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3 years ago

Solve for f

Mathematics

2 answers:

mel-nik [20]3 years ago

8 0

Answer:

f = 5/3

Step-by-step explanation:

oksano4ka [1.4K]3 years ago

5 0

Answer:

f = 5/3

Step-by-step explanation:

3/4 f = 5/4

Multiply each side by 4/3 to isolate f

4/3 *3/4 f = 5/4 *4/3

f = 5/3

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The surface area of a melting snowball decreases at a rate of3.8cm2/min. Find the rate at which its diameter decreases when the

Scorpion4ik [409]

Answer:

Step-by-step explanation:

This is a pretty basic related rates problem. I'm going to go through this just like I do in class when I'm teaching it to my students.

We see we have a snowball, which is a sphere. We are talking about the surface area of this sphere which has a formula of

$S=4\pi r^2$

In the problem we are given diameter, not radius. What we know about the relationship between a radius and a diameter is that

d = 2r so

$\frac{d}{2}=r$ Now we can have the equation in terms of diameter instead of radius. Rewriting:

$S=4\pi(\frac{d}{2})^2$ which simplifies to

$S=4\pi(\frac{d^2}{4})$ and a bit more to

$S=\pi d^2$ (the 4's cancel out by division). Now that is a simple equation for which we have to find the derivative with respect to time.

$\frac{dS}{dt}=\pi*2d\frac{dD}{dt}$ Now let's look at the problem and see what we are given as far as information.

The rate at which the surface area changes is -3.8, and we are looking for $\frac{dD}{dt}$ , the rate at which the diameter is changing, when the diameter is 13. Filling in:

$-3.8=\pi(2)(13)\frac{dD}{dt}$ and solving for the rate at which the diameter is changing:

$-\frac{3.8}{26\pi}=\frac{dD}{dt}$ and divide to get

$\frac{dD}{dt}=-.459\frac{cm}{min}$ Obviously, the negative means that the diameter is decreasing.

7 0

3 years ago

Beaker A contains 1 liter which is 15 percent oil and the rest is vinegar, thoroughly mixed up. Beaker B contains 2 liters which

Tanzania [10]

Answer:

Add 1.25 litres of oil.

Step-by-step explanation:

Contents in beaker A implies;

15% of oil in 1 litre = 0.15 litres of oil

So that, there are 0.15 litres of oil and 0.85 litres of vinegar in beaker A.

Contents in beaker B implies:

55% of oil in 2 litres = 1.1 litres of oil

So that, thee are 1.1 litres of oil and 0.9 litres of vinegar in beaker B.

Half of contents of B poured into A implies that beaker A now contains:

0.15 litres + 0.55 litres = 0.7 litres of oil

0.85 litres + 0.45 litres = 1.3 litres of vinegar

The percentage of oil in A now = $\frac{0.7}{2}$ x 100%

= 35%

To increase the percentage of oil to 60%, then:

0.7 litres + 1.25 litres = 1.95 litres of oil

But the new total litres of the content in beaker A = 3.25 litres

So that;

$\frac{1.95}{3.25}$ x 100% = 60%

Therefore, to produce a mixture which is 60% oil, add 1.25 litres of oil.

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3 years ago

What type of association does the following scatter plot represent?

yarga [219]

Answer:

Negative linear association.

Step-by-step explanation:

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3 years ago

Read 2 more answers

The product of 2 consecutive positive odd integers is 483. Write the equation that would be used to find x, the smaller integer.

Montano1993 [528]

Answer: 21

Step-by-step explanation:

Let the consecutive odd numbers be represented by x and x+2. Therefore,

x × (x+2) = 483

x² + 2x = 483

x² + 2x - 483 = 0

x² + 23x - 21x - 483 = 0

x(x + 23) - 21(x + 23) = 0

(x - 21) = 0

x = 0 + 21

x = 21

The smaller integer is 21

The larger integer is 21 + 2 = 23.

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2 years ago

The cost of 4 pounds of bananas is $3.52. What is the constant of proportionality that relates the cost of dollars, y, to the nu

Sladkaya [172]

.88
3.52 divided by 4

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3 years ago