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3 years ago

2. Allison has 22 meters of fabric to sew dresses. She uses 3 meters of fabric for each

Mathematics

2 answers:

drek231 [11]3 years ago

6 0

Answer:

Step-by-step explanation:

nekit [7.7K]3 years ago

5 0

Answer:7 meters

Step-by-step explanation:

3 doesn’t go into 22 equally, but it goes into 21

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If x^2y-3x=y^3-3, then at the point (-1,2), (dy/dx)?

zavuch27 [327]

If you're using the app, try seeing this answer through your browser: brainly.com/question/2866883

_______________

   dy
Find —— for an implicit function:
    dx

x²y – 3x = y³ – 3

First, differentiate implicitly both sides with respect to x. Keep in mind that y is not just a variable, but it is also a function of x, so you have to use the chain rule there:

$\mathsf{\dfrac{d}{dx}(x^2 y-3x)=\dfrac{d}{dx}(y^3-3)}\\\\\\
\mathsf{\dfrac{d}{dx}(x^2 y)-3\,\dfrac{d}{dx}(x)=\dfrac{d}{dx}(y^3)-\dfrac{d}{dx}(3)}$

Applying the product rule for the first term at the left-hand side:

$\mathsf{\left[\dfrac{d}{dx}(x^2)\cdot y+x^2\cdot \dfrac{d}{dx}(y)\right]-3\cdot 1=3y^2\cdot \dfrac{dy}{dx}-0}\\\\\\
\mathsf{\left[2x\cdot y+x^2\cdot \dfrac{dy}{dx}\right]-3=3y^2\cdot \dfrac{dy}{dx}}$

   dy
Now, isolate —— in the equation above:
   dx

$\mathsf{2xy+x^2\cdot \dfrac{dy}{dx}-3=3y^2\cdot \dfrac{dy}{dx}}\\\\\\
\mathsf{2xy+x^2\cdot \dfrac{dy}{dx}-3-3y^2\cdot \dfrac{dy}{dx}=0}\\\\\\
\mathsf{x^2\cdot \dfrac{dy}{dx}-3y^2\cdot \dfrac{dy}{dx}=-\,2xy+3}\\\\\\
\mathsf{(x^2-3y^2)\cdot \dfrac{dy}{dx}=-\,2xy+3}$

$\mathsf{\dfrac{dy}{dx}=\dfrac{-\,2xy+3}{x^2-3y^2}\qquad\quad for~~x^2-3y^2\ne 0}$

Compute the derivative value at the point (– 1, 2):

x = – 1 and y = 2

$\mathsf{\left.\dfrac{dy}{dx}\right|_{(-1,\,2)}=\dfrac{-\,2\cdot (-1)\cdot 2+3}{(-1)^2-3\cdot 2^2}}\\\\\\
\mathsf{\left.\dfrac{dy}{dx}\right|_{(-1,\,2)}=\dfrac{4+3}{1-12}}\\\\\\
\mathsf{\left.\dfrac{dy}{dx}\right|_{(-1,\,2)}=\dfrac{7}{-11}}\\\\\\\\ \therefore~~\mathsf{\left.\dfrac{dy}{dx}\right|_{(-1,\,2)}=-\,\dfrac{7}{11}}\quad\longleftarrow\quad\textsf{this is the answer.}$

I hope this helps. =)

Tags: <em>implicit function derivative implicit differentiation chain product rule differential integral calculus</em>

6 0

3 years ago

a pond at a hotel holds 4290 gallons. the groundskeeper drains the pond at a rate of 78 gallons per hour. how long will it take

Studentka2010 [4]

55 hours to drain it

5 0

3 years ago

How does the order of operations affect a equation? i really need to know

satela [25.4K]

Answer:

A specific order can change the answer completely

Step-by-step explanation:

7 0

3 years ago

A beekeeper has 65,000 female bees and 700 male bees in one colony. A disease kills % of the female bees and % of the male bees.

Paha777 [63]

Complete Question

A beekeeper has 65,000 female bees and 700 male bees in one colony. A disease kills 25% of the female bees and 14% of the male bees. After the disease hits the colony, the beekeeper decides to sell LaTeX: \frac{1}{2} 1 /2 of the remaining female bees to a friend.

How many total bees are left in the beekeeper’s colony after the disease and sale?

Answer:

24977 bees

Step-by-step explanation:

From the above question:

Number of female bees = 65,000

Number of male bees = 700

A disease kills 25% of the female bees and 14% of the male bees.

Number of female bees killed = 25% × 65,000

= 16,250 bees

Amount of female bees left = 65,000 - 16,250

= 48750 bees

Number of male bees killed = 14% × 700

= 98

Amount of male bees left = 700 - 98

= 602 bees

After the disease hits the colony, the beekeeper decides to sell LaTeX: \frac{1}{2} 1 /2 of the remaining female bees to a friend.

Hence:

1/2 × 48750 bees

= 24375 bees

Total bees are left in the beekeeper’s colony after the disease and sale is calculated as:

24375 female bees + 602 male bees

= 24977 bees

4 0

3 years ago

How do I find x and what is x

o-na [289]

Answer:

x = 20 degrees

Explanation:

With a 20 degree angle on the direct opposite side, it shows that x is also 20 degrees; and the other two angles would be 160 degrees.

Hope this helps :)

8 0

3 years ago

Read 2 more answers