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zzz [600]
3 years ago
10

A cable installer charges $42.50 per hour plus a $45.00 service charge your father firms hires him to hook up his company find t

he total charge if it takes the cable installer 5 hours to install
Mathematics
1 answer:
Fiesta28 [93]3 years ago
5 0
Y = 42.5x + 45.....for 5 hrs.....x = 5
y = 42.5(5) + 45
y = 212.50 + 45
y = 257.50 <===
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A bag of chips contains 53 pieces. Each person in the room receives five chips and there is three chips left over. Write and sol
Nuetrik [128]

Answer:

53-3/5

Step-by-step explanation:

7 0
3 years ago
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56" board cut in 2 pieces and one piece is longer than 3 times the ​
Aleksandr [31]

Answer:

Piece one would equal to 14" and piece two would be 42" because 42 is three times the length of 14

8 0
3 years ago
Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves
Vadim26 [7]

The expression on the left side describes a parabola. Factorize it to determine where it crosses the y-axis (i.e. the line x = 0) :

-3y² + 9y - 6 = -3 (y² - 3y + 2)

… = -3 (y - 1) (y - 2) = 0

⇒   y = 1   or   y = 2

Also, complete the square to determine the vertex of the parabola:

-3y² + 9y - 6 = -3 (y² - 3y) - 6

… = -3 (y² - 3y + 9/4 - 9/4) - 6

… = -3 (y² - 2•3/2 y + (3/2)²) + 27/4 - 6

… = -3 (y - 3/2)² + 3/4

⇒   vertex at (x, y) = (3/4, 3/2)

I've attached a sketch of the curve along with one of the shells that make up the solid. For some value of x in the interval 0 ≤ x ≤ 3/4, each cylindrical shell has

radius = x

height = y⁺ - y⁻

where y⁺ refers to the half of the parabola above the line y = 3/2, and y⁻ is the lower half. These halves are functions of x that we obtain from its equation by solving for y :

x = -3y² + 9y - 6

x = -3 (y - 3/2)² + 3/4

x - 3/4 = -3 (y - 3/2)²

-x/3 + 1/4 = (y -  3/2)²

± √(1/4 - x/3) = y - 3/2

y = 3/2 ± √(1/4 - x/3)

y⁺ and y⁻ are the solutions with the positive and negative square roots, respectively, so each shell has height

(3/2 + √(1/4 - x/3)) - (3/2 - √(1/4 - x/3)) = 2 √(1/4 - x/3)

Now set up the integral and compute the volume.

\displaystyle 2\pi \int_{x=0}^{x=3/4} 2x \sqrt{\frac14 - \frac x3} \, dx

Substitute u = 1/4 - x/3, so x = 3/4 - 3u and dx = -3 du.

\displaystyle 2\pi \int_{u=1/4-0/3}^{u=1/4-(3/4)/3} 2\left(\frac34 - 3u\right) \sqrt{u} \left(-3 \, du\right)

\displaystyle -12\pi \int_{u=1/4}^{u=0} \left(\frac34 - 3u\right) \sqrt{u} \, du

\displaystyle 12\pi \int_{u=0}^{u=1/4} \left(\frac34 u^{1/2} - 3u^{3/2}\right)  \, du

\displaystyle 12\pi \left(\frac34\cdot\frac23 u^{3/2} - 3\cdot\frac25u^{5/2}\right)  \bigg|_{u=0}^{u=1/4}

\displaystyle 12\pi \left(\frac12 u^{3/2} - \frac65u^{5/2}\right)  \bigg|_{u=0}^{u=1/4}

\displaystyle 12\pi \left(\frac12 \left(\frac14\right)^{3/2} - \frac65\left(\frac14\right)^{5/2}\right) - 12\pi (0 - 0)

\displaystyle 12\pi \left(\frac1{16} - \frac3{80}\right) = \frac{12\pi}{40} = \boxed{\frac{3\pi}{10}}

6 0
2 years ago
27j - 6 = 14j + 7 *it has to show work*
lutik1710 [3]

27j-6=14j+7

Subtract 14j from both sides

27j-6-14j=14j+7-14j

13j-6=7

Add 6 to both sides

13j-6+6=7+6

13j=13

Divide both sides by 13

13j/13=13/13

j=1


I hope that's help !

4 0
3 years ago
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Write an imequality” five times some number is less than 65”
lawyer [7]

Answer: 5x < 65

Step-by-step explanation: please give brainliest hope it helps and thankyou

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