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Aleks [24]
3 years ago
7

Vivi is a drummer for a band. She burns 756 calories while drumming for 3hours. She burns the same number of calories per hour.

How many calories does Vivi burn per hour?
Mathematics
1 answer:
lions [1.4K]3 years ago
7 0

This question uses the concept of the division.

Vivi, the band drummer, burns 765 calories in 3 hours. And she burns these calories at the same rate. Which means she burns the same amount of calories per hour.

Thus, the set up equation for this question will be:

Energy burnt in 3 hours=756 calories

Therefore, Energy burnt in 1 hour = \frac{756}{3} =252 Calories.

Thus, the required answer is that Vivi burns 252 Calories of energy per hour while drumming.

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Solve the initial value problem: y'(x)=(4y(x)+25)^(1/2) ,y(1)=6. you can't really tell, but the '1/2' is the exponent
goblinko [34]

Answer:

y(x)=x^2+5x

Step-by-step explanation:

Given: y'=\sqrt{4y+25}

Initial value: y(1)=6

Let y'=\dfrac{dy}{dx}

\dfrac{dy}{dx}=\sqrt{4y+25}

Variable separable

\dfrac{dy}{\sqrt{4y+25}}=dx

Integrate both sides

\int \dfrac{dy}{\sqrt{4y+25}}=\int dx

\sqrt{4y+25}=2x+C

Initial condition, y(1)=6

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C=5

Put C into equation

Solution:

\sqrt{4y+25}=2x+5

or

4y+25=(2x+5)^2

y(x)=\dfrac{1}{4}(2x+5)^2-\dfrac{25}{4}

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Hence, The solution is y(x)=\dfrac{1}{4}(2x+5)^2-\dfrac{25}{4} or y(x)=x^2+5x

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3 years ago
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Answer:

Step-by-step explanation:

PART 1:

Possible roots by noticing the coefficient of first term:

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1 | 1  -1  -4   4

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   1   0  -4  0

The remainder is zero, hence one factor is (x-1)

PART 3:

x^3-x^2-4x+4=(x^2-4)(x-1)\\\\x^3-x^2-4x+4=(x+2)(x-2)(x-1)

PART 4:

f(x)=(x+2)(x-2)(x-1)\\\\=(x^2-4)(x-1)\\\\=x^3-4x-x^2+4\\\\=x^3-x^2-4x+4

6 0
3 years ago
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Nina [5.8K]

Answer:

This type of transformation is a horizontal stretch.

<em></em>

Step-by-step explanation:

Given

y = x + 4

y = .5x + 4

Required

Determine the type of transformation

The first function can be expressed as:

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While the second function is:

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Solving f(0.5x), we have to substitute 0.5x for x in f(x) = x + 4

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The second function is:

g(x) = 0.5x + 4

<em>This type of transformation is a horizontal stretch.</em>

<em></em>

<em>i.e. f(x) stretched to g(x)</em>

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