The diameter of a circle with a circumference of 69.1 yds is 22.
What is circumference of a circle?
The measurement of the circle's perimeter, also known as the circle's boundary, is called its circumference . The radius of the circle is considered when applying the formula to determine the circumference of the circle.
Circumference of circle(C) = 2πR
where,
R represents the radius of the circle
We know that diameter of circle is twice of its radius i.e
Diameter(D) = 2R
Thus, C = πD
We are given Circumference(C) = 69.1yd and π= 3.14
So, using C = πD, we get
⇒69.1 = 3.14*D
⇒D = 69.1/3.14
⇒D = 22
Hence, the diameter of a circle with a circumference of 69.1 yds is 22.
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Use implicit differentiation to find
∂z/∂x and ∂z/∂y.
e^9z = xyz
e6z = xyz, implicit differentiation of the following equation-
What are equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value
To determine the value A statement is not an equation if it has no "equal to" sign.
A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.
According to our question-
Given e6z = xyz
To find ∂z/∂x → consider z as a function of x and take y to be a constant
So differentiating with respect to x, we get
e6z × 6 × ∂z/∂x = z × y + xy × 1 × ∂z/∂x
[using the chain rule on the LHS and the product rule on the RHS]
Factor out the ∂z/∂x:
∂z/∂x [6e6z - xy] = yz
∂z/∂x = yz / [6e6z - xy]
Do the same thing to find ∂z/∂y except consider z to be a function of y and take x to be a constant
Differentiating with respect to y:
e6z × 6 × ∂z/∂y = z × x + xy × 1 × ∂z/∂y
∂z/∂y [6e6z - xy] = xz
∂z/∂y = xz / [6e6z - xy]
Therefore, ∂z/∂x = yz / [6e6z - xy] and ∂z/∂y = xz / [6e6z - xy]
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In which month was the peak, the largest deposit, made? January June July August
The peak, the largest deposit, made in July
It's the tallest one in the plot.
Let's arrange the number from smallest to greatest:
50<80=80<95<100<110<250<300<320
Jan<Feb=Sep<May<Apr<Mar<June<Aug<July
So, the greatest amount of deposit was in July.
These trades took place between June and August 2020. June 1 After giving it some deliberation, Natalie decides to offer Curtis a mixer for $1,150 (mixer cost: $620) on credit with terms of n/30. 30 Curtis gives Natalie a call. He signs a one-month, 8.35% note payable since he won't be able to pay the sum due for another month. Curtis calls on July 31.
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Solve the proportion.
x/12 = 3/8
Response:
x = _____
Answer:
Step-by-step explanation:
x / 12 = 3 / 8
x = 3 / 8 x 12
x = 3 / 94
x = 32
32 / 12 = 3 / 8
how many integers $n$ less than $1000$ can be written as the sum of $j$ consecutive positive odd integers from exactly 5 values of $j\ge 1$?
The number of integers N less than 1000 that can be written as the sum of j consecutive positive odd integers from exactly 5 values of j ≥ 1 is 15.
Arithmetic sequence is a sequence of numbers/terms that has a fixed pattern, based on the operation of subtraction or addition. Thus, each sequence of numbers will have a common difference.
Formula: aₙ = a₁ + (a - 1)d,
where aₙ is the nᵗʰ term and a₁ is the first term in the sequence, and d is the common difference between terms
Sum of n terms = n (a₁ + aₙ) / 2
We want to know the number of integers N less than 1000 that can be written as the sum of j consecutive positive odd integers from exactly 5 values of j ≥ 1
First, we determine:
- the first odd integer in the list: 2n + 1, where n ≥ 1
- the last odd integer in the list: 2n + 1 + 2(j - 1) = 2(n + j) - 1
These odd integers form a sequence with the following sum:
N = n (a₁ + aₙ) / 2
= j (2n + 1 + 2(n + j) - 1) / 2
= j (2n + 1 + 2n + 2j - 1) / 2
= j (4n + 2j) / 2
= j (2n + j)
We also know that there are exactly 5 values of j that satisfy the equation, there must be either 9 or 10 factors of N.
This means N = p₁².p₂² or N = p₁.p₂⁴
If N is odd, then j is also odd, which means that 2n+j is also odd. It is valid for all odd j. Given the boundary of 1000, the possibilities of odd N are (3².5²), (3².7²), (3⁴.5), (3⁴.7), and (3⁴.11) ---> 5 possibilities
If N is even, then j is also even. If we substitute j = 2k into the N, we get:
N = j (2n + j)
= 2k (2n + k)
= 4k (n + k)
N/4 = k (n + k)
This formula implies that the new upper bound is 250. So the possibilities of even N are (2².3²), (2².5²), (2².7²), (3².5²), (2⁴.3), (2⁴.5), (2⁴.7), (2⁴.11), (2⁴.13), and (3⁴.2) ---> 10 possibilities
Thus, the total number of integer N is 5 + 10 = 15
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a point $(3\sqrt{5},d 3)$ is $3d$ units away from the origin. what is the smallest possible value of $d$?
If the point (3√5,d+3) is 3d Units away from the origin , then the smallest possible value of d is 3 .
The point (3√5,d+3) is 3d Units away from the origin , that means ,
the distance between the points (0,0) and (3√5,d+3) is 3d units ;
By using the distance formula , the given situation can be represented as
⇒ [tex](3d)^{2} =(3\sqrt{5} -0)^{2} + (d+3)^{2}[/tex] ;
On simplifying the equation ,
we get ;
⇒ [tex]9d^{2} = 45+d^{2} +6d+9[/tex] ;
⇒ [tex]4d^{2} -3d--27 = 0[/tex] ;
Writing in factor form ,
we get ;
⇒ [tex](4d+9)(d-3)= 0[/tex] ;
On solving we have [tex]d=-\frac{9}{4}[/tex] and [tex]d=3[/tex] .
Since the distance is only positive , So we can write d = 3 ;
Therefore , the smallest possible value of d is 3 .
The given question is incomplete , the complete question is
A point (3√5,d+3) is 3d Units away from the origin. What is the smallest possible value of d ?
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How many protons does tin-112 have? responses 12 12, 50 50, 62 62, 112
Answer:
50
Step-by-step explanation:
A baby weigh 3. 35 kilogram at birth. Suppoe the baby' weight contantly increae every two month by 1. 2 kilogram, what i hi weight in the ame unit in the 6th month?
After 6 months of birth the weight will become 6.95 kg.
A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set.
from given condition, a baby weigh 3. 35 kilogram at birth and the baby weight constantly increase every two month by 1. 2 kilogram.
so, the weight after 2 months of birth is 3.35 kg + 1.2 kg = 4.55 kg
and the weight after 4 months of birth is 4.55 kg + 1.2 kg = 5.75 kg
and the weight after 6 months of birth is 5.75 kg + 1.2 kg = 6.95 kg
Therefore, after 6 months of birth the weight will become 6.95 kg.
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my three-digit code is . reckha can't choose a code that is the same as mine in two or more of the three digit-positions, nor that is the same as mine except for switching the positions of two digits (so and , for example, are forbidden, but is fine). reckha can otherwise choose any three-digit code where each digit is in the set . how many codes are available for reckha?
9,900 codes that are available for reckha.
There are a total of 10,000 possible three-digit codes when each digit is in the set {0,1,2,3,4,5,6,7,8,9}. Since each digit can take 10 different values, we can use the formula 10^3 = 1000 to calculate the total number of codes.
However, since reckha cannot choose a code that is the same as yours or one that is the same as yours except for switching the positions of two digits, we have to subtract these possibilities from the total. We can calculate the number of codes forbidden by subtracting the number of codes with the same digits in all three positions (10) and the number of codes with the same digits but different positions (90) from the total. This leaves us with 10,000 - (10 + 90) = 9,900 codes that are available for reckha.
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A car travels the 200 miles along the M1 from London to Leeds. The car leaves London at 8am and travels at a constant speed of 60mph for the first 60 miles. The driver takes a break of 30mins at a motorway services before continuing the journey at a constant speed of 70mph a) Draw a distance-time graph of the journey
Answer:
I can provide you with a description of the graph.
The graph would have the distance on the y-axis and the time on the x-axis.
The first 60 miles of the journey would be represented by a straight line with a slope of 60/1=60, since the car is traveling at a constant speed of 60 mph.
The point where the first 60 miles ends would be (1,60) which is the time of one hour from London, the distance of 60 miles from London.
After the 30-minute break at the motorway services, the car would continue its journey at a constant speed of 70 mph. This part of the journey would be represented by a straight line with a slope of 70/1=70.
The point where the whole journey ends would be (4,200) which is the time of 4 hours from London, the distance of 200 miles from London.
Please note that it is assumed that the car doesn't stop during the second part of the journey.
Given that a is an odd multiple of 1183, find the greatest common divisor of 2a^2+29a+65 and a+13
The solution is 26, since gcd (26, a + 13) = 26 when a = 1183k, and k = 1,3,5,7,9...
Let d = [tex](2a^{2} +29a + 65, a+ 13)[/tex]
Now, we can split [tex]2a^{2} + 29a + 65[/tex] in the following way, so that it becomes easier to factorise.
[tex]2a^{2} + 29a + 65 = (2a^{2} + 29a + 39) + 26[/tex]
From this, we can quantify and notice that -13 is one root of this equation, while the other root is -3/2.
Therefore, [tex]2a^{2} + 29a + 39 = (a+13)(2a+3)+26[/tex]
Thus, [tex]d = ((a+13)(2a+3)+26, a+ 13)[/tex]
The greatest common divisor (GCD) of two or more numbers is the greatest common factor number that divides them, exactly. It is also called the highest common factor (HCF).
Now, we can use Euclid's Algorithm.
[tex]= gcd (2a^{2} + 29a + 65, a + 13)\\= gcd (2a^{2} + 29a + 65 - 2a(a+13), a+13)\\= gcd (3a + 65, a + 13)\\= gcd (3a + 65 - 3a(a+13), a+13)\\= gcd (26, a + 13)[/tex]
This is necessarily 1, 2, 13, or 26, which we can see by just looking at the first term. By factoring 1183 and considering that [tex]a[/tex] is an odd multiple, then we should be able to conclude the answer.
Hence, the conclusion is that the solution is 26, since gcd (26, a + 13) = 26 when a = 1183k, and k = 1,3,5,7,9...
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Which of the following is the domain of the function {(3,6),(5,7),(7,7),(8,9)}
1. {3,5,7,8}
2. {6,7,9}
3. {(6,3),(7,5),(7,7),(9,8)}
4. {1,3,5,7,9}
On solving the provided question, we can say that the roasting approach, which represents sets as 3, 5, 7, and 8, is one way to write domains
what is domain?The domain of a function is the set of possible values that it can accept. The x-values of a function like f are represented by these integers (x). A function's domain is the set of possible values on which it can be used. This set is the value that the function returns after the insertion of the x value. Y = f is the definition of a function with x as the independent variable and y as the dependent variable (x). A value of x is said to be in a function's domain if it can be successfully utilised to produce a single value of y by using the value of x.
A set of ordered pairs (x, y), {(3,6),(5,7),(7,7),(8,9)}.
The collection of x values that make up the domain of the function f(x) include,
The roasting approach, which represents sets as 3, 5, 7, and 8, is one way to write domains. Another is the arrow diagram method.
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5. Mike has read 4/9 of a book; he has read 1,089 pages. The book has how many pages?
The number of pages the book has is 2450.
How to find the number of pages in the book?Mike has read 4/9 of a book; he has read 1,089 pages. The number of pages of book can be calculated as follows;
He has read 4 / 9 of the pages of book.
Therefore,
let
x = number of pages of book
Hence,
4 / 9 x = 1089
cross multiply
4x = 1089 × 9
4x = 9801
divide both sides by 4
4x / 4 = 9801 / 4
x = 2450.25
Therefore, the book has 2450 pages.
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This is due today. I have no brain cells.
Answer:
Option B
Step-by-step explanation:
Does the point (-3,2) lie inside, outside, or an a circle with center (4,0) and radius 5 units?
Answer:
The given point is outside of the circle---------------------------------------
Find the distance between the given point (-3, 2) and the center of circle (4, 0) using distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex][tex]d=\sqrt{(4-(-3))^2+(0-2)^2} =\sqrt{7^2+(-2)^2} =\sqrt{49+4} > 7 > r=5[/tex]As we see the distance is greater than radius, hence it is outside circle.
(8 pts.) in a binomial experiment, the probability of success in any trial of the experiment is 0.7. you will conduct 10 trials of this experiment. a. what is the probability of getting exactly 5 successes? b. what is the probability of getting 6 or more successes?
a) The probability of getting exactly 5 successes is 0.1029.
b)The probability of getting 6 or more successes is 0.8497510126.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Here, p = 0.7, q = 0.3 and n = 10
a) The probability of getting exactly 5 successes
P (x= 5) = C(10, 5) (0.7)⁵ (0.3)⁵
= 10!/ 5! 5! x 0.16807 x 0.00243
= 0.1029
b)The probability of getting 6 or more successes
P(X≥6) = 1 - P(X<6)
= 1 - P(X = 0, 1,2, 3, 4, 5)
= 1 - [ P(0) + P(1) P(2) + P(3) + P(4) + P(5)]
= 1 - [C(10, 0) [tex](0.3)^{10[/tex] + C(10, 1) (0.7) [tex](0.3)^{9[/tex] + C(10, 2) (0.7)² [tex](0.3)^{8[/tex]
+ C(10, 3) (0.7)³ [tex](0.3)^{7[/tex] + C(10, 4) [tex](0.7)^4[/tex][tex](0.3)^{6[/tex] + C(10, 4) [tex](0.7)^5[/tex]
[tex](0.3)^{5[/tex] ]
= 1 - [ 0.0000059049 + 0.000137781 + 0.0014467005 +
0.009001692 + 0.036756909 + 0.1029]
= 1 - 0.1502489874
= 0.8497510126
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Explain how to solve 5x − 2 = 8 using the change of base formula . include the solution for x in your answer.
The solution to the given exponential equation is 0.791.
What is a logarithm?
The logarithm is the inverse function of exponentiation in mathematics. That is, the exponent to which b must be raised to produce x is the logarithm of a number x to the base b.
Given exponential function is
5x⁻² = 8
Divide both sides by 5:
x⁻² = 8/5
x⁻² = 1.6
Taking logarithm of base x:
[tex]log_x(x^{-2})=log_x1.6[/tex]
-2 [tex]=log_x(1.6)[/tex]
Now applying the logarithm of change of base formula:
-2 = log 1.6/log x
Divide both sides by -2:
1 = log 1.6/( -2log x)
Multiply both sides by log x:
log x = log 1.6/-2
log x = -0.1021
Now applying the formula [tex]log_xa = b[/tex] implies [tex]a = x^b[/tex]:
x = 10^(-0.1021)
x = 0.7905
x = 0.791
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students were surveyed on the number of siblings they have. the following probability model was created from the results. a 2-column table with 5 rows. column 1 is labeled number of siblings with entries 0, 1, 2, 3, 4 or more. column 2 is labeled probability with entries 0.223, 0.532, 0.121, 0.085, 0.039. what is the probability that a randomly selected student does not have 0 siblings? enter your answer as a decimal rounded to the thousandths place. p(not 0 siblings)
The likelihood that a student chosen at random has any siblings is 0.777. This is determined by deducting from 1 the probability of having no siblings (0.223).
1. Get the probability of 0 siblings : 0.223
2. Subtract the probability of 0 siblings from 1 :
1 - 0.223
= 0.777
3. Round the result to 3 decimal places :
0.777
The probability of a student not having 0 siblings can be calculated by subtracting the probability of having 0 siblings from 1. The probability model created from the survey results is a 2-column table with 5 rows. Column 1 is labeled number of siblings with entries 0, 1, 2, 3, 4 or more. Column 2 is labeled probability with entries
0.223, 0.532, 0.121, 0.085, 0.039.
The probability of having 0 siblings is 0.223. To calculate the probability of not having 0 siblings, we subtract 0.223 from 1. This gives us 0.777, which is the probability of not having 0 siblings. This result should be rounded to 3 decimal places, giving us 0.777 as the final answer.
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Solve for x. Round to the nearest tenth, if necessary.
By using a trigonometric relation, we will see that the hypotenuse of the right triangle measures 160 units.
How to find the value of x?On the image, we can see a right triangle where we know one of the angles and one of the cathetus.
We want to find the value of x, which is the hypotenuse of the right triangle, and the cathetus that we know is the adjacent cathetus to the known angle.
Then we can use the trigonometric relation:
cos(a) = (adjacent cathetus)/hypotenuse
cos(60°) = 80/x
Using that we can find the value of x, we will get:
x = 80/cos(60°) = 160
The value of x is 160 units.
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if f(x)=2(x)² + 5√(x+2), complete the following statement:
f(2)=
Answer:
x-intercept(s):
None
y-intercept(s):
(
0
,
5
√
2
)
Step-by-step explanation:
Answer:
f(2)=18
Step-by-step explanation:
f(2)=2(2)²+5√(2+2)
f(2)=2(4)+5√(4)
f(2)=8+5(2)
f(2)=8+10
f(2)=18
Suppose you know that the amount of time it takes your friend Susan to get from her residence to class averages 50 minutes, with a standard deviation of 5 minutes. What proportion of Susan's trips to class would take less than 40 minutes? What proportion of Susan's trips to class would take more than 50 minutes or less than 40 minutes?
Answer:
To solve this problem, we will use the following steps:
Step 1: We know that the amount of time it takes Susan to get from her residence to class averages 50 minutes, with a standard deviation of 5 minutes. So we can use this information to calculate the proportion of Susan's trips to class that would take less than 40 minutes.
Step 2: To calculate the proportion of Susan's trips to class that would take less than 40 minutes, we need to find the z-score for the value of 40 minutes. We can use the following formula to find the z-score:
z = (x - μ) / σ
Where x is the value we are interested in (40 minutes), μ is the mean (50 minutes), and σ is the standard deviation (5 minutes).
z = (40 - 50) / 5 = -2
Step 3: We can use a standard normal table or a calculator to find the proportion of Susan's trips to class that would take less than 40 minutes.
The proportion of Susan's trips to class that would take less than 40 minutes is 0.0228 or 2.28%.
Step 4: To calculate the proportion of Susan's trips to class that would take more than 50 minutes or less than 40 minutes, we need to find the proportion of Susan's trips to class that would take more than 50 minutes and add it to the proportion of Susan's trips to class that would take less than 40 minutes.
Step 5: To find the proportion of Susan's trips to class that would take more than 50 minutes, we need to find the z-score for the value of 50 minutes.
z = (50 - 50) / 5 = 0
Using a standard normal table or a calculator, the proportion of Susan's trips to class that would take more than 50 minutes is 0.5 or 50%.
Step 6: Finally, we can add the proportion of Susan's trips to class that would take more than 50 minutes and the proportion of Susan's trips to class that would take less than 40 minutes to find the proportion of Susan's trips to class that would take more than 50 minutes or less than 40 minutes.
0.50 + 0.0228 = 0.5228 or 52.28%
Final Answer: The proportion of Susan's trips to class that would take more than 50 minutes or less than 40 minutes is 0.5228 or 52.28%.
Which of the following is equivalent to
4x^2 6x/ 2x+2?
a. 2X - 10/2X+2
b. 2X - 5 + 10/2X+2
c. 2x-3
d. 2X + 5 - 10/2X +2
An equation Dividing 4x^2+6x by 4x+2 gives : Therefore , the expression ... 4x + 2, as follows: 4x^2 + 2x + 4x + 2 − 2, or x(4x + 2) + (4x + 2) − 2.
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
here,
the given equation is
this above equation is equivalent to
2X - 10/2X+2,
as root of both equation are same
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a fisheries biologist is stocking fish in a lake. She knows that when there are n fish per unit of water, the average weight of each fish will be W(n) = 500 -2n, measured in ounces. What is the value of n that will maximize the total fish weight per unit of water? What is that weight?
If a fisheries biologist is stocking fish in a lake. She knows that when there are n fish per unit of water. The value of n that will maximize the total fish weight per unit of water is 125 fish . The weight is 31,250g.
How to find the value of n that will maximize the total fish weight per unit of water?a. Value of n that will maximize the total fish weight per unit of water?
W(n) = 500 -2n
W=n(500 -2n)
W = 500n -2n
0=500 -4n
n =500/4
n = 125 fish
b. Weight
Weight = Number of fish/ Average weight of fish
Weight = 125 × (500/2)
Weight = 125 × 250
Weight = 31,250g
Therefore the value of n that will maximize the total fish weight per unit of water is 125 fish . The weight is 31,250.
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Write an equation in point-slope form of the line that passes through the point (-9, 1) and has a slope of
2/3
Answer:
y-1=2/3(x+9)
Step-by-step explanation:
Sorry cant really explain well but I am positive this is the right answer.
the perimeter of an isosceles triangle (2 equal sides) pqr is 9 cm. the length of side p is 4 cm and the lengths of q and r are equal
The lengths of q and r are 2.5 , 2.5 respectively if the perimeter of an isosceles triangle pqr is 9 cm.
What is a triangle ?
triangle can be defined in which it consists of three sides , three angles and the sum of three angles is always 180 degrees.
Given ,
The perimeter of an isosceles triangle (2 equal sides) pqr is 9 cm.
the length of side p is 4 cm
Let the lengths of q and r are x and y respectively.
The perimeter of an isosceles triangle = (p+2q)
So,
p+2q = 9
4+2q = 9
2q = 9-4
2q = 5
q = 5/2
q = 2.5 cm
Hence , the lengths of q and r are 2.5 , 2.5 cm respectively .
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what is the reciprocal of 12/5 in fraction form
Answer:
5/12
Step-by-step explanation:
5/12
What’s the answer ? Please help
Answer:
Step-by-step explanation:
0
How to put this in vertex form?
The vertex form of equation is discussed below,
What is Vertex form?The vertex form of a quadratic function is f(x) = a(x – h)² + k, where a, h, and k are constants. of the parabola is at (h, k).
As, A parabola has a lowest point if it opens upward.
Additionally, a parabola has a highest point if it opens downward.
The vertex of the parabola is located at this lowest or highest point.
Now, the parent function f(x) = x² has its vertex at the origin.
Also, The vertex form of a quadratic function is
f(x) = a(x – h)² + k, where a, h, and k are constants.
For example, The parent function f(x) = x² is vertically stretched by a
factor of 4/3 and then translated 2 units left and 5 units down.
So, the vertex form : g(x) = 4/3 (x+2)² - 5.
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In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12
receptionists is bell-shaped and has a mean of 64 and a standard deviation of 9. Using the Empirical Rule (as
presented in the book), what is the approximate percentage of daily phone calls numbering between 46 and
822
Do not enter the percent symbol.
ans =
%
The approximate percentage of daily phone calls numbering between 46 and 82 is 95%.
The Empirical Rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.
In this case, the mean is 64 and the standard deviation is 9. Therefore, approximately 68% of the daily phone calls answered by each receptionist fall between 64 - 9 = 55 and 64 + 9 = 73.
Additionally, approximately 95% of the data falls between 64-18 = 46 and 64 + 18 = 82.
So, the approximate percentage of daily phone calls numbering between 46 and 82 is 95%.
Learn more about the empirical rules here:
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Work backward to find the value of the varible in the eqautoin belw. Show your work. d+7x2=20
Directions: Use the Law of Sines to find each missing side or angle. Round to the nearest tenth.
Answer: 7.4
Step-by-step explanation:
[tex]\frac{x}{\sin 46^{\circ}}=\frac{5}{\sin 29^{\circ}}\\\\x=\frac{5\sin 46^{\circ}}{\sin 29^{\circ}}\\\\x \approx 7.4[/tex]
