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3 years ago

Hurryyyy uppppp i need it rnn plzzz! Solve for f: 6f + 9g = 3g + f

Mathematics

2 answers:

Naily [24]3 years ago

8 0

Answer:

$f=\frac{-6g}{5}$

Step-by-step explanation:

The given equation is: $6f + 9g = 3g + f$ .

To solve for f, first we should move all f's to the left side, and the other terms to the right side. The first goal is to reduce like term:

$6f-f=3g-9g\\5f=-6g$

Now, we isolate f, and then we'll have the final expression.

$f=\frac{-6g}{5}$

Therefore, the answer is $f=\frac{-6g}{5}$

son4ous [18]3 years ago

6 0

Answer:

f=-6/5

Step-by-step explanation:

got it from photomath

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Aubrey ran 13 1/6 miles and walked 9 5/6 miles. How much farther did Aubrey run than walk?

leonid [27]

Answer:

Aubrey ran 3 1/3 miles further than what she walked.

Step-by-step explanation:

This would be your basic subtraction problem. So, 13 1/6 - 9 5/6.

Since you can't subtract 5/6 from 1/6, let's borrow from 13. Now, instead of 13, it would be 12. Adding the whole (1) or 6/6 to the 1/6, you'll get 7/6. Now you can subtract. 7/6 - 5/6 = 2/6. Moving on, 12 - 9 = 3.

Therefore, your answer is 3 2/6. In simplified terms, it would be 3 1/3.

3 0

2 years ago

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. An industrial tank of this shape must h

mestny [16]

Answer:

Radius =6.518 feet

Height = 26.074 feet

Step-by-step explanation:

The Volume of the Solid formed = Volume of the two Hemisphere + Volume of the Cylinder

Volume of a Hemisphere $=\frac{2}{3}\pi r^3$

Volume of a Cylinder $=\pi r^2 h$

Therefore:

The Volume of the Solid formed

$=2(\frac{2}{3}\pi r^3)+\pi r^2 h\\\frac{4}{3}\pi r^3+\pi r^2 h=4640\\\pi r^2(\frac{4r}{3}+ h)=4640\\\frac{4r}{3}+ h =\frac{4640}{\pi r^2} \\h=\frac{4640}{\pi r^2}-\frac{4r}{3}$

Area of the Hemisphere = $2\pi r^2$

Curved Surface Area of the Cylinder = $2\pi rh$

Total Surface Area=

$2\pi r^2+2\pi r^2+2\pi rh\\=4\pi r^2+2\pi rh$

Cost of the Hemispherical Ends = 2 X Cost of the surface area of the sides.

Therefore total Cost, C

$=2(4\pi r^2)+2\pi rh\\C=8\pi r^2+2\pi rh$

Recall: $h=\frac{4640}{\pi r^2}-\frac{4r}{3}$

Therefore:

$C=8\pi r^2+2\pi r(\frac{4640}{\pi r^2}-\frac{4r}{3})\\C=8\pi r^2+\frac{9280}{r}-\frac{8\pi r^2}{3}\\C=\frac{9280}{r}+\frac{24\pi r^2-8\pi r^2}{3}\\C=\frac{9280}{r}+\frac{16\pi r^2}{3}\\C=\frac{27840+16\pi r^3}{3r}$

The minimum cost occurs at the point where the derivative equals zero.

$C^{'}=\frac{-27840+32\pi r^3}{3r^2}$

$When \:C^{'}=0$

$-27840+32\pi r^3=0\\27840=32\pi r^3\\r^3=27840 \div 32\pi=276.9296\\r=\sqrt[3]{276.9296} =6.518$

Recall:

$h=\frac{4640}{\pi r^2}-\frac{4r}{3}\\h=\frac{4640}{\pi*6.518^2}-\frac{4*6.518}{3}\\h=26.074 feet$

Therefore, the dimensions that will minimize the cost are:

Radius =6.518 feet

Height = 26.074 feet

5 0

2 years ago

Rewrite 3* = 243 as a logarithmic equation.

soldi70 [24.7K]

Answer:

log₃(243) = x

Step-by-step explanation:

3^x = 243

Rule: a^x = b -> logₐ(b) = x

log₃(243) = x

4 0

2 years ago

Is it possible to have a number to the power of a decimal? For example, 4 to the 0.5 power.

sp2606 [1]

in different cases it is possible

7 0

3 years ago

Read 2 more answers

All members of a class of 27 students participated in at least one event on sports day. 20 students participated in individual e

creativ13 [48]

5 students took part in both individual and team events.

Data is information that has been translated into a form that is efficient for movement or processing. Relative to today's computers and transmission media, data is information converted into binary digital form. It is acceptable for data to be used as a singular subject or a plural subject.

Given:

Total students participated = 27

20 students participated in individual events

12 students took part in team events.

We have N(All students) = 27

N(individual) = 20

N(Team)= 12

So,

$N_{\text{individual \; and \; team}} & = N_{\text{individual}} + N_{\text{team}} - N_{\text{All students}}$

=20+12-27

=32-27

Hence, 5 students took part in both individual and team events.

Learn more about data here:

brainly.com/question/10980404

#SPJ4

6 0

1 year ago