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2 years ago

Simplify (6.89 + 14.52) + (-14.52)=

Mathematics

1 answer:

FinnZ [79.3K]2 years ago

3 0

Adding 14.52 and -14.52 cancels it out

The answer is 6.89

I hope that helps!

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Let h(x)=20e^kx where k ɛ R (Picture attached. Thank you so much!)

zloy xaker [14]

Answer:

$k=0$

$\displaystyle \begin{aligned} 2k + 1& = 2\ln 20 + 1 \\ &\approx 2.3863\end{aligned}$

$\displaystyle \begin{aligned} k - 3&= \ln \frac{1}{2} - 3 \\ &\approx-3.6931 \end{aligned}$

Step-by-step explanation:

We are given the function:

$\displaystyle h(x) = 20e^{kx} \text{ where } k \in \mathbb{R}$

Given that h(1) = 20, we want to find k.

h(1) = 20 means that h(x) = 20 when x = 1. Substitute:

$\displaystyle (20) = 20e^{k(1)}$

Simplify:

$1= e^k$

Anything raised to zero (except for zero) is one. Therefore:

$k=0$

Given that h(1) = 40, we want to find 2k + 1.

Likewise, this means that h(x) = 40 when x = 1. Substitute:

$\displaystyle (40) = 20e^{k(1)}$

Simplify:

$\displaystyle 2 = e^{k}$

We can take the natural log of both sides:

$\displaystyle \ln 2 = \underbrace{k\ln e}_{\ln a^b = b\ln a}$

By definition, ln(e) = 1. Hence:

$\displaystyle k = \ln 2$

Therefore:

$2k+1 = 2\ln 2+ 1 \approx 2.3863$

Given that h(1) = 10, we want to find k - 3.

Again, this meas that h(x) = 10 when x = 1. Substitute:

$\displaystyle (10) = 20e^{k(1)}$

Simplfy:

$\displaystyle \frac{1}{2} = e^k$

Take the natural log of both sides:

$\displaystyle \ln \frac{1}{2} = k\ln e$

Therefore:

$\displaystyle k = \ln \frac{1}{2}$

Therefore:

$\displaystyle k - 3 = \ln\frac{1}{2} - 3\approx-3.6931$

3 0

2 years ago

The equation y+6=1/3(x-9) is written in point-slope form. What is the equation written in slope-intercept form?

loris [4]

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

y + 6 = $\frac{1}{3}$ (x - 9) ← distribute the parenthesis

y + 6 = $\frac{1}{3}$ x - 3 ← subtract 6 from both sides

y = $\frac{1}{3}$ x - 9 ← in slope- intercept form

7 0

3 years ago

Read 2 more answers

I need to solve for this 24+12R < 100

Sindrei [870]

Answer:

here's the answer

Step-by-step explanation:

hope this helps!

6 0

2 years ago

The answer, and work shown.

hoa [83]

Slope= 1/2
Y intercept= (0,2)

Explanation:
Slope-intercept form is y=mx+b
-2x+4y=8
-8-2x=-4y
Divide by -4
2+1/2x=y

Y=1/2x+2

5 0

2 years ago

SOLVE THIS PROBLEM ASAP PLS

deff fn [24]

Answer:

See attached

Step-by-step explanation:

-> Also see attached

Have a nice day!

I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

7 0

2 years ago