Answer:
The total charge on the rectangle is 29.33C
Step-by-step explanation:
Given
σ(x, y) = 2xy + y²
For 2 ≤ x ≤ 4, 0 ≤ y ≤ 2
The total charge on the rectangle is calculated as follows.
Charge, q = ∫∫2xy + y² dydx {0,2}{2,4}
Integrate with respect to y
q = ∫xy² + ⅓y³ dydx {0,2}{2,4}
q = ∫(2²*x + ⅓*2³) dx {2,4}
q = ∫4x + 8/3 dx {2,4}
Integrate with respect to x
q = 2x² + 8x/3 {2,4}
q = (2(4)² + 8(4)/3) - (2(2)² + 8(2)/3)
q = 29.33C
Answer:
Step-by-step explanation:
6 , -4
Reason:
If you add 6 and (-4) , you will get 2 & if you multiply 6 and -4, you will get -24
Answer:
D
Step-by-step explanation:
(f+g)(x) basically means to "ADD" f(x) and g(x).
We have

and

Now we simply add these two, adding like terms as shown below (and simplify):

Correct answer is D
Answer:
Cliff is 45 m tall.
Step-by-step explanation:
Given:
Height of Sarah = 1.8 m
Angle of elevation = 60°
Angle of elevation 50 m back = 30°
As shown in the figure we have two right angled triangles SPQ and SPR.
Let the height of the cliff be
meters and
.
Using trigonometric ratios:
tan (Ф) = opposite/adjacent
In ΔSPQ. In ΔSPR.
⇒
...equation (i) ⇒
...equation (ii)
Dividing equation (i) and (ii)
⇒ 
⇒ 
⇒ 
⇒ 
⇒ 
⇒
⇒
meters
To find
plugging
in equation (i)
⇒ 
⇒ 
⇒
meters
The height of the cliff from ground :
⇒ 
⇒ 
⇒
meters
The cliff is 45 m tall to the nearest meter.
To solve for the variable "w" you only need to use algebra to get it alone on one side of the equals sign.