All categories

2 years ago

Need to choose answers

Mathematics

1 answer:

trapecia [35]2 years ago

3 0

Answer:

Box Number 3.

Step-by-step explanation:

4 is a coefficient in 4x because 4x is really 4*x which has 4 multiplying x. This is the same as 4 working with x. Also none of the other answers are true.

You might be interested in

Five distinct numbers are randomly distributed to players numbered 1 through 5. Whenever two players compare their numbers, the

julia-pushkina [17]

Is there answer choices or ....

3 0

2 years ago

A recipe for 3 servings calls for 2 grams of chili powder, how many milligrams are needed for 6 servings

Irina18 [472]

3servings=2garms
6servings=xgrams

easy way is
3 imes 2=6 so
2 times 2=4
answer is 4 grams
the ratio and proportion way
3:2=6:x
3/2=6/x
3x=12
x=4

4 grams
now convert to miligrams
1gram=1000 milgram
4 grams=4000 miligram

answer is 4000 miligrams

4 0

2 years ago

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

2 years ago

one tamk of gasoline has an octane rating of 140 and another tank of gasoline has an octane rating of 80. To obtain a mixture of

Zarrin [17]

Answer:

20 gallons were used from the tank with the octane rating of 80.

Step-by-step explanation:

Given : One tank of gasoline has an octane rating of 140 and another tank of gasoline has an octane rating of 80. To obtain a mixture of 60 gallons with an octane rating of 120.

To find : How many gallons should be used from the tank with the octane rating of 80?

Solution : Let x be the volume of gas whose octane rating is 140 and

y be the volume of gas whose octane rating is 80.

Then, we form the equation as:

(1) $x\times140 + y\times80 = 60\times120$