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3 years ago

What is the answer help ASAP!! :))

Mathematics

1 answer:

vampirchik [111]3 years ago

8 0

Answer:

Step-by-step explanation:

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A block of ice has a square top and bottom and rectangular sides. At a certain point in

Lilit [14]

Answer:

$\frac{dV}{dt} = 360 \ cm^3/h$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Geometry

Volume of a Rectangular Prism: V = lwh

Calculus

Derivatives

Derivative Notation

Differentiating with respect to time

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

$l = 30 \ cm\\w = l\\\frac{dl}{dt} = 2 \ cm/h\\h = 20 \ cm\\\frac{dh}{dt} = 3 \ cm/h$

Step 2: Differentiate

Rewrite [VRP]: $V = l^2h$
Differentiate [Basic Power Rule]: $\frac{dV}{dt} = 2l\frac{dl}{dt} \frac{dh}{dt}$

Step 3: Solve for Rate

Substitute: $\frac{dV}{dt} = 2(30 \ cm)(2 \ cm/h)(3 \ cm/h)$
Multiply: $\frac{dV}{dt} = 360 \ cm^3/h$

Here this tells us that our volume is decreasing (ice melting) at a rate of 360 cm³ per hour.

3 0

3 years ago

Two students, Carlos and Sophie, factored the trinomial -4x2 − 10x + 6. Sophie factored it as -2(2x − 1)(x + 3) and Carlos facto

damaskus [11]

Sophie has factored the term completely while Carlos has not factored the term completely.

Step-by-step explanation:

We need to factor the trinomial:

$-4x^2-10x + 6$

Factoring:

$-4x^2-10x + 6\\Taking\,\,-2\,\,common:\\-2(2x^2+5x-3)\\Now\,\,factoring:\\-2(2x^2+6x-x-3)\\-2(2x(x+3)-1(x+3))\\-2(2x-1)(x+3)$

So, the factored form of $-4x^2-10x + 6$ is $-2(2x-1)(x+3)$

So, Sophie has factored the term completely. The terms are factored when we cannot further simplify it. Since Carlos factored (x+3)(-4x+2) 2 can be taken common from the term (-4x+2) so, it is not factored completely.

Keywords: Factoring the terms

Learn more about Factoring the terms at:

#learnwithBrainly

7 0

3 years ago

The surface area of a tabletop is 5760 square inches. What expression shows this number in scientific notation?

aniked [119]

The answer is C

5.76 x 10 ^3 means you move the decimal 3 times:

57.6> 576.0> 5760

8 0

3 years ago

The formula for the area,A, of a trapezoid is shown below, where ݄H represents its height and b1 and b2

emmainna [20.7K]

One equivalent is $A=h( \frac{ b_{1}+b_{2} }{2})$

Another example is $A= \frac{(b_{1}+b_{2})(h)}{2}$

4 0

3 years ago

How many integers $n$ satisfy $-4n\ge 12$ and $n+5>2$??

Dahasolnce [82]

-4n ≥ 12 ==> n ≤ -3

n + 5 > 2 ==> n > -3

But n cannot be both less than/equal to -3 AND greater than -3, so there are no integers n that satisfy these inequalities.

6 0

3 years ago