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3 years ago

What are the coordinates of the vertex of the table? Is it a minimum or a maximum?

Mathematics

1 answer:

Aleksandr [31]3 years ago

8 0

B.(-2,-3);maximum. that is the answer

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If the integral of the product of x squared and e raised to the negative 4 times x power, dx equals the product of negative 1 ov

Nataly_w [17]

Answer:

$A + B + E = 32$

Step-by-step explanation:

Given

$\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C$

Required

Find $A +B + E$

We have:

$\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C$

Using integration by parts

$\int {u} \, dv = uv - \int vdu$

Where

$u = x^2$ and $dv = e^{-4x}dx$

Solve for du (differentiate u)

$du = 2x\ dx$

Solve for v (integrate dv)

$v = -\frac{1}{4}e^{-4x}$

So, we have:

$\int {u} \, dv = uv - \int vdu$

$\int\limits {x^2\cdot e^{-4x}} \, dx = x^2 *-\frac{1}{4}e^{-4x} - \int -\frac{1}{4}e^{-4x} 2xdx$

$\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} - \int -\frac{1}{2}e^{-4x} xdx$

$\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} \int xe^{-4x} dx$

-----------------------------------------------------------------------

Solving

$\int xe^{-4x} dx$

Integration by parts

$u = x$ ---- $du = dx$

$dv = e^{-4x}dx$ ---------- $v = -\frac{1}{4}e^{-4x}$

So:

$\int xe^{-4x} dx = -\frac{x}{4}e^{-4x} - \int -\frac{1}{4}e^{-4x}\ dx$

$\int xe^{-4x} dx = -\frac{x}{4}e^{-4x} + \int e^{-4x}\ dx$

$\int xe^{-4x} dx = -\frac{x}{4}e^{-4x} -\frac{1}{4}e^{-4x}$

So, we have:

$\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} \int xe^{-4x} dx$

$\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} [ -\frac{x}{4}e^{-4x} -\frac{1}{4}e^{-4x}]$

Open bracket

$\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} -\frac{x}{8}e^{-4x} -\frac{1}{8}e^{-4x}$

Factor out $e^{-4x}$

$\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{x^2}{4} -\frac{x}{8} -\frac{1}{8}]e^{-4x}$

Rewrite as:

$\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{1}{4}x^2 -\frac{1}{8}x -\frac{1}{8}]e^{-4x}$

Recall that:

$\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C$

$\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{1}{64}Ax^2 -\frac{1}{64} Bx -\frac{1}{64} E]Ce^{-4x}$

By comparison:

$-\frac{1}{4}x^2 = -\frac{1}{64}Ax^2$

$-\frac{1}{8}x = -\frac{1}{64}Bx$

$-\frac{1}{8} = -\frac{1}{64}E$

Solve A, B and C

$-\frac{1}{4}x^2 = -\frac{1}{64}Ax^2$

Divide by $-x^2$

$\frac{1}{4} = \frac{1}{64}A$

Multiply by 64

$64 * \frac{1}{4} = A$

$A =16$

$-\frac{1}{8}x = -\frac{1}{64}Bx$

Divide by $-x$

$\frac{1}{8} = \frac{1}{64}B$

Multiply by 64

$64 * \frac{1}{8} = \frac{1}{64}B*64$

$B = 8$

$-\frac{1}{8} = -\frac{1}{64}E$

Multiply by -64

$-64 * -\frac{1}{8} = -\frac{1}{64}E * -64$

$E = 8$

So:

$A + B + E = 16 +8+8$

$A + B + E = 32$

4 0

3 years ago

5-7 please and thank you

Crazy boy [7]

5. 623. Just split the shape into two. then find the area of two figures that you created. Then add.
6. V = 138.125. Just multiply all the numbers together for this problem.
7. SA = 392. Use the formula 2(lw + lh + wh).

5 0

3 years ago

A square has a perimeter of 12x + 52 units. Which expression represents the side length of the square in units?

DochEvi [55]

1. Find the surface area of the rectangular prism. (1 point)
Measures are 2, 3, and 4 inches. Let W=2, L=3, H=4 
a rectangular has six sides, the total surface area is equal to 6 plains: 
2*W*L + 2*L*H + 2*L*W 
= 2*(W*L + L*H + L*W) 
= 2 * (2*3 + 3*4 + 4*2) 
= 2 * ( 6 + 12 + 8 ) 
= 2 * 26 
= 52 ................... the last choice 

2. A cube has a side length of x feet. Which expression represents the surface area of the cube? (1 point) 

Area of one face = x^2, Total Area of 6 faces = 6*x^2 = 2x^2 units 

3. Find the surface area of the cylinder. Use 3.14 for pi . (1 point) 
Length: 15 cm, Diameter: 2 cm 
A cylinder has 3 surfaces: two circles + one curved surface area 
...... two circles of 2cm diameter (1cm radius) 
A = pi*r^2 = 3.14*1*1 = 3.14 sq. cm ...... two circles' area = 6.28 sq.cm 
Curved surface area = circumference * length 
.... circumference = pi*d = 3.14 * 2 = 6.28 cm ......... length = 15 
curved surface area = 6.28*15 = 94.2 sq. cm 

Add both for total surface area = 6.28 + 94.2 = 100.48 sq.cm 

4. The bottom of a shopping bag measures 8 inches by 10 inches. The bag has a height of 12 inches. How much paper is needed to make the bag? (1 point) 
two pieces of paper ... one for bottom = 8*10 = 80 sq.in 
the other ... height * perimeter of the bottom = 12*(2*(10+8)) = 12 * 2 * 18 = 432 sq.in 
Add both: 80 + 432 = 512 sq.in <<<<<<<<<<<

4 0

3 years ago

Read 2 more answers

An investment counselor calls with a hot stock tip. He believes that if the economy remains strong, the investment will result i

Dovator [93]

Answer: expected profit = 18,000 dollars

Step-by-step explanation:

expected value formulae = x * p(x)

x= data value, p(x) = probability of data value

When the economy is strong

profit to be made = 60,000 dollars

probability that economy will be strong = 30/100 = 0.3

expected value = profit * probability at which profit is made

expected value = 0.3 * 60000

expected value = 18,000 dollars

When economy grows at moderate pace

profit to be made = 10,000

probability that economy will be moderate = 60/100 = 0.6

expected value = 0.6 * 10000

expected value = 6,000 dollars

When economy is in recession

loss to be made = -60,000

probability that economy will be in recession = 10/100=0.1

expected value = 0.1 * -60000 = -6000 dollars

negative sign denotes loss.

total investment = 18,000 + 6000 - 6000

total investment = 18,000 dollars

3 0

3 years ago

Select the correct difference. 5d^2 + 4d - 3 less 2d^2 - 3d + 4

Alex_Xolod [135]

Answer:

3 d^2 + 7 d - 7

Step-by-step explanation:

5d^2 + 4d - 3 less 2d^2 - 3d + 4

correct difference

3 d^2 + 7 d - 7

4 0

3 years ago

Read 2 more answers