Express 3^2 = x as a logarithmic equation

Which of the following integrals represents the area of the region bounded by x = 0, x = 1 and the functions f(x) = -2x4 and g(x

leva [86]

Answer:

C. $\int\limits^0_1 {-2x^4-x^2} \, dx$ is correct

Step-by-step explanation:

We are given that,

The region bounded by $x= 0, x=1, f(x)= -2x^4, g(x)=x^2$ is given in the figure below.

Now, as we have,

Area of the bounded region = $\int\limits^a_b {f(x)-g(x)} \, dx$ ,

where f(x) represents the upper curve and f(x) represents the lower curve in the bounded region.

So, as we see that,

The upper curve in the given region is $f(x)= -2x^4$ and the lower curve is $g(x)=x^2$ .

Thus, the integral showing the area of the given region is,

$\int\limits^0_1 {-2x^4-x^2} \, dx$

Hence, option C is correct.

6 0

3 years ago

Find the maximum rate of change of f at the given point and the direction in which it occurs. f(p, q) = 8qe−p + 4pe−q, (0, 0) ma

Pachacha [2.7K]

Answer:

Step-by-step explanation:

$Given \ f (p,q) = 8qe^{-p} + 4pe^{-q} \ where \ P_o(0,0) \\ \text{thus the gradient of f is: } \\ \\ \bigtriangledown f(p,q) = \Big(\dfrac{\partial f}{\partial p}, \dfrac{\partial f}{\partial q} \Big) \\ \\ \dfrac{\partial f}{\partial p} = -8qe^{-p} + 4pe^{-q} \\ \\ \dfrac{\partial f}{\partial p} = 8qe^{-p} - 4pe^{-q} \\ \\ Then: \bigtriangledown f(p.q) = (-4qe^{-p}+ 8qe^{-q}, 4qe^{-p}- 8qe^{-q}) \\ \\ f(0,0) = (-4*(0)e^{-0}+ 8*(0)e^{-(0)}, 4*(0)e^{-(0)}- 8*(0)e^{-(0)}) \\ \\ = (0+8,4-0) = (8.4)$

$\Big| \Big | \bigtriangledown f(0,0) = \sqrt{(8)^2+4^2} \\ \\ = \sqrt{64+16} \\ \\ = \sqrt{80}$

$\mathbf{the \ direction \ of \ maximum \ change \ is }= \mathbf{\sqrt{80}} \\ \\ \mathbf{direction }(8,4)$

7 0

3 years ago

Need help!! What’s the second blank?

tatuchka [14]

Answer:

The answer is 350 sqft

Step-by-step explanation:

terrace 48 sqft

back porch is = 6x6 = 36 sqft

side deck = 3x14 = 42 sqft

playroom = 16x14 = 224 sqft

Total area of the tree house: 48+36+42+224 = 350 sqft

7 0

4 years ago

Read 2 more answers

If AD=6 and AB=24, find AC

ruslelena [56]

When a perpendicular is dropped from the right-angle (C) to the opposite side AB, the metric relations apply:
BD*BA=a^2 ..........................(1)
AD*AB=b^2...........................(2)
BD*DA=DC^2........................(3)

Given AD=6, AB=24, using metric relation (2) above, we have
b^2=6*24=144
=>
b=sqrt(144)=12

By the way, we conclude that this is a 30-60-90 triangle because b/AB=(1/2)=sin(B) => B=30 degrees.

Answer: b=12

6 0

3 years ago

How long would it take to travel 630 miles at the rate of 35 miles per hour?

blsea [12.9K]

Answer:

Using formula:

$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$