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2 years ago

The decimal 5.2323… is a(n) _____number. rational irrational integer whole

Mathematics

2 answers:

Phantasy [73]2 years ago

8 0

Answer:

rational

Step-by-step explanation:

infinite decimal

recurring decimal

integer

Semmy [17]2 years ago

4 0

Answer:

it is a rational number

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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

What is the length of the diameter of a circle if the endpoints of the diameter are at the points (4, 2) and (–6, –1)?

Oksana_A [137]

Answer:

d= 10.44030651

Step-by-step explanation:

The diameter is the length between the endpoints. We can find it using the distance formula.

d= sqrt((x2-x1)^2+(y2-y1)^2 )

d = sqrt((-6-4)^2+ (-1-2)^2)

d = sqrt((-10)^2+(-3)^2)

d= sqrt(100+9)

d = sqrt(109)

d= 10.44030651

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2 years ago

A study intends to estimate a population mean with an unknown population standard deviation and a sample size of 15. Which of th

GuDViN [60]

Answer:2.624

Step-by-step explanation:

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alexgriva [62]

4 is your answer have a great day

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