Answers
Answer:
[tex]\sin(\theta)=-\sqrt5/5\text{ and } \csc(\theta)=-\sqrt5\\\cos(\theta)=2\sqrt5/5\text{ and } \sec(\theta)=\sqrt5/2\\\tan(\theta)=-1/2\text{ and } \cot(\theta)=-2[/tex]
Step-by-step explanation:
First, let's determine which quadrant our angle θ lies in.
Remember ASTC, where:
Everything is positive in QI,
Only sine (and cosecant) is positive in QII,
Only tangent (and cotangent) is positive in QIII,
And only cosine (and secant) is positive in QIV.
Since our tangent is negative, and our cosine is positive, this means that our θ must be in QIV.
In QIV, sine is negative, tangent is negative, and cosine is positive.
With that, let's figure out the remaining trig ratios.
We know that:
[tex]\tan(\theta)=-1/2[/tex]
Remember that tangent is the ratio of the opposite side to the adjacent side.
Let's figure out our hypotenuse using the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
Substitute 1 for a and 2 for b (we can ignore the negative since we're squaring anyways). This yields:
[tex](1)^2+(2)^2=c^2[/tex]
Square:
[tex]1+4=c^2[/tex]
Add:
[tex]c^2=5[/tex]
Take the square root:
[tex]c=\sqrt{5}[/tex]
So, our square root is √5.
So, our three sides are: Opposite=1, Adjacent=2, and Hypotenuse=√5.
Sine and Cosecant:
Remember that:
[tex]\sin(\theta)=opp/hyp[/tex]
Substitute 1 for the opposite and √5 for the hypotenuse. This yields:
[tex]\sin(\theta)=1/\sqrt5[/tex]
Rationalize:
[tex]\sin(\theta)=\sqrt5/5[/tex]
And since our angle is in QIV, we add a negative:
[tex]\sin(\theta)=-\sqrt5/5[/tex]
Cosecant is simply the reciprocal of sine. So:
[tex]\csc(\theta)=-\sqrt5[/tex]
Cosine and Secant:
Remember that:
[tex]\cos(\theta)=adj/hyp[/tex]
Substitute 2 for the adjacent and √5 for the hypotenuse. This yields:
[tex]\cos(\theta)=2/\sqrt5[/tex]
Rationalize:
[tex]\cos(\theta)=2\sqrt5/5[/tex]
Since our angle is in QIV, cosine stays positive.
Secant is the reciprocal of cosine. So:
[tex]\sec(\theta)=\sqrt5/2[/tex]
Tangent and Cotangent:
We were given that:
[tex]\tan(\theta)=-1/2[/tex]
To find cotangent, flip:
[tex]\cot(\theta)=-2[/tex]
And we're done!
Related Questions
Write the equation of the line passing through the points (-7,7) and (7,1).
Answers
Answer and work down below. Let me know if you have questions
can someone please help?? (assume that no variable equals 0)
Answers
Practice using a table to determine key features of the graph of a continuous function. A 2-column table with 6 rows. The first column is labeled x with entries negative 1, 0, 1, 2, 3, 4. The second column is labeled f of x with entries negative 9, negative 8, negative 7, 0, 19, 56. What is the x-intercept of the continuous function shown in the table? (0, –8) (0, 2) (–8, 0) (2, 0)
Answers
Answer:
2,0
Step-by-step explanation:
Answer:
the answer too this answer is 2.0
Step-by-step explanation:
I just did it on edge i got it right.
Drag the numbers to order them from least to greatest.
0.7
-4.5
0.3
-0.5
2.3
Answers
Answer:
-4.5 -0.5 0.3 0.7 2.3
Step-by-step explanation:
Darlene earned 6.75 interest in her savings account for a 15-month period. What was the average amount of interest Darlene earned on her savings account per month?
Answers
Find the distance benveen the points A (13, 2) and B (7, 10).
The distance between the two points is ?
Answers
B = (7, 10)
the distance between point A and point B is 10
Which expression means the same as subtract 3 from 7 and then multiply by 4
Answers
The width of a rectangle is 1.9 feet. The perimeter is 7.4 feet. What is the length?
Answers
Answer:
1.8 feet
Step-by-step explanation:
This is the answer because:
Perimeter = L + W + L + W
1) Since we know the width of the rectangle is 1.9 feet, let's add 1.9 + 1.9 which is 3.8
2) Now, we know the total perimeter is 7.4, therefore, subtract 7.4 - 3.8 which is 3.6
3) Next, divide 3.6/2 which is 1.8
4) Finally, you can check your work by adding 1.8 + 1.8 + 1.9 + 1.9 which equals 7.4
Hope this helps!
The temperature in a town is 36.1°F during the day and -8.9°F at night. Find the difference in the
temperatures.
The difference in temperature is N°r.
HELP HELP
Answers
Answer:
45 degrees
Step-by-step explanation:
A circle has a diameter of 22 cm. What is its circumference?
Use 3.14 for it, and do not round your answer. Be sure to include the correct unit in your answer.
Answers
Answer:
[tex]\boxed {\tt 69.08 \ centimeters}[/tex]
Step-by-step explanation:
The circumference of a circle can be found using the following formula:
[tex]c= \pi d[/tex]
where d is the diameter. We know the diameter of the circle is 22 centimeters. Substitute the value in for d.
[tex]d= 22 \ cm[/tex]
[tex]c= \pi* 22 \ cm[/tex]
We also know we are using 3.14 for pi. Substitute it in for pi.
[tex]c= 3.14 * 22 \ cm[/tex]
Multiply.
[tex]c=69.08 \ cm[/tex]
The circumference of the circle is 69.08 centimeters.
Answer:
Circumference = 69.08 cm
Step-by-step explanation:
Diameter = 22
Radius = 22/2
= 11
Circumference = 2πr
= 2 × 3.14 × 11
= 69.08 cm
Hoping it helps
Please follow me
Y = l x + 5 l pleaseeee
Answers
Answer:
y = x + 5
Step-by-step explanation:
We can take away the absolute value signs (as the equation does not differ with or without them).
To graph, one must remember slope-intercept form (y = mx + b)
M is the slope. When a clear "m" is not present, then one must assume that it is one, as the product of one and x is x.
B is where the y-axis intercepts the line (when x equals zero, y equals b). This is called the y-intercept. In this equation, b is five, so one point on the line is (0, 5). Then, following the slope (which is rise over run, or y over x), one must go up one, over one, up one, over one (up one unit, then to the right one unit (then mark your spot as a point)), then, draw a straight line connecting the two or more points. And there you have it!
PLEASE HELPP
What is the value of m?
13m+3−56m=−15
m=−36
m=−27
m = 27
m = 36
Answers
Answer:
m = 18/43.
Step-by-step explanation:
13m + 3 − 56m = −15
13m - 56m = -15 - 3
- 43m = -18
m = 18/43.
Answer: plz mark me as brainiest
i took the test and its 36
What is 9/10 divided by 5/10
Answers
Answer:
[tex]\frac{9}{10}[/tex] ÷ [tex]\frac{5}{10}[/tex] = 1.8 / [tex]\frac{9}{5}[/tex] (or 1 [tex]\frac{4}{5}[/tex])
Step-by-step explanation:
when you convert these fractions to decimals, you get 0.9 and 0.5. then multiply them. the answer is 1.8 as a decimal, 9/5 as a fraction, or 1 4/5 as a mixed number.
Answer:
ur mom ;),its 1.8, just delete it i swear :D
0.007 0.07 0.7 7 what’s next
Answers
Answer:
77
Step-by-step explanation:
Because your slowly moving up a place
A projectile is launched upward with a velocity of 256 feet per second from the top of a 35-foot structure. What is the maximum height attained by the projectile?
Answers
Answer:
1059 ft
Step-by-step explanation:
For problems like these, we assume the acceleration due to gravity is -32 ft/s², so the velocity will decrease to zero in time t, where ...
0 = 256 -32t
32t = 256
t = (256 ft/s)/(32 ft/s² ) = 8 s
Since velocity is linearly decreasing from 256 ft/s to 0, its average value of 128 ft/s will serve to tell us the height attained.
Height attained is ...
35 ft + (128 ft/s)(8 s) = 35 ft + 1024 ft = 1059 ft
The maximum height attained by the projectile is 1059 feet.
Please help ASAP 15 points
Answers
Alternate interior angles - <4 & <6
Vertical angles - <5 & <7
Alternate exterior angles - <1 &<7
Supplementary angles - <6 & <7
Corresponding angles - <8 & <4
Consecutive interior angles - <3 & <6
Marcia has 412 flowers for centerpieces she uses 8 flowers for each center how many center pieces can she make
Answers
Answer:
5l.5
Step-by-step explanation: 412 divieded into 8 is 51 or 51.5
Answer:
51
Step-by-step explanation:
To find how many centerpieces she can make, divide 412 by 8, since she has 412 flowers and uses 8 for each one:
412/8
= 51.5
Since centerpieces can only be whole numbers in the real world, this has to be rounded down to 51.
So, she can make 51 centerpieces.
Which number is less than 8.350
A8.503
B8.305
C8.530
D8.355
Answers
Answer:
b
Step-by-step explanation:
small town whose population was 18,395 ten years ago, has lost 270 inhabitants each year since then. what is the present population of small town?
Answers
Answer:
15965
Step-by-step explanation:
a=18395
d= -270 (lost inhabitants every year)
n=10
tn=?
We know that,
tn= a+(n-1)×d
=18395+(10-1)×(-270)
=18395+9×(-270)
= 18395 -2430
=15965
Hence,the present population of small town is 15965.
Are the lines Y= -X +5 and 2X + 2y=6 perpendicular?
Answers
Answer:
no
Step-by-step explanation:
Why did I get this question wrong?
Answers
You set up was almost accurate. Remember the arc length formula:
If f'(y) is continuous on the interval [a,b], then the length of the curve x = f(y), a ≤ y ≤ b should be;
L = ∫ᵇ ₐ √1 + [f'(y)]^2 * dy
We have to find the length of the curve given x = √y - 2y, and 1 ≤ y ≤ 4. You can tell your limits would be 1 to 4, and you are right on that part. But f'(y) would be rather...
f'(y) = 1/(2√y) - 2
So the integral would be:
∫⁴₁ √1 + (1/(2√y) - 2)² dy
Using a calculator we would receive the solution 5.832. Their is a definite curve, as represented below;
Answer:
s = ∫₁⁴ √(1 + (1/(2√y) − 2)²) dy
s = 5.8319
Step-by-step explanation:
Arc length is:
s = ∫ ds
s = ∫ √(1 + (dx/dy)²) dy
Find dx/dy:
x = √y − 2y
dx/dy = 1/(2√y) − 2
Substitute:
s = ∫₁⁴ √(1 + (1/(2√y) − 2)²) dy
Evaluate with a calculator:
s = 5.8319
Which characteristics do Jupiter and Saturn share? Check all that apply.
A.) Mostly made of gas
B.)Have few moons
C.) Same size as earth
D.) They have rings
E.) They have thick atmospheres
Answers
Answer:
correct is A, D, and E
hope it help! please make me a brainliest!
Answer:
A.) Mostly made of gas
D.) They have rings
E.) They have thick atmospheres
Step-by-step explanation:
9. An article was sold at a profit of 12%. Had it been sold for Nu 80 more, there would be a profit of
20%. Find
1) the cost price of the article
2)the selling price of the article
Answers
Answer:
The cost price of the article was Nu 1,000
The original selling price was Nu 1,120
The second selling price was Nu 1,200
Step-by-step explanation:
System of Equations
Let's call:
x = Original selling price of the article
y = Cost of the article
The first condition implies that the difference between the selling price and the cost price (the profit) is 12%. Recall the profit % is always calculated with respect to the cost, that is, the profit at the first condition is:
0.12y = Original profit
Setting up the equation, we have:
[tex]x-y=0.12y[/tex]
The second condition states the selling price is 80 Nu more than before, that is:
x+80= Second selling price of the article
y = Cost of the article (it doesn't change)
The profit of this condition is 20%, thus:
0.2y = Second profit
This produces a second equation:
[tex]x+80-y=0.2y[/tex]
Let's put both equations together to form a system of equations:
[tex]x-y=0.12y[/tex]
[tex]x+80-y=0.2y[/tex]
Operating on both equations:
[tex]x=1.12y[/tex]
[tex]x=1.2y-80[/tex]
Equating both equations, we have an equation with only y's:
[tex]1.12y=1.2y-80[/tex]
Subtracting 1.2y on each side:
[tex]1.12y-1.2y=-80[/tex]
Operating:
[tex]-0.08y=-80[/tex]
Solving:
[tex]\displaystyle y=\frac{-80}{-0.08}=1,000[/tex]
a)
The cost price of the article was Nu 1,000
b) The selling price of the article will be calculated in both cases:
Original selling price: x=1.12y= 1.12*1000=1,120
The original selling price was Nu 1,120
The second selling price was x+80=1,200
The second selling price was Nu 1,200
12 points ik its not alot but i need help please.The table shows the prices of some breakfast items at a restaurant. Sara ordered 2 eggs, a slice of bacon, and a glass of orange juice for breakfast. The sales tax for the order was $0.48. She paid for her breakfast with a $10 bill.
Item Price
One egg $1.69
Slice of bacon $1.49
Glass of orange juice $1.09
How much change should Sara receive from a $10 bill? pls show work
Answers
Answer:
The change should Sara receive from the $10 bill is $3.56.
Step-by-step explanation:
Given:
The table shows the prices of some breakfast items at a restaurant.
Item Price
One egg $1.69
Slice of bacon $1.49
Glass of orange juice
$1.09
Sara ordered 2 eggs, a slice of bacon, and a glass of orange juice for breakfast.
The sales tax for the order was $0.48.
She paid for her breakfast with a $10 bill.
Now, to find the change should Sara receive from the $10 bill.
Bill for the Sara's breakfast:
2 eggs =
A slice of bacon = $1.49.
A glass of orange = $1.09.
The sales tax = $0.48.
Total bill =
Sara paid for the breakfast bill = $10.
Now, to get the change Sara should receive we subtract the amount of bill from the money Sara paid for the bill:
Therefore, the change should Sara receive from the $10 bill is $3.56.
Answer:
Her change would be 3 dollars and 56 cents
Step-by-step explanation:
1.69 times 2 because she ordered 2 eggs
1.49 for the bacon
1.09 for the orange juice
0.48 for the sales tax
add them all up
it would equal 6.44
then subtract 6.44 from 10 which would equal 3.56
Suppose that 30% of all students who have to buy a textbook for Statistics want a new copy (the successes!), while the rest 70% want a used copy. Consider randomly selecting 15 buyers. (a) Find the mean and standard deviation for the number who want to buy a new copy of the book Mean = 15*.3 Standard deviation = sqrt(15*.3*.7) (b) Is that probability that the number of buyers who want new copies is more than two standard deviations away from the mean value? Probability= 1-.984757474+.004747562 (c) The bookstore has 13 new copies and 13 used copies in stock. If 15 people come in one by one to buy this textbook, what is the probability that all 15 will get the type of book they want from current stock? Probability= .999999483-.0352676 Hint: Consider X: the number of buyers who want a new copy. For what values of X will all 15 buyers get what they want? (d) Suppose that new copies cost $134 and used copies cost $67. Assume that the bookstore has currently 15 new copies and 15 used copies. What is the expected total revenue from the sale of the next 15 copies? Expected Revenue=
Answers
Step-by-step explanation:
a.
mean = E(X)
= no = 15 x 0.3
= 4.5
Standard deviation
= √np(1-p)
= √15x0.3x0.7
= √3.15
= 1.775
B.
Probability of number of buyers who want new copy
P(x>mean+2sd)
= P(x>4.5+2(1.775))
P(x>8.05)
= 1-(0.984757474+0.004747562)
= 0.01049
= 0.0105
C.
Σ13 (15Cx) x (0.3^x)(0.7)^15-x
= 0.9647
D. (4.5*237)+(15-4.5)*67
= 616.5+703.5
= $1320
Expected revenue from sale of next 15 copies is $1320
The product of y and 2
Answers
Answer:
2y
From: iOE your friend
*Be awesome Be you*
Find the measures of the following angles.
Answers
Answer:
1: 36° 2: 122° 3: 122° 4: 38°
Step-by-step explanation:
First start out by getting 2 and 3. so 58+angle 3 has to sum to 180° since they are supplementary and are a straight line. So 180-58=122. Angle 2 is the same since theyre vertical. then since a triangle has 180° total, you subtract from 180 to find the final angle measurement.
A school has 415 third graders and 338 second graders. How many more third
graders are there than second graders?
Answers
Answer:
75
Step-by-step explanation:
Answer:
77
Step-by-step explanation:
Just do simple subtraction 415-338=77
A man has 29 coins in his pocket, all of which are dimes (worth $ 0.10 each) and quarters (worth $ 0.25 each). If the total value of his change is $ 4.85 , how many dimes and how many quarters does he have?
Answers
Answer:
58
Step-by-step explanation:
An animator is drawing a scene in which a ladybug moves around three mushrooms. The figure shows
the starting position of the ladybug. The animator rotates the ladybug 180° around mushroom A, then
180° around mushroom B, and finally 180° around mushroom C. What are the final coordinates of the
Ladybug?
What are the final coordinates of the ladybug?
Answers
Answer:
(-1, 4)
Step-by-step explanation:
Original position of the ladybug → (-1, 4)
Animator rotates the ladybug 180° around the mushroom A.
Coordinates of the new position of the ladybug → (-5, -4)
Now this point is rotated by 180° around the mushroom B,
Coordinates of the new position → (0, 3)
Point (0, 3) has been rotated again by 180° about the mushroom C,
Coordinates of the new position → (-1, 4)
Therefore, ladybug will come back to its original position after these transformations at (-1, 4).
