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4 years ago

3.

Mathematics

1 answer:

larisa [96]4 years ago

8 0

Answer:

a. 16 gallons

b. 32

Step-by-step explanation:

Let the full capacity of the tank is x gallons.

a. It is given that 12 gallons of water fill a tank to $\frac{3}{4}$ capacity.

Hence, we can write $\frac{3x}{4} = 12$

⇒ $x = \frac{4 \times 12}{3} = 16$ gallons.

b. If the tank is filled to capacity, then there will be 16 gallons of water, with which $\frac{16}{\frac{1}{2} } = 32$ numbers of half-gallon bottles of be filled with water. (Answer)

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In a freefall skydive, a skydiver begins at an altitude of 10,000 feet. during a freefall, the skydiver drops toward earth towar

asambeis [7]

Answer:

{ $t|0\leq t\leq 50$ }

Step-by-step explanation:

We are given that

In a freefall skydive, a skydiver begins at an altitude during free fall =10,000 feet

The skydiver drops towards earth at a rate=175 ft/s

The height of the skydiver from the ground can be modeled using the function

$H(t)=10000-175t$

We have to find the domain of the function for this situation.

When t=0

Then , $H(0)=10,000 feet$

From given graph we can see that the value of t lies from 0 to 50.

Therefore, the domain of the function for this situation is given by

{ $t|0\leq t\leq 50$ }

7 0

3 years ago

Find a formula for dy/dx if sin x + cos y + sec(xy) = 251

Lena [83]

Answer:

$\displaystyle \frac{dy}{dx} = \frac{-cos(x) - ysec(xy)tan(xy)}{-sin(y) + xsec(xy)tan(xy)}$

General Formulas and Concepts:

Pre-Algebra

Distributive Property

Algebra I

Factoring

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Trig Differentiation

Derivative Rule [Chain Rule]: $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Implicit Differentiation

Step-by-step explanation:

Step 1: Define

Identify

sin(x) + cos(y) + sec(xy) = 251

Step 2: Differentiate

[Implicit Differentiation] Trig Differentiation [Chain Rule]: $\displaystyle cos(x) - sin(y)\frac{dy}{dx} + sec(xy)tan(xy) \cdot (y + x\frac{dy}{dx}) = 0$
[Subtraction Property of Equality] Isolate $\displaystyle \frac{dy}{dx}$ terms: $\displaystyle -sin(y)\frac{dy}{dx} + sec(xy)tan(xy) \cdot (y + x\frac{dy}{dx}) = -cos(x)$
[Distributive Property] Distribute sec(xy)tan(xy): $\displaystyle -sin(y)\frac{dy}{dx} + ysec(xy)tan(xy) + xsec(xy)tan(xy)\frac{dy}{dx} = -cos(x)$
[Subtraction Property of Equality] Isolate $\displaystyle \frac{dy}{dx}$ terms: $\displaystyle -sin(y)\frac{dy}{dx} + xsec(xy)tan(xy)\frac{dy}{dx} = -cos(x) - ysec(xy)tan(xy)$
Factor out $\displaystyle \frac{dy}{dx}$ : $\displaystyle \frac{dy}{dx}[-sin(y) + xsec(xy)tan(xy)] = -cos(x) - ysec(xy)tan(xy)$
[Division Property of Equality] Isolate $\displaystyle \frac{dy}{dx}$ : $\displaystyle \frac{dy}{dx} = \frac{-cos(x) - ysec(xy)tan(xy)}{-sin(y) + xsec(xy)tan(xy)}$

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Implicit Differentiation

Book: College Calculus 10e

5 0

3 years ago

Evaluate sin 45° cos 60° + tan 45°

Anna [14]

Answer:

√2/4 + 1

Step-by-step explanation:

sin 45° --> √2/2

cos 60° --> 1/2

tan 45° --> 1

with these values, we write a new expression

√2/2 × 1/2 + 1

√2/2 × 1/2 = √2/4

(by doubling the denominator, you are splitting the number in half as implied by the 1/2)

your answer is √2/4 + 1

goodluck :)

7 0

3 years ago

Which direction will the line be? 4

Allushta [10]

Step-by-step explanation:

um that's not enough information to answer that

4 0

3 years ago

Read 2 more answers

When might it be useful to know how to find the area of a real-life composite figure?

quester [9]

If you choose to become an architect, then you will need it all the time. You would need to find the area of the floors, walls, etc. which will almost always be composite figures.

5 0

3 years ago