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3 years ago

A.) all real numbers B.) y>6 C.)y is greater than or equal to -6 D.)x= √6 or -√6

Mathematics

1 answer:

Gemiola [76]3 years ago

7 0

Answer:

C.) y is greater than or equal to -6

Step-by-step explanation:

The range are all the set of y-values that are plotted on the vertical axis (y-axis).

The range starts from -6 and above. Which is y ≥ -6

Therefore, range of the function is said to be:

C.) y is greater than or equal to -6

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5) Placido pulls a rope attached to a wagon through a pulley at a rate of q m/s. With dimension as in Figure 5:

Damm [24]

The formula for the speed of the wagon can be found by using Pythagoras theorem, and chain rule of differentiation.

$(a) \ \mathrm{The \ speed \ of \ the \ wagon} , \ \dfrac{dx}{dt} = q -\dfrac{x}{\sqrt{x^2+ 5.76}}$

(b) When x = 0.6 and q = 0.5 m/s, the speed of the wagon is approximately 0.243 m/s.

Reasons:

(a) The distance from the cart to the pulley, r is given by Pythagoras's

theorem as follows;

r = √((3 - 0.6)² + x²) = √(2.4² + x²)

The speed of the wagon = $\mathbf{\dfrac{dx}{dt}}$

The speed of the rope, q = $\mathbf{\dfrac{dr}{dt}}$

By chain rule, we have;

$\dfrac{dr}{dt} = \mathbf{\dfrac{dr}{dx} + \dfrac{dx}{dt}}$

$\dfrac{dr}{dx} = \dfrac{x}{\sqrt{x^2+ 5.76}}$

Therefore;

$\dfrac{dr}{dt} = q =\dfrac{x}{\sqrt{x^2+ 5.76}}+ \dfrac{dx}{dt}$

$\mathrm{The \ speed \ of \ the \ wagon} , \ \dfrac{dx}{dt} = \underline{ q -\dfrac{x}{\sqrt{x^2+ 5.76}}}$

(b) The speed of the wagon when x = 0.6 if q = 0.5 m/s is given as follows;

$\dfrac{dx}{dt} = 0.5 -\dfrac{0.6}{\sqrt{0.6^2+ 5.76}} =\sqrt{\dfrac{1}{17} } \approx 0.243$

The speed of the wagon when x = 0.6 and q = 0.5 m/s, $\dfrac{dx}{dt}$ ≈ 0.243 m/s

Learn more here:

brainly.com/question/17081984

4 0

2 years ago

Find the area of a circle with radius, r = 41cm. Give your answer rounded to 3 SF.

joja [24]

Answer:

5283.143 cm^2

Step-by-step explanation:

Area =πr^2

22/7*41*41

=5283.143cm^2

5 0

3 years ago

What is the probability you would spin a yellow or green space on this spinner?

Ivenika [448]

Answer:

I'm pretty sure the answer is 4/8 or 1/2

5 0

3 years ago

Read 2 more answers

Your friend Ana received an 90% on a quiz. If Ana got 36 problems right, how many questions were in the quiz?

kherson [118]

Answer:

Step-by-step explanation: I just guesstimated a number and divided 36 by 40 to get .9 which means 90%

3 0

3 years ago

What are the first five terms of the sequence generated by the formula below?

Novay_Z [31]

Answer:

The correct option is:

2, 4, 12, 48, 240

Step-by-step explanation:

We have to determine the first 5 terms of the sequence by using following formula:

$a_n=2n!$

To Calculate the first 5 terms.

Put n = 1

a₁ = 2 (1)!

a₁ = 2(1)

a₁ = 2

Put n = 2

a₂ = 2 (2)!

a₂ = 2 (2·1) = 2(2)

a₂ = 4

Put n = 3

a₃ = 2(3)!

a₃ = 2(3·2·1)

a₃ = 2(6)

a₃ = 12

Put n = 4

a₄ = 2(4)!

a₄ = 2(4·3·2·1)

a₄ = 2(24)

a₄ = 48

Put n =5

a₅ = 2(5)!

a₅ = 2(5·4·3·2·1)

a₅ = 2(120)

a₅ = 240

8 0

3 years ago