Can you please help me please

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

Bernice wants to buy two

Olegator [25]

Answer:

$3.72

Step-by-step explanation:

7.75*2=15.5

15.5+0.78=16.28

20-16.28=3.72

3 0

2 years ago

Read 2 more answers

Find the mean of 100

goldfiish [28.3K]

Answer:

100.

Step-by-step explanation:

100 + 0 = 100

100 ÷ 1 = 100

8 0

2 years ago

Read 2 more answers

Consider the following.3x + 3y = 8(a) Find y' by implicit differentiation.(b) Solve the equation explicitly for y and differenti

ludmilkaskok [199]

Answer:

a.y'=-1

b.y'=-1

c.Yes

Step-by-step explanation:

We are given that consider a function

$3x+3y=8$

Implicit function: That function is a relation in which dependent variable can not be expressed in terms of independent variable

Explicit function: It is that function in which dependent variable can be expressed in terms of independent variable.

a. $3x+3y=8$

Differentiate w.r.t x then we get

$3+3\frac{dy}{dx}=0$

$3\frac{dy}{dx}=-3$

$\frac{dy}[dx}=\frac{-3}{3}=-1$

$\frac{dy}{dx}=y'=-1$

b. $3x+3y=8$

$3y=8-3x$

$y=\frac{8-3x}{3}$

Differentiate w.r.t x then we get

$\frac{dy}{dx}=\frac{-3}{3}=-1$

$\frac{dy}{dx}=y'=-1$

When we substituting the value of y obtained from part b into a solution of part a then we get

$y'=-1$

Hence, solutions are consistent.

8 0

2 years ago

There are 24 girls on the track team. First race2/3 girl ran.only1/4 girl ran in second race. 1/6 on third race. Hiw many more g

alukav5142 [94]

Answer:

10 more girls

Step-by-step explanation:

So here 2/3 of 24 ran for first race

Then it gives us that 16 girls ran for first race.

Next, 1/4 of 24 ran for second race

That is 6 girls

The remaining girls ran for the third race,

24 - 22

2 girls

16 - 6 = 10

So for first race 10 more girls ran

5 0

2 years ago

Can you please help me please ​

Can you please help me please