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2 years ago

14

Andrew adds two numbers. Each addend has seven digits. The sum has eight digits. What digit is in the ten millions place in the

sum? Explain.

1 answer:

tatuchka [14]2 years ago

4 0

Answer:

5,000,000 and 6,000,000

Step-by-step explanation:

5,000,000 and 6,000,000 is 11,000,000

or 5,000,000 and 5,000,000 is 10,000,000

and the 1 is in the ten millions place in the sum

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Wittaler [7]

Answer:

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Step-by-step explanation:

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2 years ago

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Can someone please explain this to me? Thanks!

Makovka662 [10]

Answer: Choice D

$\displaystyle F\ '(x) = 2x\sqrt{1+x^6}\\\\$

==========================================================

Explanation:

Let g(t) be the antiderivative of $g'(t) = \sqrt{1+t^3}$ . We don't need to find out what g(t) is exactly.

Recall by the fundamental theorem of calculus, we can say the following:

$\displaystyle \int_{a}^{b} g'(t)dt = g(b)-g(a)$

This theorem ties together the concepts of integrals and derivatives to show that they are basically inverse operations (more or less).

So,

$\displaystyle F(x) = \int_{\pi}^{x^2}\sqrt{1+t^3}dt\\\\ \displaystyle F(x) = \int_{\pi}^{x^2}g'(t)dt\\\\ \displaystyle F(x) = g(x^2) - g(\pi)\\\\$

From here, we apply the derivative with respect to x to both sides. Note that the $g(\pi)$ portion is a constant, so $g'(\pi) = 0$

$\displaystyle F(x) = g(x^2) - g(\pi)\\\\ \displaystyle F \ '(x) = \frac{d}{dx}[g(x^2)-g(\pi)]\\\\\displaystyle F\ '(x) = \frac{d}{dx}[g(x^2)] - \frac{d}{dx}[g(\pi)]\\\\ \displaystyle F\ '(x) = \frac{d}{dx}[x^2]*g'(x^2) - g'(\pi) \ \text{ .... chain rule}\\\\$

$\displaystyle F\ '(x) = 2x*g'(x^2) - 0\\\\ \displaystyle F\ '(x) = 2x*g'(x^2)\\\\ \displaystyle F\ '(x) = 2x\sqrt{1+(x^2)^3}\\\\ \displaystyle F\ '(x) = \boldsymbol{2x\sqrt{1+x^6}}\\\\$

Answer is choice D

5 0

1 year ago

Read 2 more answers

What is the volume, in cubic centimeters, of a cylinder with a height of 5 centimeters and a base radius of 10 centimeters, to t

stealth61 [152]

Answer:

The volume of the cylinder is <em>approximately</em> 1570.8 cm³.

General Formulas and Concepts:
<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

<u>Geometry</u>

Volume Formula [Cylinder]:
$\displaystyle V = \pi r^2 h$

<em>r</em> is radius
<em>h</em> is height

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify given variables</em>.

<em>h</em> = 5 cm

<em>r</em> = 10 cm

<u>Step 2: Find Volume</u>

[Volume Formula - Cylinder] <em>Substitute</em> in variables:
$\displaystyle V = \pi (10 \ \text{cm})^2 (5 \ \text{cm})$
[Order of Operations] Evaluate:
$\displaystyle V = 500 \pi \ \text{cm}^3$
Approximate:
$\displaystyle V \approx \boxed{ 1570.8 \ \text{cm}^3 }$

∴ the volume of a cylinder whose height is 5 cm and radius is 10 cm is <em>approximately</em> 1570.8 cm³.

___

Learn more about Geometry: brainly.com/question/9774838

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Topic: Geometry

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1 year ago

Answer the following question. 10 points!

Illusion [34]

The right answer may be option 4

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2 years ago

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What is the distance from (6, -8) to the origin?

Flauer [41]

You have to use Pythagoras' theorem for this!

The triangle formed is 6 units across, and 8 units down, which means we can form an equation like this:

a^2 + b^2 = c^2
6^2 + 8^2 = c^2
36 + 64 = c^2
100 = c^2
c = 10.

The answer is 10 :)

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2 years ago