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2 years ago

A copy machine makes 24 copies per minute. How long does it take to make 114 copies?

1 answer:

4 0

A copy machine makes 24 copies per minute is already given. So the question becomes easy because of this part. the only thing that needs to be noticed are the minute details given in the question, otherwise it is an absolutely simple problem.
24 copies can be copied by the copy machine in = 1 minute
Then
114 copies will be copied by the machine in = (1/24) * 114 minutes
= 114/24 minutes
= 4.75 minutes
So the copy machine has the capacity to copy 114 copies in 4.75 minutes.

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Find the slope of the line through (9,0) and (3,8)

timofeeve [1]

Answer: 4/-3

Step-by-step explanation:

Slope (m) = ΔY /ΔX = 4 /-3

ΔX = 3 – 9 = -6

ΔY = 8 – 0 = 8

4 0

2 years ago

What is the answer to x (x+8)=9

marta [7]

Answer:

x=1 or x=−9

Step-by-step explanation:

Let's solve your equation step-by-step.

x(x+8)=9

Step 1: Simplify both sides of the equation.

x2+8x=9

Step 2: Subtract 9 from both sides.

x2+8x−9=9−9

x2+8x−9=0

Step 3: Factor left side of equation.

(x−1)(x+9)=0

Step 4: Set factors equal to 0.

x−1=0 or x+9=0

x=1 or x=−9

8 0

2 years ago

Help and tell me why

lorasvet [3.4K]

Answer:

Step-by-step explanation:

V= lwh / 3 Write formula

V= 6*6*5 /3 Substitute

V=60

3 0

2 years ago

sandra brings cheese and crakers for lunch every 6 days, and lily brings cheese and crakers every 8 days. if they both brought c

Evgesh-ka [11]

Answer:

24 Days

Step-by-step explanation:

6 0

2 years ago

Let S be the solid beneath z = 12xy^2 and above z = 0, over the rectangle [0, 1] × [0, 1]. Find the value of m > 1 so that th

jonny [76]

Answer:

The answer is $\sqrt{\frac{6}{5}}$

Step-by-step explanation:

To calculate the volumen of the solid we solve the next double integral:

$\int\limits^1_0\int\limits^1_0 {12xy^{2} } \, dxdy$

Solving:

$\int\limits^1_0 {12x} \, dx \int\limits^1_0 {y^{2} } \, dy$

$[6x^{2} ]{{1} \atop {0}} \right. * [\frac{y^{3}}{3}]{{1} \atop {0}} \right.$

Replacing the limits:

$6*\frac{1}{3} =2$

The plane y=mx divides this volume in two equal parts. So volume of one part is 1.

Since m > 1, hence mx ≤ y ≤ 1, 0 ≤ x ≤ $\frac{1}{m}$

Solving the double integral with these new limits we have:

$\int\limits^\frac{1}{m} _0\int\limits^{1}_{mx} {12xy^{2} } \, dxdy$

This part is a little bit tricky so let's solve the integral first for dy:

$\int\limits^\frac{1}{m}_0 [{12x \frac{y^{3}}{3}}]{{1} \atop {mx}} \right.\, dx =\int\limits^\frac{1}{m}_0 [{4x y^{3 }]{{1} \atop {mx}} \right.\, dx$

Replacing the limits:

$\int\limits^\frac{1}{m}_0 {4x(1-(mx)^{3} )\, dx =\int\limits^\frac{1}{m}_0 {4x-4x(m^{3} x^{3} )\, dx =\int\limits^\frac{1}{m}_0 ({4x-4m^{3} x^{4}) \, dx$

Solving now for dx:

$[{\frac{4x^{2}}{2} -\frac{4m^{3} x^{5}}{5} ]{{\frac{1}{m} } \atop {0}} \right. = [{2x^{2} -\frac{4m^{3} x^{5}}{5} ]{{\frac{1}{m} } \atop {0}} \right.$

Replacing the limits:

$\frac{2}{m^{2} }-\frac{4m^{3}\frac{1}{m^{5}}}{5} =\frac{2}{m^{2} }-\frac{4\frac{1}{m^{2}}}{5} \\ \frac{2}{m^{2} }-\frac{4}{5m^{2} }=\frac{10m^{2}-4m^{2} }{5m^{4}} \\ \frac{6m^{2} }{5m^{4}} =\frac{6}{5m^{2}}$

As I mentioned before, this volume is equal to 1, hence:

$\frac{6}{5m^{2}}=1\\m^{2} =\frac{6}{5} \\m=\sqrt{\frac{6}{5} }$

3 0

2 years ago