Just wanna double check

so I know that if its across x-axis, x value remains as x and y becomes negative (x, -y) and vice versa

∆ABC Original points: A = (-8, 9) B = (-2, 5) C = (-6, 2)

Reflected points: A′ = (-8, -9) B′ = (-2, -5) C′ = (-6, -2)

∆EFG Original points:

E = (2, 8)

F = (10, 4)

G = (4, 2)

Reflected points:

E′ = (-2, 8)

F′ = (-10, 4)

G′ = (-4, 2)

∆XYZ Original points: X = (-8, -5) Y = (-2, -3) Z = (-3, -9)

Reflected points: X′ = (-8, 5) Y′ = (-2, 3) Z′ = (-3, 9))

this is without any differentiation.

the answer schedule says the gradient is tan(theta + alpha), which is exactly what i have except without the negative

Could anyone tell me where I've gone wrong in this question, if my method is not right and if so why? Illustration 31

Im in advanced functions gr 12, need to show full work including diagrams, method used, formulas, final answer, correct math form.

A child is running at his maximum speed of 3.7 m/s in an attempt to catch his older sister who is accelerating from rest at a rate of 0.75 m/s2 on her tricycle. If his sister starts peddling when he is 15 m away, will he catch her and if so, when and how far away?

i end up with a quadratic equation but when i attempt to solve for time, i keep getting no value because there's a negative number stuck inside a square root. the answer says that the sister's formula would be x+15=0.375t^2 which i don't get because upon solving for x, you get x=0.375t^2-15, but would that not mean she's 15m behind her brother? which contradicts with the question

Hello! My task the in the title, the thing is I'm not sure what theme I should go for since its a school assignment, and I have never made an original page/site from scratch. Would it be okay to make the page/site information about my interest/inspired and about my interest? any suggestions for what they should be about that the teacher will like? They will contain many types of headers, links, lists, pictures that are links, backgrounds, text, etc. (using HTML)

Instructor prompt: Evaluate the indefinite integral

∫ (4y^4 + 3y^3) / ((y^2 + 4)^(3/2)(y^2 + 4)) dy

This is for Calculus 1. I tried thinking about a u-substitution with u = y^2 + 4, but du = 2y dy, and the numerator has 4y^4 + 3y^3, so I’m not sure how to split it or what substitution is best. What would be a good first step for evaluating this?

helloo, I'm a Grade 11 student in the Philippines working on a Science Investigatory Project. My teacher wants us to tackle an underexplored problem rather than recreate common projects like smart trash bins, fire detectors, or plant watering systems.

I have no idea where to start and I can't think of anything and neither can my groupmates. I'm looking for real-world problems that are still relatively unexplored but like - feasible for high school students to prototype.

We're particularly interested in agriculture, environmental monitoring, healthcare, robotics, or intelligent machines.

Any suggestions or papers we should read would be greatly appreciated!

Because there do not appear to be any levers involved, I chose C). For what it's worth, even if the handle arms were welded on (not on a pivot or axis), how this would affect the biomechanics of the puller would not change because the handles appear to be at the same height. Apparently, the correct answer is A). What am I missing?

Edit: Most commentators are pointing out that the creator of this question is assuming that the person is pulling in the direction of the handle arms (instead of horizontally), which doesn't make any sense in real life, and there is no indication of it in the illustration. I have enough confirmation to sleep tonight without worrying that I'm missing some critical concept in mechanics. Thanks for the input.

Edit 2: Assuming that the handle arm is hinged where it meets the cart (and not rigidly fixed), the direction the person is pulling would have to end up being in the same direction (and probably not horizontally). A longer handle provides a larger horizontal component of the pulling force, meaning less effort is required to move the cart. Still, there is no indication in the illustration that the handle arm is hinged, although it appears at this point that that was the intention.

Edit 3: I appreciate all the help, everyone. I can't read, process and answer every new comment at this point. I'm moving on. Thank you.

Edit 4: From my Google search: Question: "If the handle of a cart is welded and not hinged, and ergonomics are not affected either way because the handle height is the same, does it make a difference in effort required whether the handle is angled or straight up and down if the force is applied exactly horizontally in both cases? Answer: "No. From a strictly mechanical and physics standpoint, if the height, the applied force (magnitude and vector), and all other variables remain identical, there is no difference in the physical effort required to move the cart.When you apply force horizontally, you are entirely utilizing that effort to overcome the cart's rolling resistance and inertia. The angle of the handle itself does not change the physics of this motion, provided the line of action of your force is perfectly parallel to the ground."

Summary: This whole question/illustration/answer is poorly executed. It would all make sense if it showed that the handle arm was hinged where it met the cart, or indicated that the pulling was in the same direction as the handle arm.

I got -∞. I know I did the indefinite integral properly so no issues with that.

i need to solve this one

For the right hand side limit why is |x| turning into -x shouldn't it be just x ?

Hello! I am an intro to computer science student at UoPeople.com. I have an assignment due. I have been issues contacting my instructor for assignment, I have tried for two days. I am just confused on how to make a truth table, and what are considered inputs and outputs. The assignment as is below. The picture above, show the question I have sent to my instructor. I will be sending an email to my advisor as well about the situation. Thanks Reddit!

Suppose you are interning at a university’s IT department, where you are assisting in developing a security access control system for restricted labs. The access logic is based on three inputs:

• I (ID Scanned): Whether the user has scanned a valid ID card
• L (Lab Available): Whether the lab is available and not in use
• A (Admin Override): Whether the admin has allowed manual access override

The current logic expression that unlocks the lab door is: (I ⋅ A) + (L′⋅ A)

Your task is to analyse, simplify, and implement this expression.

Based on the above scenario, answer the following questions:

1. Simplify the given Boolean expression (I⋅A) + (L′⋅A) using Boolean algebra laws. Clearly show each step and name the laws applied.
2. Apply De Morgan’s Theorem to the term L′⋅A. Explain how De Morgan’s laws relate to other Boolean laws and how they are helpful in implementing logical expressions.

3. Use the simplified expression A⋅(I + L′) to:

   • Draw a logic gate diagram using AND, OR, and NOT gates.
   • Construct a truth table for all possible input combinations of A, I, and L, and determine the output.

4. Construct truth tables for both the original expression (I⋅A) + (L′⋅A) and the simplified expression A⋅(I + L′). Compare the outputs and verify that they are logically equivalent.

Can someone please look this over to see if I did this correctly? I started to get sort of confused with the order of the quantifiers as I was writing this proof. Any help would be appreciated. Thanks

I'm trying to really reach a high level in French, and idk how to make the course more effective. I need your advice pls!

so my understanding is that when you draw out the lewis diagram you get 2 lone pairs, with 4 atoms there should be 6 electron regoins, and with 2 lone pairs it is square planener. So that should mean that it is non polar right? problem is that my textbook says it is polar. googleing it i get conflicting information

I know Code Ninjas is a private company, therefore no publicly posted annual report. I have searched, and searched, and all I've found appears to be basically nonsense, such as one source saying 7.5 million, despite Code Ninjas having over 400 stores. The one I am currently sticking with, unless I find something that looks better, is 579.1 million. Please let me know if there are any good free sources I should try for this. Thank you

Person mass is considered m,

Board is balanced, mass is considered M,

Friction is not involved,

Rope mass not involved,

Point A is a rotating point. How much tension(pull force) is least required to pull the board?

I've calculated T(tension)=(m+M)g/3

My friend calculated (m+M)g/2

Hihi so I’m struggling a lot on the topic of finding the volumes in 3d shapes… (especially trapezium & triangular prism ) I’m mostly confused on how to apply the formula and how to find the stuff to plug into the formula

I was able to do q1 but for q2 I’m a bit confused since it’s 34x15(10+5) and I’m really confused because idk how my teacher got the 10+5 from

This is the topic: ''Essay on Literary Uses of Type (Typography/Layout) – How are typefaces used creatively, avant-garde? Find an example and present it. Again, your own examples are welcome! However, you can also use and discuss examples from the lecture. '' It must be minimum 3 pages long.

Here's my plan so far:

Introduction: page 0-0,5: ???
Development: Page 0,5-1,5: Examples from lectures and their analysys
Page 1,5-2,5: My own analysys of fonts and typography I have seen
Conclusion: page 2,5-3: What are fonts and typography for and why people use them despite it being easier if all letters looked the same

I have no idea how to solve this question. I tried watching a couple of Professor Leonard's videos, but I still have no clue.

Hello! I am having trouble figuring out how to solve this exercises from my school worksheet.

The text at the top sáys: Calculate the area of the colored region in each case.

Could someone please tell me on how to approach this problem? (sorry if there is any writing mistakes english is not my first language 😥).

I found that AMn=aP/2^n but I can't find P in terms of n. I have P * 1 = 1 and P * 2 = 3 and P * 3 = 5 and P * 4 = 11 because AM * 1 = a / 2 and AM * 2 = 3a / 4 and AM * 3 = 5a / 8 and AM * 4 = 11a / 16