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3 years ago

Simplify 2x+3y^2 -2(x-y2)

Mathematics

1 answer:

poizon [28]3 years ago

6 0

Multiply the bracket by -2

2x+3y^2 -2(x-y2)

2x+3y^2-2x+2y^2

2x-2x+3y^2+2y^2- rearranging

3y^2+2y^2

5y^2

Answer: 5y^2

You might be interested in

Is the following number rational or irrational? -3+π

enyata [817]

Answer:

B, irrational

Step-by-step explanation:

We know that π is irrational, since it can not be written as a division between natural numbers (a sub class of Real numbers called N), it's value is 3,1415(a whole bunch of decimals after this)

If you remove the decimal part of π by subtracting the integer part of it, that is the number 3. the result will still being and irrational number

Since π= 3(the rational part) +0,1415... (the irrational part)

The resut of π-=3= 0,1415...

3 0

3 years ago

Among all right circular cones with a slant height of 24, what are the dimensions (radius and height) that maximize the volum

aleksklad [387]

Answer:

5571.99

Step-by-step explanation:

We need to use the Pythagorean theorem to solve the problem.

The theorem indicates that,

$r^2+h^2=24^2 \\r^2+h^2=576\\r^2=576-h^2$

Once this is defined, we proceed to define the volume of a cone,

$v=\frac{1}{3}\pi r^2 h$

Substituting,

$v=\frac{1}{3} \pi (576-h^2)h\\v=\frac{1}{3} \pi (576h-h^3)$

We need to find the maximum height, so we proceed to calculate h, by means of its derivative and equalizing 0,

$\frac{dv}{dh} = \frac{1}{3} \pi (576-3h^2)$

$\frac{dv}{dh} = 0$ then $\rightarrow \frac{1}{3}\pi(576-3h^2)=0$

$h_1=-8\sqrt{3}\\h_2=8\sqrt{3}$

<em>We select the positiv value.</em>

We have then,

$r^2 = 576-(8\sqrt3)^2 = 384\\r=\sqrt{384}$

We can now calculate the maximum volume,

$V_{max}= \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi (\sqrt{384})^2 (8\sqrt{3}) = 5571.99$

4 0

3 years ago

Find the general indefinite integral. (Use C for the constant of integration. Remember to use absolute values where appropriate.

Maru [420]

Answer:

$9\text{ln}|x|+2\sqrt{x}+x+C$

Step-by-step explanation:

We have been an integral $\int \frac{9+\sqrt{x}+x}{x}dx$ . We are asked to find the general solution for the given indefinite integral.

We can rewrite our given integral as:

$\int \frac{9}{x}+\frac{\sqrt{x}}{x}+\frac{x}{x}dx$

$\int \frac{9}{x}+\frac{1}{\sqrt{x}}+1dx$

Now, we will apply the sum rule of integrals as:

$\int \frac{9}{x}dx+\int \frac{1}{\sqrt{x}}dx+\int 1dx$

$9\int \frac{1}{x}dx+\int x^{-\frac{1}{2}}dx+\int 1dx$

Using common integral $\int \frac{1}{x}dx=\text{ln}|x|$ , we will get:

$9\text{ln}|x|+\int x^{-\frac{1}{2}}dx+\int 1dx$

Now, we will use power rule of integrals as:

$9\text{ln}|x|+\frac{x^{-\frac{1}{2}+1}}{-\frac{1}{2}+1}+\int 1dx$

$9\text{ln}|x|+\frac{x^{\frac{1}{2}}}{\frac{1}{2}}+\int 1dx$

$9\text{ln}|x|+2x^{\frac{1}{2}}+\int 1dx$

$9\text{ln}|x|+2\sqrt{x}+\int 1dx$

We know that integral of a constant is equal to constant times x, so integral of 1 would be x.

$9\text{ln}|x|+2\sqrt{x}+x+C$

Therefore, our required integral would be $9\text{ln}|x|+2\sqrt{x}+x+C$ .

4 0

3 years ago

Sebuah Prisma Segitiga memiliki tiga sisi masing

Veseljchak [2.6K]

Menjawab:

15cm

Penjelasan langkah demi langkah:

Keliling segitiga adalah jumlah semua sisi segitiga

P = s1 + s2 + s3

Diberikan sisi jika segitiga;

S1 = 5cm

S2 = 7cm

S3 = 3cm

Keliling = 5cm + 7cm + 3cm

Keliling = 15cm

Oleh karena itu, keliling segitiga tersebut adalah 15 cm

5 0

3 years ago

Diego pours 6.8 ounces of water from a full bottle. He estimates that he poured out 20% of the water in the bottle. About how mu

Hatshy [7]

Answer:

Full bottle can fill 34 ounces water and 27.2 ounces left in the bottle

Step-by-step explanation:

Full bottle : 100%

6.8 ounces: 20%

100% / 20% = 5

Full bottle = 6.8 x 5 = 34 ounces

water remain in bottle = 34 -6.8 = 27.2 ounces

5 0

4 years ago