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write a numerical expression for each word phrase Three less than the product of eight and six

Sergio [31]

(8*6)-3 is your answer

4 0

3 years ago

The line integral of (2x+9z) ds where the curve is given by the parametric equations x=t, y=t^2, z=t^3 for t between 0 and 1. Pl

Naya [18.7K]

Let r = (t,t^2,t^3)

Then r' = (1, 2t, 3t^2)

General Line integral is:
$\int_a^b f(r) |r'| dt$

The limits are 0 to 1
f(r) = 2x + 9z = 2t +9t^3
|r'| is magnitude of derivative vector $\sqrt{(x')^2 + (y')^2 + (z')^2}$

$\int_0^1 (2t+9t^3) \sqrt{1+4t^2 +9t^4} dt$

Fortunately, this simplifies nicely with a 'u' substitution.

Let u = 1+4t^2 +9t^4

du = 8t + 36t^3 dt

$\int_0^1 \frac{2t+9t^3}{8t+36t^3} \sqrt{u} du \\ \\ \int_0^1 \frac{2t+9t^3}{4(2t+9t^3)} \sqrt{u} du \\ \\ \frac{1}{4} \int_0^1 \sqrt{u} du$

After integrating using power rule, replace 'u' with function for 't' and evaluate limits:
$=\frac{1}{4} |_0^1 (\frac{2}{3}) (1+4t^2 +9t^4)^{3/2} \\ \\ =\frac{1}{6} (14^{3/2} - 1)$

7 0

3 years ago

Part A: Factor x2y2 + 6xy2 + 8y2. Show your work. (4 points) Part B: Factor x2 + 8x + 16. Show your work. (3 points) Part C: Fac

skad [1K]

Answer:

Part A : y²(x + 2)(x + 4)

Part B: (x + 4) (x + 4)

Part C: (x + 4) (x - 4)

Step-by-step explanation:

Part A: Factor x²y²+ 6xy²+ 8y²

x²y²+ 6xy²+ 8y²

y² is very common across the quadratic equation , hence

= y² (x² + 6x + 8)

= (y²) (x² + 6x + 8)

= (y²) (x² + 2x +4x + 8)

= (y²) (x² + 2x)+(4x + 8)

= (y²) (x(x + 2)+ 4(x + 2))

= y²(x+2)(x+4)

Part B: Factor x² + 8x + 16

x² + 8x + 16

= x² + 4x + 4x + 16

= (x² + 4x) + (4x + 16)

= x( x + 4) + 4(x + 4)

= (x + 4) (x + 4)

Part C: Factor x² − 16

= x² − 16

= x² + 0x − 16

= x² + 4x - 4x - 16

= (x² + 4x) - (4x - 16)

= x (x + 4) - 4(x + 4)

= (x + 4) (x - 4)

6 0

3 years ago

4. If your company purchases an annuity that will pay $50,000/year for 10 years at a 11% discount rate, what is the value of the

julsineya [31]

Answer:

The value of the annuity is $326,852.3766.

Step-by-step explanation:

Here is the required formula to find the present value of annuity:

We can find the present value of annuity:

$PV = P + P (\frac{1-(1+r)^{-(n-1)} }{r})$

Here:

P = $50,000

n = represents the number of number of periods

r = 0.11

$PV = 50,000 + 50,5000 (\frac{1-(1+0.11)^{-(10-1)} }{0.11})$

PV = $326,852.3766

The value of the annuity is $326,852.3766 i.e. PV = $326,852.3766.

Keywords: discount rate, present value of annuity

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4 0

3 years ago

How do you get the numbers 4 5 13 to equal 5

MAVERICK [17]

You can subtract 4 from 13 then subtract 4 again

3 0

3 years ago