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3 years ago

What is 8.49x10^-7 in decimal form?

Mathematics

2 answers:

vlabodo [156]3 years ago

3 0

8.49 x 10^-7 = 0.000000849

answer

0.0000000849

Aloiza [94]3 years ago

3 0

It’s b, when you see a 10^-7 that means you have to start at that decimal and count in between the 0’s until you count to -7

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Paulo and Marie are collecting quarters. The number of quarters Paulo has is 3 times the quantity of 5 fewer than the number of

Hatshy [7]

P = 3(m - 5)

p is the number of quarters that paulo has

m is the number of quarters that marie has

5 0

3 years ago

<img src="https://tex.z-dn.net/?f=%5Clim_%7Bx%5Cto%20%5C%200%7D%20%5Cfrac%7B%5Csqrt%7Bcos2x%7D-%5Csqrt%5B3%5D%7Bcos3x%7D%20%7D%7

salantis [7]

Answer:

$\displaystyle \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \frac{1}{2}$

General Formulas and Concepts:

Calculus

Limits

Limit Rule [Variable Direct Substitution]: $\displaystyle \lim_{x \to c} x = c$

L'Hopital's Rule

Differentiation

Derivatives
Derivative Notation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]: $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

We are given the limit:

$\displaystyle \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)}$

When we directly plug in x = 0, we see that we would have an indeterminate form:

$\displaystyle \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \frac{0}{0}$

This tells us we need to use L'Hoptial's Rule. Let's differentiate the limit:

$\displaystyle \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \displaystyle \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)}$

Plugging in x = 0 again, we would get:

$\displaystyle \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)} = \frac{0}{0}$

Since we reached another indeterminate form, let's apply L'Hoptial's Rule again:

$\displaystyle \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)} = \lim_{x \to 0} \frac{\frac{-[cos^2(2x) + 1]}{[cos(2x)]^{\frac{2}{3}}} + \frac{cos^2(3x) + 2}{[cos(3x)]^{\frac{5}{3}}}}{2cos(x^2) - 4x^2sin(x^2)}$

Substitute in x = 0 once more:

$\displaystyle \lim_{x \to 0} \frac{\frac{-[cos^2(2x) + 1]}{[cos(2x)]^{\frac{2}{3}}} + \frac{cos^2(3x) + 2}{[cos(3x)]^{\frac{5}{3}}}}{2cos(x^2) - 4x^2sin(x^2)} = \frac{1}{2}$

And we have our final answer.

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

Unit: Limits

6 0

3 years ago

Fifteen 7th graders were asked how many hours they spend doing homework each week and how many hours they spend watching televis

timama [110]

Answer:

18 > 14, true

12 - 16 = -4, true

Mean:

Homework = (4 + 6*2+10*3+12*2+14*4+16*2+18)/15 = 11.73
Television = (0 + 10*3+12*1+16*3+18*4+20*3)/15 = 14.8

The difference:

14.8 - 11.73 > 1, NOT true

True

3 0

3 years ago

Find the measure of an interior angle of a regular nonagon (9-sided polygon).

Scrat [10]

The measure of an interior angle of a regular nonagon (9-sided polygon) is 140°

<h3>How to determine the angle</h3>

The formula for sum of interior angles of a polygon is given as;

= ( n -2) × 180

Recall that a nonagon has nine sides, so , n = 9

Substitute the value into the formula

= ( 9 -2) × 180

= 7× 180

= 1260°

Since the sum of the angles = 1260°

One of the angles = 1260/ 9 = 140°

Therefore, the measure of an interior angle of a regular nonagon (9-sided polygon) is 140°

Learn more about polygons here:

brainly.com/question/224658

#SPJ1

7 0

2 years ago

Please solve! Evaluate the function.

nikitadnepr [17]

Answer:

(h o g)(5) = 20

Step-by-step explanation:

(h o g)(5) = h(g(5)) This is two ways of writing the expression

g(x) = $\sqrt{5x}$ h(x) = 3x + 5 g(x) and h(x) are your "plug-ins" for the expression

g(5) = $\sqrt{5(5)}$ = $\sqrt{25}$ = 5 This is how you would solve for plugging in 5 to g(x)

Whatever you get for g(5) {the answer to it} is what you will be plugging into h(x); x being equal to g(5).

h(5) = 3(5) + 5 = 15 + 5 = 20

6 0

3 years ago