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11111nata11111 [884]
3 years ago
5

Carlos takes classes at both Westside Community College and Pinewood Community College. At Westside, class fees are $ 98 per cre

dit hour, and at Pinewood, class fees are $ 115 per credit hour. Carlos is taking a combined total of 13 credit hours at the two schools. Write an expression for the combined total dollar amount he paid for his class fees.
Mathematics
1 answer:
Sholpan [36]3 years ago
7 0

Answer:

x + y = 13

98x + 115y = z

Step-by-step explanation:

Let x represent the time spent taking class in Westside community college

Let y represent the time spent taking class in Pinewood community college

Let z represent the combined total amount paid for the class fees.

The total combined time for the two school is given as:

x + y = 13.

For the combined total amount; we multiply the price for each school with the time spent on the school and sum them together.

Westside: 98 * x = 98x

Pinewood: 115 * y = 115y

The combined total amount represented as z is given as:

z = 98x + 115y

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F(x) = 3x + x3
____ [38]

Answer:

Please check the explanation.

Step-by-step explanation:

Given

f(x) = 3x + x³

Taking differentiate

\frac{d}{dx}\left(3x+x^3\right)

\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'

=\frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(x^3\right)

solving

\frac{d}{dx}\left(3x\right)

\mathrm{Take\:the\:constant\:out}:\quad \left(a\cdot f\right)'=a\cdot f\:'

=3\frac{d}{dx}\left(x\right)

\mathrm{Apply\:the\:common\:derivative}:\quad \frac{d}{dx}\left(x\right)=1

=3\cdot \:1

=3

now solving

\frac{d}{dx}\left(x^3\right)

\mathrm{Apply\:the\:Power\:Rule}:\quad \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1}

=3x^{3-1}

=3x^2

Thus, the expression becomes

\frac{d}{dx}\left(3x+x^3\right)=\frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(x^3\right)

                    =3+3x^2

Thus,

f'(x) = 3 + 3x²

Given that f'(x) = 15

substituting the value  f'(x) = 15 in f'(x) = 3 + 3x²

f'(x) = 3 + 3x²

15 =  3 + 3x²

switch sides

3 + 3x² = 15

3x² = 15-3

3x² = 12

Divide both sides by 3

x² = 4

\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}

x=\sqrt{4},\:x=-\sqrt{4}

x=2,\:x=-2

Thus, the value of x​ will be:

x=2,\:x=-2

5 0
3 years ago
Where did the Industrial Revolution begin?
garri49 [273]

Answer:

england

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Please help me with this question <br><br> image attached
Sveta_85 [38]

Answer: 60°


Step-by-step explanation: use exterior angle property,

therefore, y+70°=130°

                        y=130°-70°

                        y=60°


7 0
3 years ago
So I have another trigonometry question PLZ HELP ME I'm clueless at this rate I have like a little idea but I'm lost, SO PLZZZ!
Sergio039 [100]

Answer:

1) The windsurfer is approximately 580 ft from each lifeguard stand.

2) The distance between the Earth and Mercury is approximately 61 million miles.

Step-by-step explanation:

The image other two situations described is presented in the attached image to this answer.

1) From the attached image, the windsurfer forms a right angled triangle with each of the lifeguard stand and the midpoint between the two lifeguard stands.

Hence, the angle at the top of the triangle is half of 30°, 15° and the distance from the midpoint of the lifeguard stands to the lifeguard stands is 300/2 = 150 ft.

Let the required distance of the windsurfer from each of the lifeguard stands be x.

Using trigonometric relations,

Sin 15° = (150/x)

x = 150 ÷ sin 15° = 150 ÷ 0.2588

x = 579.6 ft = 580 ft to the nearest whole number

2) From the image, the Sun, Earth and Mercury form a triangle.

Let the possible distance between the Earth and Mercury be y.

Using cosine rule,

y² = 36² + 93² - (2×36×93×cos 22°)

y² = 3,736.5769098208

y = √3,736.5769098208 = 61.13 million miles = 61 million miles to the nearest million miles.

Hope this Helps!!!

5 0
3 years ago
DUE IN 27 minutes PLEASE HELP EASYY
trapecia [35]

Answer:

6 + 0 = 0 + 6 = 6

12 X (3 X 9)

2 + 6x

3 + 7 + 8 = 7 + __ + 3

27 - 108

-15 - 5m

(6 + 5) + 1

8x + 28

26 X 1 = 1 X 26 = 26

24 + 4s

Step-by-step explanation:

i hope this helps :))

7 0
3 years ago
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