Answers
Answer:
a) [tex]cos(\alpha)=-\frac{3}{5}\\[/tex]
b) [tex]\sin(\beta)= \frac{\sqrt{3} }{2}[/tex]
c) [tex]\frac{4+3\sqrt{3} }{10}\\[/tex]
d) [tex]\alpha\approx 53.1^o[/tex]
Step-by-step explanation:
a) The problem tells us that angle [tex]\alpha[/tex] is in the second quadrant. We know that in that quadrant the cosine is negative.
We can use the Pythagorean identity:
[tex]tan^2(\alpha)+1=sec^2(\alpha)\\(-\frac{4}{3})^2 +1=sec^2(\alpha)\\sec^2(\alpha)=\frac{16}{9} +1\\sec^2(\alpha)=\frac{25}{9} \\sec(\alpha) =+/- \frac{5}{3}\\cos(\alpha)=+/- \frac{3}{5}[/tex]
Where we have used that the secant of an angle is the reciprocal of the cos of the angle.
Since we know that the cosine must be negative because the angle is in the second quadrant, then we take the negative answer:
[tex]cos(\alpha)=-\frac{3}{5}[/tex]
b) This angle is in the first quadrant (where the sine function is positive. They give us the value of the cosine of the angle, so we can use the Pythagorean identity to find the value of the sine of that angle:
[tex]cos (\beta)=\frac{1}{2} \\\\sin^2(\beta)=1-cos^2(\beta)\\sin^2(\beta)=1-\frac{1}{4} \\\\sin^2(\beta)=\frac{3}{4} \\sin(\beta)=+/- \frac{\sqrt{3} }{2} \\sin(\beta)= \frac{\sqrt{3} }{2}[/tex]
where we took the positive value, since we know that the angle is in the first quadrant.
c) We can now find [tex]sin(\alpha -\beta)[/tex] by using the identity:
[tex]sin(\alpha -\beta)=sin(\alpha)\,cos(\beta)-cos(\alpha)\,sin(\beta)\\[/tex]
Notice that we need to find [tex]sin(\alpha)[/tex], which we do via the Pythagorean identity and knowing the value of the cosine found in part a) above:
[tex]sin(\alpha)=\sqrt{1-cos^2(\alpha)} \\sin(\alpha)=\sqrt{1-\frac{9}{25} )} \\sin(\alpha)=\sqrt{\frac{16}{25} )} \\sin(\alpha)=\frac{4}{5}[/tex]
Then:
[tex]sin(\alpha -\beta)=\frac{4}{5}\,\frac{1}{2} -(-\frac{3}{5}) \,\frac{\sqrt{3} }{2} \\sin(\alpha -\beta)=\frac{2}{5}+\frac{3\sqrt{3} }{10}=\frac{4+3\sqrt{3} }{10}[/tex]
d)
Since [tex]sin(\alpha)=\frac{4}{5}[/tex]
then [tex]\alpha=arcsin(\frac{4}{5} )\approx 53.1^o[/tex]
Related Questions
Please help me match these formulas thank you :)
Answers
Answer:
Circle Circumference: 5
Triangle: 8
Circle Area: 3
Regular Polygon: 7
Parallelogram:6
Equilateral triangle: 1
Trapezoid:4
Rectangle:2
Step-by-step explanation:
I don't know how I would do a step by step explanation
Please help :) Is the relationship shown by the data linear? If so model the data with an equation.
Answers
Answer:
y-5=5/4(x-1)
Step-by-step explanation:
the slope is 1.25
m=y2-y1/x2-x1=10-5/5-1=5/4=1.25
y-5=(5)/(4)(x-1)=
y=(5)/(4)x+(15)/(4) this one is linear
it is a linear function and the
Find the smallest number by which 8788 must be multiplied so that the quotient is a perfect cube. Also, find the cube root of the perfect cube so obtained.
Answers
Answer:
Hi ,
Cube of a number :
_______________
For a given number x we define cube
of x = x × x × x , denoted by x^3.
A given Natural number is a perfect
Cube if it can be expressed as the
product of triplets of equal factors.
Now ,
Write given number as product of
prime .
8788 = 2 × 4394
= 2 × 2 × 2197
= 2 × 2 × 13 × 169
= 2 × 2 × 13 × 13 × 13
= 2 × 2 × ( 13 × 13 × 13 )
Here we have only triplet of equal
factors i.e 13
To make 8788 into perfect Cube we
have multiply with 2.
Now ,
2 × 8788 = ( 2 × 2 × 2 ) × ( 13 × 13 × 13 )
17576 = ( 2 × 13 )^3 = ( 26 )^3 perfect
Cube
I hope this will useful to you.
If d = the number of dogs, which variable expression represents the phrase below? the sum of the number of dogs and the 6 cats.
Answers
Answer:
D.
Step-by-step explanation:
" Sum" means "+".
The sum of the number of dogs and the 6 cats.
d + 6
Answer:
Option D
Step-by-step explanation:
Sum is Adding (+)
So,
The expression becomes
=> d+6
In 1787, if an enslaved African was considered 3/5th of a person for representation in Congress,how many enslaved Africans would have been considered equivalent to 6 white Americans?
Answers
Answer:
10
Step-by-step explanation:
3/5 is 0.6 and 10 time 0.6 is 6.
hope this helps
What value from the set {2, 4, 6, 8} can be substituted for x to make an inequality x > 7 true?
Answers
Answer:
8
Step-by-step explanation:
8 is greater than 7
Find the value of x.
Answers
Answer:
x = √21.
Step-by-step explanation:
Triangles ADB and BCD are similar.
So their corresponding sides are in the same ratio:
x / 7 = 3 / x
x^2 = 21
x = √21.
If m∠ABC = 45° and m∠ECD = 45°, which statement explains whether the AA similarity postulate can be used to determine whether ΔBAC ~ ΔEDC? answers: Yes, the AA similarity postulate can be used because a reflection over line f will establish that segment AB ≅ segment DE. Yes, the AA similarity postulate can be used because a reflection over line f will establish that ∠ABC ≅ ∠DEC. No, the AA similarity postulate cannot be used because a reflection over line f will establish that segment AB and segment DE are not congruent. No, the AA similarity postulate cannot be used because a reflection over line f will establish that ∠ABC and ∠DEC are not congruent.
please answer ASAP please i need HELP ASAP thank you
Answers
Answer:
No, the AA similarity postulate cannot be used because a reflection over line f will establish that ∠ABC and ∠DEC are not congruent.
Step-by-step explanation:
Data provided in the question
m∠ABC = 45°
m∠ECD = 45°
Based on the above information, the ΔBAC ~ ΔEDC could be determined by seeing the given options
As we can see that from the last option the AA could not be postulated as it creates a reflection over the line plus the ∠ABC and ∠DEC is not congruent
Therefore the last option is correct
No, the AA similarity postulate cannot be used because a reflection over line f will establish that ∠ABC and ∠DEC are not congruent. Therefore the option D is correct.
What is the congruent triangle?Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.
Data given in the question
m∠ABC = 45°
m∠ECD = 45°
Based on the above information, the ΔBAC ~ ΔEDC could be determined by seeing the given options one by one.
As we can conclude that from the last option the AA could not be postulated as it creates a reflection over the line plus the ∠ABC and ∠DEC is not congruent.
No, the AA similarity postulate cannot be used because a reflection over line f will establish that ∠ABC and ∠DEC are not congruent.
Therefore the option D is correct.
Read more about similar triangles at:
brainly.com/question/14926756
#SPJ5
The sales tax for an item was $19.20 and it costs $480 before tax. Find the sales tax rate. Write your answer as a percentage
Answers
Answer:
sales tax rate = 4%
Step-by-step explanation:
In this problem formula to express one term in percentage is used
To express x as percentage of y is given by (x/y*100) %
______________________________________________
Cost of item = $480
sales tax = $19.20
we have to find sales tax rate.
sales tax rate is percentage of cost price which will levied as tax .
thus, we have to find sales tax as percentage of cost price.
using the percentage cost as given above
sales tax as percentage = sales tax/ cost of item *100
sales tax as percentage = 19.20/480 *100 = 4%
Thus, sales tax rate is 4%.
It means that if cost price of item is $100 then $4 will be the sales tax for the item.
PLEASE HELP! 10 POINTS!The graphs of f(x) and g(x) are shown below:
What are the solutions to the equation f(x) = g(x)?
Ox= -3,4
x = -4.2.5
X = -0.8, 2.5
X = 8.-8
Answers
Answer:
x = -4, 2.5
Step-by-step explanation:
To find the solution, look for the points where the line crosses the parabola. As this question only asks for the x-values, find the distance to the left and right of the y-axis. Here, it's -4 on the left and 2.5 on the right.
In a class of students, the following data table summarizes how many students have a
brother or a sister. What is the probability that a student who has a brother also has a
sister?
Has a brother | Does not have a brother
Has a sister
6
2
Does not have a sister
8
13
Answers
Answer:
[tex]Probability = \frac{6}{29}[/tex]
Step-by-step explanation:
Given
------------------------------Has a brother | Does not have a brother
Has a sister --------------------------- 6 ----------------- 8
Does not have a sister -----------2 ------------------ 13
Required
Probability of having a sister and a brother
First, the total number of students has to be calculated;
Total = 6 + 2+ 8 + 13
Total = 29
Number of students that have a sister and a brother is represented with data in row 1 and column 1 i.e. 6
At this point, the probability can then be calculated;
Probability = Number of students that have a sister and a brother divided by Total number of students
[tex]Probability = \frac{6}{29}[/tex]
Find the volume of a sphere 8 feet in diameter use 3.14 round your answer to the nearest tenth
(A) 150.7
(B) 267.9
(C) 83.7
(D)67.0
What one is it help me please
Answers
Answer:
B 267.9
Step-by-step explanation:
the formula is again the same, so you plug 4 in (because the radius is half the diameter) and solve to get around 267.9
Help asap please will give brainliest
Answers
Answer:
d. (x+2)/(-x²-5)
Step-by-step explanation
ƒ(x) = x + 2/(2x²)
The function is undefined when x = 0.
b. ƒ(x) = (2x + 4)/(3x + 3)
The function is undefined when 3x + 3 = 0, i.e., when x = -1.
c. ƒ(x) = (6x - 5)/(x² - 7)
The function is undefined when x² - 7 = 0, i.e., when x = √7.
d. ƒ(x) = (x+2)/(-x²-5) = -(x+2)/(x² + 5)
The function would be undefined if x² + 5 = 0, i.e., if x² = -5. However, the square of a real number cannot be negative.
This function has no excluded values.
True or false? It's possible to create a regular tessellation with a regular octagon.
Answers
It is possible to create a regular tessellation with a regular octagon, is false.
What is regular tessellation?A tessellation or tiling is the seamless covering of an area, frequently a flat, including one or much more geometric forms, known as tiles.
It is impossible to create a regular tessellation with a regular octagon because when an octagon is arranged, a gap is there.
Then the statement is false.
More about the regular tessellation link is given below.
https://brainly.com/question/12926513
#SPJ2
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the rectangle: A(2, -3), B(4, -3), C(4,5), and D(2,5) What is the perimeter of rectangle ABCD
Answers
Answer:
20
Step-by-step explanation:
(2,-3) to (4,-3) = 2
(4,-3) to (4,5) = 8
(4,5) to (2,5) = 2
(2,5) to (2,-3) = 8
Total =20
Answer:
20
Step-by-step explanation:
khan said so trust me
6f = 24 pls help!!!!!!!!!!!!!!
Answers
Answer:
f=4
Step-by-step explanation:
6f = 24
÷6 ÷6
f=4
Answer:
f = 4
Step-by-step explanation:
6f = 24
f = 24/6
f = 4
When I square my number, I get the same answer as when I multiply my number by 10 and then add 144. My number is positive. What is it?
Answers
Answer:
your number is 18
Step-by-step explanation:
x^2 = (x × 10 ) + 144
x^2 = 10x + 144
x^2 - 10x - 144 = 0
using quadratic method
your answer should be
(x- 18) ( x+8 )
a. 1620
b. 180
c. 38
d. 29
Answers
Answer:
V =1620 pi cm^2
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
V = pi ( 9)^2 * 20
V =1620 pi cm^2
Please help with this
Answers
Answer:
5/2
Step-by-step explanation:
We take the ratio of a side of ABC over the same side on DEF
AB/ DE
35/14
Divide top and bottom by 7
5/2
Given the following system of equations, solve it by using substitution and elimination. Do
you get the same answer? Why or why not? Explain using complete sentences.
2x+3y = -14
3x + y =-14
Answers
Step-by-step explanation:
2x+3y=-14------equation i ×1
3x+y=-14--------equation ii ×3
2x+3y=-14
9x+3y=-42
-7x =- 28
x=4
Substitute for x in equation ii
3x+y= -14
3(4)+y=-14
12+y=-14
y=-14-12
y=- 26
Please help i will mark brainliest!
Answers
Answer:
A. and C. are true i think :/
Step-by-step explanation:
im not 100% sure though but again, good lucks!
(NEED HELP ASAP)Determine whether the situation calls for a survey, an observational study, or an experiment. You want to find new car buyers' opinions on the most important options. Question 7 options: survey observational study experiment
Answers
Answer: The answer is "experiment."
Step-by-step explanation:
This procedure is being used in order to validate a hypothesis, particularly in a research study. In the situation above, you have to validate whether a new reading program can increase reading comprehension or not.
The experiment consists of independent, dependent, and controlled variables. The independent variables are the ones being changed by the researcher, while the dependent variables tell whether the changes in the independent variable is significant. The controlled variables are the ones that are constant.
The dependent variable above is reading comprehension, while the new reading program is the independent variable. Examples of controlled variables are the ages of the participants. The age directly affects the reading comprehension, thus it has to be considered.
In a newspaper, it was reported that yearly robberies in Springfield were down 2% to 245 in 2014 from 2013. How many robberies were there in Springfield in 2013?
Answers
Answer:
250
Step-by-step explanation:
245 / 0.98 = 250
What is the standard form of this function? f(x) = -(x − 4)2 + 2 A. f(x) = -x2 + 4x − 30 B. f(x) = x2 + 8x − 14 C. f(x) = -x2 + 8x − 14 D. f(x) = x2 + 4x − 30
Answers
Answer:
C
Step-by-step explanation:
Standard form is f(x) = ax² + bx + c.
f(x) = -(x - 4)² + 2
= -(x² - 8x + 16) + 2
= -x² + 8x - 16 + 2
= -x² + 8x - 14
Hi,
the correct answer is C
This is the correct equation: f(x) = -x^2 + 8x - 14
XD
P.S. (on the image I sent the answer was B but on your test the correct one is C. The equation is still the same.)
air flows through a duct at 2400 cubic feet per minute after several feet in a few vent the air flow decreases to 1680 cubic feet what is the percent drop that has occurred
Answers
Answer:
I think the answer is 7.2%
Step-by-step explanation:
2400-1680=720
720/100=7.2
7.2 is the answer
Hope this helps!
Owners of a recreation area are filling a small pond with water. Let y represent the total amount of water in the pond (in liters). Let x represent the total number of minutes that water has been added. Suppose that x and y are related by the equation y=400+32x . Answer the questions below. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number. What is the change per minute in the amount of water in the pond? What was the starting amount of water in the pond?
Answers
Answer:
32400Step-by-step explanation:
Lets start by defining the numbers in the equation.
This equation is in slope-intercept form meaning that it is y=mx+b or y = b+mx they are both the same
In slope-intercept form,
m = slope or rateand b = y-intercept
Th equation is y=400+32x so now we know
b=400and m=32For the first question the change per minute is the rate so it is 32.
For the second question the starting amount is the same as the y-intercept so it is 400.
Need help with this question please:
Answers
Answer:
If the data is collected in a biased manner, or the number of observations is too small, the graph could be skewed. To ensure the data is not skewed, collect a large representative unbiased sample. Hope this helps
Step-by-step explanation:
help will give brainliest
Answers
Answer: A. (-3,7)
Step-by-step explanation:
No work needed, you just need to look at the coordinate plane.
Coordinate II is x as a negative and y as a positive
Answer:
D, (5,-1)
5 is in the x axis
-1 is in the y axis
This point is it the second quadent
Hope this helps ( if incorrect try a)
Which statement best describes Cheryl's commute? A. Cheryl accelerated to 65 mph, made a stop for 5.5 minutes, and then decelerated to 45 mph. B. Cheryl drove at a speed of 65 mph for 1 minute, drove at a constant speed for 5.5 minutes, and then drove at a speed of 45 mph for 2.5 minutes. C. Cheryl accelerated to 65 mph, drove at a constant speed for 5.5 minutes, and then decelerated to 45 mph. D. Cheryl drove at a speed of 65 mph for 1 minute, made a stop for 5.5 minutes, and then drove at a speed of 45 mph for 2.5 minutes.
Answers
Answer:
C. Cheryl accelerated to 65 mph, drove at a constant speed for 5.5 minutes, and then decelerated to 45 mph.
Step-by-step explanation:
Assume the graph of Cheryl's commute was like the one below.
We see that she started at 0 mph.
One minute later, she was up to 65 mph, so she had accelerated (increased her speed).
At 6.5 min (5,5 min later) her speed was still 65 mph, so she was driving at a constant speed.
Over the next 2.5 min, her speed dropped to 45 mph, so she was decelerating.
Answer:
D
Step-by-step explanation:
on Edmentum
can someone simplify (3x)^4
Answers
Answer:
81x^4
Step-by-step explanation:
Apply the product rule to 3x
3^4x^4
Raise 3 to the power of 4
81x^4
please mark me brainliest!