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2 years ago

The seven-digit number 1113A8B can be divided by 4, 5, and 9 What is the sum of the digits A and B?

Mathematics

1 answer:

Gennadij [26K]2 years ago

7 0

Answer:

Step-by-step explanation:

This seven-digit number can be divided by 4, 5 and 9.

This means that 4, 5 and 9 are ALL factors.

Find the least common multiply (LCM) of 4, 5 and 9.

Multiples of 4: 4 , 8 , 12 , 16 , 20

Multiples of 5: 5 , 10 , 15 , 20

Find a multiple of 9 that is also a multiple of 20. All multiples of 20 have the factors 4 and 5.

9 X 20 = 180

The seven-digit number must be a multiple of 180 to have the factor 4, 5 and 9. You can find the multiples of 180 until the number looks like 1113A8B, but there are better methods.

All multiples of 180 end in the digit "0". Therefore B = 0.

1113A80

Since 9 is one of the factors, the rules for a number divisible for 3 apply. (9 is a multiple of 3).

You know that a number is divisible by 3 when its digits add to a number divisible by 3.

Find the sum of the digits:

1+1+1+3+A+8+0 = A + 14

A + 14 must be divisible by 3.

Therefore, A has to be either 1, 4, or 7.

If A = 1

1113180 ÷ 180 = 6184.333

If A = 4

1113480÷ 180= 6186

If A = 7

1113780 ÷ 180 = 6187.7

A = 4 because that number is divisible by 180.

Add A = 4 and B = 0.

A + B

= 4 + 0

= 4

The sum of digits A and B is 4.

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Determine the area enclosed by y=2x+3, the x-axis and the ordinates x=3 and x=4

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Answer:

$\displaystyle \int\limits^4_3 {2x + 3} \, dx = 10$

General Formulas and Concepts:
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Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Integration Property [Addition/Subtraction]: $\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx$

Area of a Region Formula: $\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx$

Step-by-step explanation:

Step 1: Define

Identify.

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x-interval [3, 4]

x-axis

See attachment for graph.

Step 2: Find Area

Substitute in variables [Area of a Region Formula]: $\displaystyle A = \int\limits^4_3 {2x + 3} \, dx$
[Integral] Rewrite [Integration Property - Addition/Subtraction]: $\displaystyle A = \int\limits^4_3 {2x} \, dx + \int\limits^4_3 {3} \, dx$
[Integrals] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle A = 2 \int\limits^4_3 {x} \, dx + 3 \int\limits^4_3 {} \, dx$
[Integrals] Integrate [Integration Rule - Reverse Power Rule]: $\displaystyle A = 2 \bigg( \frac{x^2}{2} \bigg) \bigg| \limits^4_3 + 3(x) \bigg| \limits^4_3$
[Integrals] Integrate [Integration Rule - FTC 1]: $\displaystyle A = 2 \bigg( \frac{7}{2} \bigg) + 3(1)$
Simplify: $\displaystyle A = 10$

∴ the area bounded by the region y = 2x + 3, x-axis, and the coordinates x = 3 and x = 4 is equal to 10.

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Learn more about integration: brainly.com/question/26401241

Learn more about calculus: brainly.com/question/20197752

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

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