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3 years ago

Machine A takes a hours to make 100 bolts, and machine B takes b hours to make 100 bolts. How many

Mathematics

1 answer:

Temka [501]3 years ago

4 0

Answer:

100(1/a + 1/b)

Step-by-step explanation:

Machine A takes a hours to make 100 bolts

Then machine A makes 100/a bolts in one hour

Machine B takes b hours to make 100 bolts

Then machine B makes 100/b bolts in one hour

Two machines will make:

100/a + 100/b = 100(1/a + 1/b)

bolts in one hour

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yarga [219]

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Step-by-step explanation:

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3 years ago

Find the value of k so that 48x-ky=11 and (k+2)x+16y=-19 are perpendicular lines.

Rufina [12.5K]

Answer: k = -1 +/- √769

Step-by-step explanation:

48x - ky = 11

-48x -48x

-ky = -48x + 11

$\frac{-ky}{-k} = \frac{-48x}{-k} + \frac{11}{-k}$

$y =\frac{48x}{k} - \frac{11}{k}$

Slope: $\frac{48}{k}$

*************************************************************************

(k + 2)x + 16y = -19

- (k + 2)x -(k + 2)x

16y = -(k + 2)x - 19

$\frac{16y}{16} = -\frac{(k + 2)x}{16} - \frac{19}{16}$

$y = -\frac{(k + 2)x}{16} - \frac{19}{16}$

Slope: $-\frac{(k + 2)}{16}$

**********************************************************************************

$\frac{48}{k}$ and $-\frac{(k + 2)}{16}$ are perpendicular so they have opposite signs and are reciprocals of each other. When multiplied by its reciprocal, their product equals -1.

$-\frac{(k + 2)}{16}$ * $\frac{k}{48}$ = -1

$\frac{(k + 2)k}{16(48)}$ = 1

Cross multiply, then solve for the variable.

(k + 2)(k) = 16(48)

k² + 2k - 768 = 0

Use quadratic formula to solve:

k = -1 +/- √769

5 0

3 years ago

timama [110]

Answer:

25π units^2

Step-by-step explanation:

The shape is a quarter circle with radius 10 units.

area of circle = πr^2

area of a quarter circle = (1/4)π(10 units)^2

area = 25π units^2

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3 years ago

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3 years ago

3 over 4 open parentheses 1 half x space minus space 12 close parentheses space plus space 4 over 5

lesantik [10]

For this case we have the following expression:

$\frac {3} {4} (\frac {1} {2} x-12) + \frac {4} {5}$