The hydrostatic force on the window is approximately 47,481 Newtons.
We can use the formula for hydrostatic force, which is:
F = ρghA
where F is the hydrostatic force, ρ is the density of the fluid (water in this case), g is the acceleration due to gravity, h is the depth of the window, and A is the area of the window.
First, we need to find the area of the window. Since the window is a semi-circle with diameter 70 centimeters, the radius is 35 centimeters, and the area is:
A = (π/2)r^2
= (π/2)(35 cm)^2
= 1225π/2 cm^2
Next, we need to convert the depth of the window to meters:
h = 2.5 m
We also need the density of water, which is approximately:
ρ = 1000 kg/m^3
Finally, we need the acceleration due to gravity, which we can assume is:
g = 9.8 m/s^2
Now we can plug these values into the formula:
F = ρghA
= (1000 kg/m^3)(9.8 m/s^2)(2.5 m)(1225π/2 cm^2)
≈ 47,481 N
Therefore, the hydrostatic force on the window is approximately 47,481 Newtons.
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What are the plotting points?
Answer: plot points (0,-2) (1.-5) (2.-8) (-1.1) (-2.1) makes a upside down V
-3|0+2|+4=-2
-3|1 +2|+4= -5
-3|2+2|+4= -8
-3|-1+2|+4=1
+3|-2+2|+4=1
Step-by-step explanation:
Julian wants to ride his bicycle 20.6 miles this week. He has already ridden 8 miles. If he rides for 3 more days, write and solve an equation which can be used to determine xx, the average number of miles he would have to ride each day to meet his goal.
Answer:
Step-by-step explanation:
Our equation will be 3x+8=20.6
3x=12.6
x=4.2
For what value of mc009-1 is the function one-to-one?
(1, 2), (2, 3), (3, 5), (4, 7), (5, 11), (6, c)
2
5
11
13
Using the concept of an one-to-one function, it will be one-to-one for c = 13.
What is an one-to-one function?A function is said to be one-to-one if each output is mapped to only one input.
In this problem, outputs 2, 5 and 11 have already been matched to inputs 1, 3 and 5, respectively, hence the output for input 6 has to be c = 13 for a one-to-one function.
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Fyodor and his three sons, Ivan, Dmitri and Alyosha, are standing exactly on the corners of a rectangular room. Fyodor is $3$ meters from Dmitri and $5$ meters from Ivan. What is the minimum possible distance that Fyodor could be from Alyosha, in meters
The minimum possible distance that Fyodor could be from Alyosha is 4 meters.
Given Information and Deduction
It is given that Fyodor is 3 meters in distance away from Dmitri and 5 meters from Ivan.
Now, since we know that the longest side of a right angle triangle formed by the dividing the rectangular room into two parts using a diagonal is the hypotenuse. Thus, if we want to find the minimum possible distance between Fyodor and Alyosha, we will have to assume that Ivan is standing diagonally opposite to Fyodor, as shown in the figure below.
Calculating the Minimum Distance
According to Pythagoras Theorem,
(hypotenuse)² = (base)² + (perpendicular)²
Here, the hypotenuse is the distance between Fyodor and Ivan.
Perpendicular and the base are the distances between Fyodor and Dmitri, and Fyodor and Alyosha respectively.
⇒ base = √(hypotenuse)² -(perpendicular)²
⇒ base = √(5)²-(3)²
⇒ base = √(25-9)
⇒ base = √16
⇒ base = 4 meters
Therefore, the minimum possible distance between Fyodor and Alyosha is 4 meters.
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120 is increased by b% then increased by 25%. What is the result?
Answer:
150 + 1.5d
Step-by-step explanation:
increase 120 by d%
d% = d/100
So, increasing 120 by d % means
120 + (d/100 * 120)
= 120 + 1.2d
Then increase this by 25%
= (120 + 1.2d) + 25/100(120 + 1.2d)
= 120 + 1.2d + (120+1.2d)/4
= 120 + 1.2d + 30 + 0.3d
= 120 + 30 + 1.2d + 0.3d
= 150 + 1.5d
Which represents the inverse of the function f(x) = 4x?
O h(x) = x + 4
O h(x) = x -4
O h(x) = 3/4x
O h(x) = 1/4x
Answer:
last answer:
h(x) = 1/4 x
Step-by-step explanation:
First, change f(x) to y.
f(x) = 4x
y = 4x
Then switch the x and y.
y = 4x
x = 4y
Last, solve for y.
x = 4y
x/4 = 4y/4
x/4 = y
y = x/4
This is the same as:
y = 1/4 x
h(x) = 1/4 x
We can learn a lot about a population if we select a ______ of it. Group of answer choices population subset data set case
We can learn a lot about a population if we select a subset of it.
What is a subset?One kind of set is a sample space. It is a clear listing of every event that could occur in a statistical experiment. A statistical experiment's events are a subset of the sample space.
A subset is a smaller group of results that are part of the bigger group.
Subsets are events, and events are subsets. A subset is an event of a sample space, and an event is a potential result of an experiment. A random experiment's sample space is a set (S) that contains all of the experiment's potential outcomes.
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The following statistics describe the hourly wages paid by two firms. Firm A Firm B Sample size 50 40 Sample mean $16.5 $16 Population standard deviation $0.9 $0.85 The test statistic used to evaluate whether there is any significant difference between the mean hourly wages is:
The t-test statistic is used to evaluate whether there is any significant difference between the mean hourly wages.
What is t-test?To evaluate whether there is a statistically significant difference between the means of two variables, a t-test is an inferential statistic that is utilized.
A statistical test for assessing hypotheses is the t-test.
The difference between the means from each data set, the standard deviation of each group, and the total number of data values are the three basic data values needed to do a t-test.
There are independent and dependent T-tests.
The problem statement is established mathematically by using a sample from each of the two sets in the t-test. It presupposes that the two means are equal, which is the null hypothesis.
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PLEASE HELP IM SUPER STUCK
Answer:
27 cm³
Step-by-step explanation:
To find the volume, multiply the length, the width, and the depth together.
3*3*3=27
The volume of the cube is 27 cm³
Hope this helps!
Which geometric series results in a sum of -69, 905?
O A.
SOB.
O C.
O D.
10
k=0
(-4)*
- }(4) *
Σ-1(5)
k=0
Σ 1 (-5)*
k=0
The geometric series which result in a sum of -69,905 is: D. [tex]\sum^{9}_{k=0} -\frac{1}{5} (4)^k[/tex]
The standard form of a geometric series.Mathematically, the standard form of a geometric series can be represented by the following expression:
[tex]\sum^{n-1}_{k=0}a_1(r)^k[/tex]
Where:
a₁ is the first term of a geometric series.r is the common ratio.Also, the sum of a geometric series is given by:
[tex]S=\frac{a_1(1-r^n)}{1-r}[/tex]
For option A, we have:
r = -5, n = 8, a₁ = 1/4 = 0.25
[tex]S=\frac{0.25(1-(-5)^8)}{1-(-5)}[/tex]
S = -24,414.
For option B, we have:
r = 5, n = 12, a₁ = -1/4 = -0.25
[tex]S=\frac{-0.25(1- 5)^{12})}{1-5}[/tex]
S = -15,258789.
For option C, we have:
r = -4, n = 11, a₁ = 1/5 = 0.2
[tex]S=\frac{0.2(1-(-4)^{11})}{1-(-4)}[/tex]
S = -279,620.
For option D, we have:
r = 4, n = 10, a₁ = -1/5 = -0.2
[tex]S=\frac{-0.2(1-4^{10})}{1-4}[/tex]
S = -69,905.
In conclusion, the geometric series which result in a sum of -69,905 is [tex]\sum^{9}_{k=0} -\frac{1}{5} (4)^k[/tex]
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Find the sum.
10+12+14+...+78
Answer:
1540
Step-by-step explanation:
This is an arithmetic progression.
a = first term = 10
Common difference = d = second term - first term
= 12 - 10
d = 2
Last term = l = 78
First we have to find how many terms are there in the sequence using the formula: l = a + (n-1)*d
78 = 10 + (n -1) * 2
78 -10 = (n -1)*2
68 = (n -1) *2
68 ÷2 = n -1
34 = n - 1
34 + 1 = n
n = 35
There are 35 terms.
[tex]\sf \boxed{\test{\bf Sum = $\dfrac{n}{2}(a +l)$}}[/tex][tex]\sf \boxed{\text{\bf Sum =$\dfrac{n}{2}(a+l) $}}[/tex]
[tex]\sf =\dfrac{35}{2}(10+78)\\\\ =\dfrac{35}{2}*88\\\\ = 35 * 44\\\\= 1540[/tex]
Step-by-step explanation:
This is an arithmetic progression.
a = first term = 10
Common difference = d = second term - first term
= 12 - 10
d = 2
Last term = l = 78
First we have to find how many terms are there in the sequence using the formula: l = a + (n-1)*d
78 = 10 + (n -1) * 2
78 -10 = (n -1)*2
68 = (n -1) *2
68 ÷2 = n -1
34 = n - 1
34 + 1 = n
n = 35
There are 35 terms.
\sf \boxed{\test{\bf Sum = $\dfrac{n}{2}(a +l)$}} \sf \boxed{\text{\bf Sum =$\dfrac{n}{2}(a+l) $}}
Sum =
2
n
(a+l)
\begin{gathered}\sf =\dfrac{35}{2}(10+78)\\\\ =\dfrac{35}{2}*88\\\\ = 35 * 44\\\\= 1540\end{gathered}
=
2
35
(10+78)
=
2
35
∗88
=35∗44
=1540
What is the solution for the compound 5/2+x>1/3 or x+2 < -29/6
Answer:
x < -41/6 or x > -13/6.
Step-by-step explanation:
5/2+x>1/3
x > 1/3 - 5/2
x > 2/6 - 15/6
x > -13/6
x+2 < -29/6
x < -29/6 - 2
x < -41/6
The answer is x < -41/6 or x > -13/6.
Answer:
x > -13/6 or x < -41/6
Step-by-step explanation:
5/2+x>1/3 or x+2 < -29/6
x > 1/3 - 5/2 or x < -29/6 - 2
x > 2/6 - 15/6 or x < -29/6 - 12/6
x > -13/6 or x < -41/6
Simplify.
Rewrite the expression in the form y^n.
(y^2)^3 =
Answer:
[tex]y^6[/tex]
Step-by-step explanation:
So there is an exponent identity that states: [tex](x^b)^a = x^{a*b}[/tex] which means this question becomes: [tex](y^2)^3 = y^{2*3} = y^6[/tex].
Just so you completely understand why this works, it might help to express y^2, as what it truly represents: [tex]y^2=y*y[/tex]. So using this definition we can substitute it into the equation so it becomes: [tex](y*y)^3[/tex]. Now let's use the definition of exponents like we just did with the y, to redefine this in terms of multiplication: [tex](y*y)^3 = (y * y) * (y * y) * (y * y)[/tex]. We can just multiply all these out, and we get: [tex]y * y * y * y * y * y =y^6[/tex].
To make it a bit more general when we have the exponent: [tex]x^b[/tex] it can be expressed as: [tex](x*x*x...\text{ b amount of times})[/tex] now when we raise it to the power of a. we get: [tex](x * x * x...\text{ b amount of times})^a[/tex] which can further be rewritten using the definition of an exponent to become the equation: [tex](x*x*x\text... \text{ b amount of times}) * (x * x * x...\text{ b amount of times})...\text{ a amount of times}[/tex] which just simplifies to: [tex]x*x*x*x...\text{ a times b amount of times}[/tex]. Hopefully this makes the identity a bit more understandable
math related!!!!! Pls help look at pic >>>>>
Manju and Arif are playing a game in which one of them thinks of a number from the grid shown
below and the other has to guess it using some clues that are given. Manju thinks of a number
and gives the following clues:
It is a multiple of 3.
It is even.
It is in the third row.
What is Manju's number?
The number from the grid that fulfills all the given clues is; 12
How to find the multiple of a number?
The grid is shown in the attached image.
Now, we are told that Manju and Arif are thinking of a number on the grid and the clues are;
It is a multiple of 3.
It is even.
It is in the third row.
Now, looking at the third row, we see the numbers as;
11, 12, 13, 14, 15
Now, the only number that fulfills all the given clues is 12.
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A desk is on sale for $595, which is 32% less than the regular price. What is the regular price?
Answer:
875
Step-by-step explanation:
1-0.32=0.68 so its 0.68 of its original price.
x*0.68=595 x is the original price
x=595/0.68
x=875
Wright in point-slope form, slope-intercept form and in standard form an equation that passes through (-1, 2) with slope 4
Point-slope form
[tex]y-2=4(x+1)[/tex]
Slope-intercept form
[tex]y-2=4x+4 \\ \\ y=4x+6[/tex]
Standard form
[tex]4x-y+6=0[/tex]
Answer:
[tex]\textsf{Point-slope form}: \quad \sf y-2=4(x+1)[/tex]
[tex]\textsf{Slope-intercept form}: \quad \sf y=4x+6[/tex]
[tex]\textsf{Standard form}: \quad \sf 4x-y=-6[/tex]
Step-by-step explanation:
Given information:
Slope = 4Point on line = (-1, 2)Point-slope form of linear equation:
[tex]\sf y-y_1=m(x-x_1)[/tex]
(where m is the slope and (x₁, y₁) is a point on the line)
Substitute the given slope and point into the formula:
[tex]\implies \sf y-2=4(x-(-1))[/tex]
[tex]\implies \sf y-2=4(x+1)[/tex]
Slope-intercept form of a linear equation:
[tex]\sf y=mx+b[/tex]
(where m is the slope and b is the y-intercept)
Substitute the given slope and point into the formula and solve for b:
[tex]\implies \sf 2=4(-1)+b[/tex]
[tex]\implies \sf b=6[/tex]
Therefore:
[tex]\sf y=4x+6[/tex]
Standard form of a linear equation:
[tex]\sf Ax+By=C[/tex]
(where A, B and C are constants and A must be positive)
Rearrange the found slope-intercept form of the equation into standard form:
[tex]\implies \sf y=4x+6[/tex]
[tex]\implies \sf 4x-y+6=0[/tex]
[tex]\implies \sf 4x-y=-6[/tex]
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in order to solve the following system of equations by subtraction, which of the following could you do before subtracting the equations so that one variable will be eliminated when you subtract them?
4x-2y=7
3x-3y=15
The following system of equation can be solved by first substituting the dependent variable in the other equation . The solution yields x = -1.5 and y = 6.5 .
What is the solution of the given system of equation ?The two equations are given as -
4x-2y=7
3x-3y=15
First substituting the value of x from the first equation and then putting that value in the second equation for the following system of equation.
From first equation,
⇒ 4x = 7 + 2y
∴ x = (7 + 2y)/4
Putting this value of x in second equation,
⇒ 3*(7 + 2y)/4 - 3y = 15
⇒ 3*(7 + 2y) - 12y = 60
⇒ 21 + 6y - 12y = 60
⇒ -6y = 39
∴ y = -6.5
∴ x = (7 + 2y)/4 = -1.5
Thus x = -1.5 and y = -6.5
Therefore, the following system of equation can be solved by first substituting the dependent variable in the other equation . The solution yields x = -1.5 and y = 6.5 .
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8. A can do a piece of work in 16 days, B in 10 days. A and B work at it together for 6 days and then C finishes it in 3 days. In how many days could C have done it alone? (a) 120 days (c) 140 days (b) 130 days (d) 150 days
Answer: 120 days
Step-by-step explanation:
A can complete it in 16 days.
=100/16 =6.25%/day.
B has ten days to do it.
10% every day is equal to 100/10.
So they would each contribute 16.25 percent per day as a group.
then for six days,
16.25*6 =97.50percent
97.50% of the work has been finished, in other words.
The amount of work left is now 100-97.5 = 2.5.
C finishes up the remaining job in 3 days
3.5% in 3 days, to be exact.
Consequently, he will finish his entire project in 120 days.
[2.5 * 40 = 100 percent; 40 * 3 = 120 days]
Multiply two and six eighths multiplied by six.
A. fourteen and five eighths
B. sixteen and two eighths
C. sixteen and four eighths
D. seventeen and three eighths
Answer:
C . Sixteen and four eighths.
Step-by-step explanation:
2 6/8 * 6
= 22/8 * 6
= 6*22 / 8
= 132/8
= 16 4/8.
WILL VOTE BRAINLIEST FOR THE FIRST RIGHT ANSWER
Answer:
last choice
Step-by-step explanation:
The domain is the set of x values: from -3 to 3.
The range is the set of y values: from 1 to 10.
Answer: last choice
Suppose you are saving your money to pay for a vacation for your family. so far, you have saved. you plan on saving more each month so you can pay for the vacation at the end of the year. assume that you save more each month than the previous month.
part a: write a formula that would show the amount you will have saved after year.
part b: if the vacation costs a total of , will you be able to pay for it after year?
part c: explain why or why not. show your work to support your answer.
440 repeat 11 more times.
400+(400*.1)=440 repeat 11 more times. Remember to use a new value each time.
Vacations can get expensive fast. The average cost per person for a week-long vacation is about $1,200 annually. So, if you've got a family of five, you'll need to sock away at least $6,000 for transportation, hotels, meals, and amusement parks.
Financial experts suggest that the average family vacation costs between 5-10% of your total income. If your family makes $40,000 per year then experts say your yearly family vacation budget should average between $2,000-$4000.
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Find 0 Round to the nearest degree.
OA. 68°
OB. 69°
OC. 22°
OD. 21°
Answer:
A
Step-by-step explanation:
[tex]\cos \theta=\frac{3}{8} \\ \\ \theta=\cos^{-1} \left(\frac{3}{8} \right) \\ \\ \theta \approx 68^{\circ}[/tex]
A score that is three standard deviations above the mean would have a z score of
a. -3
b. 3
c. 0
d. 1
The value of z-score for a score that is three standard deviations above the mean is 3.
In this question,
A z-score measures exactly how many standard deviations a data point is above or below the mean. It allows us to calculate the probability of a score occurring within our normal distribution and enables us to compare two scores that are from different normal distributions.
Let x be the score
let μ be the mean and
let σ be the standard deviations
Now, x = μ + 3σ
The formula of z-score is
[tex]z_{score} = \frac{x-\mu}{\sigma}[/tex]
⇒ [tex]z_{score} = \frac{\mu + 3\sigma -\mu}{\sigma}[/tex]
⇒ [tex]z_{score} = \frac{ 3\sigma }{\sigma}[/tex]
⇒ [tex]z_{score} = 3[/tex]
Hence we can conclude that the value of z-score for a score that is three standard deviations above the mean is 3.
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Explain why Rolle's Theorem does not apply to the function even though there exist a and b such that f(a)
Rolle's Theorem does not apply to the function because there are points on the interval (a,b) where f is not differentiable.
Given the function is [tex]f(x)=\sqrt{(2-x^{\frac{2}{3}})^{3}}[/tex] and the Rolle's Theorem does not apply to the function.
Rolle's theorem is used to determine if a function is continuous and also differentiable.
The condition for Rolle's theorem to be true as:
f(a)=f(b)f(x) must be continuous in [a,b].f(x) must be differentiable in (a,b).To apply the Rolle’s Theorem we need to have function that is differentiable on the given open interval.
If we look closely at the given function we can see that the first derivative of the given function is:
[tex]\begin{aligned}f(x)&=\sqrt{(2-x^{\frac{2}{3}})^3}\\ f(x)&=(2-x^{\frac{2}{3}})^{\frac{3}{2}}\\ f'(x)&=\frac{3}{2}(2-x^{\frac{2}{3}})^{\frac{1}{2}}\cdot \frac{2}{3}\cdot (-x)^{\frac{1}{3}}\\ f'(x)&=\frac{-\sqrt{2-x^{\frac{2}{3}}}}{\sqrt[3]{x}}\end[/tex]
From this point of view we can see that the given function is not defined for x=0.
Hence, all the assumptions are not satisfied we can reach a conclusion that we cannot apply the Rolle's Theorem.
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Which of the following polynomials has a remainder of 24 when divided by x+2?
A. 4x3+2x2+5
B. 3x3+6x−2
C. −2x3+4x2+3x−2
D. x3−2x2−4x+1
Option C is the correct choice [tex]-2x^4+4x^2+3x-2[/tex],
Remainder of a polynomial by substitution
For a polynomial f(x) to give a remainder of 24 when divided by x + 2:
f(-2) = 24
By testing, substitute x = -2 into the equation [tex]-2x^4+4x^2+3x-2[/tex]
[tex]f(x) = -2x^3+4x^2+3x-2\\\\f(-2)=-2(-2)^3+4(-2)^2+3(-2)-2\\\\f(-2)=-2(-8)+4(4)-6-2\\\\f(-2)=16+16-8\\\\f(-2)=32-8\\\\f(-2)=24[/tex]
Since f(-2) = 24 when x = -2 is substituted into [tex]-2x^4+4x^2+3x-2[/tex], then [tex]-2x^4+4x^2+3x-2[/tex] has a remainder of 24 when divided by x+2
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I cant figure this out
The length and width of the rectangle with an area of 120 units² are 12 units and 10 units respectively.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the width, hence:
length = x + 2
The area of a rectangle is the product of its length and its width.
Area = length * width
Area = x(x + 2)
120 = x² + 2x
x² + 2x - 120 = 0
x = 10, length = 10 + 2 = 12
The length and width of the rectangle with an area of 120 units² are 12 units and 10 units respectively.
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When bowling, the scoring rule for a spare is 10 points and then the points scored in the next delivery. Group of answer choices True False
The given statement is True for the scoring rule in bowling.
Scoring Rule in Bowling
The number of frames in a game of bowling is ten. According to the scoring rule in bowling, the bowler will have two opportunities to use their bowling ball to remove as many pins as they can throughout each frame.
Every bowler will complete their frame in a predefined order before the next frame starts in games with more than one bowler, which is typical.
Rule for Spare
A bowler is given a strike if they can remove all 10 pins with their first ball. A spare is achieved when the bowler uses both of the two balls in a frame to remove all 10 pins.
Depending on whether the next two balls (for a strike) or the next ball (for a goal) are scored, bonus points are given for both of these (for a spare), as per the scoring rule.
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What are the coordinates of vertex A of square ABCD
A(-1,-6)
B(-1,-2)
C(-1,6)
D(-2,1)
The given points on the final image A''B''C''D'', and the transformation gives;
The coordinates of the vertex A of square ABCD is the option;
D. A(-2, 1)
How can the coordinate of the point A on the pre-image be found?From the figure, we have;
A''(-5, -3), B''(-3, -1), C''(-1, -3), D''(-3, -5)
The given transformation is presented as follows;
[tex] T_{ (- 4 , \: - 1)} \circ \:R_ {( O , \: 90^{ \circ} )}[/tex]
The formula for a rotation of 90° about the origin is presented as follows;
(x, y) rotation of 90°→ (-y, x)Therefore;
(-y, x) reverse rotation of 90°→ (x, y)Therefore;
A''(-5, -3) → A'(-5 + 4, -3 + 1) = A'(-1, -2)
B''(-3, -1) → B'(-3 + 4, -1 + 1) = B'(1, 0)
C''(-1, -3) → C'(-1 + 4, -3 + 1) = C'(3, -2)
D''(-3, -5) → D'(-3 + 4, -5 + 1) = D'(1, -4)
A'(-1, -2) rotation of 90° reverse → A(-2, 1)The coordinates of the vertex A of square ABCD is therefore;
D. A(-2, 1)
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Square A"B"C"D" has vertex A" at (-5, -3), the coordinates of vertex A before the transformation is A(-2, 1)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Rigid transformation is a transformation that preserves the shape and size of a figure such as translation, reflection and rotation.
Square A"B"C"D" has vertex A" at (-5, -3), the coordinates of vertex A before the transformation is A(-2, 1)
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Answer:
7.7 km
Explanation:
Use cosine rule as here given two sides and one angle.
Cosine rule states:
a² = b² + c² - 2bc cos(A)
While solving, treat a = 7.5 km as to that opposite angle is given of 68°
then b = missing side, c = 5.2 km, A = 68°
Applying rule:
7.5² = b² + 5.2² - 2(b)(5.2) cos(68)
56.25 = b² + 27.04 - 3.8959b
56.25 - 27.04 = b² - 3.8959b
b² - 3.8959b = 29.21
b² - 3.8959b - 29.21 = 0
apply quadratic equation, Here [a = 1, b = - 3.8959, c = -29.21]
[tex]\sf b = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad\:when \:\ ax^2 + bx + c = 0[/tex]
[tex]\sf b = \dfrac{ -(-3.8959) \pm \sqrt{(-3.8959)^2 - 4(1)(-29.21)}}{2(1)}[/tex]
[tex]\sf b = 7.69 291 \quad or \quad b = -3.797[/tex]
[tex]\sf b = 7.7 \quad (rounded \ to \ nearest \ tenth)[/tex]
As length cannot be negative. Hence the value of b is only 7.7 km
The answer is 7.7 km.
Let's apply the Cosine Law in this situation.
a² = b² + c² - 2bc cos(A)
Now, substitute the values based on the given diagram.
(7.5)² = b² + (5.2)² - 2(b)(5.2)(cos 68°)56.25 = b² + 27.04 - 3.896bb² - 3.896b - 29.21 = 0Here, using the Quadratic Equation, we can solve :
b = 3.896 ± √(3.896)² - 4(1)(-29.21) / 2b = 3.896 ± √15.178816 + 116.84 / 2b = 3.896 ± √132.018816 / 2b = 3.896 + 11.49 / 2b = 7.7 km