To find the value of x in the triangle, we can use the law of sines, which states that in any triangle ABC, the following relationship holds:
a/sin A = b/sin B = c/sin C
where a, b, and c are the side lengths of the triangle opposite to the angles A, B, and C, respectively.
In this case, we can write:
x/sin 80° = 7/sin 50°
Using the properties of sines, we can simplify this expression to:
x = (7 x sin 80°) / sin 50°
Using a calculator, we can evaluate this expression to get:
x ≈ 9.05
Therefore, the value of x in the triangle is approximately 9.05.
A wire connects the top of a flag pole to the ground, as shown below. Calculate the height, k, of the flag pole. Give your answer in metres to 1 d.p. 74° 2.5 m k Not drawn accurately.
The flag pole is 6.8 meters tall.
Define Triangle-Based FunctionsTrigonometric functions are mathematical formulas that connect the angles and side lengths of a right triangle. The six trigonometric functions are sin, cos, tangent, cosec, sec, and cotangent.
Sine (sin): sin()=perpendicular/hypotenuseThe adjacent side/ hypotenuse is the cosine (cos) symbol.Tangent (tan): tan() = adjacent/oppositeThe cosecant formula is csc() = 1/sin().Secant (sec): sec(cos) = 1/sec(cos)A cotangent is defined as cot() = 1/tan().Height,p of the flagpole should be calculated.
Given;
base,b=2.9m
Angle subtended=67
Using trigonomteric identity
tan67=Height/base
Tan67=h/b
Tan67=h/2.9
h=2.9tan67
h=6.8m
Height pf the flag pole is 6.8m.
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The complete question is attached below:
HELP PLEASE 20PTS!!!!!!!!!!!!
Answer: -125
Step-by-step explanation:
-5*-5=25
But, because its squared you have to multiply 25 * -5
A negative times a positive is a negative so,
25 * -5 = -125
Hope this helped!
9x9x9x9x9x9x9( write in exponential form)
Im quite confused in this topic
The equation [tex]p^{2} =5a[/tex] represents the perimeter, p, of a square with an area, A, a square stained glass had an area of 20ft. What is the perimenter of the window?
The area of the stained glass is given as 20ft².
Let's start by finding the length of one side of the square stained glass. Since the area of a square is given by the formula A = s^2, where s is the length of one side of the square, we have:
s^2 = A
s^2 = 20ft²
s = sqrt(20)ft
s = 2sqrt(5)ft
Now, we can use the given equation p^2 = 5A to find the perimeter p of the square, by substituting the value of A:
p^2 = 5A
p^2 = 5(20ft²)
p^2 = 100ft²
p = sqrt(100ft²)
p = 10ft
Therefore, the perimeter of the square stained glass is 10 feet.
What is the correct mathematical description for the expression 25 ÷ 5 + (6 x 2) − 4.5?
25 divided by 5 plus 6 times 2 minus 4 and 5 tenths
25 divided by the sum of 5 and 6 times 2 minus 4 and 5 tenths
25 divided by 5 plus 6 times the difference of 2 and 4 and 5 tenths
25 divided by 5 plus the product of 6 and 2 minus 4 and 5 tenths
Ans :-
25 divided by 5 plus 6 times 2 minus 4 and 5 tenths[tex] \: [/tex]
Solution:-
[tex] \sf{25 ÷ 5 + (6 \times 2) − 4.5}[/tex][tex] \: [/tex]
[tex] \sf{( 25 ÷ 5 ) + ( 6×2 ) - 4.5}[/tex][tex] \: [/tex]
[tex] \sf \: 5 + 12 - 4.5[/tex][tex] \: [/tex]
[tex] \sf \: 17 - 4.5[/tex][tex] \: [/tex]
[tex] \boxed{ \sf \red{ \bold{ \: 12.5 \: }}}[/tex][tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
hope it helps ∼
3 out of every 7 trucks on the road are followed by a car, while 3 out of every 9 cars are followed by a truck. what fraction of vehicles on the road are trucks?
The fraction of vehicles on the road are trucks is 3/7
Let's assume there are a total of x vehicles on the road.
According to the first statement, 3/7 of those vehicles are trucks followed by a car. This means that (3/7)x trucks are on the road and are followed by a car.
According to the second statement, 3/9 of the vehicles are cars followed by a truck. This means that (3/9)x cars are on the road and are followed by a truck.
We know that the total number of vehicles on the road is x. So we can write
(3/7)x + (3/9)x = x
Simplifying this equation
(27/63)x + (21/63)x = x
(48/63)x = x
We can then solve for x
x = 63
So there are 63 vehicles on the road.
To find out what fraction of vehicles on the road are trucks, we need to determine what fraction of those 63 vehicles are trucks.
According to the first statement, 3/7 of the vehicles are trucks followed by a car.
So the fraction of vehicles that are trucks is 3/7
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El valor de las razones trigonométricas no depende del tamaño del triángulo sino de la medida del ángulo ¿ es verdad o falso ? argumenten su respuestas
Answer: Falso. Las razones trigonométricas dependen tanto del tamaño del triángulo como de la medida del ángulo. Esto se debe a que las razones trigonométricas de un triángulo se calculan relacionando los lados del triángulo con el ángulo. Por lo tanto, si cambia el tamaño del triángulo, los lados cambiarán y, por consiguiente, las razones trigonométricas también cambiarán.
Step-by-step explanation:
Hiro's recipe for granola bars uses 2 cups of oatmeal for every 12 bars. How many bars can Hiro make with 6 cups of oatmeal? With 8 cups of oatmeal?
question 3 Multiply and simplify if necessary. 3.1.1 3a²bc² (3a²-4b-c)
Answer:
3a⁴bc-3a²4b²c²-3a²bc³
Step-by-step explanation:
remove brackets by multiplying by the numbers out the brackets.As they are no like terms that is where we end our answers
Find the value of X
(2x+60) 6x°
Answer:
x=15
Step-by-step explanation:
(2x+60)=6x
2x+60=6x
subtract 2x from both sides
60=4x
divide by 4
15=x
Do all rational and irrational numbers have decimal expansions?
Yes, all rational and irrational numbers have decimal expansions. Rational numbers can be expressed as terminating or repeating decimals, while irrational numbers have non-repeating, non-terminating decimal expansions.
In decimal form, rational numbers have a finite or repeating pattern of digits after the decimal point, while irrational numbers have an infinite, non-repeating pattern of digits after the decimal point. For example, the rational number 1/4 is expressed as 0.25, while the irrational number pi is expressed as 3.14159265358979323846... where the decimal goes on infinitely without repeating. In conclusion, every real number can be represented in decimal form, either as a terminating or repeating decimal, or as a non-repeating, non-terminating decimal.
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Help pls
Been trying A WHILE
Step-by-step explanation:
c = y axis intercept = 6 ( from the graph)
slope = rise/run = 6/3 = 2 ( using points (-3,0) and (0,6) )
then
y = 2x + 6
a local paint company surveyed people and found that 53% prefer brand a paint. a sample of 6 was taken. what is the probability that at least 1 person prefers brand a paint?
By using the complement probability that none of the 6 people prefer brand A paint, the probability that at least 1 person in a sample of 6 prefers brand A paint is 0.9939 or approximately 99.39%.
To find the probability that at least 1 person in the sample of 6 prefers brand A paint, we need to find the probability of the complement event that none of the 6 people prefer brand A paint, and subtract it from 1.
The probability that one person prefers brand A paint is 0.53, and the probability that one person does not prefer brand A paint is 0.47. Since we are dealing with a binomial distribution, we can use the formula for the probability of k successes in n trials:
P(k successes) = n! / (k! * (n - k)!) * p^k * (1 - p)^(n - k)
Using this formula, we can calculate the probability of 0 people preferring brand A paint:
P(0 people prefer brand A) = 6! / (0! * 6!) * 0.53^0 * 0.47^6 = 0.0061
Therefore, the probability of at least 1 person preferring brand A paint is:
P(at least 1 person prefers brand A) = 1 - P(0 people prefer brand A) = 1 - 0.0061 = 0.9939
So, the probability that at least 1 person prefers brand A paint is 0.9939 or approximately 99.39%.
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work out the size of angle x and work out the size of angle y
Answer:
X = 34, Y=56
Step-by-step explanation:
BOA is an isosceles triangle.
Angle CBO = 90°
Angle DBO = 90 - 56 = 34
Angle ODB = 34° and ODB is x
Angle EBD is also 90°
Y = 180 - (90+34) = 56
The value of x is 34 degree and y is 56 degree.
What is a Tangent?Tangents to circles are lines that cross the circle at a single point. Point of tangency refers to the location where a tangent and a circle converge. The circle's radius, where the tangent intersects it, is perpendicular to the tangent. Any curved form can be considered a tangent.
We have, BOA is an isosceles triangle.
< CBO = 90°
So, < DBO = 90 - 56
<DBO = 34
and, <ODB = 34°
Now, let the angle ODB be x
As, from the figure < EBD is also 90°
So, <y = 180 - (90+34) (Angle sum property)
<y = 56
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47 feet wide how many yards and feet is that.
pls show your work thanks....................?
Answer:
15 yards and 2 feet
Step-by-step explanation:
There are 3 feet in a yard
47/3= 15 and R 2
15 yard and 2 feet
The roof will be covered with sheets of plywood that are 4 feet x 8 feet x 1/2
inch. Plywood is placed over the top chords of the roof trusses to form the
covering or "decking" of the roof.
How many sheets of plywood will be needed to form the decking? Include all
calculations and/or explanations necessary to support your answer.
Answer:
The length and width of the roof can be used to calculate the total square footage of the roof. For example, if the roof is 20 feet long and 10 feet wide, the total square footage would be 200 square feet.
Once the total square footage is known, the number of sheets of plywood needed can be calculated. Each sheet of plywood is 4 feet x 8 feet, or 32 square feet. Therefore, 200 square feet of roof would require (200/32 = 6.25) 6.25 sheets of plywood. In order to cover the entire roof, 7 sheets of plywood would need to be used.
Step-by-step explanation:
if you are going to receive $2,000 in six years from now, how much is that worth today, assuming 5 nnual simple interest? review later $1,538.46 $1,780.32 $1,904.76 $2,600.00
The initial amount is worth $ 1538.46
Simple interest:Simple interest is a type of interest that is calculated only on the principal amount of a loan or investment, without taking into account any additional interest that may be added over time.
Simple interest is calculated as a percentage of the principal amount and is usually expressed as an annual rate.
The formula to calculate simple interest is:
Simple Interest = Principal x Rate x Time/ 100
Here we have
You are going to receive $2,000 in 6 years from now
The annual simple interest rate is 5%
Let 'P' be the initial or principal amount
Using the formula, I = PTR/100
Simple interest will gain on 'P' at 5% for 6 years
=> I = P(6)(5)/100
=> I = 0.3P
And total amount = P + 0.3P = 1.3P
It is given that after 6 years we get $ 2000
=> 1.3P = 2000
=> P = 1538.46
Therefore,
The initial amount is worth $ 1538.46
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What is the answer to this question? If m angle J +(7x+13) , mangleK = (83-2x) and the sum of the measures of the angle is 141 degrees find the measure of each angle>
The expression has basic mathematical operators. is The measurement of the two angles ∠J and ∠K is 76° and 65° respectively.
What is Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Given to us
∠J = (7x + 13)°,
∠K = (83 - 2x)°,
the sum of the two angles is 141°.
As it is given that the sum of the two angles is 141°, therefore, the expression for the sum of the two angles can be written as,
∠J + ∠K = 141°
(7x + 13)° + (83 - 2x)° = 141°
7x + 13 +83 - 2x = 141
5x = 141 - 83 - 13
5x = 45
x = 9
Now, we got the value of x, substitute the value of x in given measurements, therefore,
∠J = (7x + 13)°
∠J = 7(9) + 13
∠J = 63 + 13
∠J = 76°
∠K = (83 - 2x)°
∠K = (83 - 2(9))°
∠K = (83 - 18)°
∠K = 65°
Hence, the measurement of the two angles ∠J and ∠K is 76° and 65° respectively.
Factor in the trinomial form of ax²+bx+c
4x²+15x+9
Answer:
( 4x + 3 ) ( x + 3 )
Step-by-step explanation:
9 × 4 = 36
Factors of 36 = { 1, 2, 3, 4, 6, 9, 12, 18, 36 }
3 and 12 add up to 15
4x² + 15x + 9
4x² + 3x + 12x + 9
( 4x² + 3x ) + ( 12x + 9 )
x (4x + 3) + 3 ( 4x + 3 )
( 4x + 3 ) ( x + 3 )
A taxpayer had a taxable income of $61,900, and her spouse had a taxable
income of $59,400. If they wish to file their tax return jointly, which tax bracket
will they fall into?
Married Filing Jointly
Taxable
income is
over
But not
over
$0
16,700
16,700
67,900
67,900 137,050
137,050 208,850
208,850 372,950
372,950
← PREVIOUS
Bracket
10%
15%
25%
28%
33%
35%
X
Answer:
The combined taxable income of the couple is $61,900 + $59,400 = $121,300. This falls in the tax bracket for Married Filing Jointly between $67,900 and $137,050. Therefore, their tax rate will be 25%.
Step-by-step explanation:
The rate of tax couple has to pay is 25 percent.
What is tax?In mathematics, the tax calculation is related to the selling price and income of taxpayers. It is a charge imposed by the government on the citizens for the collection of funds for public welfare and expenditure activities. There are two types of taxes: direct tax and indirect tax.
The combined taxable income of the couple is $61,900 + $59,400 = $121,300.
This falls in the tax bracket for Married Filing Jointly between $67,900 and $137,050.
Therefore, their tax rate will be 25%.
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the physician orders medication l 400 mg po twice daily. the pharmacy supplies medication l with a dosage strength of 2 grams per 5 ml. how many milliliters does the nurse advise the patient to take with each dose? enter the numeral only, not the units.
The nurse will advise the patient to take 1 ml of medication with each dose.
The physician orders medication at 400 mg po twice daily. The pharmacy supplies medication with a dosage strength of 2 grams per 5 ml.
How many milliliters does the nurse advise the patient to take with each dose?
The nurse should advise the patient to take 1 ml of medication with each dose.
To find the number of milliliters, the following formula will be used.
Dose × Volume/Strength
Given, Dose = 400 mg
Strength = 2 grams per 5 ml
Volume = ?
To convert 400 mg to grams, divide by 1000.
400 mg = 400/1000 = 0.4 g
Now, put the values in the formula,
0.4 g × Volume / 2 g/ 5 ml= 5/2 × 0.4/1= 5/2 × 0.4= 1 ml
Hence, the nurse will advise the patient to take 1 ml of medication with each dose.
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Find the distance between D and E.
Find the bearing of E from D.
The distance DE is 338.25m
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary. . The ratio of corresponding sides of Similar triangles are equal.
Therefore AB /DE = CB/CE
CE = 80+250
= 330
represent DE by x
82/x = 80/330
330× 82 = 80x
80x = 27060
x = 338.25
Therefore the distance DE is 338.25m
Using cosine rule to find the angle of D
c² = a²+b² +2abcos C
330² = 300²+ 338.25²+2× 300× 338.25cos D
108900 = 90000 + 114413.1 + 202950cosD
202950cos D = 108900-204413.1
202950cos D = -955131
cos D = -955131/202950
cosD = -0.471
D = cos^-1( 0.471)
D = 62° ( nearest degree)
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1. The number of red balloons is 3/5 to the number of green balloons. If there are a total of 320 balloons. How many greens balloons are there?
2. Tammi has a bowl of fruit which has only apples and bananas. The ratio is 2 apples to each banana. If there are a total of 15 fruits in the bowl, how many apples are there?
there are 200 green balloons, there are 120 red balloons , there are 10 apples and 5 bananas in the bowl, for a total of 15 fruits. To solve this problem, we need to use the given ratio and the total number of balloons to find the number of green balloons.
Let's assume the number of green balloons is x. Then, the number of red balloons is 3/5 of x, or (3/5)x.
The total number of balloons is 320, so we can write an equation based on the given information:
x + (3/5)x = 320
To solve for x, we can simplify the equation:
(8/5)x = 320
x = 200
Therefore, there are 200 green balloons.
To check our answer, we can use the ratio given in the problem:
(3/5)x = (3/5) * 200 = 120
So there are 120 red balloons.
Let's assume the number of bananas is x. According to the given ratio, the number of apples is twice that of bananas, or 2x.
The total number of fruits in the bowl is 15, so we can write an equation based on the given information:
x + 2x = 15
To solve for x, we can simplify the equation:
3x = 15
x = 5
Therefore, there are 5 bananas in the bowl.
To find the number of apples, we can use the ratio given in the problem:
2x = 2 * 5 = 10
So there are 10 apples in the bowl.
To check our answer, we can verify that the ratio of apples to bananas is 2:1:
10/5 = 2
Therefore, there are 10 apples and 5 bananas in the bowl, for a total of 15 fruits.
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The total expenditure is R1 149 390bn,calculate the total amount allocated to the Department of Health which is 12. 6%
The total amount allocated to the Department of Health is R145,026,540,000, calculated by multiplying the total expenditure by the percentage allocated to the department expressed as a decimal.
To calculate the total amount allocated to the Department of Health, we need to multiply the total expenditure by the percentage allocated to the department, which is 12.6%.
Then, we must divide the percentage by 100 to get the decimal equivalent:
12.6/100 = 0.126
Next, we can calculate the total amount allocated to the Department of Health by multiplying the total expenditure by the decimal equivalent of the percentage:
Total amount allocated to the Department of Health = 0.126 x R1 149 390bn
Simplifying this expression, we get:
Total amount allocated to the Department of Health = R145,026,540,000
Therefore, the total amount allocated to the Department of Health is R145,026,540,000.
The calculation involves multiplying the total expenditure by the decimal equivalent of the percentage allocated to the department, which gives the amount allocated to the Department of Health.
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Marissa spent $45 on a hat and a shirt.
The hat cost $10. What is x, the cost of
the shirt in dollars? What is the answer
Answer:
To determine the cost of the shirt, we can set up an equation using algebra. Let x be the cost of the shirt in dollars. We know that Marissa spent a total of 45 on the hat and the shirt, and the hat cost 10. Therefore, we can write the equation:
x + 10 = 45
To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting 10 from both sides:
x = 35
Thus, the cost of the shirt is $35.
I need help. We're learning circles and I cant get these
Applying the appropriate circle theorem, the values are:
1. x = 9; 2. Measure of arc DL = 66°; 3.x = 11; 4. x = 0; 5. x = 15
What is the Central Angle Theorem?The central angle theorem is a circle theorem that states that the measure of the central angle is the same as the measure of the arc it intercepts.
1. 63 + 44 + 7x + 10 = 180
117 + 7x = 180
7x = 180 - 117
7x = 63
x = 9
2. Measure of arc DL = 2(33) [based on the inscribed angle theorem]
Measure of arc DL = 66°
3. 9x + 3 = 1/2(154 + 50) [based on the angle of intersecting chords theorem]
Solve for x:
9x + 3 = 102
9x = 102 - 3
9x = 99
x = 11
4. 35 = 1/2(171 + 2x - 101) [based on the secant-tangent theore]
Solve for x:
70 = 2x + 70
70 - 70 = 2x
2x = 0
x = 0
5. 8 * x = 12 * 10 [based on the intersecting chords theorem]
8x = 120
x = 15
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Hello! When using compelting the square, arent you just technically putting the standard form equation you have into vertex form?
Answer:
Hello! Yes, when completing the square, you are essentially transforming a quadratic equation from standard form to vertex form. The vertex form of a quadratic equation is given by:
y = a(x - h)^2 + k
where (h, k) represents the vertex of the parabola and 'a' is a constant that determines the shape and direction of the parabola.
To convert a quadratic equation from standard form (ax^2 + bx + c) to vertex form, we follow these steps:
1. Divide both sides of the equation by 'a' to make the coefficient of x^2 equal to 1.
2. Move the constant term (c/a) to the right-hand side of the equation.
3. Complete the square by adding and subtracting (b/2a)^2 on the left-hand side of the equation.
4. Factor the left-hand side of the equation as a perfect square trinomial.
5. Write the equation in vertex form by identifying the values of 'a', 'h', and 'k'.
tyler's playlist has 36 songs. noah's playlist has one quater as many songs as tyler's plaslist. how many songs are on noahs playlist?
According to the question, Tyler's playlist has 36 songs. Noah's playlist has one-quarter as many songs as Tyler's playlist. then Noah's playlist has 9 songs.
Let the number of songs on Noah's playlist be represented by x.
To solve the question, we'll set up an equation, which is given as:
36 / 4 = x
Simplifying the above equation we get:
9 = x
Therefore, Noah's playlist has 9 songs.
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What is the surface area of this right triangular prism?
Enter your answer in the box.
in²
The surface area of right triangular prism of height 3 in, base 8 in, slop 5 in and width 4 in is 76 in².
What is surface area?Surface area is a measure of the total area occupied by the surfaces of a three-dimensional object.
It is the sum of the areas of all the faces, including the base(s), of the object.
The units for measuring surface area are squared units, such as square meters or square inches.
To find the surface area of a right triangular prism, we need to add the areas of all of its faces.The prism has two congruent triangular faces and three rectangular faces.
The area of every single triangle face is (1/2)bh, where b is the base of the triangle and h is its height.
In this case, the base is 8 in and the height is 5 in, so the area of each triangular face is (1/2)(8)(5) = 20 inches². Since there are two triangular faces, their combined area is 2(20) = 40 inches².
The area of each rectangular face is lw.
In this case, the width is 4 in and the height is 3 in, so the area of each rectangular face is (4)(3) = 12 inches². Since there are three rectangular faces, their combined area is 3(12) = 36 inches²
Therefore, the total surface area of the right triangular prism is the sum of the areas of all its faces:
Surface area = 2(triangular face area) + 3(rectangular face area)
Surface area = 2(20) + 3(12)
Surface area = 40 + 36
Surface area = 76 inches²
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Consider the parametric curve x = 4t 3 − 3t, y = t 5 − 5t, t ∈ R. (a) Find the points where the tangent line is horizontal or vertical. (b) Determine the intervals where the slope of the tangent line to the curve is positive or negative. (c) Determine the intervals where the curve is concave upward or downward. (d) Sketch the curve.
The points where the tangent line is vertical are (13/16, -5/16) and (-13/16, 5/16) and The slope of the tangent line is positive on the intervals t < -1 and t > 1, and negative on the interval -1 < t < 1.
How can we analyzing the properties of a parametric curve?(a) To find where the tangent line is horizontal, we need to find values of t where the derivative of y with respect to x (dy/dx) is equal to 0.
We have:
dy/dx = (dy/dt)/(dx/dt) = (5t^4 - 5)/(12t^2 - 3)
Setting dy/dx = 0, we get:
5t^4 - 5 = 0
t^4 = 1
t = ±1 or t = ±i
Substituting t = 1 into the parametric equations gives us the point (1,-4). Substituting t = -1 gives us the point (-1,4). Substituting t = i or t = -i gives us points on the imaginary axis, which are not part of the real plane.
Therefore, the points where the tangent line is horizontal are (1,-4) and (-1,4).
To find where the tangent line is vertical, we need to find values of t where dx/dt is equal to 0.
We have:
dx/dt = 12t^2 - 3
Setting dx/dt = 0, we get:
t^2 = 1/4
t = ±1/2
Substituting t = 1/2 into the parametric equations gives us the point (13/16, -5/16). Substituting t = -1/2 gives us the point (-13/16, 5/16).
Therefore, the points where the tangent line is vertical are (13/16, -5/16) and (-13/16, 5/16).
(b) To determine the intervals where the slope of the tangent line is positive or negative, we need to examine the sign of the derivative dy/dx.
From part (a), we know that dy/dx is equal to:
dy/dx = (5t^4 - 5)/(12t^2 - 3)
The denominator is always positive, so the sign of dy/dx is determined by the numerator.
For t < -1, we have 5t^4 - 5 > 0, so dy/dx > 0.
For -1 < t < 1, we have 5t^4 - 5 < 0, so dy/dx < 0.
For t > 1, we have 5t^4 - 5 > 0, so dy/dx > 0.
Therefore, the slope of the tangent line is positive on the intervals t < -1 and t > 1, and negative on the interval -1 < t < 1.
(c) To determine the intervals where the curve is concave upward or downward, we need to examine the sign of the second derivative d^2y/dx^2.
We have:
d^2y/dx^2 = ((d^2y/dt^2)(dx/dt) - (dy/dt)(d^2x/dt^2)) / (dx/dt)^3
Calculating the second derivatives, we get:
d^2y/dt^2 = 20t^3
d^2x/dt^2 = 24t
Substituting these into the expression for d^2y/dx^2, we get:
d^2y/dx^2 = (20t^3)(12t^2 - 3) - (5t^4 - 5)(24t) / (12t^2 - 3)^3
Simplifying this expression, we get:
d^2
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