Answer:
8.5$
Step-by-step explanation:
85 diveded by 10 is 8.5$.
Answer:
$2353 at 12.5% and $7647 at 8.25%
Step-by-step explanation:
I'll say a is the amount he invested in one market, and b is the amount in the other.
a + b = 10000, or b = 10000 - a
multiplying the investments with the percentages and adding them together will give the total earned interest.
(a × 0.125) + (b × 0.0825) = 925
0.125a + 0.0825b = 925
Use substitution to solve for a.
0.125a + 0.0825(10000 - a) = 925
0.125 a + 825 - 0.0825a = 925
0.0425a = 100
a = 2352.94
Use substitution to find b
b = 10000 - 2352.94
b = 7647.06
The questions are to the nearest dollar so round a and b.
$2353 and $7647
Answer:
84 juice bottles
Step-by-step explanation:
Given the ratio of grapefruit juice, pineapple juice, and tomato juice bottles as
3:1:2
Let the total number of bottles available be R
If there are 14 pineapple juice bottles, then
1/(3 + 1 + 2) * R = 14
1/6 * R = 14
multiply both sides by 6
R = 14 * 6
= 84
This means there are 84 bottles in all
Answer:
a. y= e raise to power y
c. y = e^ky
Step-by-step explanation:
The first derivative is obtained by making the exponent the coefficient and decreasing the exponent by 1 . In simple form the first derivative of
x³ would be 2x³-² or 2x².
But when we take the first derivative of y= e raise to power y
we get y= e raise to power y. This is because the derivative of e raise to power is equal to e raise to power y.
On simplification
y= e^y
Applying ln to both sides
lny= ln (e^y)
lny= 1
Now we can apply chain rule to solve ln of y
lny = 1
1/y y~= 1
y`= y
therefore
derivative of e^y = e^y
The chain rule states that when we have a function having one variable and one exponent then we first take the derivative w.r.t to the exponent and then with respect to the function.
Similarly when we take the first derivative of y= e raise to power ky
we get y=k multiplied with e raise to power ky. This is because the derivative of e raise to a constant and power is equal to constant multiplied with e raise to power y.
On simplification
y= k e^ky
Applying ln to both sides
lny=k ln (e^y)
lny=ln k
Now we can apply chain rule to solve ln of y ( ln of constant would give a constant)
lny = ln k
1/y y~= k
y`=k y
therefore
derivative of e^ky = ke^ky
