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2 years ago

Please help me! I'm stuck! If you answer both a and b, you get brainliest and points!

Mathematics

1 answer:

Rufina [12.5K]2 years ago

7 0

The water is flowing into the pool at 1.5 gallons per minute and it would take 20 minutes to be filled.

<h3>What is an Equation</h3>

An equation is used to show the relationship between two or more numbers and variables.

The pool holds 30 gallons of water. After 5 minutes, the pool is about one fourth full. Hence:

Time to full the pool = 5 minutes * 4 = 20 minutes

Rate of water flow = 30 gallons/20 minutes = 1.5 gallons per minute

The water is flowing into the pool at 1.5 gallons per minute and it would take 20 minutes to be filled.

Find out more on Equation at: brainly.com/question/13763238

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A closed box with a square base is to have a volume of 13 comma 500 cm cubed. The material for the top and bottom of the box cos

andrezito [222]

Answer:

x = 1,5 cm

h = 6 cm

C(min) = 135 $

Step-by-step explanation:

Volume of the box is :

V(b) = 13,5 cm³

Aea of the top is equal to area of the base,

Let call " x " side of the base then as it is square area is A₁ = x²

Sides areas are 4 each one equal to x * h (where h is the high of the box)

And volume of the box is 13,5 cm³ = x²*h

Then h = 13,5/x²

Side area is : A₂ = x* 13,5/x²

A(b) = A₁ + A₂

Total area of the box as functon of x is:

A(x) = 2*x² + 4* 13,5 / x

And finally cost of the box is

C(x) = 10*2*x² + 2.50*4*13.5/x

C(x) = 20*x² + 135/x

Taking derivatives on both sides of the equation:

C´(x) = 40*x - 135*/x²

C´(x) = 0 ⇒ 40*x - 135*/x² = 0 ⇒ 40*x³ = 135

x³ = 3.375

x = 1,5 cm

And h = 13,5/x² ⇒ h = 13,5/ (1,5)²

h = 6 cm

C(min) = 20*x² + 135/x

C(min) = 45 + 90

C(min) = 135 $

8 0

3 years ago

Juliette is making a fruit salas. She purchased 9 and 2/3 ounces each of 6 different fruits. how many ounches of fruit did she p

Rom4ik [11]

Juliette purchased approximately 58 ounces of fruit

5 0

3 years ago

Read 2 more answers

A recipe for salad dressing calls for 3 tablespoons of oil for every 2 tablespoons of vinegar. The line represents the relations

pochemuha

Answer:

3:2, 3 to 2

Step-by-step explanation:

4 0

3 years ago

Derivative of tan(2x+3) using first principle

kodGreya [7K]

$f(x)=\tan(2x+3)$

The derivative is given by the limit

$f'(x)=\displaystyle\lim_{h\to0}\frac{f(x+h)-f(x)}h$

You have

$\displaystyle\lim_{h\to0}\frac{\tan(2(x+h)+3)-\tan(2x+3)}h$
$\displaystyle\lim_{h\to0}\frac{\tan((2x+3)+2h)-\tan(2x+3)}h$

Use the angle sum identity for tangent. I don't remember it off the top of my head, but I do remember the ones for (co)sine.

$\tan(a+b)=\dfrac{\sin(a+b)}{\cos(a+b)}=\dfrac{\sin a\cos b+\cos a\sin b}{\cos a\cos b-\sin a\sin b}=\dfrac{\tan a+\tan b}{1-\tan a\tan b}$

By this identity, you have

$\tan((2x+3)+2h)=\dfrac{\tan(2x+3)+\tan2h}{1-\tan(2x+3)\tan2h}$

So in the limit you get

$\displaystyle\lim_{h\to0}\frac{\dfrac{\tan(2x+3)+\tan2h}{1-\tan(2x+3)\tan2h}-\tan(2x+3)}h$
$\displaystyle\lim_{h\to0}\frac{\tan(2x+3)+\tan2h-\tan(2x+3)(1-\tan(2x+3)\tan2h)}{h(1-\tan(2x+3)\tan2h)}$
$\displaystyle\lim_{h\to0}\frac{\tan2h+\tan^2(2x+3)\tan2h}{h(1-\tan(2x+3)\tan2h)}$
$\displaystyle\lim_{h\to0}\frac{\tan2h}h\times\lim_{h\to0}\frac{1+\tan^2(2x+3)}{1-\tan(2x+3)\tan2h}$
$\displaystyle\frac12\lim_{h\to0}\frac1{\cos2h}\times\lim_{h\to0}\frac{\sin2h}{2h}\times\lim_{h\to0}\frac{\sec^2(2x+3)}{1-\tan(2x+3)\tan2h}$

The first two limits are both 1, and the single term in the last limit approaches 0 as $h\to0$ , so you're left with

$f'(x)=\dfrac12\sec^2(2x+3)$

which agrees with the result you get from applying the chain rule.

7 0

3 years ago

Find the source area of the space figure represented by the net

sergejj [24]

I assume you meant "surface area" :)

Looking at the net, it looks like if you folded it back together it would form to become a triangular prism.

To calculate the surface area of a triangular prism, you would use the formula: A = bh + 2ls + lb, where b is the base of the triangular faces, h is the height of the prism, l is the length of the prism, and s is the side length of the prism.

I attached a picture to help you see what these labels are.

Looking at the diagram you've provided, we can assume that b = 7 cm, h = 4 cm, l = 8 cm, and s = 5 cm. Substitute these into the formula.

A = bh + 2ls + lb ==> A = (7)(4) + 2(8)(5) + (8)(7)

Multiply from left to right.

28 + 80 + 56

Add.

164

The surface area of this triangular prism is A) 164 cm^2.

6 0

3 years ago