To convert 2x = 2y into polar form, replace x with r cos(theta) and y with r sin(theta), then simplify, resulting in the polar equation cos(theta) = sin(theta) or theta = pi/4 + kpi, where k is an integer.
To convert the equation 2x = 2y to polar form, we need to use the relationship between Cartesian coordinates (x, y) and polar coordinates (r, (theta)). The transformations are given by x = r cos(theta) and y = r sin(theta).
Starting with our original equation 2x = 2y, we can substitute the transformations into the equation, which gives us 2(r cos(theta)) = 2(r sin(theta)). We can divide both sides by 2 to simplify, which results in r cos(theta) = r sin(theta). Since r cannot be 0 (because then both x and y would be 0, which does not satisfy the original equation), we can divide both sides by r, leading to cos(theta) = sin(theta). This equation implies that tan(theta) = 1. When tan(theta) equals 1, theta can be written as theta = arctan(1) or theta = pi/4 + kpi, where k is an integer representing the multiple full rotations around the circle.
What is the sum of the polynomials?
(7x3 – 4x2) + (2x3 – 4x2)
Answer:
ANswer is D on edgeunity
Step-by-step explanation:
What are the factors of 18??
What is the value of r? 35(r−7)=1
The answer is 8 and 2 over 3.
What is .62 rounded to the nearest tenth?
The table below shows the ticket rates for whale watching trips offered by Dolphin Tricks & Tours.
Age Ticket Price
Under three years free
Three to twelve years $35
Over twelve years $46
On a certain day, the company took 88 people on whale watching trips. There were 44 children aged twelve and under, of which some children were under three years. If x represents the number of children under three years, which equation can be used to find the value of x, where C represents the total amount of money collected from tickets that day?
...?
Answer:
What if it was $32 and $44, 82 and 54?
Step-by-step explanation:
On a certain day, the company took 82 people on whale watching trips. There were 54 children aged 12 and under, of which some children were under three years. If x represents the number of children under three years, which equation can be used to find the value of x, where C represents the total amount of money collected from tickets that day?
30 g equals how many dg
A standard deck of 52 playing cards contains 13 cards in each of four suits: diamonds, hearts, clubs, and spades. Two cards are chosen from the deck at random. What is the approximate probability of choosing one club and one heart?
The approximate probability of choosing one club followed by one heart from a standard deck of 52 playing cards is 5.9%.
The student's question pertains to the calculation of the probability of choosing one club and one heart from a standard deck of 52 playing cards. We start by recognizing that there are 13 clubs and 13 hearts in the deck, with each of the four suits represented equally.
Firstly, the probability of choosing a club (P(club)) is 13/52. After a club is chosen, there are 51 cards left in the deck. The number of hearts remains the same at 13 (since a club was chosen first). So, the probability of then picking a heart (P(heart)) is 13/51.
The two events, choosing a club and then a heart, are dependent events because the outcome of the second event depends on the outcome of the first. Hence, to find the combined probability, we multiply the probabilities of each event.
The probability of choosing one club followed by one heart is therefore P(club) imes P(heart) = (13/52) imes (13/51), which simplifies to approximately 0.059, or 5.9%.
A rock is kicked horizontally at 15 m/s from a hill with a 45degree slope. How long does it take for the rock to hit the ground?
Final answer:
The rock takes 2 seconds to hit the ground.
Explanation:
In order to find the time it takes for the rock to hit the ground, we can analyze the vertical motion of the rock. Since the rock is kicked horizontally, its initial velocity in the vertical direction is zero. The acceleration due to gravity is -9.8 m/s^2.
Using the equation h = ut + (1/2)gt^2, where h is the height, u is the initial velocity, g is the acceleration due to gravity, and t is the time, we can plug in the values to find the time.
Since the rock is kicked horizontally, the initial velocity in the vertical direction (uy) is zero, so the equation becomes h = (1/2)gt^2. We know that h = 0 since the rock is at the ground, and g = -9.8 m/s^2. Plugging these values into the equation, we get 0 = (1/2)(-9.8)t^2.
Solving for t, we find that t = 0 or t = 2 seconds. Since time cannot be negative, the rock takes 2 seconds to hit the ground.
I need help!
Secant DB intersects secant DZ at point D. Find the length of DA.
Answer:
[tex]DA=3[/tex]
Step-by-step explanation:
We have been given an image of a circle and we are told that Secant DB intersects secant DZ at point D.
We will use intersecting secants theorem to solve our given problem.
Intersecting secants theorem states that if two secants say MN and KL intersect at a point 'X' outside the circle, then product of XN and MX equals the product of XL and KX.
Using intersecting secants theorem we can set an equation as:
[tex]DA\cdot DB=DY\cdot DZ[/tex]
Upon substituting our given values in above equation we will get,
[tex]3x\cdot (3x+8)=x\cdot (32+x)[/tex]
Upon dividing both sides of our equation by x we will get,
[tex]\frac{3x\cdot (3x+8)}{x}=\frac{x\cdot (32+x)}{x}[/tex]
[tex]3\cdot (3x+8)=32+x[/tex]
Upon using distributive property [tex]a(b+c)=a*b+a*c[/tex] we will get,
[tex]9x+24=32+x[/tex]
[tex]9x-x+24-24=32-24+x-x[/tex]
[tex]8x=8[/tex]
Upon dividing both sides of our equation by 8 we will get,
[tex]\frac{8x}{8}=\frac{8}{8}[/tex]
[tex]x=1[/tex]
Since the length of DA is 3x, so upon multiplying 3 by 1 we will get,
[tex]\text{Length of DA}=3\cdot 1=3[/tex]
Therefore, the length of DA is 3 units.
if the tax that you pay when you purchase an item is 12% of the sale price, write an expression that gives the tax on the item with a price p. write another expression that gives the total price ofthe item, including tax.
- what operations are involved in th expression you wrote
-determine the total price, including tax, of an item that costs 75.
-explain how the order of operation helped you solve this problem.
The tax on an item of price p is calculated as 0.12p and the total price is p + 0.12p. On calculating for an item that costs 75, the total cost with tax is 84. The order of operations (PEMDAS/BODMAS) was used to solve the problem accurately
Explanation:The tax on the item with a price p can be given by the expression 0.12p, using the operation of multiplication. The total price of the item, including tax would be p + 0.12p. This is done by using both addition and multiplication operations.
To determine the total price, including tax, of an item that costs 75, we substitute 75 for p in the second expression: 75 + 0.12*75 = 75 + 9 = 84. Therefore, an item that costs 75 before tax would cost 84 with tax.
Order of operations is important in this problem to ensure accurate calculations. According to PEMDAS/BODMAS rules (Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction), multiplication should be carried out before the addition, hence why 0.12*75 was calculated before adding the result to the initial cost of the item (75).
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The taxation on an item with a price tag of 'p' can be represented as 0.12p. The total cost, counting tax, is depicted as 1.12p. Applying these expressions, an item priced at 75 would cost 84 including the 12% tax.
Explanation:The tax on an item with a price p can be expressed as 0.12p. This is because 12% is equivalent to 0.12 in decimal form. To find the total price of the item, including tax, you would add the original price (p) to the tax (0.12p). This can be written as p + 0.12p, or simplified further to 1.12p.
The operations involved in these expressions include multiplication and addition. To determine the total price, including tax, of an item that costs 75, you would plug in 75 for p in the total price expression, 1.12p. This works out to 1.12 * 75 = 84. The order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) dictates that you perform multiplication before addition in the total price expression. Since there are no parentheses or exponents, you would multiply 0.12 by p (or the price of the item), and then add that result to p, to find the total price including tax.
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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) = f(b).
f(x) = cot (x/2) , [π, 9π]
There are around 132 births in the united states per minute. how many births per day
WILL MARK BRAINLIEST Harry had $32. He spent all the money on buying 3 notebooks for $x each and 4 packs of index cards for $y each. If Harry had bought 5 notebooks and 5 packs of index cards, he would have run short of $18. A student concluded that the price of each notebook is $5 and the price of each pack of index cards is $1. Which statement best justifies whether the student's conclusion is correct or incorrect? The student's conclusion is incorrect because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 50 is (8, 2). The student's conclusion is incorrect because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 18 is (8, 2). The student's conclusion is correct because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 18 is (5, 1). The student's conclusion is correct because the solution to the system of equations 3x − 4y = 32 and 5x − 5y = 50 is (5, 1).
Solve: log2 (x) +log2(x+7) =3
(2 is the base) ...?
Final answer:
To solve the equation log2 (x) + log2(x+7) = 3, you can combine the logarithmic terms using the property log(a) + log(b) = log(a*b). By applying this property and solving the resulting quadratic equation, we find that x = 1.
Explanation:
To solve the equation log2 (x) + log2(x+7) = 3, we need to combine the logarithmic terms using the property log(a) + log(b) = log(a*b). Applying this property, we get log2 (x*(x+7)) = 3. Next, we can rewrite this equation in exponential form as 2^3 = x * (x+7). Simplifying further, we have 8 = x^2 + 7x. Rearranging the equation, we get a quadratic equation x^2 + 7x - 8 = 0. Solving this quadratic equation, we find that x = -8 or x = 1. However, since the logarithm of a negative number is undefined, the solution is x = 1.
Find the coordinates for the midpoint of the segment with endpoints given.
P1 P2 M
(10, 6) (-4, 8) ( , ) ...?
A pumpkin with a mass of 2.5 kg was pushed toward a wall. The average acceleration of the pumpkin was 10.7 m/s². How much force was applied to the pumpkin to make it move?
A circle has an area of 98mm^2. Find the circumference of the circle
Find the sum: –1.54 + 5.093 ...?
Tina lives in a state that charges her 4.5% state income tax on her federal taxable income. If her federal taxable income is $61,600, how much does Tina pay in state income tax?
a. $1,545
b. $227
c. $4,372
d. $2,772
Crafty Grandma Edith sat her family down during Thanksgiving and told them they couldn’t have any pumpkin pie until they worked out this puzzle. Her 6-year-old granddaughter was the first to solve it! Can you work out what 9183 equals?
8809=6
7111=0
9881=5
6660=4
5531=0
2516=1
3590=2
6855=3
1012=1
5731=0
9191=2
9183=?
How many different 12-member juries can be made from 150 people? Please explain how. Thank you (:
Sarah is driving her car very smoothly from
Austin to Dallas one day. At 6:00 pm she is
travelling at 20 mph, while 25 minutes later
she is travelling at 40 mph.
Calculus tells us that at some time between
6:00 pm and and 6:25 pm her acceleration is
exactly x mph/h. Determine x.
The acceleration (x) is approximately 48 mph/hr, determined by dividing the change in velocity (20 mph) by the change in time (0.41667 hr).
Explanation:The subject of this problem is acceleration, which in this context refers to the rate at which Sarah increased her speed during a particular period of time. Here, the change in speed was from 20 mph to 40 mph, a difference of 20 mph. The time over which this change occurred was 25 minutes, but since acceleration is usually measured in hours, we need to convert this to 25/60 = 0.4167 hours.
The formula for acceleration is change in speed/ change in time.
Therefore, to calculate the acceleration, we divide the change in speed (20 mph) by the time (0.4167 hr) to get x = 20 mph / 0.4167 hr = 47.99 mph/hr or approximately 48 mph/hr, which is the acceleration.
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Trent purchases 44 euros worth of souvenirs while on vacation in France. If $1 U.S. = 0.678 euros , find the cost of the souvenirs in US dollars. Round to the nearest cent
Using the exchange rate $1 U.S. = 0.678 euros, the cost of the souvenirs in US dollars is calculated by dividing the total in euros (44 euros) by the exchange rate (0.678). The result is approximately $64.89.
Explanation:To find the cost of the souvenirs in US dollars, we must first understand the exchange rate provided $1 U.S. = 0.678 euros. This means that one dollar buys 0.678 euros. To convert the euros to dollars, we divide the amount in euros by the exchange rate. Here's how you can do it:
Step 1: Note down the total amount in euros which is 44 euros.Step 2: Note down the exchange rate $1 U.S. = 0.678 euros. Step 3: Divide the total amount in euros (44 euros) by the exchange rate (0.678).When you carry out the calculation, you'll get approximately $64.89. Therefore, the cost of the souvenirs in US dollars is around $64.89.
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Which of the following is a factor of 2x4 + 22x3 + 60x2?
2x3
x4
x + 4
x + 5
the correct answer is x+5 :DDD it was also the correct answer on the test !
Final answer:
To determine which of the given options is a factor of the expression 2x⁴ + 22x³ + 60x², we can use synthetic division. The only option that is a factor of the given expression is x⁴.
Explanation:
To determine which of the given options is a factor of the expression 2x⁴ + 22x³ + 60x², we can use synthetic division. Let's test each option:
2x³: When we divide 2x⁴ + 22x³ + 60x² by 2x3, the remainder is not zero. Therefore, 2x3 is not a factor.
x⁴: When we divide 2x⁴ + 22x³ + 60x²by x4, the remainder is zero. Therefore, x4 is a factor.
x + 4: When we divide 2x⁴ + 22x³ + 60x² by x + 4, the remainder is not zero. Therefore, x + 4 is not a factor.
x + 5: When we divide 2x⁴ + 22x³ + 60x² by x + 5, the remainder is not zero. Therefore, x + 5 is not a factor.
Based on the results, the only option that is a factor of the given expression is x⁴.
Which information from this passage about enkai is most important to include in a summary of the overall story?the tribe’s relationship with enkai is crucial to them.the tribe’s behavior affects enkai’s mood.enkai has moods that are reflected in the weather.enkai can be the black god or the red god
a 14 foot ladder is leaning against a building. the ladder makes a 45 degree angle with the building. how far up the building does the ladder reach?
Using the sine function and known angle and ladder length, the distance up the building the ladder reaches is \(7\sqrt{2}\) feet.
The correct answer is option C) \(7\sqrt{2}\) feet.
To find how far up the building the ladder reaches, we can use trigonometric functions, specifically the sine function since we have the angle and the length of the ladder.
Given:
- Length of the ladder (hypotenuse) = 14 feet
- Angle with the building = 45 degrees
Let [tex]\(x\)[/tex]be the distance up the building that the ladder reaches.
Using the sine function [tex](\(\sin\))[/tex] in a right triangle:
[tex]\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \][/tex]
Substituting the known values:
[tex]\[ \sin(45^\circ) = \frac{x}{14} \][/tex]
Since [tex]\(\sin(45^\circ) = \frac{\sqrt{2}}{2}\),[/tex] we have:
[tex]\[ \frac{\sqrt{2}}{2} = \frac{x}{14} \][/tex]
To solve for [tex]\(x\),[/tex] multiply both sides by 14:
[tex]\[ x = 14 \times \frac{\sqrt{2}}{2} \][/tex]
[tex]\[ x = 7\sqrt{2} \, \text{feet} \][/tex]
Therefore, the ladder reaches [tex]\(7\sqrt{2}\)[/tex] feet up the building.
Therefore the correct answer is option C) [tex]\(7\sqrt{2}\)[/tex]feet.
The question probable may be:
A 14 foot ladder is leaning against a building. The ladder makes a 45 degree angle with the building. How far up the building does the ladder reach?
A. 7 feet
B. 28sqrt(2) feet
c. 7sqrt(2) feet
D. 14sqrt(2) feet.
one side of a rectangle is 4cm shorter than three times the other side, find the side lengths if the area is 319
1) A method for solving a system of equations where you look at the equations and reason out the answer without doing any formal mathematics .
Will give brainliest answer, need an answer ASAP
You can factor, that takes almost no effort
Hope this helps
Answer:
inspection method
Step-by-step explanation:
Given f(x)=x^3-6x^2+9x and g(x)=4.
Find the coordinates of the points common to the graphs of f and g.
-find all zeros of f
-if the domain of f is limited to the closed interval [0,2], what is the range of f?
To find the coordinates of the points common to the graphs of f and g, set f(x) equal to g(x) and solve for x. The zeros of f(x) are approximately x = -1, 2, and 2.98. The range of f when the domain is limited to [0,2] is approximately [-1,9].
To find the coordinates of the points common to the graphs of f and g, we will set f(x) equal to g(x) and solve for x.
f(x) = g(x)
[tex]x^3-6x^2+9x = 4\\x^3-6x^2+9x-4 = 0[/tex]
Using a graphing calculator or software, we can find that the zeros of f(x) are approximately x = -1, 2, and 2.98.
The range of f when the domain is limited to the closed interval [0,2] is the set of y-values that f(x) takes on within that interval.
By using the First Derivative Test, we can determine that the range of f in the interval [0,2] is approximately [-1,9].
If a person shoots a basketball overhand from a position of 8 feet from the floor, then the path of the basketball through the hoop can be modeled by the parabola y=(-16x^2/0.434v^2)+1.15x+8, where v is the velocity of the ball in ft/sec, y is the height of the hoop and x is the distance away from the hoop. If the basketball hoop is 10 feet high and located 17 feet away, what initial velocity v should the basketball have to go through the hoop?
The correct initial velocity (v) for the basketball to go through the hoop is approximately 0.0406 ft/s.
To find the initial velocity v, we can use the given information and set up the equation using the height of the hoop and the distance away from the hoop. The equation of the path of the basketball is given by:
y = -16x^2/(0.434v^2) + 1.15x + 8
Given that the hoop is 10 feet high and located 17 feet away, we can substitute these values into the equation:
10 = -16(17)^2/(0.434v^2) + 1.15(17) + 8
Now, we can solve this equation for the initial velocity v. First, simplify the equation:
10 = -16(17)^2/(0.434v^2) + 19.55 + 8
Combine the constant terms on the right side:
10 = -16(17)^2/(0.434v^2) + 27.55
Now, isolate the term with v on one side:
(16(17)^2)/(0.434v^2) = 17.55
Next, multiply both sides by (0.434v^2)/(16(17)^2) to solve for v^2:
v^2 = (16(17)^2)/(0.434 * 17.55)
Now, take the square root of both sides to find v:
v = sqrt((16(17)^2)/(0.434 * 17.55))
Calculating this expression will give you the initial velocity v. Let's calculate:
v ≈ 0.0406 ft/s
The initial velocity v of the basketball should be approximately [tex]\(14.86 \, \text{ft/sec}\)[/tex] for it to go through the hoop.
Explanation:To find the initial velocity v required for the basketball to go through the hoop, we utilize the parabolic model [tex]\(y = -\frac{16x^2}{0.434v^2} + 1.15x + 8\)[/tex]. Given that the height of the hoop (y) is 10 feet and the distance away from the hoop (x) is 17 feet, we substitute these values into the equation:
[tex]\[10 = -\frac{16 \cdot 17^2}{0.434v^2} + 1.15 \cdot 17 + 8.\][/tex]
First, simplify the equation:
[tex]\[10 = -\frac{16 \cdot 17^2}{0.434v^2} + 1.15 \cdot 17 + 8.\][/tex]
Combine like terms:
[tex]\[10 = -\frac{16 \cdot 17^2}{0.434v^2} + 19.55.\][/tex]
Isolate the fraction:
[tex]\[\frac{16 \cdot 17^2}{0.434v^2} = 9.55.\][/tex]
Now, solve for v²:
[tex]\[v^2 = \frac{16 \cdot 17^2}{0.434 \cdot 9.55}.\][/tex]
Finally, find v by taking the square root:
[tex]\[v \approx \sqrt{\frac{16 \cdot 17^2}{0.434 \cdot 9.55}} \approx 14.86 \, \text{ft/sec}.\][/tex]
The calculation shows that an initial velocity of approximately [tex]\(14.86 \, \text{ft/sec}\)[/tex] is required for the basketball to follow the modeled path and successfully go through the hoop.