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3 years ago

What is the quotient of the given expression?

1 answer:

6 0

Answer:3x^3 – 5x^2 + 10x – 3) – (3x. Dividing the new leading term, –6x2, by the divisor's leading term, 3x, I get –2x, so I put this on top: (–6x^2) ÷ (3x) = –2x, which goes. Then I multiply –2x by 3x + 1 to get –6x2 – 2x ...

Step-by-step explanation:

3x^3 – 5x^2 + 10x – 3) – (3x. Dividing the new leading term, –6x2, by the divisor's leading term, 3x, I get –2x, so I put this on top: (–6x^2) ÷ (3x) = –2x, which goes. Then I multiply –2x by 3x + 1 to get –6x2 – 2x ...

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10. A triangle has sides with lengths 3,5, 7. Is this an acute, obtuse, or right<br> triangle?

satela [25.4K]

Answer:

OBTUSE

Step-by-step explanation:

You would first have to figure this put via Pythagorean theroem. Basically do this (attachment)***C IS THE LARGEST NUMBER*** and know that c^2 < a^2 + b^2 (less than) = ACUTE, c^2 > a^2 + b^2 (greater than) = OBTUSE, and c^2 = a^2 + b^2 is RIGHT. If it is Right with all different numbers, it is SCALENE.

8 0

3 years ago

Find the rate of change of f(x, y, z) = xyz in the direction normal to the surface yx2 + xy2 + yz2 = 3 at (1, 1, 2).

Paladinen [302]

Answer:

Rate of change = 18/√74

Step-by-step explanation:

The rate of change of f at x_o in the direction of the unit vector v is given by: ∇f(x_o) × v

Now, for us to get the direction of the unit vector, since we are told that f(x, y, z) = xyz in the direction normal to the surface yx² + xy² + yz² = 3, we will use; g(x, y, z) = yx² + xy² + yz² = 3 and k =3 to give;

∇g(x,y,z) = (2xy + y², (x² + 2xy + z²), 2yz)

So;

∇g(1, 1, 2) = (2(1 × 1) + 1²) , (1² + 2(1 × 1) + 2²), 2(1 × 2))

This gives;

∇g(1, 1, 2) = (3, 7, 4)

Now,

||∇g(1, 1, 2)|| = √(3² + 7² + 4²)

||∇g(1, 1, 2)|| = √74

Normal vector would be given by the formula;

v = [∇g(1, 1, 2)]/[||∇g(1, 1, 2)||]

Thus;

v = (3, 7, 4)/√74

Let's not forget that our ∇f(1, 1, 2) = (1, 1, 2)

Thus, rate of change is given by;

∇f(1, 1, 2) × v = (1, 1, 2) × (3, 7, 4)/√74

This gives;

Rate of change = [(1 × 3) + (1 × 7) + (2 × 4)]/√74 = 18/√74

7 0

3 years ago

Select the correct expressions. 1 Identify each expression that represents the slope of a tangent to the curve y= * +1 at any po

Olegator [25]

The expressions which represents the slope of a tangent to the curve $y=\frac{1}{x+1}$ at any point (x, y) are:

$f'(x) =limh \rightarrow 0\frac{-h}{h(x+1)(x+h+1)}\\\\f'(x) =limh \rightarrow 0\frac{-h}{x^2h+2xh+xh^2+h^2 +1}$

<h3>The slope of a tangent to the curve.</h3>

Mathematically, the slope of a tangent line to the curve is given by this equation:

$f'(x) =limh \rightarrow 0\frac{f(x+h)-f(x)}{h}$

Given the function:

$f(x)=y=\frac{1}{x+1}$

When (x + h), we have:

$f(x+h)=y=\frac{1}{x+h+1}$

Next, we would find the derivative of f(x):

$f'(x) =limh \rightarrow 0\frac{\frac{1}{x+h+1} -\frac{1}{x+1}}{h}\\\\f'(x) =limh \rightarrow 0\frac{x+1 -(x+h+1)}{h(x+1)(x+h+1)}\\\\f'(x) =limh \rightarrow 0\frac{x+1 -x-h-1}{h(x+1)(x+h+1)}\\\\f'(x) =limh \rightarrow 0\frac{-h}{h(x+1)(x+h+1)}\\\\f'(x) =limh \rightarrow 0\frac{-h}{x^2h+2xh+xh^2+h^2 +1}\\\\f'(x) = \frac{-1}{(x+1)(x+1)} \\\\f'(x) = \frac{-1}{(x+1)^2}$

Read more on slope of a tangent here: brainly.com/question/26015157

#SPJ1

5 0

3 years ago

How many many weeks are in 105 days?

In-s [12.5K]

Answer: 15 weeks

Step-by-step explanation:

Because there are 7 days in a week, simply divide 105/7 to get 15 weeks.

Hope it helps <3

5 0

3 years ago

Read 2 more answers

Mike is putting a ladder up against his mothers house to clean the roof. His mothers house is 24 feet tall and he is placing the

levacccp [35]

The length of the ladder is 25 feet.

<u>Explanation:</u>

Height of the House, h = 24 feet

Distance between the house and the ladder, b = 7 feet

length of the ladder, x = ?

The house makes 90° with the base of the ladder.

Using pythagoras theorm,

x² = h² + b²

x² = (24)² + (7)²

x = √625

x = 25

Therefore, the length of the ladder is 25 feet.

3 0

3 years ago