To determine which of the given lines are tangent to circle p, we need to first find the equation of the circle.
The equation given is (x^3)(y^2)=25, which can be rewritten as y^2=25/(x^3).
Taking the derivative of this equation with respect to x,
we get: 2y(dy/dx) = -(75)/(x^4).
Simplifying this, we get dy/dx = -(75y)/(2x^4).
Now we can substitute the slope of each given line into this equation and find the corresponding value of y. If this value of y satisfies the equation of the circle, then the line is tangent to the circle at that point. We find that only the line y = 5x + 1 satisfies this condition, and therefore it is the only line that is tangent to circle p.
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(√x)5 help please fast
Answer:
x2√x
Step-by-step explanation:
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
PLEASE HELP WITH THIS PROBLEM
Answer:
Step-by-step explanation:
6y = x + 1
y = 1/6 x + 1/6
slope of a perpendicular line = -6
y-5 = -6(x-(-6)
y-5 = -6(x+6)
y-5 = -6x - 36
y = -6x -36 + 5
y = -6x - 31
slope of a paralle line = 1/6
y-5 = 1/6(x-(-6)
y-5 = 1/6(x+6)
y -5 = 1/6 x + 1
y = 1/6 x + 1 + 5
y = 1/6 x + 6
help me please [giving brainliest to best answer with step by step]
Hi there!
\(\large\boxed{3\text{ } \frac{3}{4} cm^3}\)
Knowing that one cube has side-lengths of 1/2, we can calculate the dimensions for the prism:
Length: 1/2 × 5 = 2.5 cm
Height: 1/2 × 3 = 1.5 cm
Width: 1/2 × 2 = 1 cm
Use this formula to solve for the volume:
V = l × w × h
Thus:
V = 2.5 × 1.5 × 1 = 3.75 cm³
Convert to fraction:
75/100 = 3/4
Thus, the volume in mixed-numbers is 3 3/4 cm³.
Marty went on a bike ride to the store 8 miles away. If it took Marty 34 of an hour to get there and 12 of an hour to get back, what was his average rate of speed (miles per hour) for the entire trip?
Answer:
um
Step-by-step explanation:
i dont know
help me please: tan3x-tanx-1=0
Answer: \(x=0.30714\dots +\pi n\)
Step-by-step explanation:
\(\Rightarrow \tan3x-\tan x-1=0\\\\\Rightarrow \dfrac{3\tan x-\tan ^3x}{1-3\tan ^2x}-\tan x-1=0\\\\\Rightarrow 3\tan x-\tan ^3x+( 1-3\tan ^2x)(-1-\tan x)=0\\\Rightarrow 3\tan x-\tan ^3x-1-\tan x+3\tan ^2x+3\tan ^3 x=0\\\Rightarrow 2\tan ^3x+3\tan ^2x+2\tan x-1=0\\\Rightarrow \tan \left(x\right)\approx \:0.31718\)
- 8x + 1 = 5(x + 1) - 13(x-3)
Answer:
steps for solving
1 Distribute
2
Distribute
3
Add the numbers
4
Combine like terms
5
Subtract
1
from both sides
6
Simplify
7
Add
8x
to both sides
8
Simplify
9
Divide both sides by the same factor
Step-by-step explanation:
x = 43/16
brainiest pls
A rectangular garden 30 m by 40 m has two paths of equal width crossing through it as shown. Find the width of each path if the total area covered by the paths is 325 m^2
The width of the two paths is 5 m.
A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x2 is a non-zero term(a ≠ 0). For writing a quadratic equation in standard form, the x2 term is written first, followed by the x term, and finally, the constant term is written. The numeric values of a, b, c are generally not written as fractions or decimals but are written as integral values.
Let the width of the two paths be x.
Thus, the total area covered by the paths is = (30×x) + (40×x) - x²
The total area covered by the paths is 325 m².
Equate both of them.
⇒ (30×x) + (40×x) - x² = 325
⇒ 30x + 40x - x² = 325
⇒ x² -70x + 325 = 0
Solving the above equation, we get
x = 65 or x = 5
The valid solution is x = 5.
Thus, the width of the two paths is 5 m.
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16x2 + 5 = 40x what is x equal to
Answer:
37/40
Step-by-step explanation:
16*2+5=40x
32+5=40x
39=40x
x=37/40. is your answer
Which of the expressions below is equal to 10x+30? Select all that apply.
how many square miles of land did the railroad companies get for each mile of track they laid?
The amount of land the railroad companies received for each mile of track they laid varied depending on the specific circumstances and agreements.
However, a common benchmark used during the construction of railroads in the United States was the granting of land through the Homestead Act of 1862. Under this act, railroad companies were granted approximately 6,400 acres (10 square miles) of land for every mile of track laid. This land was typically located alongside the tracks and served as an incentive for the companies to expand and develop the rail network across the country.
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why would you use a trigonometric function to set-up an application problem instead of a non-trigonometric function
Trigonometric functions are used to model relationships between angles and sides of a right triangle. They are particularly useful in solving problems that involve angles, distances, heights, and lengths that are difficult to measure directly.
For example, consider a problem that involves finding the height of a building. By measuring the length of the shadow cast by the building at a particular time of day, the angle of the sun's rays can be calculated using trigonometry. Once the angle is known, the height of the building can be determined using the tangent function.
In contrast, a non-trigonometric function may not be able to model the relationship between the given quantities in such problems, and may not provide an accurate solution. Therefore, when a problem involves angles or distances that are not directly measurable, trigonometric functions are typically the best tool for setting up and solving the problem.
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Find the quotient of 3,976 ÷ 28 = ________. Use the partial quotients strategy to help you.
Answer:
142
Step-by-step explanation:
Hope this helps
What happens to the standard error of an estimate when the sample size in a SRS decreases?A. The standard error gets smaller
B. The precision of the estimate increases
C. The standard error stays roughly the same
D. The precision of the estimate decreases
The precision of the estimate decreases when standard error of an estimate when the sample size in a SRS decreases. So, the correct answer is D).
The standard error of an estimate measures the variability of sample means around the population mean. As the sample size in a simple random sample (SRS) decreases, the sample mean becomes less representative of the population mean, resulting in more variability or less precision in the estimate.
The standard error increases as the sample size decreases because there is more uncertainty in the estimate due to the smaller sample size. Therefore, decreasing the sample size will increase the margin of error and decrease the precision of the estimate. So, the correct option is D).
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who is good at math?! IM GIVING BRAINLIEST! comment or answer on the question so we can talk cuz i need help!!
Answer:
Wheres the question then i'll help
Step-by-step explanation:
Two pools are being filled with water. To start, the first pool contains 915 Liters of water and the second pool is empty. Water is being added to the first pool at a rate of 15.25 liters per minute. Water is being added to the second pool at a rate of 45.75 Liters per minute. After how many minutes will the two pools have the same amount of water? How much water will be in each pool when they have the same amount?
a) 30 minutes are taken to have the same amount of water.
b) Both pools have an amount of 1372.5 liters when 30 minutes have passed.
What is Linear Function?A linear function is one that produces a straight line when plotted. Generally, it is a polynomial function with a maximum degree of 1 or 0.
Now in the given question ,
a) Physically speaking, the capacity (Q) of each pool, in liters, is equal to the product of flow rate , in liters per minute, and time (t), in minutes. Hence, we derive the following functions :
First pool,
\(Q_1=915+15.25t\\\) ...... (1)
Second pool,
\(Q_2=45.75t\) ....... (2)
The following expression can be used to calculate how long it will take to find two pools with the same amount of water:
\(Q_1=Q_2\) ........ (3)
By putting value of (1) and (2) in (3),
915 + 15.25 t = 45.75 t
30.5 t = 915
t = 915 ÷ 30.5
t = 30 minutes
30 minutes are taken to have the same amount of water.
b) By (2) and knowing that t = 30 , then we have the corresponding amount:
\(Q_2=45.75t\\\\Q_2=45.75*30\\\\Q_2=1372.5L\)
Both pools have an amount of 1372.5 liters when 30 minutes have passed.
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what role do your needs and wants play when creating a budget?
Your needs are essential expenses such as rent, utilities, groceries, and transportation.
These should be prioritized in your budget as they are necessary for your survival. On the other hand, your wants are non-essential expenses such as eating out, entertainment, and shopping. While it is important to treat yourself, it is also important to allocate a reasonable amount of money towards your wants. Needs and wants play a crucial role in creating a budget. A budget helps allocate financial resources according to one's priorities. Needs are essential items required for daily living, such as housing, food, and utilities. Wants are desires or non-essential items, like vacations or entertainment. While creating a budget, it's important to prioritize needs over wants to ensure financial stability. Understanding the difference between the two and allocating funds accordingly helps in maintaining a balanced lifestyle, promoting healthy spending habits, and achieving long-term financial goals. A well-structured budget ensures that you can fulfill both your needs and some wants within the allotted resources.
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Needs and wants play a vital role in creating a budget by helping you prioritize your spending, make trade-offs, and allocate your financial resources effectively. By considering both your essential expenses and desired extras, you can create a balanced budget that reflects your financial goals and values.
When creating a budget, your needs and wants play a crucial role in determining how you allocate your financial resources. Here's how they factor in:
Identifying Needs: Your needs are the essential expenses required for your basic well-being and survival. These typically include housing, utilities, food, transportation, healthcare, insurance, debt repayments, and other necessary expenses. Understanding your needs helps you prioritize allocating funds to cover these essential costs first. Ensuring your needs are met is the foundation of any budget.
Prioritizing Wants: Wants, on the other hand, are things you desire or would like to have but are not essential for your survival or basic well-being. This category includes discretionary expenses such as entertainment, dining out, travel, hobbies, luxury items, and other non-essential purchases. While wants are not as critical as needs, they contribute to your overall quality of life. Allocating a portion of your budget for wants allows you to enjoy these extras within your financial means.
Trade-offs and Decision Making: Budgeting requires making decisions about how to allocate limited resources. By considering your needs and wants, you can evaluate trade-offs between various expenses. If your needs are not being fully met within your current budget, you may need to reduce or eliminate some wants temporarily to ensure your essential expenses are covered. On the other hand, if your needs are comfortably met, you have more flexibility to allocate funds toward wants or savings.
Flexibility and Adjustments: Needs and wants can evolve over time. When creating a budget, it's important to regularly reassess and adjust it to align with your changing circumstances and priorities. For instance, if your income increases, you might have more room to allocate additional funds toward wants or savings. Similarly, if your needs change, such as due to a job loss or a new family member, you may need to make adjustments to ensure your budget remains sustainable.
In summary, needs and wants play a vital role in creating a budget by helping you prioritize your spending, make trade-offs, and allocate your financial resources effectively. By considering both your essential expenses and desired extras, you can create a balanced budget that reflects your financial goals and values.
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I have no clue what the answer
carney needs $60 to buy her mother a gift. She has saved 25% of that amount so far. Bow much has she saved so far - i really need HELPPP
Answer:
25 percent off 60.00 is 45.00
Step-by-step explanation:
In 1833 A ship arrived in Calcutta with 120 tons remaining of its cargo of ice one third of the original cargo was lost because it had melted on the voyage how many tons of ice was the ship carrying when it set sail
Therefore, the ship was carrying 180 tons of ice when it set sail.
In 1833, a ship arrived in Calcutta with 120 tons of remaining cargo of ice, and one third of the original cargo was lost due to melting on the voyage.
We need to determine the original amount of cargo of ice the ship was carrying when it set sail.
Let's solve this problem step-by-step.
Step 1:
Let's denote the original amount of cargo of ice the ship was carrying when it set sail as x.
Step 2:
One-third of the original cargo was lost due to melting on the voyage.
Thus, the remaining two-thirds cargo of ice reached Calcutta.
Hence, the remaining cargo of ice was 120 tons.
We can write it mathematically as; 2/3 x = 120 tons
Step 3:
Solving for x, the original amount of cargo of ice the ship was carrying, we can cross-multiply the above equation as: 2x = 3 × 120 tons
2x = 360 tons
x = 360/2 tons
x = 180 tons
The original amount of cargo of ice the ship was carrying when it set sail was 180 tons.
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a nurse manager approves two staff nurses to attend a national conference
The nurse manager approves two staff nurses to attend a national conference.
The nurse manager has given their authorization or consent for two staff nurses to participate in and attend a national conference. This decision indicates that the nurse manager recognizes the value and relevance of the conference for professional development and sees the benefit of the staff nurses' participation. By approving their attendance, the nurse manager demonstrates support for their growth, learning, and exposure to new knowledge, experiences, and networking opportunities available at the conference.
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A movie is 1 7/8 hours long. After 45 minutes, how much of the movie is left?
help me please ……………..
Answer:
I can t see it
Step-by-step explanation:
the phone calls to a computer software help desk occur at a rate of 3 per minute in the afternoon. compute the probability that the number of calls between 2:00 pm and 2:10 pm is: (a) exactly 25. (b) more than 25.
The probability that the number of phone calls between 2:00 pm and 2:10 pm is exactly 25 is 1/110,592,893.
To calculate this probability, use the Poisson distribution formula: P(x) = (e^-λ * λ^x) / x!, where λ = 3 x 10 = 30. Therefore, P(25) = (e^-30 * 30^25) / 25! = 1/110,592,893.
The probability that the number of phone calls between 2:00 pm and 2:10 pm is more than 25 is the sum of probabilities of all calls more than 25. That is, the probability is 1 - (e^-30 * (30^0 + 30^1 + 30^2 + ... + 30^25)) / (0! + 1! + 2! + ... + 25!).
By using the same Poisson distribution formula, the probability is 1 - 0.99988822 = 0.00011178.
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A balloon has a circumference of 16 cm. Use the circumference to approximate the surface area of the balloon to the nearest square centimeter.
804 cm2
326 cm2
256 cm2
81 cm2
Answer:
The answer is 256 cm 2.....
Solve: 8y - 3 > 10y + 21
Translate this phrase into an algebraic expression, Nine more than the quotient of a number and 7 is 6
Answer:
x/7 + 9 = 6
Step-by-step explanation:
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If a train travels 165 km in 1 hour 50 minutes at a constant speed, calculate how far it could travel in 3 hours
The train travel 270 Km in 3 hours.
What is speed- distance?Speed = Distance/Time Distance = Speed X TimeTime = Distance / SpeedGiven:
Distance = 165 Km
Time= 1 hour 50 min
= 1 5/6 hour = 11/6 hour
So, speed= distance/ time
speed = 165 / (11/6)
= 165 x 6/11
= 15 x 6
= 90 Km/ h
Then, In three hour the train travels
Distance= 90 x 3
Distance= 2700 Km
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Recall that in Problem 3 of the reading questions for Section 2.1, you found that if f(x) = ln(x), then f'(2) = 1/2. Use this to find a formula for the tangent line to f(x) = ln(x) at x = 2.
formula for the tangent line is y=x-1 and differentiation of ln(x) is 1/x
A straight line without crossing the curve , it touches the curve at one single point is called tangent . Finding the derivative of a function or a variable in mathematics is called differentiation.
The ratio of the vertical to the horizontal distance between any two points on it is called slope of ray or line or line segment in analytical geometry.
y-y1 = m(x-x1)
If the function passes through (1,0) and the slope equals to 1 is:
y-0 = 1(x-1)
y=x-1
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Tangents are straight lines that only touch curves at a single spot rather than crossing them. Differentiation in mathematics refers to the process of determining a function's or variable's derivative.
The slope of a ray, line, or line segment in analytical geometry is the ratio of the vertical to the horizontal distance between any two locations on it.
y-y1 = m(x-x1) (x-x1)
If a function goes through the point (1, 0) and its slope is 1, then:
y-0 = 1(x-1) (x-1)
y=x-1
how to solve for x? i need help please help fast
Hi!
x² = 11,2² - 8,5²
x² = 125,44 - 72,25
x² = 53,19 |√
x ≈ 7,3
Determine the number of operations needed to solve 7c = 84
Answer:
12
Step-by-step explanation:
7c=84
c=84/7
c=12
Answer:
2
Step-by-step explanation:
You need division and multiplication (division for 84/7 and multiplication to identify 7c = 7 x c), which means 2.
Hope that helps!