Consider the graph below: Point T(-2; 3) is a point on the Cartesian Plane such that B is the angle of inclination of OT. T(-2;3) у х 2.1 Calculate the following without the use of a calculator: a) tanſ b) 13 sin B.cosB (2)
Answers
Answer:
(a) - 3/2
(b) - 78/25
Step-by-step explanation:
According to the trigonometry, the tangent of any angle is the ratio of rise to the run of the right angle triangle .
The sine of an angle is the ratio of rise to the hypotenuse of the right angle triangle.
The cosine of an angle is the ratio of run to the hypotenuse of the right angle triangle.
(a)
[tex]tan\beta = \frac{3}{-2} = \frac{-3}{2}[/tex]
(b)
[tex]13 sin\beta cos \beta = 13\times \frac{3}{\sqrt{3^2+2^2}}\times\frac{-2}{\sqrt{3^2+2^2}}\\\\13 sin\beta cos\beta = \frac{- 78}{25}[/tex]
Related Questions
If you apply these changes to the linear parent function f(x)=x what is the equation of the new function vertically compressed by a factor of 3 reflect over the x axis
Answers
Answer:
Because this gravity of. The earth
Qual é a frequência de cada gênero de leitura citados?
Answers
Answer:
i velo you
Step-by-step explanation:
If the coordinates of a point p(m-3, -6) = p(-7, -6), then find the value of m
Answers
Answer:
[tex]m =-4[/tex]
Step-by-step explanation:
Given
[tex]p(m-3 , -6) = p(-7 , -6)[/tex]
Required
Find m
[tex]p(m-3 , -6) = p(-7 , -6)[/tex]
By comparison:
[tex]m-3 = -7[/tex]
Add 3 to both sides
[tex]m = -7+3[/tex]
[tex]m =-4[/tex]
What is the value of angle v?
Answers
Answer:
x = 5
Step-by-step explanation:
a) The third interior angle of this triangle is 180 - 20 x.
The three interior angles must sum up to 180 degrees.
Therefore, 60 + 7x + 5 + 180 - 20x = 180, or
65 + 180 - 13x = 180, or
65 - 13x = 0
Finally, 13x = 65, and so x = 5
Difference Quotient. Correct answer is shown. It says multiply by conjugate but I don’t understand what that is and how they did it. TIA
Answers
9514 1404 393
Answer:
3/(√(3(x+h)) +√(3x))
Step-by-step explanation:
The conjugate of a binomial is the same sum, but with the sign changed. That is (a +b) and (a -b) are a conjugate pair: each is the conjugate of the other.
The purpose of multiplying expressions involving roots or complex numbers by their conjugate is to take advantage of the relation ...
(a +b)(a -b) = a² -b²
Here. you want to eliminate the h from under the radical, so squaring the radical containing h is useful for the purpose. Hence the conjugate gets involved.
"Multiply by the conjugate" means multiply both the numerator and the denominator by the conjugate. (Effectively, multiply by 1.)
__
[tex]\displaystyle\frac{f(x+h)-f(x)}{h}=\frac{\sqrt{3(x+h)}-\sqrt{3x}}{h}\\\\=\frac{(\sqrt{3(x+h)}-\sqrt{3x})(\sqrt{3(x+h)}+\sqrt{3x})}{h(\sqrt{3(x+h)}+\sqrt{3x})}=\frac{3(x+h)-3x}{h(\sqrt{3(x+h)}+\sqrt{3x})}\\\\=\frac{3h}{h(\sqrt{3(x+h)}+\sqrt{3x})}=\boxed{\frac{3}{\sqrt{3(x+h)}+\sqrt{3x}}}[/tex]
_____
Additional comment
In the end, you will want the limit as h → 0, which will be 3/(2√(3x)). You will notice that h=0 no longer makes the denominator zero, so the limit is found by simple evaluation.
When the "binomial" is a complex number of the form a+bi, its conjugate is a-bi, regardless of the sign of b. That is, the conjugate of a complex number is found by negating its imaginary part. The sign of the real part is left alone.
A study is conducted to see how effective aspirin is in reducing temperature in children. A sample of 6 children suffering from influenza had their temperatures taken immediately before and 1 hour after administration of aspirin. The results are given below. We would like to conduct a paired differences t-test for this situation. The data follows:
Patient Temperature Before Temperature After Difference
1 103.7 102.6 1.1
2 103.7 102.7 1
3 100.7 98.8 1.9
4 102.7 103.5 -0.8
5 102.7 101.3 1.4
6 100.7 99.4 1.3
Mean 102.4 101.4 1
Std. Dev. 1.4 1.9 0.9
Required:
Calculate the appropriate test statistic of a matched pairs t-test for this data to see if taking aspirin will reduce a child's fever.
Answers
Answer:
Then t(s) is in the rejection region for H₀ we reject H₀ and conclude that the aspirin will reduce a child´s fever
Step-by-step explanation:
Tem.Before Tem.After diff.
103.7 102.6 1.1
103.7 102.7 1
100.7 98.8 1.9
102.7 103.5 -0.8
100.7 99.4 1.3
102.4 101.41 (Mean)
1.4 1.9 0.9 Std. Dev.
n = 6
df = 6 - 1 = 5
CI we propose to be 95 %
Then α = 5 % α = 0.05
The test is a one-tail test ( we want to know if taking aspirin will reduce a child´s fever
Hypothesis test
Null Hypothesis H₀ μd = 0
Alternative Hypothesis Hₐ μd > 0
(NOTE:) μd (average) = Temp Before - Temp. after
Therefore if μd > 0 means that there is a statistical difference between values before ( bigger ) and after or that the aspirin will reduce a child´s fever
To find t(c) from t-student table df = 5 and α = 0.05
t(c) = 2.015
To compute t(s)
t(s) = μd/ sd/√n t(s) = 0.98/ 0.9/√6
t(s) = 2.66
Comparing t(s) and t(c)
t(s) > t(c)
Then t(s) is in the rejection region for H₀ we reject H₀ and conclude that the aspirin will reduce a child´s fever
Please help me
A. 7ft
B. 11ft
C. 15ft
D. 10ft
Answers
Answer:
A. 7ftStep-by-step explanation:
Have a good grades and study well sweetie
answered by: sugaxchimWhich of the following is the equation of a line in slope-intercept form for a
line with slope = and yintercept at (0, -1)?
O A. y - x-
1
B. y = 4x-1
O c. y= |x-1
O D. y=x+1
Answers
Answer:
y=1/4x - 1
Step-by-step explanation:
going off of the picture, I'd say this is your answer
i need help with this on my homework
Answers
ko iê ế t??????????????? t
Triangles A B C and A double-prime B double-prime C double-prime are shown. Triangle A double-prime B double-prime C double-prime is smaller and to the right of triangle A B C. Which transformations could have taken place to map △ABC to △A"B"C"? a reflection and a dilation a rotation and a dilation a translation and a dilation a reflection and a translation
Answers
C. a translation and a dilation
Step-by-step explanation:
the other person isn't wrong they just put it in the wrong order
Answer:c
Step-by-step explanation:took the test
Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced.
To buy a car, you borrow $27,000 with a term of five years at an APR of 6%. What is your monthly payment? (Round your answer to the nearest cent.)
$
How much total interest is paid? (Round your answer to the nearest cent.)
$
Answers
Answer:
The correct answer is -
monthly payment = 521.99
total pain intrest = 4319.14
Step-by-step explanation:
Given:
a or the borrowed amount = 27000
r or the interest rate = 6%
n = 5 years or 60 months
Monthly payment = ?
total intreset = ?
Formula:
The formula for the monthly payment is -
[tex]\frac{a}{\frac{{[(1+r)^n]-1}}{[r(1+r)^n]}} = P[/tex]
or, [tex]\frac{ar}{[1-(1+r)^{-60}}[/tex] = P
Where, the amount of the loan = a
r = 0.005 (6% annual rate—expressed as 0.06—divided by 12 monthly payments per year)
n = 60 months
Solution:
Putting all the values in the either of the following formula will give monthly payments:
[tex]\frac{27000}{\frac{{[(1+0.005)^{60}]-1}}{[0.005(1+0.005)^{60}]}} = P[/tex] or [tex]\frac{ar}{[1-(1+r)^{-60}}[/tex]
= 521.9856 or to the nearest cent 521.99.
The total intrest would be -
= (monthly payment*number of month) - amount borrowed
= 521.99*12-27000
= 31319.14-27000
= 4319.14
Another name for NQ is? (Geometry)
Answers
Answer:
NQ : Summary
CodeNQOne-letter codeXMolecule name2-HYDROXYNAPHTHOQUINONESynonyms2-HYDROXY-1,4-NAPHTHOQUINONESystematic namesProgram Version Name ACDLabs 10.04 2-hydroxynaphthalene-1,4-dione OpenEye OEToolkits 1.5.0 2-hydroxynaphthalene-1,4-dione
Factor t^2 - 5t + 6. Type your answer in the space provided. Do not type spaces in your answer. Use only lowercase letters and include all necessary parentheses, variables and operation signs. For example, if the answer is (x +1)(x+2), type (x+1)(x+2).
Answers
Answer:
(x-3) * (x-2
Step-by-step explanation:
An electrician leans an extension ladder against the outside wall of a house so that it
reaches an electric box 30 feet up. The ladder makes an angle of 68° with the ground.
Find the length of the ladder. Round your answer to the nearest hundredth of a foot if
necessary.
Answers
Answer: [tex]32.36\ ft[/tex]
Step-by-step explanation:
Given
Ladder is leaned and make an angle of [tex]68^{\circ}[/tex]
Electric box is 30 ft up the ground.
Suppose x is the length of ladder
From the figure, we can write
[tex]\Rightarrow \sin 68^{\circ}=\dfrac{30}{x}\\\\\Rightarrow x=\dfrac{30}{\sin 68^{\circ}}\\\\\Rightarrow x=32.36\ ft[/tex]
The Sine or Sinθ in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. The length of the ladder is 32.356 feet.
What is Sine (Sinθ)?The Sine or Sinθ in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,
[tex]\rm{Sine(\theta) = \dfrac{Perpendicular}{Hypotenuse}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The hypotenuse is the longest side of the triangle.
As it is given that the height of the electric box from the bottom is 30 feet, while the ladder makes an angle of 68° with the ground.
The length of the ladder can be found using the trigonometric functions, therefore, the length of the ladder can be written as,
[tex]\rm Sine(\theta) = \dfrac{Perpendicular}{Hypotenuse}\\\\\\Sine(\angle C) = \dfrac{AB}{\text{Length of the ladder}}\\\\\\{\text{Length of the ladder}}= \dfrac{AB}{Sine(\angle C) }\\\\\\{\text{Length of the ladder}}= \dfrac{30}{Sine(68^o) }\\\\\\{\text{Length of the ladder}}= 32.356\ feet[/tex]
Hence, the length of the ladder is 32.356 feet.
Learn more about Sine:
https://brainly.com/question/21286835
The table below represents a linear function f(x) and the equation represents a function g(x):
x f(x)
−1 −9
0 −1
1 7
g(x)
g(x) = 3x − 2
Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x).
Part B: Which function has a greater y-intercept? Justify your answer.
Answers
Answer:
(a) The slope of f(x) is greater than the slope of g(x)
(b) f(x) has a greater y intercept
Step-by-step explanation:
Given
[tex]\begin{array}{cc}x & {f(x)} & -1&-9&0&-1&1&7 \ \end{array}[/tex]
[tex]g(x) = 3x - 2[/tex]
Solving (a): Compare the slopes
The slope (m) of f(x) is calculated as;
[tex]m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}[/tex]
This gives:
[tex]m = \frac{f(0) - f(1)}{0 - 1}[/tex]
[tex]m = \frac{f(0) - f(1)}{- 1}[/tex]
Substitute values for f(0) and f(1)
[tex]m = \frac{-1 - 7}{- 1}[/tex]
[tex]m = \frac{-8}{- 1}[/tex]
[tex]m = 8[/tex]
The slope of g(x) can be gotten using the following comparison
[tex]g(x) = mx + b[/tex]
[tex]m \to slope[/tex]
So:
[tex]g(x) = 3x -2[/tex]
[tex]m = 3[/tex]
[tex]m_{f(x)} > m_{g(x)}[/tex]
Solving (b): Compare the y intercept
y intercept is when [tex]x = 0[/tex]
From the table of f(x)
[tex]f(0) = -1[/tex]
From the equation of g(x)
[tex]g(x) = 3x -2[/tex]
[tex]g(0) = 3*0-2[/tex]
[tex]g(0) =-2[/tex]
[tex]f(0) > g(0)[/tex]
Please help me answer e, f and number 3. See the image below
Answers
Answer:
Prat two of e) 6/12 Both the numerator and denominator were multipled by three, the number of boxes we split each box into.
F) we can multiply both the numerator and denominator without changing the values, so 2a/2b or 10a/10b
An assembly line consists of 21 tasks grouped into 5 workstations. The sum of the 21 task times is 85 minutes. The largest assigned cycle time is 20 minutes. What is the efficiency of this line
Answers
Answer:
The efficiency of this line is 0.85 = 85%.
Step-by-step explanation:
Efficiency:
The efficiency is given by the following formula:
[tex]E = \frac{T_t}{tn}[/tex]
In which [tex]T_t[/tex] is the total task time, [tex]t[/tex] is the largest assigned cycle time and n is the number of workstations.
5 workstations
This means that [tex]n = 5[/tex]
The sum of the 21 task times is 85 minutes.
This means that [tex]T_t = 85[/tex]
The largest assigned cycle time is 20 minutes.
This means that [tex]n = 20[/tex]
What is the efficiency of this line?
[tex]E = \frac{T_t}{tn} = \frac{85}{20*5} = \frac{85}{100} = 0.85[/tex]
The efficiency of this line is 0.85 = 85%.
Find the product of -9 and -3.
1. 0-3
2. 27
3. 0-27
4. 3
Answers
27 is the answer
gbu...
Answer:
- 9 × - 3 = 27
Step-by-step explanation:
when we multiply two negative numbers then the sign of the product convert to positive sign
I.e( - )×( - )= (+) product
create a frequency table and probability models to determine the probability the following outcome police officer kept recording of 75 drivers at a stop sign they observed 21 people who came to complete stop 46 who made a rolling stop and 8 that did not appear to a brake at all what is the probability that a randomly selected driver will come to complete stop
Answers
Answer:
0.28 = 28% probability that a randomly selected driver will come to complete stop
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
Recording of 75 drivers.
Of those, 21 came to a complete stop.
Then
21/75 = 0.28
0.28 = 28% probability that a randomly selected driver will come to complete stop
Select the correct answer.
What is this expression in simplified form?
5v2.9v6
OA. 45v3
OB. 90
O C. 90v3
OD. 45V2
Answers
Answer:
C. 90√3
Step-by-step explanation:
5√2 . 9√6 = 45√12 = 45×2√3
= 90√3
The simplified form is 90√3.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
Given expression is, 5√2×9√6
=5×9×√(2×6)
=45×√12
=45×2√3
=90√3
Hence, the simplified form is 90√3 .
To learn more on multiplication click:
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Last question! Please show work. Really need to get this done in 1 hour
Answers
Answer:
x=1; y=2; z=3
Step-by-step explanation:
Rearrange for convince:
2y-4z+6x = -2
-4y+2z-3x=-5
-6y+3z+4x=1
Now we take to pairs and eliminate the same var.:
2y-4z+6x = -2 *2
-4y+2z-3x=-5
and
-4y+2z-3x=-5 *-3
-6y+3z+4x=1. *2
We get:
4y-8z+12y=-4
-4y+2z-3x=-5
= -6z+9x=-9
and
12y-6x+9x=15
-12y+6x+8x=2
= 17x=17
We now know x = 1, so z is:
-6z+9=-9
-6z=-18
z=3
Let’s grab the first formula and find y:
6+2y-12=-2
6+2y=10
2y=4
y = 2
Please help with question 2
Answers
Answer:
Step-by-step explanation:
7*(4) - 2(-3) - (-3)^2
28 + 6 - 9
34 - 9 = 25
9 Two people start writing reports on the same day. Both write 200-page reports. Writer A averages 8 pages a day, and writer B averages 5 pages per day. How much sooner will Writer A finish her report than will Writer B?
Answers
Answer:
15 days
+
Step-by-step explanation:
A
200 pages / (8 pages / day) =
= 200 pages days / 8 pages =
= 200 days / 8 = 25 days
B
200 pages / (5 pages / day) =
= 200 pages days / 5 pages =
= 200 days / 5 = 40 days
40-25 = 15 days
A will finish 15 days sooner than B.
A will finish her report 15 days sooner than B.
What is the ratio?The ratio is defined as a relationship between two quantities, it is expressed one divided by the other.
Writer A averages 8 pages a day,
Number of pages per day written by writer A = 8 per day
Writer A will finish her report = Total pages / per day written by writer A
⇒ 200 pages / (8 pages / day)
⇒ 200 pages days / 8 pages
⇒ 200 days / 8
⇒ 25 days
Writer B averages 5 pages a day
Number of pages per day written by writer B = 5 per day
Writer B will finish her report = Total pages / per day written by writer A
⇒ 200 pages / (5 pages / day)
⇒ 200 pages days / 5 pages
⇒ 200 days / 5
⇒ 40 days
Difference between both of time when they finished their report = 40-25 = 15 days
Hence, A will finish her report 15 days sooner than B.
Learn more about Ratio here:
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If ∠P, ∠Q, and ∠R are given, as well as the value of p, then explain whether the Law of Sines or the Law of Cosines should be used to solve for q.
Law of Sines, two angles and an opposite side are known
Law of Sines, two sides and an opposite angle are known
Law of Cosines, two sides and the included angle are known
Law of Cosines, all sides are known
Answers
Answer:
Law of Sines, two angles and an opposite side are known
Step-by-step explanation:
Law of Sines, two angles and an opposite side are known
q/sinQ = p/sinP
q = p/sinP * sinQ
Stan knows that segment AB∥segment CD. He wants to use the definition of a parallelogram to prove that quadrilateral ABCD is a parallelogram. Which equation can he use?
Answers
Answer:
[tex]\frac{q - r}{m- n} = \frac{p - s}{m - n}[/tex]
Step-by-step explanation:
Given
See attachment for parallelogram
Required
Proof that ABCD is a parallelogram
We know that opposite sides are equal and parallel.
First, we calculate the slope of BC
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, we have:
[tex]m = \frac{q - r}{m- n}[/tex]
Next, the slope of AD using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, we have:
[tex]m = \frac{p - s}{m - n}[/tex]
For ABCD to be a parallelogram; then:
[tex]\frac{q - r}{m- n} = \frac{p - s}{m - n}[/tex]
Plzzz help!!!!!!!!!!!!!!!!
Answers
Answer:
B) The function has a maximum value of (1)
Step-by-step explanation:
The given function has a maximum value, as its curve is inverted. The maximum value is the largest (y) value that a function can attain. As one can see, this value is (1), because the (y-coordinate) of the highest point on its curve is (1). This function has no minimum value, its endpoints go on infinitely in a negative direction.
If we know the values of the sine and cosine of x and y, we can find the value of cos(x - y) by using the ____ Formula for Cosine. State the formula: cos(x - y) = ____.
Answers
Answer:
[tex]\cos(x - y) = \cos(x)\cos(y) + \sin(x)\sin(y)[/tex]
Step-by-step explanation:
Given
[tex]\cos(x - y)[/tex]
Required
State the formula
From trigonometry identity, the formula of [tex]\cos(x - y)[/tex] is:
[tex]\cos(x - y) = \cos(x)\cos(y) + \sin(x)\sin(y)[/tex]
43
d. 34
Clear my choice
For the discrete series given as, X variable values - 32 with frequemcy 2,37 with frequency 5,
46 with frequency 3 and 48 with frequency 9, mode is
Select one:
O a. 9
O b. 48
O c. 37
O d. 5
Answers
Given:
The frequency distribution table is:
Values of variable X Frequency
32 2
37 5
46 3
48 9
To find:
The mode of the given data set.
Solution:
We know that mode is the most frequent value of the data set.
In the given data set highest frequency is 9 that is corresponding to the value 48.
Therefore, the mode of the given data set is 48. Hence, the correct option is (b).
HELP I NEED TO PASS!!!!!
A. g(x) = 2x-1
B. g(x) = 2x + 1
C. g(x) = 2x –1
D. g(x) = 2x+1
Answers
Factor completely, then place the factors in the proper location on the grid. 25a2 +9b2 + 30ab
Answers
Answer:
(5a+3b)(5a+3b) or SQ(5a+3b)
Step-by-step explanation:
Now you can plot by referring to the above factors