Help me find the volume please!

Operations with rational expressions

Scorpion4ik [409]

$$\frac{50-2 w^{2}}{3 w^{2}+9 w-30} \cdot \frac{w^{2}+5 w-14}{6 w-30}=-\frac{w+7}{9}$

Solution:

Given expression:

$$\frac{50-2 w^{2}}{3 w^{2}+9 w-30} \cdot \frac{w^{2}+5 w-14}{6 w-30}$

To solve the given expression:

First simplify: $\frac{50-2 w^{2}}{3 w^{2}+9 w-30}$

$$\frac{50-2 w^{2}}{3 w^{2}+9 w-30}=-\frac{2(w+5)(w-5)}{3(w-2)(w+5)}$

Cancel the common factor (w + 5).

$$=-\frac{2(w-5)}{3(w-2)}$

Now substitute this in the given expression.

$$\frac{50-2 w^{2}}{3 w^{2}+9 w-30} \cdot \frac{w^{2}+5 w-14}{6 w-30}=-\frac{2(w-5)}{3(w-2)} \cdot \frac{w^{2}+5 w-14}{6 w-30}$

Multiply the fractions $\frac{a}{b} \cdot \frac{c}{d}=\frac{a \cdot c}{b \cdot d}$

$$=-\frac{2(w-5)\left(w^{2}+5 w-14\right)}{3(w-2)(6 w-30)}$

Factor the denominator $3(w-2)(6 w-30) =18(w-2)(w-5)$

$$=-\frac{2(w-5)\left(w^{2}+5 w-14\right)}{18(w-2)(w-5)}$

Cancel the common factor 2(w – 5).

$$=-\frac{w^{2}+5 w-14}{9(w-2)}$

Factor the numerator $w^{2}+5 w-14=(w-2)(w+7)$

$$=-\frac{(w-2)(w+7)}{9(w-2)}$

Cancel the common factor (w – 2).

$$=-\frac{w+7}{9}$

$$\frac{50-2 w^{2}}{3 w^{2}+9 w-30} \cdot \frac{w^{2}+5 w-14}{6 w-30}=-\frac{w+7}{9}$

3 0

3 years ago

Approved Sites

NNADVOKAT [17]

Answer:

12323232321

Step-by-step explanation:

4 0

4 years ago

For what value of a does<br> 9 = (1/27) a+3

Temka [501]

Answer: a = 162

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

At sunrise, the temperature was –4.8°C. During the day, the temperature rose 6.3°C and then fell 5.6°C.

marta [7]

Initial temperature = (-4.8)

Rise = 6.3

So, temp. after rise = -4.8 + 6.3 = 1.5

Again, fall = (-5.6)

So, temp after fall = 1.5 - 5.6 = (-4.1)

6 0

3 years ago

What is the ratio of the area of the inner square to the area of the outer square?

Nadusha1986 [10]

The area of the inner square to the area of the outer square ratio is: $\frac{(a-b)^2+b^2}{a^2}$

Given a figure in which an inner square is inscribed inside the outer square.

The area of a square is the product of the two sides of the square. Also known as side square.

Firstly, we will find the side of the inner square by finding the distance between the points (0,b) and (a-b,0)

S₁=√(a-b-0)²+(b-0)²

S₁=√(a-b)²+b²

Now, we will find the area of the inner square, we get

The area of the inner square=(side)²

A₁=(S₁)²

A₁=(√(a-b)²+b²)²

A₁=(a-b)²+b²square cm.

Further, we will find the side of the outer square by finding the distance between the points (0,0) and (a,0).

S₂=√(a-0)²+0²

S₂=√a²

S₂=a

Furthermore, we will find the area of the outer square, we get

The area of the outer square=(side)²

A₂=(S₂)²

A₂=a² square cm.

Hence, the area of the inner square to the area of the outer square ratio is $\frac{(a-b)^2+b^2}{a^2}$ .

Learn more about the area of the square from here brainly.com/question/4102299

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5 0

2 years ago