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2 years ago

Identify the GCF of 6x2y2 − 8xy2 + 10xy3. 6x2y2 2x2y 2xy2 6xy2

Mathematics

2 answers:

gladu [14]2 years ago

8 0

Answer:

Option C is correct.

Step-by-step explanation:

Given Expression: 6x²y² - 8xy² + 10xy³

We have to find GCF of the expression

GCF means Greatest common factor of the given expression.

Consider,

6x²y² - 8xy² + 10xy³

= 2×3×x×x×y×y - 2×2×2×x×y×y + 2×5×x×y×y×y

= 2×x×y×y ( 3x - 4 + 5y )

= 2xy² ( 3x -4 + 5y )

GCF = 2xy²

Therefore, Option C is correct.

sattari [20]2 years ago

3 0

First find GCF of the numbers:-

GCF of 2, 6 and 8 = 2
GCF od x^2 x and x is x
GCF of y^2, y^2 and y^3 is y^2

so the answer is 2xy^2

The third choice.

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Which expression represents the lateral surface area of the cone?

Brrunno [24]

Answer:

Option "3" is the correct answer to the following question:

Step-by-step explanation:

Given:

Radius of cone (r) = 6 centimeter

height of cone (h) = 8 centimeter

slant height of cone (l) = 10 centimeter

Find:

Lateral surface area of the cone = ?

Computation:

⇒ Lateral surface area of the cone = $\pi$ rl

⇒ Lateral surface area of the cone = $\pi$ (6 centimeters) (10 centimeters)

⇒ Therefore, option "3" is the correct answer.

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2 years ago

F(x, y) = x2 + y2 + 4x − 4y, x2 + y2 ≤ 81 find the extreme values of f on the region described by the inequality.

Whitepunk [10]

Take partial derivatives and set them equal to 0:

$\nabla F(x,y)=\langle2x+4,2y-4\rangle=\mathbf 0$

We find one critical point within the boundary of the disk at $(x,y)=(-2,2)$ . The Hessian matrix for this function is

$\mathbf H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}2&0\\0&2\end{bmatrix}$

which is positive definite, and incidentally independent of $x$ and $y$ , so $F(x,y)$ attains a minimum $F(-2,2)=-8$ .

Meanwhile, we can parameterize the boundary by $\mathbf r(t)=\langle9\cos t,9\sin t\rangle$ with $0\le t\le2\pi$ , which gives

$F(x,y)=F(x(t),y(t))=f(t)=81\cos^2t+81\sin^2t+36\cos t-36\sin t=81+36(\cos t-\sin t)$

with critical points at

$f'(t)=0\implies 36(-\sin t-\cos t)=0\implies\sin t+\cos t=0\implies t=\dfrac{3\pi}4,\dfrac{7\pi}4$

At these points, we get

$f\left(\dfrac{3\pi}4\right)=81-36\sqrt2\approx30.0883$
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so we attain a maximum only when $t=\dfrac{7\pi}4$ , which translates to $(x,y)=\left(\dfrac9{\sqrt2},-\dfrac9{\sqrt2}\right)$ .

3 0

2 years ago

4. Priya is teaching her younger cousin to ride a bike. She wants to stay on roads that are not too steep and easy enough for a

taurus [48]

Answer:

Having 2 meters and 25 meters legs and 3 meters and 30 meters legs.

Step-by-step explanation:

Priya thinks that an angle of elevation of 7 Degrees or less will be safe for a learner of bike riding.

Now, a 7-degree elevation angle in a right triangle will have a 3 : 25 ratio of its legs.

Therefore, the list of 2 right triangles that would be safe for a new rider will be having 2 meters and 25 meters legs and 3 meters and 30 meters legs.

I both cases the angle of elevation will be less than 7 degrees. (Answer)

4 0

2 years ago

A zookeeper is monitoring the population of birds. The flock needs to have exactly three times more females than males to thrive

KIM [24]

Answer:

The constraints are

$0 < x\leq 20$ and $0 < y\leq 60$

Step-by-step explanation:

Let

x ----> represent the number of male birds

y ----> represent the number of female birds

we know that

The flock needs to have exactly three times more females than males to thrive

$y=3x$ ----> equation A

The zoo only has room for a maximum of 20 male birds

$0 < x\leq 20$ ----> inequality B

we know that

The maximum number of male birds is 20

For x=20

substitute in the equation A

$y=3(20)=60$

The maximum number of female birds is 60

$0 < y\leq 60$ ----> inequality C

therefore

The constraints are

$0 < x\leq 20$ and $0 < y\leq 60$

4 0

2 years ago

Asap pls help and explain

eduard

Answer:

the answer would be 90

Step-by-step explanation:

100 giants fills 5/8 (100/160) of the theater leaving 3/8 of the theater for the elves.

3/8 times 240 elves is 90 elves.

If there were 150 elves that would also be 5/8 filled plus the original 5/8 filled with 100 giants! Some elves might suffer!!!

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2 years ago