Answer:
[tex] \rm \displaystyle x \approx \bigg \{ {59.3}^{ \circ} + \frac{n\pi}{2} , - {14.3}^{ \circ} + \frac{n\pi}{2} \bigg \}[/tex]
Step-by-step explanation:
we would like to solve the following trigonometric equation:
[tex] \rm \displaystyle \sin(x) \cos(3x) + \cos(x) \sin(3x) = \tan( {140}^{ \circ} ) [/tex]
the left hand side can be rewritten using angle sum indentity of sin which is given by:
[tex] \rm \displaystyle \sin( \alpha + \beta ) = \sin( \alpha ) \cos( \beta ) + \cos( \alpha ) \sin( \beta ) [/tex]
therefore Let
[tex] \alpha = x[/tex][tex] \beta = 3x[/tex]Thus substitute:
[tex] \rm \displaystyle \sin(x + 3x) = \tan( {140}^{ \circ} ) [/tex]
simplify addition:
[tex] \rm \displaystyle \sin(4x) = \tan( {140}^{ \circ} ) [/tex]
keep in mind that sin(t)=sin(π-t) saying that there're two equation to solve:
[tex] \begin{cases} \rm \displaystyle \sin(4x) = \tan( {140}^{ \circ} ) \\ \\ \displaystyle \sin(\pi - 4x) = \tan( {140}^{ \circ} ) \end{cases}[/tex]
take inverse trig and that yields:
[tex] \begin{cases} \rm \displaystyle 4x= { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) \\ \\ \displaystyle \pi - 4x = { \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) \end{cases}[/tex]
add π to both sides of the second equation and that yields:
[tex] \begin{cases} \rm \displaystyle 4x= { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) \\ \\ \displaystyle - 4x = { \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) + \pi\end{cases}[/tex]
sin function has a period of 2nπ thus add the period:
[tex] \begin{cases} \rm \displaystyle 4x= { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) + 2n\pi\\ \\ \displaystyle - 4x = { \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) + \pi + 2n\pi\end{cases}[/tex]
divide I equation by 4 and II by -4 which yields:
[tex] \begin{cases} \rm \displaystyle x= \frac{ { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) }{4} + \frac{n\pi}{2} \\ \\ \displaystyle x = - \frac{{ \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) + \pi}{4} - \frac{n\pi}{2} \end{cases}[/tex]
recall that,-½(nπ)=½(nπ) therefore,
[tex] \begin{cases} \rm \displaystyle x= \frac{ { \sin}^{ - 1} ( \tan( {140}^{ \circ} ) ) }{4} + \frac{n\pi}{2} \\ \\ \displaystyle x = - \frac{{ \sin}^{ - 1}( \tan( {140}^{ \circ} ) ) + \pi}{4} + \frac{n\pi}{2} \end{cases}[/tex]
by using a calculator we acquire:
[tex] \begin{cases} \rm \displaystyle x \approx - {14.3}^{ \circ} + \frac{n\pi}{2} \\ \\ \displaystyle x \approx {59.3}^{ \circ} + \frac{n\pi}{2} \end{cases}[/tex]
hence,
the general solution for: for the trig equation are
[tex] \rm \displaystyle x \approx \bigg \{ {59.3}^{ \circ} + \frac{n\pi}{2} , - {14.3}^{ \circ} + \frac{n\pi}{2} \bigg \}[/tex]
what would the equation, slope, and point be for this graph?
Answer:
slope is Δy/Δx =
-5/1 = -5
the B intercept is 4
y = -5x + 4
Step-by-step explanation:
Aaron, Blaine, and Cruz are solving the equation 4 7 (7 − n) = −1. Aaron started his solution by multiplying both sides of the equation by 7 4 . Blaine started by using the distributive property to multiply 4 7 by both 7 and −n. Cruz started by dividing both sides of the equation by 4 7 .
Answer:
D. All three chose a valid first step toward solving the equation.
Step-by-step explanation:
Aaron, Blaine, and Cruz are solving the equation 4/7 (7 − n) = −1. Aaron started his solution by multiplying both sides of the equation by 7/4 . Blaine started by using the distributive property to multiply 4/7 by both 7 and −n. Cruz started by dividing both sides of the equation by 4/7 .
Which of the following is true?
A. Blaine and Cruz made an error in picking their first steps.
B. Cruz made an error in picking his first step.
C. All three made an error because the right side equals -1.
D. All three chose a valid first step toward solving the equation.
Given:
4/7(7 - n) = -1
Aaron:
4/7(7 - n) = -1
Multiple both sides by 7/4
4/7(7 - n) * 7/4 = -1 * 7/4
7 - n = -7/4
- n = -7/4 - 7
- n = (-7-28)/4
- n = -35/4
n = 35/4
Blaine:
4/7(7 - n) = -1
4/7(7 - n) × 7 = -1 × 7
4(7 - n) = -7
28 - 4n = -7
-4n = -7 - 28
- 4n = - 35
n = -35/-4
n = 35/4
Cruz:
4/7(7 - n) = -1
Divide both sides by 4/7
4/7(7 - n) ÷ 4/7 = -1 ÷ 4/7
4/7(7 - n) × 7/4 = -1 × 7/4
7 - n = -7/4
- n = (-7-28)/4
- n = -35/4
n = 35/4
D. All three chose a valid first step toward solving the equation.
Answer:
D-All three chose a valid first step toward solving the equation.
Step-by-step explanation:
Hope I Helped
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
1.-4,-1,1,6
2.by substituting the values given, we get
32-|15+8|
32-|23|
32-23=9
3.-15+7=8
4..27-(-12)=27+12=39
5.-6.05+(-2.1)
-6.05-2.1=-8.15
6.-3/4-(-2/5)
-3/4+2/5
=-7/20
7.-9(-12)
=108
8.(3.8)(-4.1)
-15.58
9.(-8x)(-2y)+(-3y)(z)
(16xy)+(-3zy)
(16xy)-(3zy)
10.by substituting the value given,we get
2.5*(-3.2)+5
-8+5
-3
so here are the answers,mark as brainliest if u find it useful
thank you
Teresa earns $8.23 per hour. Calculate her wage for a week where she
works 14h 30min.
Answer:
$119.335
Step-by-step explanation:
8.23 per hour
14h 30 mins = 14.5 hrs
8.23*14.5 = 119.335
Answer:
238.67
Step-by-step explanation:
Which term of the AP. 8 , -4 , -16 , -28 ,......... is -880 ?
Answer: 75th term
Step-by-step explanation:
If you look at the first terms, you can see that we're subtracting 12 from the previous term to get the number. Knowing this, we can write an expression for the nth term. The expression would be -12n + 20. Since this specific term has value of -880, we set -880 equal to the value of -12n+20. By setting your equation like this -12n + 20 = -880 and solving, you get n = 75, which means the 75th term has a value of -880.
Mean of Frequency Tables
1. At a party, thirty people have an age of 30, forty have an age of 40 and fifty an age of fifty. What is their average age?
2. In a hardware shop, there are 30 spanners costing £6, 55 hacksaws costings £9 and 10 soldering irons costings £20. What is the average cost per item?
3. Using this frequency table, find the average height of a turnip.
Height (to nearest cm)
6cm 7cm 8cm 9cm 10cm
Frequency:
3 8 12 4 1
Answer: 1. 41.67years
2. £9.21
3. 7.75cm
Step-by-step explanation:
1. At a party, thirty people have an age of 30, forty have an age of 40 and fifty an age of fifty. What is their average age?
Total ages = (30 × 30) + (40 × 40) + (50 × 50) = 900 + 1600 + 2500 = 5000
Total number of people = 30 + 40 + 50 = 120
Average age = Total ages / Total number of people
= 5000/120
= 41.67 years
2. In a hardware shop, there are 30 spanners costing £6, 55 hacksaws costings £9 and 10 soldering irons costings £20. What is the average cost per item?
Total cost of items = (30 × £6) + (55 × £9) + (10 × £20) = £180 + £495 + £200 = £875
Total number of items = 30 + 55 + 10 = 95
Average cost per item = £875/95 = £9.21
3. Using this frequency table, find the average height of a turnip.
Height (to nearest cm)
6cm 7cm 8cm 9cm 10cm
Frequency: 3 8 12 4 1
Total height = (3 × 6cm) + (8 × 7cm) + (12 × 8cm) + (4 × 9cm) + (1 × 10cm) = 18cm + 57cm + 96cm + 36cm + 10cm = 217cm
Total number of turnips = 3 + 8 + 12 + 4 + 1 = 28
Average height = 217cm/28 = 7.75cm
what is the circumference of a circle with a diameter of 2 feet? use 3.14 for pie
A. 6.28ft
B. 12.56ft
C. 5.14ft
D.3.14ft
Answer:
C = 6.28 ft
Step-by-step explanation:
The circumference of a circle is given by
C = pi *d where d is the diameter
C = 3.14(2)
C = 6.28 ft
what is the circumference of a circle with a diameter of 2 feet? use 3.14 for pie
A. 6.28ft
B. 12.56ft
C. 5.14ft
D.3.14ft
To Find :The circumference of the circle Solution :Formula for getting the circumference
[tex] \: \: \: \: \: \: \: \: \: \star \: \orange{\underline{ \purple{ \boxed{ \red{\sf Circumference \: of \: the \: circle = 2πr}}}}}[/tex]
Given data :
Diameter = 2 ft
π = 3.14
Radius = diameter/2 = 2 ft/2 = 1 ft
So the circumference is
Circumference = 2πrCircumference = 2 × 3.14 × 1 Circumference = 6.28 ftTherefore, the perimeter is 6.28 ft
Please answer this!!!
Answer:
12/13
Step-by-step explanation:
we know this is a right triangle, and we know that the hypotenuse is the longest side. so we can already say that the hypotenuse of the triangle is DF or 78.
when you draw it out, you find that the shortest leg is 30 and the second is 72 and the hypotenuse is 78. we also know that cosine is adjacent/hypotenuse. once you draw the triangle and notice which side is adjacent to angle F, just fit it into the formula and you get:
cos F = 72/78
cos F = 12/13
Answer: Choice C. [tex]\frac{12}{13}[/tex]
Step-by-step explanation:
It helps to draw a right triangle with hypotenuse DF=78, and adjacent EF=72.Plug in cosine adjacent over hypotenuse and simplify.7) 5(r + 2) = 8 + 57
Step-by-step explanation:
5r + 10 = 65
5r =65 - 10
r = 55/5
r = 11
Answer:
r=11
Step-by-step explanation:
you first have to work with the brackets and then group the like terms
5(r+2)=8+57
5r+10=65
5r/5=65-10
5r/5=55/5
r=11
I hope this helps
A car travels a distance of 800m in 40s find its speed
Answer:
the answer is 20m/s
Step-by-step explanation:
speed = distance/time which equals to speed = 800/40, so the answer is 20m/s
Answer:
20m /s
Step-by-step explanation:
Speed = [tex]\frac{Distance}{time}[/tex]
[tex]= \frac{800}{40}=\frac{80}{4}= 20[/tex]
I need help asap!!Explain how to do the problem
Answer:
Step-by-step explanation:
the scale factor is 2. one length is 10, and the other is 5. pythagorean therom approved.
Translate the phrase into an algebraic expression.
The product of 9 and y
Answer:9*y or 9y
Step-by-step explanation:
Cos 600 degrees solved by double angle formula (20 points)
show work please :)))
Answer:
[tex] \rm\cos({600}^{ \circ} ) =-1/2 [/tex]
Step-by-step explanation:
we would like to solve the following using double-angle formula:
[tex] \displaystyle \cos( {600}^{ \circ} ) [/tex]
there're 4 double Angle formulas of cos function which are given by:
[tex] \displaystyle \cos(2 \theta) = \begin{cases} i)\cos^{2} ( \theta) - { \sin}^{2}( \theta) \\ii) 2 { \cos}^{2}( \theta) - 1 \\iii) 1 - { \sin}^{2} \theta \\ iv)\dfrac{1 - { \tan}^{2} \theta}{1 + { \tan}^{2} \theta } \end{cases}[/tex]
since the question doesn't allude which one we need to utilize utilize so I would like to apply the second one, therefore
step-1: assign variables
to do so rewrite the given function:
[tex] \displaystyle \cos( {2(300)}^{ \circ} ) [/tex]
so,
[tex] \theta = {300}^{ \circ} [/tex]Step-2: substitute:
[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = 2 \cos ^{2} {300}^{ \circ} - 1[/tex]
recall unit circle thus cos300 is ½:
[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = 2 \left( \dfrac{1}{2} \right)^2 - 1[/tex]
simplify square:
[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = 2\cdot \dfrac{1}{4} - 1[/tex]
reduce fraction:
[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = \dfrac{1}{2} - 1[/tex]
simplify substraction and hence,
[tex] \rm\cos({600}^{ \circ} ) = \boxed{-\frac{1}{2}}[/tex]
Which statement about this system of equations is true?
5
A.
The system has no solution.
The system has a unique solution at (0,0).
B.
C. The system has a unique solution at (0,3).
D. The system has infinitely many solutions.
Answer:
A
Step-by-step explanation:
No solution because the line will never intersect each other (cuz the gradient is the same)
Write the equation of the sinusoidal function shown.
Answer: A
It looks at though the graph moved down a unit, so definitely a (-1) at the end of the function. If you move the graph up a unit, you will notice that the y = cos x format, therefore, it's not C or D.The amplitude of the function is 1. So B and D are out because their amplitudes are 2.Therefore, the answer is A.
Jesse travels 3.0 meters east and then turns and travels 4.0 meters north. The trip requires 35 seconds. What is his velocity?
Using Pythagorean triplet
[tex]\\ \sf\longmapsto AB^2=AC^2-BC^2[/tex]
[tex]\\ \sf\longmapsto AB^2=4^2-3^2[/tex]
[tex]\\ \sf\longmapsto AB^2=16-9[/tex]
[tex]\\ \sf\longmapsto AB^2=7[/tex]
[tex]\\ \sf\longmapsto AB=\sqrt{7}[/tex]
Now time=35[tex]\\ \sf\longmapsto Velocity=\dfrac{Displacement}{Time}[/tex]
[tex]\\ \sf\longmapsto Velocity=\dfrac{\sqrt{7}}{35}[/tex]
[tex]\\ \sf\longmapsto Velocity=\dfrac{2.6}{35}[/tex]
[tex]\\ \sf\longmapsto Velocity=0.07m/s[/tex]
An isosceles triangle has one angle of 30 degrees. Calculate the possible sizes of the other 2 angles
Answer:
75 and 75
Step-by-step explanation:
Answer:
Hello,
Step-by-step explanation:
2 solutions:
30° is angle of the base: other angle of the base is 30° and the main angle is 180°-30°-30°=120°30° is the main angle, angles of the base are (180°-30°)/2=75° and 75°.Match the expression with its name. 6x3 - 9x + 3
Answer:
x is 1.7 add it by three and its 18 you can do this by doing 9 times 1.7 which gets you 15 and add it with three and it equals 6 times 3
Step-by-step explanation:
**25 POINTS**
Which of the following lists of ordered pairs is a function?
Answer: A
Step-by-step explanation: A function is when every domain (x value) corresponds to one range (y value) so that it passes the vertical line test
Through (-1,2) parallel to the line x=5. Find an equation of a line that satisfies the given conditions.
Answer:
x= -1
Step-by-step explanation:
Since x= 5 is a vertical line, the unknown line would also be a vertical line with an equation of x=___ as they are parallel to each other.
Given that the line passes through (-1, 2), the equation of the line is x= -1.
Parallel lines have the same slope and will never meet.
Can some help me with this question :)
Answer:
3/7
Step-by-step explanation:
I think its only 3/7
Cause 9/18=1/2
3/5=0.6
2/10=1/5
and 8/24=1/3
Answer:
[tex] \frac{8}{24} [/tex]
[tex] \frac{2}{10} [/tex]
[tex] \frac{9}{18} [/tex]
Simplify the following:
a. 9 sinA +33 cosec A + 10 sin A - 13 cosec A
Answer:
19 sin + 20 cosec
explanation
9 sin A + 10 sinA + 33 -13 cosecA
19 sin + 20 cosec
Four friends equally divided a whole pizza for lunch. Binli ate 1 of his 3
share and took the rest of his share home. What fraction of the whole pizza did he eat for lunch?
Please help! Will give brainiest!!!
Answer:
He ate 1/12 of the pizza
Step-by-step explanation:
Divide the pizza by 4 to get the share each friend got
1/4
Then Binli ate 1/3 of his share
1/4 * 1/3 = 1/12
He ate 1/12 of the pizza
Graph the line that passes through (5, 5), and is perpendicular to a line whose slope is –2.
Answer:
y = 1/2x + 5/2
Step-by-step explanation:
y = 1/2x + b
5 = 1/2(5) + b
5 = 5/2 + b
5/2 = b
Help plz Algebra 1
Simplify numbers 10 and 13 <3
Answer:
10t+2
Step-by-step explanation:
2-5t+8+5t-8
10t+2
what is the value of x
Answer:
-10
Step-by-step explanation:
Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result. Therefore, the value of x is -10.
Which expression is equivalent to
X^4
Jdnzusjdnekdjdnkdkelef
2. Write down the supplementary angle of each of the following angles are 105 degree.
Answer:
75
Step-by-step explanation:
Answer:
75°Step-by-step explanation:
Supplementary angles add up to 180°.
The angle x, supplementary with 105°:
x + 105° = 180°x = 180° - 105°x = 75°9. Find the zero of the polynomial in each of the following
i)f(x) = 3x- 5
Answer:
[tex]f(x) = 3x - 5[/tex]
For a zero, f(x) = 0:
[tex]{ \tt{0 = 3x - 5}} \\ { \tt{x = \frac{5}{3} }}[/tex]
What is the image of (-5,-5) after a dilation by a scale factor of 3 centered at the origin
Answer:
(-15,-15)
Explanation:
The dilation of 3 to the image means that each coordinate point is multiplied by 3. So, multiplying -5*3 gets you -15.
