Use a definite integral to find an expression that represents the area of the region between the given curve and the x-axis on t

he interval [0,b].
y=6x^2

Mathematics

1 answer:

miss Akunina [59]2 years ago

4 0

$\bf y=6x^2\qquad \cfrac{dy}{dx}=12x\qquad [0,b]\\\\
-----------------------------\\\\
\displaystyle \int\limits_{0}^{b}\ 12x\cdot dx$

You might be interested in

You drive from your home to a vacation resort 420 miles away. You return on the same highway. The average velocity on the return

attashe74 [19]

<h2>Time required to complete the round trip $T=\frac{420}{x}+\frac{420}{(x-15)}$ where x is average velocity on the outgoing trip.</h2>

Step-by-step explanation:

Let average velocity of outgoing trip = x mph

The average velocity on the return trip is 15 miles per hour slower than the average velocity on the outgoing trip.

Average velocity of return trip = (x-15) mph

Distance to vacation place = 420 miles

Distance to vacation place = Time for outgoing trip x average velocity of outgoing trip

$420=t_1\times x\\\\t_1=\frac{420}{x}$

Distance to vacation place = Time for return trip x average velocity of return trip

$420=t_2\times (x-15)\\\\t_2=\frac{420}{(x-15)}$

We have total time T = t₁ + t₂

That is

$T=\frac{420}{x}+\frac{420}{(x-15)}$

Time required to complete the round trip $T=\frac{420}{x}+\frac{420}{(x-15)}$ where x is average velocity on the outgoing trip.

8 0

2 years ago

What is the percent of change if 90 is decreased to 82

Sedbober [7]

Answer: - 8.89%

I am going to explain you in detail ir order to help you to be able to do this kind of problems by yourself.

The definition of percent change, %, is:

          change
% = ---------------- * 100
        base value

The base value is from where you start or the value for which you want to asses the variation.

So, in this case the base value is 90 (starting value).

The change is final value - initial value = 82 - 90 = - 8. The negative sign means that the value decreased.

So, following the formula you get:

         82 - 90                - 8
% = ----------- * 100 = -------- * 100 = - 8.89
            90                     90

Answer: the percent of change is - 8.89 %, meaning that the value decreased 8.89%.

4 0

3 years ago

Read 2 more answers

7 less than twice a number.

tino4ka555 [31]

Answer:

7-2x..I'm not entirely sure coz the question isn't given

4 0

2 years ago

Solve 15 ≥ -3x or 2/5x ≥ -2. <br><br> A.) {x | x ≤ -5}<br> B.) {x | x ≥ -5}<br> C.) {all reals}

Lapatulllka [165]

$15 \geq -3x\quad|:(-3)\qquad\vee\qquad \dfrac{2}{5}x \geq -2\quad|\cdot5\\\\\\
-5 \leq x\qquad\vee\qquad 2x \geq -10\quad|:2\\\\\\
-5 \leq x\qquad\vee\qquad x \geq -5\\\\\\x\geq -5\qquad\implies\qquad\boxed{\{x | x \geq -5\}}$

Answer B.

6 0

3 years ago

Read 2 more answers

Find the value of x in the triangle shown below.

nika2105 [10]

Answer:

$x = \sqrt{28}$