Parametric equations for the tangent line to the curve with the given parametric equations at the specified point are
x=s
y=1-4s
z=0
Derivatives of a function in parametric form: There are instances when rather than defining a function explicitly or implicitly we define it using a third variable. This representation is when a function y(x) is represented via a third variable which is known as the parameter is a parametric form. A relation between x and y can be expressible in the form x = f(t) and y = g(t) is a parametric form representation with parameter as t
In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters.
At the point (0, 1,0) t = 0
Find the tangent vector:
[tex]\frac{dx}{dt}=1=x_t\\y_t=\frac{dy}{dt}=-4e^{-4t}\\\\Z_t=5-5t^4[/tex]
The tangent vector for all points is
[tex]v(t)=i-4e^{-4t}j+(5-5t^4)k\\\\v(0)=i-4j[/tex]
The vector equation of the tangent line is
(x,y,z0=(0,1,0)+s(i-4j)
The parametric equation for this line is
x=s
y=1-4s
z=0
The complete question is -
Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = t, y = e−4t, z = 5t − t5; (0, 1, 0) x(t), y(t), z(t) = t,1−4t,5t Illustrate by graphing both the curve and the tangent line on a common screen.
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The souvenir shop at the ballpark sells signed baseballs for $2 each and
signed miniature bats for $6 each. Jay can spend at most $12 to buy no more than 4
items. Create a system of inequalities to model this situation, and then graph the
solution set. Which solution results in Jay spending all his money to buy 4 items?
The solution results in Jay spending all his money to buy 4 items is (3, 1)
How to determine teh system of inequalitiesFrom the question, we have the following parameters that can be used in our computation:
Signed baseballs = x
Signed miniature bats = y
Using the above as a guide, we have the following:
2x + 6y <= 12
x + y <= 4
Next, we graph the system (see attachment)
The solution results in Jay spending all his money to buy 4 items is (3, 1)
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Half of seven added to product of x and 4 is less than 1
Answer:
The equation to represent the given statement is:
(7/2) + (4 * x) < 1
We can simplify the equation as follows:
(7/2) = 3.5
And then:
3.5 + (4 * x) < 1
Finally:
3.5 - 1 < - (4 * x)
2.5 < - (4 * x)
Dividing both sides by -4:
-2.5/4 > x
-0.625 > x
∡Step-by-step explanation:
This means that for the equation to be true, the value of x must be less than -0.625.
In this figure, h = 3, and r = 4.
What is the exact surface area of the cone?
Enter your answer in the box.
units²
The exact surface area of the cone is 113.097 units².
What is Surface Area?The area of a three dimensional object on it's outer surface is called the surface area of the object.
Base of a cone is circle.
Base area = π r²
= π (4)² = 16π
Lateral surface area = π r √(h² + r²)
= 4π √(3² + 4²)
= 4π √25
= 4π × 5
= 20π
Total surface area = 16π + 20π
= 36π
= 113.097 units²
Hence the total surface area of the given cone is 113.097 units².
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given a standard deck of cards find the probability of randomly drawingan ace of hearts from the deck
Answer:
Since there are 54 cards in a standard deck, and only 1 ace of hearts:
You would have 1/54 of a chance of drawing the ace of hearts.
You would also have 1.85% of a chance drawing the ace of hearts.
Step-by-step explanation:
Hope it helps! =D
Answer questions 31 and 32.
30. Angle 1 and angle 9 are equal to each other. Then the correct option is C.
31. The value of the expression x + y will be 165°. Then the correct option is C.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Corresponding angle - If two lines are parallel then the third line. The corresponding angles are equal angles.
30. Angle 1 and angle 9 are the corresponding angles. Then they are equal to each other.
Thus, the correct option is C.
31. Angle x and angle 55° are the corresponding angle.
x = 55°
And angle 70° and angle (180° - y) is the corresponding angle. Then the equations are given as,
70° = 180° - y
y = 110°
Then the value of the expression x + y is given as,
x + y = 55° + 110°
x + y = 165°
Thus, the correct option is B.
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Which methods will determine 70% of 42?
A: Determine 1% of 42, and multiply the result by 7
B: Determine 10% of 42, and multiply the result bv 7.
C: Determine 10% of 42, and multiply the result by 70
D: Determine 10% of 42, and multiply the result by 70.
Rewrite the statement (p v ~q) -> (r v q) without using ^, ->, or <->.
The statement (p v ~q) -> (r v q) can be reworded as: "If either p is true or not q is true, then either r is true or q is true."
What is a conditional statement?A conditional statements are made up of two parts, a hypothesis (represented by p) and a conclusion (represented by q).. We will set down all potential combinations of truth values for our hypothesis and conclusion in a truth table and use those to determine the conditional statement's overall truth.
When a set of conditions are satisfied, a conditional assertion is judged to be true. Sometimes called if-then statements, they begin with a hypothesis and end with a conclusion. For instance, you might explain to a friend that getting a sunburn happens if you walk outside without sunscreen.
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Graph 3x-4y=8 2-48-3=y
The graph of the given equation are attached below.
What is graph?A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
For example, if the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.
If we know that the function crosses x axis at some point, then for polynomial functions, we have those as roots of the polynomial.
We are given the equation as;
3x - 4y = 8
3=y
From 3x – 4y = 8
⇒ -4y = -3x + 8
y = (3/4x) + -2
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The Blue Knights soccer team is practicing kicking the soccer ball into the goal. To begin, each player attempts kicks for 2 minutes and then reports the fraction of goals they made. Brad, Alice, and Andre report the following fractions: Player Goals Made Brad 4 5 Alice 1 2 Andre 4 6 Graph each fraction on a number line. 1. Which of these players made the greatest fraction of goal i don't know the answerr
According to the information, the player who scored the most goals in relation to the number of shots he took was Brad.
How to identify the player who scored the most goals?To find the player who scored the most goals in relation to the number of shots we must divide the fraction and place the number on the line. Once we have graphed this data, the highest number would be the one who scored the most goals compared to his attempts.
According to the above, the divisions would be:
4 / 5 = 0.81 / 2 = 0.54 / 6 = 1.6According to the above, Brad was the one who scored the most goals.
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arulfo deposited 55 into a savings account according to the rulw of 72 what interest rate will cause his money to double in approximately 23 years
The 3.13% interest rate will cause his money to double in approximately 23 years.
What is compound interest?The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.
Given that Arnulfo deposited $55 into a savings account for which interest is compounded semiannually.
According to the rule of 72, we should divide 72 by the interest rate to determine how many years it will take to double our money at a specific interest rate (r).
time is taken to double the money = 72/r,
where r represents the interest rate and time is in years.
As we have been given that it will take approximately 23 years to double Arnulfo's money, so we can set an equation as:
23 = 72/r
r = 72/23
r = 3.13
Hence the interest rate is 3.13%.
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The complete question is,
Arnulfo deposited $55 into a savings account for which interest is compounded semiannually. according to the rule of 72, what interest rate will cause his money to double in approximately 23 years?
Write a word problem for 3(2x)=6x
Multiply a number by 2 and then find the product of the number obtained with 3 is the statement required
What is an Algebraic Expression?An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.
Given here: The equation 3(2x)=6x
Clearly here the associative property of multiplication is used above
First, a number x is multiplied by 2
Then the number obtained above i.e 2x is multiplied again by 3
Thus the word problem can be of the form
Multiply a number by 2 and then find the product of the number obtained with 3
Hence, Multiply a number by 2 and then find the product of the number obtained with 3 is the statement required
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About how many millimeters long is the missing side of the right triangle, to the nearest tenth?
5 mm
7 mm
Using Pythagoras theorem, The missing side of the right triangle is 4,9 mm long.
The Pythagoras Theorem is what?Pythagoras' Theorem states that the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides. The Perpendicular, Base, and Hypotenuse are the names of the three sides of this triangle. The hypotenuse in this example is the longest side because it is located across from the 90° angle. A right triangle's positive integer sides (let's say sides a, b, and c) are squared to produce a Pythagorean triple equation.
Right triangles are what the provided triangle is.
The Pythagorean Theorem is used:
[tex]a^{2} + b^{2} = c^{2}[/tex]
[tex](5)^{2} + (7)^{2} = c^{2}[/tex]
25 + 49 =[tex]c^{2}[/tex]
c = 4.9
Hence, the missing side of the right triangle is 4,9 mm long.
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a grain silo is in the shape of a cylindrical prism. the silo is 90ft in diameter and 275ft in height. using the standard acceleration of gravity as , find the total weight exerted to the floor of the silo. additionally, of grain weighs 49lbs
The total weight exerted on the floor of the silo is 138,973,475 lbs
The volume of the cylindrical silo is given by the formula:
V = πr^2h
where r is the radius, h is the height and π (Pi) is approximately 3.14.
First, find the radius:
r = D/2 = 90ft / 2 = 45ft
Next, find the volume:
V = π * 45^2 * 275 = 31,875 * 3.14 * 275 = 2836275 cubic feet
Finally, calculate the weight of the grain:
W = V * w_grain/ft^3 = 2836275 * 49lbs/ft^3 = 138,973,475 lbs
This is the total weight exerted on the floor of the silo.
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determine the required value of the missing probability to make the distribution a discrete probability distribution.
The discrete probability distribution of 4 which is given as P(4) is 0.22.
In order to make a discrete probability distribution, the sum of all probabilities must equal 1. We can calculate the missing probability P(4) by subtracting the sum of the known probabilities from the value 1. So,
P(4) = 1 - (0.28 + 0.36 + 0.14)
= 1 - 0.78
= 0.22.
A discrete probability distribution is a mathematical function that assigns a probability to each outcome of a discrete random variable. In this case, the random variable is the value of x, and the corresponding probabilities are P(x).
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Complete Question:
Determine the required value of the missing probability to make the distribution a discrete probability distribution.
x P(x)
3 0.28
4 ?
5 0.36
6 0.14
P(4) = ______ ?
Pam wants to put a banner across her garage door, as shown below, to congratulate her son for his college graduation. The garage door is 12 feet high and 16 feet wide. How long should the banner be to fit the garage door? A house is shown with a banner over the garage door. The garage door is marked 16 ft wide and 12 ft high.
The banner should be 56 feet long to fit the garage door.
What is the perimeter of rectangle?The perimeter of a rectangle is the total length of all the sides of the rectangle.
P = 2 (L + B)
P = perimeter of rectangle, L = Length of rectangle, B = Breadth of rectangle
Given length of garage door = 12 feet
Given breadth of garage door = 16 feet
P = 2 (L + B)
P = 2 ( 12 + 16)
P = 2 (28)
P = 56 feet
Hence, The total length of the banner should be 56 feet to cover the entire door.
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HELPPP
Question #5
Suppose that you have "P" pieces of candy to distribute it evenly among your 5 friends. You can give each friend at most 8 pieces
of candy. Write an inequality to model this situation. Do not solve.
Answer:
[tex] \frac{p}{5} \times 8 = \frac{8p}{5} [/tex]
A container can hold 40 litres of milk and container can hold 60 litres of milk . What is the maximum capacity of a jar that can be used to measure the milk of both containers ?
The capacity of the two containers can be measured with a jar with a maximum capacity of 20 litres.
How to determine the maximum capacity of a jar that can be used to measure two milk jars
In this problem we find the case of two containers with different capacity, one with a capacity of 40 litres and other with a capacity of 60 litres, we can measure each of them based on the number of adds needed to fill each container. The number of adds (n) is equal to the container capacity (C), in litres, divided by the jar capacity (c), in litres:
n = C / c
If we assume that the number of adds is a natural numbers, then we determine the greatest common factor of both container capacities. First, decompose each number related to each container:
40 = 2³ × 5
60 = 2² × 3 × 5
Second, find the common factors and create the resulting product:
G.C.F. = 2² × 5
G.C.F. = 20
A jar with a maximum capacity of 20 litres can be used to measure the capacity of both containers.
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Drag each number tile to the box with the matching expression.
3
1
2
3
1
3
3
1
4
3
1
6
3
2
3
12
1
2
−
9
1
4
5
3
4
−
2
5
12
The first box is satisfied by 3 1/4
The second box is satisfied by 3 1/3
What is a fraction?
A fraction is a mathematical expression that represents a part of a whole or a ratio of two numbers. It consists of two parts: the numerator and the denominator.
The numerator represents the number of parts being considered, and the denominator represents the total number of parts in the whole. If we work on the boxes that we can see in the question then we end up with the values as shown above.
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NO LINKS!!
Shown in the figure is a cross-section of a design for a two-story home. The center height h of the second story has not yet been determined. Find h such that the story will have the same cross-sectional area as the first story.
h = _________ ft
Answer:
13 ft
-----------------------------
Area of the cross-section of the first story is:
A = lw A = 30*8 A = 240Area of the cross-section of the second story is the sum of rectangular and triangular sections:
A = lw + 1/2*bhA = 30*3 + 1/2*30*(h - 3)A = 90 + 15(h - 3)A = 90 + 15h - 45A = 15h + 45Since both story's have same cross-section area, we have equation:
15h + 45 = 24015h = 195h = 195/15h = 13The height of the second story is 13 inches.
What is area?Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.
Given that, the first story has length=30 inches and width=8 inches.
Now, area of the cross-section of the first story is
A = Length×Width
A = 30×8
A = 240 square inches
Area of the cross-section of the second story is the sum of rectangular and triangular sections:
A = Length×Width + 1/2×Base×Height
A = 30×3 + 1/2×30×(h - 3)
A = 90 + 15(h - 3)
A = 90 + 15h - 45
A = 15h + 45
Since both story's have same cross-section area, we have equation:
15h + 45 = 240
15h = 195
h = 195/15
h = 13 inches
Therefore, the height of the second story is 13 inches.
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a) b) c) d) By how much is 78 greater than-12? By how much is -23 less than 23? What must be added to -6 to give 105? What must be added to 15 to give -30?
The yield to maturity (YTM) on Billy Bob, Inc.'s bonds was 6.02%. It was reported at interest rates rose 52 basis points. If BBI's bonds YTM changed by the same amount, what would you expect the YTM to be after the increase? (answer in % format to the nearest basis point, i.e. xx.xx, with no % sign needed).
BBI's bonds after the increase given the rise in basis points, would be 6. 54 %
What are basis points ?Basis points (bps) are a unit of measurement used to express the change in the value of a financial instrument, such as a bond or stock, or the difference in interest rates or yields. One basis point is equal to 0.01% (1/100th of 1%) and is used to express small changes in the value of a financial instrument.
A rise by 52 basis points would lead to BBI's bond YTM being:
= 6. 02 + 0.52
= 6. 54 %
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How many kilometers per hour is this? Km/h
The speed of a car is 0.61 kilometer per hour.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
From the figure, time =1.68 minutes and distance =17 meter
Now, in kilometer per hour is
Here, speed = Distance/Time
= 17 meter/1.68 minute
= 0.017 km/0.028 hours
= 0.017/0.028
= 0.61 kilometer per hour
Therefore, the speed is 0.61 kilometer per hour.
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What is the quotient of 5.688\times 10^95.688×10 9 and 7.9 \times 10^27.9×10 2 expressed in scientific notation?
[tex]\cfrac{5.688\times 10^{9}}{7.9\times 10^{2}}\implies \cfrac{5.688}{7.9}\times \cfrac{ 10^{9}}{ 10^{2}}\implies 0.72\times 10^{9-2} \\\\\\ 0.72\times 10^{7}\implies 7200000\implies 7.2\times 10^{6}[/tex]
WILL GIVE BRAINLIEST cylinder has a volume of 1 and one sixteenth in3 and a radius of one fourth in. What is the height of a cylinder? Approximate using pi equals 22 over 7.
119 twelfths inches
119 over 22 inches
119 over 44 inches
119 over 56 inches
The height of the cylinder is 119/22 inches or 5.41 inches.
What is the area and volume of a right circular cylinder?The volume of a Right Circular Cylinder. In general, the volume of a right cylinder is the area of the base times the height of the cylinder. The area of the circular base is given by the formula A = πr2. Substitute to get V = πr²h.
Given here: Volume of the cylinder = 1¹/₁₆ in³ and radius of 1/4
We know the volume of the cylinder is equal to
V=πr²h
17/16 = 22/7 × 1/16×h
h=17×7 /22
h=119/22
h=5.41 inches
Hence, The height of the cylinder is 119/22 inches or 5.41 inches.
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The answer is B, 119/22 inches
Id like to order 5 halves of a cupcake for my family plus some extra for my 2 friends. They'll each like a quarter of a cupcake
The total number of cupcakes needed will be 3 cupcakes.
How to calculate the fractionA fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
Since you 5 halves of a cupcake for my family plus some extra for my 2 friends, the total number of cupcakes needed will be:
= 5 ( 1 /2) + 2 ( 1 / 4)
= 2 1/2 + 1/2
= 3
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Complete question
Id like to order 5 halves of a cupcake for my family plus some extra for my 2 friends. They'll each like a quarter of a cupcake. What is the total cupcakes needed?
one kilogram is 2.2 pounds what is the kilogram per pound
Here we have a relation to perform changes of units, we will see that:
1 pound = 0.455 kilograms
How many kilograms are in one pound?We know that one kilogram is 2.2 pounds, and we want find what is the "kilogram per pound".
We can write the relation:
1 kilogram = 2.2 pounds
To get the "kilogram per pound" we need to have a "1" on the right side, so we can divide both sides by 2.2, then we will get:
(1 kg)/2.2 = (2.2 lb)/2.2
0.455 kg = 1lb
This means that one pound is equalto 0.455 kilograms.
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Garrett bought 4 pounds of red apples and g pounds of green apples. Choose the expression that shows how many pounds of apples Garrett bought in all.
An expression that shows the total pounds of apples Garrett bought in all include the following: D. 4 + g.
How to write an equation to model this situation?In order to write an equation that model this situation, we would assign a variable to the total pounds of green apples and the total pounds of red apples respectively, and then translate the word problem into algebraic equation as follows:
Let the variable r represent the total pounds of red apples.Let the variable g represent the total pounds of green apples.Since Garrett bought 4 pounds of red apples and g pounds of green apples, an equation that models the total pounds of apples that he bought is given by:
Total pounds of apples = r + g
Total pounds of apples = 4 + g
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in the board game perfection, individuals must attempt to fit a number of shaped plastic pieces into their matching holes on a board before the buzzer goes off and makes the board spring upward. to make things interesting, a student sets the buzzer to a random time increment anywhere between 20 and 60 seconds. consider time until the buzzer sounds a random variable where any time between 20 and 60 has an equal likelihood.
The probabilities are equal, the expected time until the buzzer goes off simplifies to E(X) = 40.5.
Let X be a random variable representing the time until the buzzer goes off. X follows a uniform distribution, since any time between 20 and 60 seconds is equally likely. This can be represented by the formula P(X=x) = 1/41, where 41 is the total number of possible times (41 = 60 - 20 + 1).
Using this formula, the probability of the buzzer going off at any particular time can be calculated. For example, the probability of the buzzer going off at 23 seconds is P(X=23) = 1/41. The expected time until the buzzer goes off can also be found by taking the sum of each possible time multiplied by its individual probability. This is calculated as E(X) = Σ(x*P(X=x)). Since all the probabilities are equal, the expected time until the buzzer goes off simplifies to E(X) = 40.5.
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Alice wants to bake 9 cakes for a party. Alice needs 1/3 cups of sugar for each cake. How much sugar will she need for the 9 cakes?
Answer:
Step-by-step explanation:
Answer:
8 2/3
Step-by-step explanation:
Since she has 1/3 already, we need more. So here, we SUBRACT.
Subtract 9 with 1/3.
You'll get 8 2/3
Use a calculator to find the values of the inverse function in radians.
tan -¹(3.23)
The values of the inverse function in radians is 1.27
How to determine the value of the inverseFrom the question, we have the following parameters that can be used in our computation:
tan -¹(3.23)
Using the above as a guide, we have the following:
arctan(3.23)
Using a calculator, we have
arctan(3.23) = 1.27 radians
Hence, the values of the inverse function in radians is 1.27
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