What values of the variables highlighted would create an equation infinitely many solutions

Find the equation of the tangent line to the curve 4x3+2y2−11=4xy−x at the point (−1,2).

katrin [286]

Hello : let : y = f(x) so : y' = f'(x)
calculate : f'(x) and : f'(-1) given f(-1) = 2

by derivate : 4x3+2y2−11=4xy−x
12x² +4yy' = 4y +4xy' - 1
4yy' - 4xy' = - 12x² +4y -1
y' ( 4y - 4x) = 4y -12x² -1 ...(*)
if x = -1 y = 2 subsct in : (*)
y' (4(2)-4(-1)) = 4(2)-12(-1)² - 1
2y' = - 9
y' = - 9/2 = f'(- 1) ( the slope of the tangent )
of the tangent line to the curve at the point (−1,2) is :
y - 2 = (-9/2)(x +1)

5 0

3 years ago

A scale factor can never by greater than 1. True False

mr Goodwill [35]

True the scale factor can never ever be greater than 1.
Hope this helped <3

4 0

3 years ago

A survey was conducted that asked 1011 people how many books they had read in the past year. results indicated that x overbarequ

Tcecarenko [31]

Since we do not know the population standard deviation, we will use the t-distribution to construct the 90% confidence interval of the mean number of books people read. The value of $t_{\frac{\alpha }{2}}$ with 1010 degrees of freedom and with alpha equals to 0.10 is 1.64

First, we need to solve for the margin of error, E.
$E=t_{\frac{\alpha }{2}}\cdot \frac{s}{\sqrt{n}}=1.64\cdot \frac{16.6}{\sqrt{1011}}=0.86$

The lower bound of the confidence interval is
$LB=\overline{x}-E=14.8-0.86=13.94$

The upper bound of the confidence interval is
$LB=\overline{x}+E=14.8+0.86=15.66$

Therefore, the 90% confidence interval is (13.94, 15.66).

We are 90% confident that the interval from 13.94 books to 15.66 books does contain the true value of the population mean number of books people read.

4 0

4 years ago

Help Determine which equation is parallel to line jk and which is perpendicular to line jk.

alukav5142 [94]

Answer:

5x + 3y = 13 parallel.

6x - 10y = 7 perpendicular.

Step-by-step explanation:

Two lines with slopes $m_1$ and $m_2$ are parallel when $m_1=m_2$ and are perpendicular when $m_1*m_2=-1$