Answer:
the answer is 56.25
Step-by-step explanation:
.32x=18
×=56.25
What is one possible value of the
y-intercept of the line passing
through the point (2, 2) and in
between the points (4, 4) and (6, 4)?
In a two digit number, t = the tens digit and u = the ones digit. Which of the expressions below shows the value of its reversal?
10u + t is the expressions shows the value of the reversal of digits in a two digit number, t = the tens digit and u = the ones digit. This can be obtained by multiplying 10 with the tens digit and adding unit digit.
Which is the required expressions?
Given that, in a two digit number,
t = the tens digit
u = the ones digit
The expression for the digit will be ,
10×t + u = 10t + u
The value of its reversal,
u = the tens digit
t = the ones digit
10×u + t = 10u + t is the required expression
For example,
37 = 10×3 + 7 = 30 + 7 and its reverse 73 = 10×7 + 3 = 70 + 3
Hence 10u + t is the expressions shows the value of the reversal of digits in a two digit number, t = the tens digit and u = the ones digit.
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Cylinder A has a radius of 7 inches and a height of 5 inches. Cylinder B has a volume of 490π. What is the percentage change in volume from cylinder A to cylinder B?
50% decrease
75% increase
150% decrease
100% increase
The percentage change in volume from cylinder A to cylinder B; D: 100%
How to find the percentage change in Volume?
Formula for Volume of a Cylinder is;
V = πr²h
Thus, volume of Cylinder A is;
V_a = π * 7² * 5
V_a = 245π
Thus, percentage change in volume is;
[245π/(490π - 490π)] * 100%
Percentage change in volume = 100%
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Answer:
100% increase
Step-by-step explanation:
I got it right on the test.
Look at the image below.
6
13
12
Find the area of the parallelogram.
square units
Answer: 72 square units
Step-by-step explanation:
[tex]A=Bh=6(12)=72[/tex]
Answer:
72 SQUARE UNITS
Step-by-step explanation:
A right cylinder and an oblique cylinder have the same radius and the same height. How do the volumes of the two
cylinders compare?
A. The volumes are the same, based on Cavalieri's principle.
B. The volumes are not the same, because Cavalieri's principle does not apply to oblique solids.
C. The volumes are not the same, because the two solids do not have the same cross-sectional
area at every level parallel to the bases.
D. The volumes are not the same, because an oblique solid has less volume thanits corresponding
right solid with the same height.
Answer:
A. The volumes are the same, based on Cavalieri's principle.
Step-by-step explanation:
Cavalieri's principle tells us the volumes of solids will be identical if their cross sectional areas are identical at every height.
ApplicationA right cylinder and an oblique cylinder of the same height and radius will both have circular cross sections of the given radius at any height. Since the radius is the same, the area of the circle is the same. Hence the requirements of Cavalieri's principle are met, and the cylinders have the same volume.
(-1,-2) or (1,0) ????
Answer:
(-1,-2)
Step-by-step explanation:
See attached graph.
The equation 4x2 8x 15 = 0 is being rewritten in vertex form. fill in the missing step. given 4x2 8x 15 = 0 step 1 4(x2 2x ___) 15 ___ = 0 step 2 ✔ step 3 4(x 1)2 11 = 0 4(x2 2x 1) 15 − 4 = 0 4(x2 2x 1) 15 − 1 = 0 4(x2 2x 2) 15 − 2 = 0 4(x2 2x 4) 15 − 4 = 0
Answer:
a) is the correct answer
43. Consider the equation 4(x-8)+y=9(x-2)
[Part 1]
Find an expression for y of the form ax+b expression for y such that the equation has infinitely many solutions. Is there more than one such solution? Explain your reasoning using complete sentences.
[Part 2]
Find an expression for y of the form ax+b expression for y such that the equation has no real solutions. Is there more than one such solution? Explain your reasoning using complete sentences.
The expression of the equation 4(x - 8) + y = 9(x - 2) in slope intercept form is; y = 5x + 14
How to write an equation in Slope Intercept form?We want to express 4(x - 8) + y = 9(x - 2) in slope intercept form of y = mx + b.
Let us expand the equation to get;
4x - 32 + y = 9x - 18
Isolate y to get;
y = 9x - 4x - 18 + 32
y = 5x + 14
Thus;
Slope = 5
y - intercept = 14
x - intercept = -2.8
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5 circles are shown. Circle D has a secant with length 12. Circle E has a radius with length 6. Circle H has a secant with length 6. Circle F has a diameter with length 12. Circle G has a diameter with length 12.
Circle A has a radius of 6. Which circles are congruent to circle A? Check all that apply.
circle D
circle E
circle F
circle G
circle H
The circle E, circle F and circle G are the circles which are congruent (similar) to the circle A has a radius of 6.
Let us discuss about the structure of each circles.
Circle DThe circle D has the secant with the length 12. The secant means the straight line joining two points on the circle. So, we can't conclude that the secant will always be the diameter. Hence, it has different shape compared to circle A.
Circle EThe circle E has the radius with length 6. The radius is same as the radius of the circle A. So, it is similar to the circle A.
Circle HThe circle D has the secant with the length 6. Similar to the condition of circle D, it is not congruent to circle A.
Circle FThe circle F has the diameter with length 12. Which means, the radius of this circle is with length 6. Hence, it is similar to the circle A.
Circle GThe circle G has the diameter with length 12. Which means, the radius of this circle is with length 6. Hence, it is similar to the circle A.
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Answer:
Circles E and F are congruent to circle A
please help me with this problem
please show steps so i know for next time
=========================================================
Explanation:
You could use the AC method to factor this, but the quadratic formula is the most efficient route in my opinion. This will avoid any guess-and-check.
Compare the original equation to the form [tex]a\text{x}^2 + b\text{x} + c = 0[/tex]
We have a = 9, b = 6, and c = -8
Those values lead to...
[tex]\text{x} = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\text{x} = \frac{-6\pm\sqrt{(6)^2-4(9)(-8)}}{2(9)}\\\\\text{x} = \frac{-6\pm\sqrt{324}}{18}\\\\\text{x} = \frac{-6\pm18}{18}\\\\\text{x} = \frac{-6+18}{18} \ \text{ or } \ \text{x} = \frac{-6-18}{18}\\\\\text{x} = \frac{12}{18} \ \text{ or } \ \text{x} = \frac{-24}{18}\\\\\boldsymbol{\text{x} = \frac{2}{3} \ \text{ or } \ \text{x} = -\frac{4}{3}}\\\\[/tex]
Side notes:
2/3 = 0.667 approximately-4/3 = 1.333 approximatelySince your teacher did not give rounding instructions, I'll assume s/he wants the fraction form of each x value (rather than the decimal form). Be sure to follow all instructions given, and ask for clarification if need.To confirm the solutions, replace every copy of x with either 2/3 or -4/3 (pick one value only). Simplifying the left hand side should lead to 0. I'll let you check each answer.(The two triangles are not the same)
In the quadrilateral ABCD, in which angle A = 60° and angle B = 50°. The measure of angles C and D are,
∠C = 200° and ∠D = 50°
In the quadrilateral ABCD, it is given that,
A = 60° and angle B = 50°
Now, since AC is the angle bisector of angles A and C, we have,
∠DAC = ∠BAC ......... (1)
And ∠ACD = ∠ACB ............ (2)
Also, AC divides the quadrilateral ABCD into two triangles, ΔABC and ΔACD.
In ΔABC, ∠BAC = 30° [from (2)] and ∠ABC = 50°
Using angle sum property of a triangle, we have,
∠BAC + ∠ABC + ∠ACB = 180°
⇒ 30° + 50° + ∠ACB = 180°
80° + ∠ACB = 180°
∠ACB = 180° - 80°
∠ACB = 100°
From (1), ∠ACD = ∠ACB = 100°
∠C = ∠ACD + ∠ACB
⇒ ∠C = 100° + 100°
∠C = 200°
Now, according to the angle sum property of a quadrilateral,
∠A + ∠B + ∠C + ∠D = 360°
Substituting the values of ∠A, ∠B, and ∠C, we get,
60° + 50° + 200° + ∠D = 360°
310° + ∠D = 360°
∠D = 360° - 310°
∠D = 50°
Hence, in quadrilateral ABCD, ∠C = 200° and ∠D = 50°
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The primary goal of a data _____ is to create new questions using data.
The primary goal of a data scientist is to create new questions using data.
Who is a data scientist?In the data ecosystem, a data scientist is one who creates new questions using data.
Who is a data analyst?Unlike a data scientist, a data analyst uses existing data questions to find answers through insightful analysis of data.
Who are data designers?Data designers design databases and database-specific constructs, and the procedures for storing, retrieving, and deleting persistent objects.
Who are data engineers?Data engineers build data systems to collect, manage, and convert data into information for both data scientists and analysts.
Thus, the primary goal of a data scientist is to create new questions using data.
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Question Completion with Answer Options:a) scientist
b) engineer
c) designer
d) analyst
A map's numerical coordinates are in kilometres. Town A is at (16.3, 2.9) and town B is at
(4.5, 6.3). A road is to be constructed on a direct line between the two towns. Each town is
responsible for the construction up to the mid-point at a cost of $150 000 for each kilometre.
Determine the cost for each town.
Answer:
$92,250 per town
Step-by-step explanation:
See attached image.
The two towns may be connected with a straight line, the road, that can be made into the hypotenuse of a right triangle. The twio sides are calculated from the coordinates and shown in the image. Then use the phythagorean theorem to calculate the hypotenuse. The towns are 12.3 km apart. The total road cost would be:
($150,000/km)(12.3 km) = $1,845,000, or $92,250 per town.
Find the measure of each numbered angle.
Answer:
m∠1 = 51°
m∠2 = 16°
Step-by-step explanation:
First ,check the attached photo.
=================
In the right triangle ABC :
m∠1 = 90 - 39
= 51°
……………………
In the right triangle ABD :
m∠2 = 90 - 74
= 16°
Answer:
• ∠ 1 = 51°
• ∠ 2 = 16°
Step-by-step explanation:
• ∠ 1, the 39° angle, and the right angle marked in red are angles of a triangle.
∴ ∠ 1 + 90° + 39° = 180° [Angles in a triangle add up to 180°]
⇒ ∠ 1 = 180° - 90° - 39°
⇒ ∠ 1 = 51°
• The small triangle on the top-left of the image consists of ∠ 2, a right-angle (marked in red) and a 74° angle.
∴ ∠ 2 + 90° + 74° = 180° [Angles in a triangle add up to 180°]
⇒ ∠ 2 = 180° - 90° - 74°
⇒ ∠ 2 = 16°
Can someone help me do these problems I’m having a hard time doing it and show work please !
The expression which expresses the number of square feet of wallpaper needed is 12[tex]x^{2}[/tex]-21.
Given that the length of family room is 3x, breadth be 3x , height be x and the length and breadth of door be 7 feet and 3 feet.
We are required to find the expression which shows the square feet of wallpaper needed for the walls of the family room.
Because the wallpaper is not usually used on the floor and the ceiling and on doors so we will deduct the area of ceiling , floor and door from the surface area of whole room or we will just find the area of four walls one by one and then deduct the area of door from it.
Area of four walls only=2(lh+bh)
=2(3x*x+3x*x)
=2(3[tex]x^{2}[/tex]+3[tex]x^{2}[/tex])
=2*6[tex]x^{2}[/tex]
=12[tex]x^{2}[/tex]
Area of door=length*breadth
=3*7
=21 [tex]feet^{2}[/tex]
Required area=12[tex]x^{2}[/tex]-21.
Hence the expression which expresses the number of square feet of wallpaper needed is 12[tex]x^{2}[/tex]-21.
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The population of a bacteria culture quadriples every 30 minutes. If the culture started with 8 cells, how many cells will be in the culture after 3 hours?
Using an exponential function, it is found that there will be 32,768 bacteria after 3 hours.
What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex]
In which:
a is the initial value.b is the rate of change.x is the number of time periods.For this problem, the parameters are:
a = 8, b = 4.
3 hours is 6 periods of 30 minutes, hence the amount is:
[tex]y = 8 \times 4^6 = 32768[/tex]
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A cylindrical pain can has a diameter of 12 centimeters and height of centimetrs which is closest to the volume of the paint can in cubic centimeters
The volume of the cylinder having diameter 12 cm and height of 4 cm is 452 [tex]cm^{3}[/tex].
Given diameter of cylinder be 12 cm and height of cylinder be 4cm.
We are required to find the volume of cylinder.
Volume is the quantity of substance a container can hold in its capacity.
Diameter=12 cm
Radius=6 cm (Radius is always equal to half of diameter)
Volume of cylinder=π[tex]r^{2} h[/tex]
We have to just put the values of r, h and π in the formula to get the volume of the cylinder.
Volume=π[tex](6)^{2} 4[/tex]
=3.14*4*36
=452.57 [tex]cm^{3}[/tex]
After rounding off we will get 452 [tex]cm^{3}[/tex].
Hence the volume of cylinder is 452 [tex]cm^{3}[/tex].
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Question is incomplete as it should include height of cylinder be 4cm.
The seismic activity density of a region is the ratio of the number of earthquakes during a given time span to the land area affected. A state had 424 earthquakes over a given time span and a land area of 71,300 square miles.
What is the seismic activity density for this state? Round to the nearest ten thousandth, if necessary.
0.0046 earthquakes per square mile
0.0059 earthquakes per square mile
168.1604 earthquakes per square mile
179.0049 earthquakes per square mile
Using proportions, it is found that the seismic activity density for this state is of 0.0059 earthquakes per square mile.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
In this problem, the density is the proportion given by the number of earthquakes divided by the area, hence:
424/71,300 = 0.0059 earthquakes per square mile.
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Answer: Using proportions, it is found that the seismic activity density for this state is of 0.0059 earthquakes per square mile.
Step-by-step explanation:
If AB is the midsegment of ∆XYZ, then find AB and x.
Answer:
AB = 17, x = 6
Step-by-step explanation:
3x - 1 = 34 / 2
3x - 1 = 17
3x = 18
x = 6
AB = 17
x = 6
each snack pack of crackers to the number of calories in each snack pack of trail mix.
A number line goes from 65 to 115. Crackers's whiskers range from 70 to 100, and the box ranges from 75 to 85. A line divides the box at 80. Cookies's whiskers range from 70 to 115, and the box ranges from 90 to 105. A line divides the box at 100.
Which statement is true about the box plots?
The interquartile range of the trail mix data is greater than the range of the cracker data.
The value 70 is an outlier in the trail mix data.
The upper quartile of the trail mix data is equal to the maximum value of the cracker data.
The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.
Based on the interquartile range, the true statement about the box plots is: D. Number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.
How to Find the Interquartile Range in a Box Plot?The interquartile range is the range of the box, which is the difference between the upper and lower quartile. Interquartile range is a measure of variation. The larger the value, the more the variation of the data.
Interquartile range for cracker = 85 - 75 = 10
Interquartile range for trail mix = 105 - 90 = 15
This means that the variation for trail mix is greater.
Therefore, the statement that is true is: D. Number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.
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Answer:d
Step-by-step explanation:
A pharmaceutical scientist studying two medications wonders how long different amounts of each medicine stay in someone's bloodstream. The amount of time (in hours) one medication stays in the bloodstream can be modeled by f(x)=-1.25\cdot \ln{\left(\dfrac{1}{x}\right)}f(x)=−1.25⋅ln( x 1 )f, left parenthesis, x, right parenthesis, equals, minus, 1, point, 25, dot, natural log, left parenthesis, start fraction, 1, divided by, x, end fraction, right parenthesis, where xxx is the initial amount of the medicine (in milligrams). The corresponding function for the other medication is g(x)=-1.8\cdot\ln\left(\dfrac{2.1}{x}\right)g(x)=−1.8⋅ln( x 2.1 )g, left parenthesis, x, right parenthesis, equals, minus, 1, point, 8, dot, natural log, left parenthesis, start fraction, 2, point, 1, divided by, x, end fraction, right parenthesis. Here are the graphs of
The amount of medication that stays in the bloodstream is the same at 3.04 hours for the two medications
How to compare both functions?The functions are given as:
[tex]f(x)=-1.25\cdot \ln{\left(\dfrac{1}{x}\right)}[/tex]
[tex]g(x)=-1.8\cdot\ln\left(\dfrac{2.1}{x}\right)[/tex]
Next, we represent both functions on a graph.
From the attached graph, we can see that both functions intersect at (11.34, 3.04)
This means that the amount of medication that stays in the bloodstream is the same at 3.04 hours for the two medications
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Complete question
A pharmaceutical scientist studying two medications wonders how long different amounts of each medicine stay in someone's bloodstream. The amount of time (in hours) one medication stays in the bloodstream can be modeled by [tex]f(x)=-1.25\cdot \ln{\left(\dfrac{1}{x}\right)}[/tex] where x is the initial amount of the medicine (in milligrams). The corresponding function for the other medication is [tex]g(x)=-1.8\cdot\ln\left(\dfrac{2.1}{x}\right)[/tex]. Here are the graphs of
Answer:
It gives the initial amount + It gives the solution
Step-by-step explanation:
It gives the initial amount + It gives the solution
We know from the graph given and the data provided that the function can automatically be proven true.
It cannot describe the amount of time as the data says X is how much of the medicine is given, not the time.
It can't be the equal ratio because, for example, 1 milligram of medicine doesn't equal 1h of time in the body.
All you need to do for this is educational guessing, reasoning, and the process of elimination. Hope this helped! have a great day :7)
What are the potential solutions of log4X+log4(x+6)=2?
Ox=-2 and x=-8
Ox=-2 and x = 8
O x=2 and x=-8
Ox=2 and x=8
Answer:
x = 2 ; x = -8
Step-by-step explanation:
Log rule: Log a + log b = log a*b[tex]\sf \ log_4 \ x +log_4 \ (x +6) = 2\\\\ log_4 \ (x)*(x +6) = 2\\\\[/tex]
log₄ ( x² + 6x) = 2
4² = x² + 6x
x² + 6x - 16 = 0
x² - 2x + 8x - 16 = 0
x(x - 2) + 8(x - 2) = 0
(x - 2) (x + 8) = 0
x - 2 = 0 or x + 8 = 0
x = 2 or x = - 8
Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the help!
Answer:
b. -x + y = 0
Step-by-step explanation:
Direct variation:
Direct variation means "y varies directly as x”:
[tex]y \propto x \implies y=kx[/tex]
where k is the (non-zero) constant of variation.
To determine which of the given equations represents a direct variation, isolate y for each and compare with the direct variation equation.
Equation a
[tex]y=\dfrac{4}{3}x-2[/tex]
This is not a direct variation equation as there is an addition of -2.
Equation b
[tex]-x+y=0[/tex]
[tex]\implies y=x[/tex]
This is a direct variation equation where the constant of variation is 1.
Equation c
[tex]xy=8[/tex]
[tex]\implies y=\dfrac{8}{x}[/tex]
This is not a direct variation equation as y is inversely proportional to x.
Equation d
[tex]y=14[/tex]
This equation does not include the variable x, and so is therefore not a direct variation equation.
If y varies inversely with x then the line must be linear and increasing
And the y intercept must be 0 in y=mx+c
#1
y=4/3x-2c=-2
Not direct#2
y=xYes
#3
y=8/xNo
#4
y=14Parallel to x axis no direct variation
Identify the equation that describes the line in slope-intercept form. slope = 2 , point (- 1, 2) is on the line
Answer:
[tex]y=2x+4[/tex]
Step-by-step explanation:
Given a slope and a point on the line, you can use point slope form and then rearrage your terms into slope-intercept formSLOPE-INTERCEPT FORM: [tex]y=mx+b[/tex], where "m" is your slope and "b" is your y-interceptPOINT-SLOPE FORM: [tex](y-y_{1}) =m(x-x_{1})[/tex], where [tex]y_{1}[/tex] represents the y-coordinate of your point, [tex]x_{1}[/tex] represents the x-coordinate of your point, and [tex]m[/tex] represents the slope[tex](y-2)= 2(x-(-1))[/tex]
Point-slope form[tex](y-2)=2(x+1)[/tex]
[tex]y-2=2x+2[/tex]
[tex]y=2x+4[/tex]
Slope-intercept formWrite down two irrational numbers with a sum of 4
Answer:
π & 4-π
Step-by-step explanation:
Taking, a = π & b = 4-π ,a + b = π + 4 - π = 4find the distance formula
Answer:
d=(x^2-x^1)+(y^2-y^1)^2
Answer:
[tex]\mathfrak{Distance \: between \: two \:points}[/tex]
The distance between two points [tex]A(x_1,y_1)[/tex] and [tex]B(x_2,y_2)[/tex] is given by the formula,
[tex]AB= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2 }[/tex]
Proof: Let X'OX and YOY' be the x-axis and y-axis respectively. Then, O is the origin.
Let[tex]A(x_1,y_1) [/tex] and [tex]B(x_2,y_2)[/tex]
be the given points.
Draw AL perpendicular to OX, BM perpendicular to OX and AN perpendicular to BM
Now,[tex]OL=x_1,OM=x_2,AL=y_1 \: and \: BM=y_2[/tex]
[tex] \therefore{AN=LM=(OM-OL)=(x_2-x_1)}[/tex]
[tex] \: \: \: BN=(BM-NM)=(BM-AL)=(y_2-y_1)[/tex]
In right angled triangle [tex] \triangle \: ANB[/tex],by Pythagorean theorem,
We have,
[tex] \: \: \: AB^2=AN^2+BN^2[/tex]
[tex]or,AB^2=(x_2-x_1)^2+(y_2-y_1)^2[/tex]
[tex] \therefore \: AB= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} [/tex]
Thus ,the distance between the points A(x_1,y_1) and B(x_2,y_2) is given by,
[tex] \implies \boxed{AB= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }[/tex]
Identify the segments that are parallel, if any, if ∠EDA≅∠HCB.
In the above question, (image attached) The option that shows the segments that are parallel, if any, if ∠EDA≅∠HCB is option A: None of these.
What is the line segment about?Note that by examining the the image if ∠EDA≅∠HCB, the two lines can never intersect even if they go a longer distance.
The reason why is that there are no parallel lines on it and as such, they cannot intercept.
Hence, In the above question, (image attached) The option that shows the segments that are parallel, if any, if ∠EDA≅∠HCB is option A: None of these.
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Divide 24x2y + 8xy2 + 8xy by -4xy.
What is the quotient?
The quotient of 24x2y + 8xy2 + 8xy and -4xy is -6x - 2y - 2
How to determine the quotient?The statement is given as:
Divide 24x2y + 8xy2 + 8xy by -4xy
The quotient is represented as:
Quotient = (24x^2y + 8xy^2 + 8xy)/(-4xy)
Factor out -4xy
Quotient = (-4xy)(-6x - 2y - 2)/(-4xy)
Evaluate the quotient
Quotient = -6x - 2y - 2
Hence, the quotient of 24x2y + 8xy2 + 8xy and -4xy is -6x - 2y - 2
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How many ways can 8 people stand in a line if Alice and Bob refuse to stand next to each other.
Answer:
there are 6 people that need to sit down so let's see how we can fill those seeds we will start while finding seats for Alice and bob they can't sit next to each other so will remove one of the seeds them both in the remaining 5 then at a seat between them to ensure that they are not next to each other they are 5 ways to choose seat and 4 ways from those that we make giving 20 ways to seats
Step-by-step explanation:
once a lies and verb are ct we can arrange the remaining people in 4 is equal to 24 west in each other four seats for the total of 20 into 24 4 80 ways to seat everyone
Let sine of theta equals the quantity 2 times radical 2 end quantity over 5 and pi over 2 is less than theta is less than pi. determine the exact value of sine of the quantity theta over 2 end quantity.
The exact value of the trigonometric relation sin(θ/2) is √[(1 + √(17)/5)) / 2]
Given data:
The trigonometric relation is :
sin(θ) = (2√2) / 5 and π/2 < θ< π
Using the half-angle identity for sine:
sin(θ/2) = ± √[(1 - cos(θ)) / 2]
To determine the sign, look at the quadrant in which theta lies. Since π/2 < θ< π, θis in the second quadrant, where the sine function is positive. Therefore, we take the positive sign.
Now, let's calculate the cosine of θ. Using the Pythagorean identity for sine and cosine, we have:
sin²(θ) + cos²(θ) = 1
(2√2/5)² + cos²(θ) = 1
8/25 + cos²(θ) = 1
cos²(θ) = 1 - 8/25
cos²(θ) = 17/25
Taking the square root:
cos(θ) = ± √(17)/5
Since theta is in the second quadrant, take the negative sign:
cos(θ) = -√(17)/5
Now, substituting the values into the half-angle identity, we get:
sin(θ/2) = ± √[(1 - cos(θ)) / 2]
sin(θ/2) = ± √[(1 - (-√(17)/5))) / 2]
sin(θ/2) = ± √[(1 + √(17)/5)) / 2]
Since θ is in the second quadrant, where the sine function is positive, take the positive sign:
sin(θ/2) = √[(1 + √(17)/5)) / 2]
Therefore, the exact value of sin(θ/2) is √[(1 + √(17)/5)) / 2].
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