Factor perfect square trinomials

Rewrite the statement in mathematical notation. (Let y be the distance from the top of the ladder to the floor, x be the distanc

In-s [12.5K]

Answer:

$\frac{dy}{dt}=\frac{6y}{x}\text{ ft per sec}$

Step-by-step explanation:

Let L be the length of the ladder,

Given,

x = the distance from the base of the ladder to the wall, and t be time.

y = distance from the base of the ladder to the wall,

So, by the Pythagoras theorem,

$L^2 = y^2 + x^2$

$\implies L = \sqrt{y^2 + x^2}$ ,

Differentiating with respect to time (t),

$\frac{dL}{dt}=\frac{d}{dt}(\sqrt{x^2 + y^2})$

$=\frac{1}{2\sqrt{x^2 + y^2}}\frac{d}{dt}(x^2 + y^2)$

$=\frac{1}{2\sqrt{x^2 + y^2}}(2x\frac{dx}{dt}+2y\frac{dy}{dt})$

$=\frac{1}{\sqrt{x^2 +y^2}}(x\frac{dx}{dt}+y\frac{dy}{dt})$

Here,

$\frac{dy}{dt}=-6\text{ ft per sec}$

Also, $\frac{dL}{dt} = 0$ ( Ladder length = constant ),

$\implies \frac{1}{\sqrt{x^2 +y^2}}(x(-6)+y\frac{dy}{dt})=0$

$-6x + y\frac{dy}{dt}=0$

$y\frac{dy}{dt}=6x$

$\implies \frac{dy}{dt}=\frac{6y}{x}\text{ ft per sec}$

Which is the required notation.

8 0

3 years ago

The common difference in an arithmetic sequence is –2 and the first term is 47. What is the 29th term?

BlackZzzverrR [31]

An arithmetic sequence is an ordered list of numbers where the next number is found by adding on to the last number (ex: 2,5,8,11... is a sequence where 3 is added on to find the next number).

The equation for an arithmetic sequence is
$A_{n}=A_{1}+(n-1)d$

$A_{n}$ is the "n-th" number in the sequence (ex: is the first term in the sequence)
d is the number you add (common difference) to find the next number
The first number in the sequence is 47 so $A_{1}=47$
d=-2 because the question gives you that

$A_{n}=A_{1}+(n-1)d$
 $A_{29}=47+(29-1)(-2)$
 $A_{29}=47+(28)(-2)$
 $A_{29}=47+-56$
 $A_{29}=-9$

The answer is A. -9.

 

The answer is C. 158

For the second one, it gives you $A_{1}=4$ and $A_{}=18$
You can use this to find d

 $A_{n}=A_{1}+(n-1)d$
 $A_{3}=4+(3-1)d$
 $18=4+(3-1)d$
 $18=4+2d$
 $14=2d$
 $7=d$

Now you can just solve using the equation normally.
 $A_{n}=A_{1}+(n-1)d$
 $A_{23}=4+(23-1)(7)$
 $A_{23}=4+(22)(7)$
 $A_{23}=4+154$
 $A_{23}=158$

The answer is C. 158

8 0

3 years ago

Read 2 more answers

Follow the process of completing the square to solve 2x2 + 8x - 12 = 0. After adding B2 to both sides of the equation in step 4,

Sladkaya [172]

Answer:

Step-by-step explanation:

I dont quite understand the problem but this is one way to solve it using completing the square:-

2x^2 + 8x - 12 = 0

2(x^2 + 4x) - 12 = 0

2((x + 2)^2 - 4) = 12

2(x + 2)^2 - 8 + 8 = 12 + 8

2(x + 2)^2 = 20

6 0

3 years ago

Kade has 100 flag pins. He has 221 frog pins and 10 dinosaur pins. How many flag and frog pins does Kade have?

bazaltina [42]

Answer:

321

Step-by-step explanation:

because 100+221 equals 321

Hope this helped.

5 0

3 years ago

Write the equation of the line that passes through (-1,2) and (2,8) in any form NEED HELLP ASAP!!!

Tems11 [23]

Answer: y=2x+4 for parallel and y=-1/2x+1 1/2

Step-by-step explanation: you need to do an equation using the slope which you can find by using y2-y1/x2-x1

from there you have to use y-y1=m(x-x1)

4 0

3 years ago