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3 years ago

Solve 2 | 2x + 10|+ 4 > 10

Mathematics

1 answer:

Valentin [98]3 years ago

8 0

Answer:

x>−72 or x<−132

Step-by-step explanation:

I believe that is the answer

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) The density of oil in a circular oil slick on the surface of the ocean at a distance of r meters from the center of the slick

Feliz [49]

Answer:

Therefore the mass of the of the oil is 409.59 kg.

Step-by-step explanation:

Let us consider a circular disk. The inner radius of the disk be r and the outer diameter of the disk be (r+Δr).

The area of the disk

=The area of the outer circle - The area of the inner circle

= $\pi (r+\triangle r)^2- \pi r^2$

$=\pi [r^2+2r\triangle r+(\triangle r)^2-r^2]$

$=\pi [2r\triangle r+(\triangle r)^2]$

Since (Δr)² is very small, So it is ignorable.

∴ $A=2\pi r\triangle r$

The density $\delta (r)= \frac{40}{1+r^2}$

We know,

Mass= Area× density

$=(2r \pi \triangle r)(\frac{40}{1+r^2}})$

Total mass $M=\sum_{i=1}^n \frac{80r_i\pi }{1+r^2}\triangle r_i$

Therefore

$\sum_{i=1}^n \frac{80r_i\pi }{1+r^2}\triangle r_i=\int_0^5 \frac{80r\pi }{1+r^2}dr$

$=40\pi[ln(1+r^2)]_0^5$

$=40\pi [ln(1+5^2)-ln(1+0^2)]$

$=40\pi ln(26)$

= 409.59 kg (approx)

Therefore the mass of the of the oil is 409.59 kg.

3 0

2 years ago

Madison had $187.56 in her checking account. She deposited $49.73 and then used her debit card to spend $18.65. What is Madison'

masha68 [24]

First you would find the sum of 187.56 and 49.73 which is 237.29 then you subtract this number from 18.65 which is 218.64 that's your answer

4 0

3 years ago

Read 2 more answers

Select all factors of the following polynomial:

Lena [83]

Step-by-step explanation:

4p³ + 36p² + 32p

= 4p(p² + 9p + 8)

= 4p(p + 1)(p + 8).

8 0

2 years ago

Can someoneee please help me

icang [17]

9514 1404 393

Answer:

37°

Step-by-step explanation:

The diagonals of a rhombus are angle bisectors. Angle 1 matches the other half of angle L.

∠1 = 37°

Angle 2 is the complement, 53°, and angle 3 is the same as angle 2, 53°.

The diagonals of a rhombus are perpendicular bisectors of each other, so angle 4 is 90°.

7 0

3 years ago

Let f(x, y) = (x + y)e x 2−y 2 and R be the rectangle enclosed by the lines x − y = 0, x − y = 2, x + y = 0, and x + y = 3.

dalvyx [7]

Answer:

(1/4)*(e⁶ - 7)

Step-by-step explanation:

a) Given

x − y = 0 if x = 0 ⇒ y = 0

x − y = 2 if x = 0 ⇒ y = -2; if y = 0 ⇒ x = 2

x + y = 0 if x = 0 ⇒ y = 0

x + y = 3 if x = 0 ⇒ y = 3; if y = 0 ⇒ x = 3

then we show the region R in the pics 1 and 2.

b) We make the change of variables as follows

u = x + y

v= x - y

x - y = 0 ⇒ v = 0

x − y = 2 ⇒ v = 2

x + y = 0 ⇒ u = 0

x + y = 3 ⇒ u = 3

Where u is the horizontal axis and v is the vertical axis, the new region S is shown in the pic 3.

c) We evaluate ∫∫R (x + y)*e∧(x² - y²)dA

The procedure is shown in the pic 4, where we have to calculate the Jacobian in order to use it to get the answer.

7 0

3 years ago