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3 years ago

Choose the expression that represents a linear expression.

Mathematics

2 answers:

tresset_1 [31]3 years ago

6 0

Answer:

Step-by-step explanation:

A linear expression has the highest power of the variable to 1, i.e ax+b

Then only the first option is in a linear expression format

9x-2

eduard3 years ago

5 0

Answer:

9x-2

Step-by-step explanation:

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Evaluate 5z^2 when z = 3 and when z = -3

erastova [34]

When Z=3 it is 45 and when Z=-3 it is also 45.

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3 years ago

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A light bulb is designed by revolving the graph of:

nadya68 [22]

Answer:

$\displaystyle 0.251327 \ in. \ of \ glass$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Terms/Coefficients
Expand by FOIL (First Outside Inside Last)
Factoring

Calculus

Differentiation

Derivative Notation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integration

Integration Property: $\displaystyle \int\limits^a_b {cf(x)} \, dx = c \int\limits^a_b {f(x)} \, dx$

Fundamental Theorem of Calculus: $\displaystyle \int\limits^a_b {f(x)} \, dx = F(b) - F(a)$

Area between Two Curves

Volumes of Revolution

Arc Length Formula: $\displaystyle AL = \int\limits^a_b {\sqrt{1+ [f'(x)]^2}} \, dx$

Surface Area Formula: $\displaystyle SA = 2\pi \int\limits^a_b {f(x) \sqrt{1+ [f'(x)]^2}} \, dx$

Step-by-step explanation:

Step 1: Define

$\displaystyle y = \frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}\\Interval: [0, \frac{1}{3}]$

Step 2: Differentiate

Basic Power Rule: $\displaystyle y' = \frac{1}{2} \cdot \frac{1}{3}x^{\frac{1}{2} - 1} - \frac{3}{2} \cdot x^{\frac{3}{2} - 1}$
[Derivative] Simplify: $\displaystyle y' = \frac{1}{6}x^{\frac{-1}{2}} - \frac{3}{2}x^{\frac{1}{2}}$
[Derivative] Simplify: $\displaystyle y' = \frac{1}{6\sqrt{x}} - \frac{3\sqrt{x}}{2}}$

Step 3: Integrate Pt. 1

Substitute [Surface Area]: $\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{1+ [\frac{1}{6\sqrt{x}} - \frac{3\sqrt{x}}{2}}]^2}} \, dx$
[Integral - √Radical] Expand/Add: $\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{\frac{81x^2+18x+1}{36x}} \, dx$
[Integral - √Radical] Factor: $\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{\frac{(9x + 1)^2}{36x}} \, dx$
[Integral - Simplify]: $\displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {-\frac{|9x + 1|(3x - 1)}{18}} \, dx$
[Integral] Integration Property: $\displaystyle SA = \frac{- \pi}{9} \int\limits^{\frac{1}{3}}_0 {|9x + 1|(3x - 1)} \, dx$

Step 4: Integrate Pt. 2

[Integral] Define: $\displaystyle \int {|9x + 1|(3x - 1)} \, dx$
[Integral] Assumption of Positive/Correction Factors: $\displaystyle \frac{9x + 1}{|9x + 1|} \int {(9x + 1)(3x - 1)} \, dx$
[Integral] Expand - FOIL: $\displaystyle \frac{9x + 1}{|9x + 1|} \int {27x^2 - 6x - 1} \, dx$
[Integral] Integrate - Basic Power Rule: $\displaystyle \frac{9x + 1}{|9x + 1|} (9x^3 - 3x^2 - x)$
[Expression] Multiply: $\displaystyle \frac{(9x + 1)(9x^3 - 3x^2 - x)}{|9x + 1|}$

Step 5: Integrate Pt. 3

[Integral] Substitute/Integral - FTC: $\displaystyle SA = \frac{- \pi}{9} (\frac{(9x + 1)(9x^3 - 3x^2 - x)}{|9x + 1|})|\limits_{0}^{\frac{1}{3}}$
[Integrate] Evaluate FTC: $\displaystyle SA = \frac{- \pi}{9} (\frac{-1}{3})$
[Expression] Multiply: $\displaystyle SA = \frac{\pi}{27} \ ft^2$

It is in ft² because it is given that our axis are in ft.

Step 6: Find Amount of Glass

Convert ft² to in² and multiply by 0.015 in (given) to find amount of glass.

Convert ft² to in²: $\displaystyle \frac{\pi}{27} \ ft^2 \ \div 144 \ in^2/ft^2 = \frac{16 \pi}{3} \ in^2$
Multiply: $\displaystyle \frac{16 \pi}{3} \ in^2 \cdot 0.015 \ in = 0.251327 \ in. \ of \ glass$

And we have our final answer! Hope this helped on your Calc BC journey!

5 0

3 years ago

What are the coordinates of the image of vertex R after a reflection across the y-axis?

vfiekz [6]

Consider any point P(x, y) in the coordinate axis.

The reflection of this point across the y-axis is the point P'(-x, y).

(x, y) and (-x, y) are the 'mirror' images of each other, with the y'axis as the 'mirror'.

For example the coordinates of the image of P(4, 13) after the reflection across the y-axis is P'(-4, 13)

or, if P(-5, -9), then P'(5, -9)

Answer: if coordinates of V are (h, k), coordinates of V' are (-h, k)

3 0

3 years ago

Read 2 more answers

Pls answer this asap

zimovet [89]

Answer:

$20.44

Step-by-step explanation:

first solve for the whole thing

10 x 6 = 60

now to the red part

2 x 1.5 = 3

now the blue

r^2 * pi = a

2^2 * 3.14

4 * 3.14 = 12.56

now add red and blue

3 + 12.56 = 15.56

now subtract that sum from the whole

60 - 15.56 = 44.44

now do

44.44 / 10 = 4.444

now see how much it would cost for the grass

4.444 * 4.60 = 20.4424 ≈ 20.44

it would cost $20.44 to get the grass reseeded

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3 years ago

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after every eighth visit to a restaurant you receive a free beverage.after every tenth visit you receive a free appetizer. if yo

Alik [6]

On the 40th and the 80th you will receive both a free beverage and a free appetizer. You can find this by simply finding the multiples of both number up to 100 (or a little more than 100) to find out on which dates you'd get bothe an appetizer and beverage for free. Here are the multiples of both, to prove this answer.

8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104.
10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100.

Thus making 40 and 80 the answers. I hope this helps!

3 0

3 years ago