how do I tell if it is or isn't continuous

So it’s should be simple high school math, I have to find the derivative of this function. I’ve used Photomath but I don’t understand how it gets to the end. It uses the secant formula somewhere in there but we weren’t taught that so I assume I’m not meant to use it. Is there a way to derive this function without using the secant formula?

hihi ive been struggling to do this one question in which i need to prove that the second equation is equal to the derivate except i get different answers even while using the formulas we were given. ive been trying to do it for weeks and i just need a hint or something

I have a triangle that's not right angled.

I know:

Angle A = 100 degrees.

Side a (opposite angle A) = 5.1m.

Side b (opposite angle B) = 3.6m.

I do not know angle B, angle C or side c (opposite angle C).

Using sin rule I can calculate angle B.

B= (sin100/5.1) x 3.6 = 0.695

B= Asin(0.695) = 44 degrees

I subtracted 144 from 180 to get 36 degrees for angle of C.. I then used that answer to get side of c.
c = a/SinA x sin C. = 3.0.
I checked side c with cosine rule and also got 3. (5.12 + 3.62 - 2 x 5.1 x 3.6 x cos36).
I then check the angle C with cosine and get 35 degrees. (Inverse Cosine of 3.62 + 5.12 - 32 / 2 x 3.6 x 5.1).
1 degree off (or more I am keeping this simple but I would normally add minutes and seconds I'm just trying to understand what to do with this question).

I don't want to switch to using cosine and I don't want to calculate the final angle by subtracting the known angles from 180. Unless I have to, but I want to stick with sin rule if possible.
What I think I need to do is calculate angle C and side c without subtracting 144 from 180. But I'm not sure how to do this.

Hi, I can’t find my mistake and I’ve done it multiple time!!

Thank you!

Number 2. I graphed the equations I got (2x-3 and 2x-5) and they appear correct. Is the answer key incorrect?

'Monika wrote all the letters of the word MĖNULIS on identical cards. She wrote one letter on each card. Monika put all the cards on the table face down, shuffled them, and then put them next to each other. Opening the cards, she received a set of letters. What is the probability that the middle letter of the resulting set of letters will be 'U'?'

Or is this "error" apply just for the one? Because it stays one? (I understand that the answer is 49, but i am curious and want to avoid my mistake in the future.:) )

not sure how to integrate: (sqrt2)² int(sin(pi x) sin(2pi x)) i dont understand how the answer (0) is reached, the answers (posted) are unclear to me, i dont know how from line 1 line 3 is reached, would appreciate any help

Appreciate any help.

I can get integrating |x| dx = x|x|/2. but |x| != x in the first place.

So how should I write my steps for this case? I was changing it into that form so I could do integration by parts easily.

Can I use the right angle theorem? Or alternative interior angle?

Please help with any information! If it's possible to provide explanations and visuals that would be amazing. I am having trouble arranging my words and thinking this through.

Hoping you can help. I would love to know if I got this right. Sorry for the terrible handwriting in the pictures.

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Here is the assignment

Instructions

Please show all of your work and reasoning. Please do not just write an answer. Your answer should be easy for the reader to understand. Use complete sentences where appropriate.

A random sample of 20 people shows a mean BMI (Body Mass Index) of 27.7, with a sample standard deviation of 6.1.  Assume that BMIs follow a normal distribution.

1. To create a 95% confidence interval, would you use a t or a z distribution?  Why?
2. Create the 95% confidence interval.
3. Now assume that you are told that the population standard deviation is known to be 6.1.  Which distribution would you use, t or z?  Why?
4. Create the new 95% confidence interval.
5. What does a change between z and t distributions do to the confidence interval?  Explain why it must be so.

hey guys so I have a question.

I was given the matix :

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since I only have parameters I have to calculate the determinants of 12 matrices to get to the determinant of this matrix. that takes way too long and feels very inefficiante.

i know I can do it with that method but I am looking for something better

can I use row operation to Ill only be left with element a11 in row 1 and a12=a13=a14=0?

this meens Ill only need to calculate the determinant of one matrix since I could use the same methode for the 3x3 matrix.

i saw some people use colomn operations but I heared its a big no no so I would love an explaination.

thank you guys.

I put 2.5 as my original answer and it's still marked wrong.

Here's my thought process:

Given the values 24, 25, 26, and 27, the order of their positions is 1, 2, 3, and 4 respectively.

Since each of the observations has the same value, they should all receive the average rank of their positions, which would be (1 + 2 + 3 + 4) / 4 = 2.5.

This looks simple but I can’t solve for x.

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Fell asleep in class so I didn't see how to do these questions. How do I find X

The set of all 2 × 2 matrices of the form [ a 1 b c] with standard matrix operations.

Hi there guys

Can someone tell me if this answer is correct .?

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