The Pythagorean Identity states that: (sin x)^2 + (cos x)^2 = 1
Given cos 0 = 5/3, find sin 0
sin 0 = ?/?
Simplify the fraction.
Answers
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:sin(\theta) = \cfrac{2}{3} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: \cos {}^{2} ( \theta) + \sin {}^{2} ( \theta) = 1[/tex]
[tex]\qquad \tt \rightarrow \: {\bigg( \cfrac{ \sqrt{5}}{3} \bigg) }^{2} + \sin {}^{2} ( \theta) = 1[/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{5}{9} + \sin {}^{2} ( \theta) = 1[/tex]
[tex]\qquad \tt \rightarrow \: \sin {}^{2} ( \theta) = 1 - \cfrac{5}{9} [/tex]
[tex]\qquad \tt \rightarrow \: \sin {}^{2} ( \theta) = \cfrac{9 - 5}{9} [/tex]
[tex]\qquad \tt \rightarrow \: \sin {}^{2} ( \theta) = \cfrac{4}{9} [/tex]
[tex]\qquad \tt \rightarrow \: \sin {}^{} ( \theta) = \sqrt \cfrac{4}{9} [/tex]
[tex]\qquad \tt \rightarrow \: \sin {}^{} ( \theta) = \pm \cfrac{2}{3} [/tex]
Generally, only positive value is taken :
[tex]\qquad \tt \rightarrow \: \sin {}^{} ( \theta) = \cfrac{2}{3} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Related Questions
What is the area of this triangle?
Answers
Answer:
sum of all sides
Step-by-step explanation:
x1y2 + x3y3 + x1y1
In formula P = 2L + 2W
A. solve for L
B. solve for W
C. Find P if L=12 and W=8
Answers
Answer:
P=2l+2W
if l=12 and W=8
then,
P=2L+2W
=2.18+2.8
=36+16
=52
on a day in winnipeg with 10 1/2 h of daylight, it was sunny for 1/3 of that time. for how many hours was it sunny that day
Answers
Considering the multiplication of mixed fractions, [tex]\frac{21}{6}[/tex] or 3.5 hours was sunny that day.
Multiplication of mixed fractionsTo multiply mixed fractions, it is necessary to transform these fractions into improper fractions. To do this, the whole part is multiplied by the denominator of the fraction that accompanies it. The result of the multiplication is added to the numerator of the fraction that accompanies it, and it will be the denominator of the new fraction, while the denominator remains the same.
After transforming the mixed fractions to be multiplied into improper fractions, they are multiplied. To do this, it is necessary to multiply the numerators of the two fractions, and the denominators of the fractions. If the resulting product needs to be simplified to lowest terms, divide the numerator and denominator by common factors.
Sunny hoursOn a day in winnipeg with 10[tex]\frac{1}{2}[/tex] h of daylight, it was sunny for [tex]\frac{1}{3}[/tex] of that time. This is:
10[tex]\frac{1}{2}[/tex] h × [tex]\frac{1}{3}[/tex]
Solving:
10[tex]\frac{1}{2}[/tex] h × [tex]\frac{1}{3}[/tex] = [tex]\frac{10x2+1}{2}[/tex] × [tex]\frac{1}{3}[/tex] = [tex]\frac{21}{2}[/tex] × [tex]\frac{1}{3}[/tex] = [tex]\frac{21x1}{2x3}[/tex]= [tex]\frac{21}{6}[/tex]= 3.5
Finally, [tex]\frac{21}{6}[/tex] or 3.5 hours was sunny that day.
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(5+3√2)² simplify the following
Answers
Answer:
[tex](5+3\sqrt{2} )^{2} =43+30\sqrt{2}[/tex]
≈85.43
Step-by-step explanation:
apply the binomial theorem to the square
[tex]=(5)^{2} +2(5)(3\sqrt{2} )+(3\sqrt{2} )^{2}[/tex]
[tex]=25+30\sqrt{2} +18\\[/tex]
[tex]=43+30\sqrt{2}[/tex]
≈85.43
Hope this helps
Hello!
Here, we apply the algebraic identity :
[tex]\boxed {(a + b)^{2} = a^{2} + 2ab + b^{2}}[/tex]
Let's solve!
⇒ (5 + 3√2)²
⇒ (5)² + 2(5)(3√2) + (3√2)²
⇒ 25 + 30√2 + 18
⇒ [tex]\boxed {43 + 30\sqrt{2}}[/tex]
∴ The final answer will be 43 + 30√2.
The owner of a fitness watch would like to determine if the mean number of steps he takes per day differs from the recommended 10,000 steps per day, using α = 0.01. He selects a random sample of 50 days with the intention of testing the hypotheses H0:μ = 10,000 steps versus Ha:μ ≠ 10,000 steps where μ = the true mean number of steps taken per day.
Which of the following values of the alternative hypothesis would yield the greatest power to reject the null hypothesis?
A. u = 9,000
B. u = 9,500
C. u = 10,000
D. u = 10,500
Answers
Answer:
ok so it could be Careful because think about it 10000x 0.01...
Answer:10,000
Step-by-step explanation:
What is the average of the following numbers?
2, 5, 8, 1
Answers
Answer:
average of the no. = sum of all no. / no. of terms
= 2 + 5 + 8 + 1 / 4
= 16/4
= 4
4 is the answer
The standard deviation for a set of data is 9.5. The mean is 205.
What is the margin of error?
Answers
If the standard deviation for a set of data is 9.5. The margin of error is: 19.5.
Margin of errorUsing this formula
Margin of error=Standard deviation×Mean
Let plug in the formula
Margin of error=205 × 9.5%
Margin of error = 19.475
Margin of error = 19.5 (Approximately)
Therefore If the standard deviation for a set of data is 9.5. The margin of error is: 19.5.
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In how many ways can $9$ friends sit at a circular table if two of them, Anna and Bob, insist on having exactly two people seated between them? (As usual, two seatings are considered the same if one is a rotation of the other.)
Answers
There are 10,080 different ways in which the friends can seat on the circular table.
In how many ways the friends can seat?
There are 9 friends, such that two of them need to be separated by exactly two people.
Because the table is circular, we can consider the first position as the position where Bob is.
Now let's count the number of options for each of the other 8 positions. (counting to the left).
The next two positions have 7 and 6 options respectively (as these can be taken by any of the other 7 friends)
For the next seat, we could seat Anna or one of the remaining 5 friends.
Let's assume we seat Anna there, then for each of the next positions, we will have, respectively, 5, 4, 3, 2, 1 options.
The total number of combinations is given by the product between the numbers of options, so we have:
C = 7*6*5*4*3*2*1
But we also need to consider the case where Anna is on the first position (and Bob on the third), so we just need to add a factor equal to 2.
C = 2*(7*6*5*4*3*2*1) = 10,080
There are 10,080 different ways in which the friends can seat on the circular table.
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How many kilometers are in 462 meters? How many kilometers are in 462 meters ?
Answers
Answer:
0.462
Step-by-step explanation:
1km=1000m
so to get from metres to kilometres you divide by 1000
so 462÷1000=0.462
how many units are -7 and its opposite from zero?
Answers
Answer:
-7 is -7 units away from zero. Its opposite is 7 from zero.
Step-by-step explanation: Count from 0 how many digits away it is
Galaxy Star Corporation purchased goods for $100,000 from Sunrise
Materials. Galaxy Star Corporation can avail a discount of 2.5% if the
payment is made within 20 days. However, the full payment will be made
if the payment is made after 20 days.
If Galaxy Star Corporation pays within 20 days, which of the
following entries will it pass?
Answers
The entry that it will pass on the accounting book based on the information about Galaxy Star Corporation is the credit sales.
What is a credit sale?It should be noted that credit sales are the sales where the amount that is owed will be paid at alter date.
From the information given, we were informed that the payment will be made after 20 days. Therefore, the appropriate entry will be in town credit sales.
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Find the perimeter of a rectangle whose leath in 223 and width is 3/2. Find the perimeter of a rectangle whose leath in 223 and width is 3/2 .
Answers
Answer:
449 units
Step-by-step explanation:
Perimeter of a rectangle = 2(a+b)
= 2(223+3/2)
=449 units
A tunnel is constructed with a semielliptical arch. The width of the tunnel is 60 feet, and the maximum height at the center of the tunnel is 25 feet. What is the height of the tunnel 5 feet from the edge? Round your answer to the hundredths place.
9.99 feet
13.82 feet
24.65 feet
25.01 feet
Answers
The height of the tunnel 5 feet from the edge is 13.82 feet option second 13.82 feet is correct.
What is an ellipse?An ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called focus adds up to a constant. It is taken from the cone by cutting it at an angle.
We have:
A tunnel is constructed with a semi-elliptical arch. The width of the tunnel is 60 feet, and the maximum height at the center of the tunnel is 25 feet.
2a = 60 (width of the tunnel is 60 feet)
a = 30
And the maximum height at the center of the tunnel is 25 feet
b = 25
Let's assume the center of the ellipse is at the origin.
So the equation of the ellipse:
[tex]\rm \dfrac{x^2}{30^2}+\dfrac{y^2}{25^2}=1[/tex]
Now plug x = a - 5 = 30 - 5 = 25
[tex]\rm \dfrac{25^2}{30^2}+\dfrac{y^2}{25^2}=1[/tex]
After solving:
[tex]\rm \dfrac{y^2}{25^2}=1-\dfrac{25}{36}[/tex]
[tex]\rm y^2=\dfrac{6875}{36}[/tex]
y = ±13.819 ≈ ±13.82
Height cannot be negative
y = 13.82 feet
Thus, the height of the tunnel 5 feet from the edge is 13.82 feet option second 13.82 feet is correct.
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if a polyhedron has a volume of 35 cm^3 and is dilated by a factor of 5/2, what will be the volume of the dilated polyhedron? Round your answer to the nearest thousandth if necessary.
Answers
If a polyhedron has a volume of 35 cm cube and is dilated by a factor of 5/2 then the volume of dilated polyhedron will be 50.6 cm cube.
Given Volume of polyhedron=35 cm cube . Factor from which is dilated 5/2.
If the polyhedron is dilated by factor 5/2 then the volume of the polyhedron will change by the cube of that factor because when it is dilated by factor its material also increases.
Volume =35[tex]cm^{3}[/tex]
After dilation
Volume=35+[tex](5/2)^{3}[/tex]
=35+15.625
=50.625
After Rounding nearest to thousand we will get 50.6 [tex]cm^{3}[/tex].
Hence after dilation the volume which is 35 cm cube will change from 35 to 50.6[tex]cm^{3}[/tex].
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Use slopes and y-intercepts to determine if the lines 10x+3y=−3 and 5x−4y=−3 are parallel.
Answers
Answer:
They are not parallel
Step-by-step explanation:
original equation
10x + 3y = -3
subtract 10x
3y = -10x - 3
divide by 3
y = -10/3x - 1
original equation
5x - 4y = -3
subtract 5x
-4y = -5x-3
divide by -4
y = 5/4x + 3/4
the slopes are not equal to each other (5/4x and -10/3x) so they are not parallel
what is ⅛ in a percentage form
Answers
Answer:
12.5%
Step-by-step explanation:
1/8 × 100% = 12.5%
So 9f you multiply an eighth by one hundred percent and simplify accurately you'll get 12.5%
How would you multiply 4x 2
—
3
( 4 x 2 by 3 (fractions))
Answers
Answer:
8/3
Step-by-step explanation:
4 x 2 = 8, so (4 × 2)/2 = 8/3.
Christina knits a scarf for each of her 7 friends. Altogether, the scarfs had a total length of 39.9 ft. if each scarf has the same length. how long was each scarf? write answer in inches
Answers
The length of each scarf knitted for the 7 friends given the total length of the scarf altogether is 5.7 ft
Length of each scarfNumber of friends = 7Total length of scarf = 39.9 ftLength of each scarf = Total length of scarf / Number of friends
= 39.9 ft / 7
= 5.7 ft
Therefore, the length of each scarf knitted for the 7 friends given the total length of the scarf altogether is 5.7 ft
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Find area bounded between y=x^2 and y=-(x+2)^2+4
Answers
By applying definite integrals and integration rules, the area bounded between the curves f(x) = x² and g(x) = -(x+2)² + 4 is equal to 8 square units.
How to determine the between the two integrals
The points of intersection between the two curves are (x, y) = (0, 0) and (x, y) = (-2, 4). The curve is f(x) = x² and upper curve is g(x) = -(x+2)² + 4. The area between the two curves is defined by this definite integral:
[tex]A = \int\limits^{0}_{-2} {f(x) - g(x)} \, dx[/tex]
[tex]A = \int\limits^{0}_{-2} {f(x)} \, dx - \int\limits^{0}_{-2} {g(x)} \, dx[/tex]
[tex]A = \int\limits^0_{-2} {[-(x+2)^{2}+4]} \, dx -\int\limits^0_{-2} {x^{2}} \, dx[/tex]
[tex]A = -\frac{(x+2)^{3}}{3}|_{-2}^{0} + 4\cdot x|_{-2}^{0}-\frac{x^{3}}{3}|_{-2}^{0}[/tex]
[tex]A = - \frac{2^{3}}{3} + 0 + 4\cdot [0 - (-2)] - 0 + \frac{(-2)^{3}}{3}[/tex]
[tex]A = -\frac{8}{3} + 8 -\frac{8}{3}[/tex]
A = 8
By applying definite integrals and integration rules, the area bounded between the curves f(x) = x² and g(x) = -(x+2)² + 4 is equal to 8 square units.
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A class of students consists of 9 men and 51 women. Write a proper fraction to represent the part of the class that is women. Reduce the fraction. Change the fraction to a percent.
Answers
Answer:
85%
Step-by-step explanation:
9+51 = 60
(51/3) ÷ (60/3) = 17/20
(17/20)% = 85%
AABC=AADC, LACB=143, AC=33 LACD=?
Answers
Answer:
I think the best answer is 143
7 of 9 For each 48 mm of coloured fabric Fiona uses to make her curtains, she also uses 1.2 cm of white fabric. Express the amount of white fabric to coloured fabric as a ratio in its simplest form. 7 of 9 For each 48 mm of coloured fabric Fiona uses to make her curtains , she also uses 1.2 cm of white fabric . Express the amount of white fabric to coloured fabric as a ratio in its simplest form
Answers
Answer:
amount of coloured fabric in mm = 48
amount of white fabric in mm = 12
ratio = white fabric : coloured fabric = 12 : 48 = 1:4
Initially, there were only 86 weeds in the garden. The weeds grew at a rate of 8% each week. The following function represents the weekly weed growth: f(x) = 86(1.08)x. Rewrite the function to show how quickly the weeds grow each day.f(x) = 86(1.08)7x; grows approximately at a rate of 5.6% daily
f(x) = 86(1.087)x; grows approximately at a rate of 0.56% daily
f(x) = 86(1.01)x; grows approximately at a rate of 0.1% daily
Feedback for this selection: Don't forget to multiply the power by 7.
f(x) = 86(1.01)7x; grows approximately at a rate of 1% daily
please explain how you got the answer!
Answers
The function represents the weekly weed growth f(x) = 86(1.01)^7x; They grow at approximately the rate of 1% per day.
What is a function?The function is a type of relation, or rule, that maps one input to specific single output.
The following function represents the weekly weed growth:
f(x) = 86(1.08)x.
we'll represent the growth function by day g(x). If x is to represent days, then x/7 represents weeks.
We can write,
g(x) = f(x/7) = 86·1.08^(x/7)
g(x) = 86·(1.08^(1/7))^x
g(x) = 86·1.011055^x
The function represents the weekly weed growth f(x) = 86(1.01)^7x; They grow at approximately the rate of 1% per day.
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3. What's the difference between 126 1/4 and 78 2/3?
O A. 57 7/12
OB. 47 7/12
O C. 58 5/12
O D. 48 1/3
Answers
Answer:
B. 47 7/12
Step-by-step explanation:
=126 1/4 - 78 2/3
Change the two mix fraction to improper fractions.
= 505/4 - 236/3
= 1515-944/12
= 571/12
= 47 7/12
2) An electronic gadgets distributor distributes various brands of mobiles to retailers.
The data for the number of smartphones distributed in nine months (Jan-Sep) are
collected to make a box-and-whisker plot. Read the plot and answer the questions.
H
20
30
40
a) Write the median from the above given plot.
b) What is the least number of smartphones distributed?
c) Write the third quartile from the given plot.
50
t>
60
Answers
The median is 40, the least number of smartphones distributed is 33, and the third quartile is 48.
What is the box and whisker plot?A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have a box and whisker plot shown in the picture.
From the box plot, the line between the box ends represents the median of the data.
The median = 40
The least number of smartphones distributed = 33
Q3 = 48
Thus, the median is 40, the least number of smartphones distributed is 33, and the third quartile is 48.
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Please help !!! I will give 20 points to correct answer !!!!
Answers
Answer:
the answer above the image
Answer:
a=-4/3, 14/3
Step-by-step explanation:
absolute value only makes the answer become positive whether the value inside is negative or positive.
so -3a+5=9 or -3a+5=-9 all works
-3a+5=9
-3a=4
a=-4/3
If -3a+5=-9
-3a=-14
a=14/3
Question in image, it asks to show your work
Answers
Answer:
• f(g(x)) = [tex]\sqrt{x^{2} + 1}[/tex] + 8
• g(f(x)) = 16[tex]\sqrt{x}[/tex] + x + 65
Step-by-step explanation:
• f(g(x)) = f(x² + 1)
= [tex]\sqrt{x^{2} + 1}[/tex] + 8
• g(f(x)) = g([tex]\sqrt{x + 8}[/tex] )
= [tex](\sqrt{x } + 8)^{2}[/tex] + 1
= x + 16[tex]\sqrt{x}[/tex] + 64 + 1
= 16[tex]\sqrt{x}[/tex] + x + 65
The slope equals zero and it passes through the point (x, y) = (1, −6).
Answers
Answer:
i think the answe is. y=0x-6
What is the solution, if any, to the inequality |3x|_>0
O all real numbers
O no solution
O x_>0
O x≤0
Answers
Answer:
C , x>0
Step-by-step explanation:
anything times 0 is 0 and 3x has to be larger than 0
Which function has a restricted domain?
Answers
For more explanation, please see the attachment