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2 years ago

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Write the equation of the circle with center (2, -3) and a radius of 4. A) (x + 2)2 + (y - 3)2 = 4 Eliminate B) (x - 2)2 + (y +

3)2 = 4 C) (x + 2)2 + (y - 3)2 = 16 D) (x - 2)2 + (y + 3)2 = 16

1 answer:

bekas [8.4K]2 years ago

7 0

The answer is: [D]: " (x − 2)² + (y + 3)² = 16 " .
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Q2. A train travels at a constant speed of 45 m/s. a) Calculate the distance travelled by the train in:

alex41 [277]

Answer:

i) 1350 m

ii) 5400 m

Step-by-step explanation:

<u>Formula for Speed</u>

$\boxed{\sf Speed=\dfrac{Distance}{Time}}$

Rearrange the formula so that Distance is the subject:

$\implies \sf Distance = Speed \times Time$

<h3><u>Question (i)</u></h3>

Given:

Speed = 45 m/s (meters per second)
Time = 30 seconds

Substitute the given values into the formula for distance:

$\implies \sf Distance = 45 \times 30 = 1350\:m$

<h3><u>Question (ii)</u></h3>

Given:

Speed = 45 m/s (meters per second)
Time = 2 minutes

As the time is given in a different unit of time as the speed, we must first convert the time into seconds:

1 minute = 60 seconds

⇒ 2 minutes = 60 × 2 = 120 seconds

Therefore:

Speed = 45 m/s (meters per second)
Time = 120 seconds

Substitute the values into the formula for distance:

$\implies \sf Distance = 45 \times 120 = 5400\:m$

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7 months ago

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Tell whether the points appear to represent a linear function, an exponential function, or neither? Explain please.

mario62 [17]

Answer:

Exponential

Step-by-step explanation:

Linear is easy to remember because it goes in a straight LINE.

Only other option is a quadratic and this does not create a parabola

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2 years ago

The scatter plot shows a regression line of advertising dollars spent and sales. If the company were to spend $275,000 on advert

Misha Larkins [42]

Answer: need the graph please

Step-by-step explanation:

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3 years ago

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Which of the following equations is equivalent to 3x + 4y = 15?

Ray Of Light [21]

Letter A is the answer because
4y = 15 - 3x
so y = 15/4 -3x/4

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2 years ago

Show that cos(3x) = cos3(x) − 3 sin2(x)cos(x). (Hint: Use cos(2x) = cos2(x) − sin2(x) and the cosine sum

otez555 [7]

<u>Step-by-step explanation:</u>

To prove:

$\cos 3x=\cos^3x-3\sin^2 x\cos x$

Identities used:

$\cos(A+B)=\cos A\cos B+\sin A\sin B$ ......(1)

$\sin 2A=2\sin A\cos A$ ........(2)

$\cos 2A=\cos^2A-\sin^2 A$ .......(3)

Taking the LHS:

$\Rightarrow \cos 3x=\cos (x+2x)$

Using identity 1:

$\Rightarrow \cos (x+2x)=\cos x\cos 2x-\sin x\sin 2x$

Using identities 2 and 3:

$\Rightarrow \cos x(\cos ^2x-\sin^2 x)-\sin x(2\sin x\cos x)\\\\\Rightarrow \cos^3x-\sin^2x\cos x-2\sin^2 x\cos x\\\\\Rightarrow \cos^3x-3\sin^2x\cos x$

As, LHS = RHS

Hence proved

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2 years ago