You invest $40,000 in two funds paying 4% and 52% simple interest. The total annual interest is $2080. How much do you invest in
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At the start, the tank contains
(0.02 g/L) * (1000 L) = 20 g
of chlorine. Let <em>c</em> (<em>t</em> ) denote the amount of chlorine (in grams) in the tank at time <em>t </em>.
Pure water is pumped into the tank, so no chlorine is flowing into it, but is flowing out at a rate of
(<em>c</em> (<em>t</em> )/(1000 + (10 - 25)<em>t</em> ) g/L) * (25 L/s) = 5<em>c</em> (<em>t</em> ) /(200 - 3<em>t</em> ) g/s
In case it's unclear why this is the case:
The amount of liquid in the tank at the start is 1000 L. If water is pumped in at a rate of 10 L/s, then after <em>t</em> s there will be (1000 + 10<em>t</em> ) L of liquid in the tank. But we're also removing 25 L from the tank per second, so there is a net "gain" of 10 - 25 = -15 L of liquid each second. So the volume of liquid in the tank at time <em>t</em> is (1000 - 15<em>t </em>) L. Then the concentration of chlorine per unit volume is <em>c</em> (<em>t</em> ) divided by this volume.
So the amount of chlorine in the tank changes according to
which is a linear equation. Move the non-derivative term to the left, then multiply both sides by the integrating factor 1/(200 - 5<em>t</em> )^(5/3), then integrate both sides to solve for <em>c</em> (<em>t</em> ):
There are 20 g of chlorine at the start, so <em>c</em> (0) = 20. Use this to solve for <em>C</em> :
Answer:
Step-by-step explanation:
The functions are given f and g using coordinates.
Whenever we will ask for f(a), we look for "a" in the x coordinate of the function f and find the corresponding value. THAT IS THE ANSWER.
If we ask for g(b), we look for "b" in the x coordinate of the function g and find the corresponding value. THAT IS THE ANSWER.
So,
The total length of the steel used in the frame is 270 cm, if the decorative steel up of 6 stems and each stem is 45 cm.
Step-by-step explanation:
The given is,
Decorative steel made from circular circle of 6 stems
The length of the stem is 45 cm
Step:1
We need to find the total length of the steel used in the decorative steel,
Let, T - Total length of the steel
L - Length of the stem
n - Number of stems used in steel frame
Step:2
Formula to find the total length of the steel is,
×
From given,
= 45 cm
= 6 stems
Substitute the values in formula,
( 45 × 6 )
= 270
270 cm
Result:
The total length of the steel used in the frame is 270 cm.