Step-by-step explanation:
∫₀³⁰ (r/V C₀ e^(-rt/V)) dt
If u = -rt/V, then du = -r/V dt.
∫ -C₀ e^u du
-C₀ ∫ e^u du
-C₀ e^u + C
-C₀ e^(-rt/V) + C
Evaluate between t=0 and t=30.
-C₀ e^(-30r/V) − -C₀ e^(-0r/V)
-C₀ e^(-30r/V) + C₀
C₀ (-e^(-30r/V) + 1)
I got the same answer. Try changing the lowercase v to an uppercase V.
Answer:
Step-by-step explanation:
This is a question that uses the Pythagorean Theorem.
a = 35 feet
b = x which is the height of the tree.
c = 3*x + 1 so we are trying to find x. Substitute into a b and c
a^2 + b^2 = c^2
35^2 + x^2 = (3x + 1)^2
35^2 + x^2 = 9x^2 + 6x + 1 Subtract x^2 from both sides.
35^2 = 8x^2 + 6x + 1 Subtract 35^2 from both sides.
0 = 8x^2 + 6x + 1 - 35^2
0 = 8x^2 + 6x - 1224
Does this factor?
(x + 12.75)(x - 12)
x - 12 = 0 is the only value that works.
x = 12
The tree is 12 feet high.
Note: I used the quadratic formula to solve this.
This is a simple problem
First, take common sense and apply it here. The problem doesn't specifically tell you what the shape ACTUALLY is, but we can also apply what we know about geometry here, as well as what we know in general. Fish tanks most commonly come in 2 shapes: Square's and Rectangles. Fish tanks are what we call "3D" objects (meaning it's just not flat like a piece of paper", and the shapes are known as "Cubes and Rectangular Prisms".
Well, we know that squares/cubes have to have even sides. The problem states the tank is 5(l) by 2(w) by 2(h). This means it CAN'T be a cube, thus meaning it's a rectangular prism.
Now, to calculate volume, we have to know the formula. For this, the formula for volume is as follows: V=lwh
This means Volume=Length*Width*Height
So, do replace the words with what you know you already have. Let's make a list:
Length=5
Width=2
Height=2
V=lwh-----V=5*2*2
Now, work it out. 5*2=10*2=20, Left to right
Your answer here is V=20
~Hope this helps!
a[n] = 7n - 16
The fifth term is a[5]
a[5] = 7(5) - 16 = 35 - 16 = 19
Answer: C. 19
Ok I will add u to if you can help me with my test
