pythagoras Theorem
[tex]c^{2}=a^{2}+a^{2}[/tex]
we have
[tex]a=3\sqrt{3}\ units[/tex]
substitute
[tex]c^{2}=(3\sqrt{3})^{2}+(3\sqrt{3})^{2}[/tex]
[tex]c^{2}=54[/tex]
[tex]c=\sqrt{54}\ units[/tex]
simplify
[tex]c=3\sqrt{6}\ units[/tex]