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Natasha_Volkova [10]
3 years ago
15

The length of a rectangle is increasing at a rate of 6 cm/s and its width is increasing at a rate of 5 cm/s. When

Mathematics
1 answer:
atroni [7]3 years ago
8 0

Answer:

The area of the rectangle is increasing at a rate of 84 square centimeters per second.

Step-by-step explanation:

The area for a rectangle is given by the formula:

A=w\ell

Where <em>w</em> is the width and <em>l</em> is the length.

We are given that the length of the rectangle is increasing at a rate of 6 cm/s and that the width is increasing at a rate of 5 cm/s. In other words, dl/dt = 6 and dw/dt = 5.

First, differentiate the equation with respect to <em>t</em>, where <em>w</em> and <em>l</em> are both functions of <em>t: </em>

\displaystyle \frac{dA}{dt}=\frac{d}{dt}\left[w\ell]

By the Product Rule:

\displaystyle \frac{dA}{dt}=\frac{dw}{dt}\ell +\frac{d\ell}{dt}w

Since we know that dl/dt = 6 and that dw/dt = 5:

\displaystyle \frac{dA}{dt}=5\ell + 6w

We want to find the rate at which the area is increasing when the length is 12 cm and the width is 4 cm. Substitute:

\displaystyle \frac{dA}{dt}=5(12)+6(4)=84\text{ cm}^2\text{/s}

The area of the rectangle is increasing at a rate of 84 square centimeters per second.

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Please answer these and I will give brainliest!!!
ollegr [7]

Answer:

#1. 1232 feet per minute

#2. $14.81 per second

#3. 46.93 feet per second

Hope This Helps!

And that it's right!

4 0
3 years ago
PLSS HELP
Dmitry [639]

Answer:

$8,000

Step-by-step explanation:

Let the store earned $x in December.

Therefore,

Money spent to buy new inventory =\frac{1}{4} x

Remaining money = x - \frac{1}{4} x =\frac{3}{4} x

Money used to pay bills =\frac{1}{2} \times \frac{3}{4} x=\frac{3}{8} x

Money still left over = $3,000

Total money earned in December = \frac{1}{4} x+ \frac{3}{8} x+3,000

\therefore x= \frac{1}{4} x+ \frac{3}{8} x+3,000

\therefore x= \frac{2}{8} x+ \frac{3}{8} x+3,000

\therefore x= \frac{5}{8} x+ 3,000

\therefore x- \frac{5}{8} x=3,000

\therefore \frac{8x-5x}{8} =3,000

\therefore \frac{3x}{8} =3,000

\therefore x =3,000\times \frac {8}{3}

\therefore x =1,000\times 8

\therefore x =\$8,000

Thus, total money earned in December is $8,000.

3 0
2 years ago
The slope point equation of a line passing through the points (-3, -1) and (2, -6) is:
evablogger [386]

Answer:

y = -1x -4

Step-by-step explanation:

The point slope equation is y - y1 = m(x -x1).

You will have to plug in the points (-3, -1) and (2, -6).

y - (-1) = m (x - (-3))

To find "m", find y over x.

m = (y2 - y1) / ( x2 - x1)

m = (-6 + 1)/(2 + 3)

m = -5/5

m = -1

Then plug in "m"

y + 1 = -1(x + 3)

then distribute the "m" into the parenthesis and isolate y or subtract 1 from both sides.

y + 1 = -1x - 3

y = -1x -4

4 0
3 years ago
which of these shows the result of using the first equation to substitute for y in the second equation, then combining like term
Furkat [3]

Answer:

C. \Rightarrow \bold{8x = 16}

Step-by-step explanation:

Given the two equations:

y=2x ........ (1)\\ 2x+3y=16.......(2)

To find:

The correct option when value of y is substituted to 2nd equation using the 1st equation.

Solution:

First of all, let us learn about the substitution method.

Substitution method is the method to provide solutions to two variables when we have two equations and two variables.

In substitution method, we find the value of one variable in terms of the other variable and put this value in the other equation.

Now, the other equation becomes only single variable and then we solve for the variable's value.

Here, we have two equations and value of one varible is:

y=2x

Let us put value of y in 2nd equation:

2x+3y=16\\\Rightarrow 2x + 3(2x) = 16\\\Rightarrow 2x + 6x = 16\\\Rightarrow \bold{8x=16}

So, the correct answer is option C. \Rightarrow \bold{8x = 16}

7 0
3 years ago
Lesson 6.2 math 7th grade
Daniel [21]
What about lesson 6.2 math 7th grade??

5 0
3 years ago
Read 2 more answers
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