1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
alina1380 [7]
3 years ago
5

Let 3z=(2w-5)^3. If dw/dt =1/3, find dz/dt when z=9

Mathematics
1 answer:
jekas [21]3 years ago
5 0

3<em>z</em> = (2<em>w</em> - 5)³

When <em>z</em> = 9, we have

27 = (2<em>w</em> - 5)³   →   3 = 2<em>w</em> - 5   →   <em>w</em> = 4

Differentiate both sides with respect to <em>t</em> :

3 d<em>z</em>/d<em>t</em> = 3 (2<em>w</em> - 5)² d<em>w</em>/d<em>t</em>

d<em>z</em>/d<em>t</em> = (2<em>w</em> - 5)² d<em>w</em>/d<em>t</em>

Plug in everything you know and solve for d<em>z</em>/d<em>t</em> :

d<em>z</em>/d<em>t</em> = 3² • (1/3)

d<em>z</em>/d<em>t</em> = 3

You might be interested in
Why can a fraction, a decimal, or a percent be written in equivalent forms?
Inessa [10]

Answer:

Because there are many ways you can simplify an equation, and it will still be the same.

5 0
3 years ago
Pleeeeeeeeaaaseeeeee help meeeeeeee!!!!!!!!!
zaharov [31]

Answer:

Option D.

A =96\pi\ cm^2

Step-by-step explanation:

The area of the circular bases is:

A_c = 2\pi(a) ^ 2

Where

a=4\ cm is the radius of the circle

Then

A = 2\pi(4) ^ 2

A = 32\pi\ cm^2

The area of the rectangle is:

A_r=b * 2\pi r

Where

b=8\ cm

b is the width of the rectangle and 2\pi r is the length

Then the area of the rectangle is:

A_r=8 * 2\pi (4)

A_r=64\pi\ cm^2

Finally the total area is:

A = A_c + A_r\\\\A = 32\pi\ cm^2 + 64\pi\ cm^2\\\\

A =96\pi\ cm^2

7 0
4 years ago
Read 2 more answers
Which of the following situations could be represented by the expression - 14+ (- 7)?
RUDIKE [14]

Answer:

Matt's

Step-by-step explanation:

he has to give away $14 (-14)

and also $7 (-7)

The others have positive numbers.

4 0
3 years ago
The sides of a triangle are x , x +1 , 2 x -1 and its area is x root of 10 .Find the value of x.
VARVARA [1.3K]


Ok, I'm going to start off saying there is probably an easier way of doing this that's right in front of my face, but I can't see it so I'm going to use Heron's formula, which is A=√[s(s-a)(s-b)(s-c)] where A is the area, s is the semiperimeter (half of the perimeter), and a, b, and c are the side lengths.

Substitute the known values into the formula:

x√10=√{[(x+x+1+2x-1)/2][({x+x+1+2x-1}/2)-x][({x+x+1+2x-1}/2)-(x+1)][({x+x+1+2x-1}/2)-(2x-1)]}

Simplify:

<span>x√10=√{[4x/2][(4x/2)-x][(4x/2)-(x+1)][(4x/2)-(2x-1)]}</span>

<span>x√10=√[2x(2x-x)(2x-x-1)(2x-2x+1)]</span>

<span>x√10=√[2x(x)(x-1)(1)]</span>

<span>x√10=√[2x²(x-1)]</span>

<span>x√10=√(2x³-2x²)</span>

<span>10x²=2x³-2x²</span>

<span>2x³-12x²=0</span>

<span>2x²(x-6)=0</span>

<span>2x²=0 or x-6=0</span>

<span>x=0 or x=6</span>

<span>Therefore, x=6 (you can't have a length of 0).</span>

6 0
3 years ago
Danielle has a $30 gift card to T-Shirt-paradise . She wants to use it to buy a rock band T-shirt and a glitter T-shirt. The roc
hammer [34]
X= $18.05. Hope this helps! can i please get brainliest
5 0
3 years ago
Other questions:
  • What 2 integers are located 4 units away from -6 on a number line?
    13·1 answer
  • Y=f(x)=(4)^x find f(x) when x=-2
    8·1 answer
  • Which will not result in a value of zero?
    12·2 answers
  • Two numbers have a difference of 42. What is the sum of their squares if it is a minimum?
    15·2 answers
  • In the auditorium there are 27 red chairs and 63 blue chairs. what is the ratio of the number of red chairs to the number of blu
    8·1 answer
  • If 5 cans of baked beans cost $2.85, how<br> many cans of baked beans can be bought<br> for $19.38?
    10·1 answer
  • A scientist measured the wavelength of an X-ray as 0.0000000065 meters. ​ ​Write the number in scientific notation.
    5·1 answer
  • Darius buys a bottle of a chemical solution that contains 70% percent alcohol. The bottle contains 500 milliliters of solution.
    7·1 answer
  • The formula for the slant height of a cone is t equals StartFraction S minus pi r squared Over pi EndFraction. , where S is surf
    13·2 answers
  • #10 HELP PLEASE THANKS!
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!