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2 years ago

List the single-digit divisors of 2100. I really need help

Mathematics

1 answer:

liberstina [14]2 years ago

5 0

Answer:

1, 2, 3, 4, 5, 6, 7

Step-by-step explanation:

Prime factors of 2100 are:

2100 = 2*2*3*5*5*7

The single-digit divisors are:

1, 2, 3, 2*2= 4, 5, 2*3= 6, 7

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Another solution is you divide 2100 by all numbers 1 through 9 and list those divisible:

2100/1 = 2100, yes
2100/2 = 1050, yes
2100/3 = 700, yes
2100/4 = 525, yes
2100/5 = 420, yes
2100/6 = 350, yes
2100/7 = 300, yes
2100/8 = 262.5, no
2100/9 = 233.33, no

So all the numbers from 1 to 7

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3 years ago

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

zloy xaker [14]

Answer:

$k=0$

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

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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:

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

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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:

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$\displaystyle k = \ln 2$

Therefore:

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

Simplfy:

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Take the natural log of both sides:

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

Therefore:

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

Therefore:

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

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2 years ago

The sum of two numbers is 70. one number is 4 times as large as the other. What are the numbers?

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