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2 years ago

A copy machine makes 24 copies per minute. How many copies does it make in 5 minutes and 15 seconds?

Mathematics

1 answer:

liubo4ka [24]2 years ago

8 0

Answer: it makes 126 copies

Explanation:

15/60=6/24

5x24=120

6+120= 126

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A cyclist rides at an average speed of 18 miles per hour. if she wants to bike 212 km, how long (in hours) must she ride?

SOVA2 [1]

The cyclist would ride 7.31836 to travel 212 km.

8 0

3 years ago

Read 2 more answers

maks197457 [2]

Answer:

A. 3:7

Step-by-step explanation:

The volume of the smaller cube is 216 m³.

The volume of the larger cube is 2744 m³

Let the similarity ratio be $l:L$

The volume of these two cubes are in the ratio:

$l^3:L^3=216:2744$

This implies that:

$(\frac{l}{L})^3 =\frac{216}{2744}$

We take the cube root of both sides to obtain:

$\frac{l}{L} =\sqrt[3]{\frac{216}{2744}}$

$\frac{l}{L} =\frac{6}{14}$

This simplifies to:

$\frac{l}{L} =\frac{3}{7}$

Therefore the ratio is 3:7

6 0

4 years ago

What is the value of x?<br><br> Enter your answer in the box.

Delicious77 [7]

Answer: 24

15/5=x/8

Step-by-step explanation:

The triangles are similar and the right hand triangle is 3 times larger than the other.

Similar because two angles are equal so the third is also. One angle is marked as equal, and one is formed by intersecting lines and so is equal to the corresponding angle.

8 0

3 years ago

Read 2 more answers

Determine whether the equation is exact. If it is, then solve it. e Superscript t Baseline (7 y minus 3 t )dt plus (2 plus 7 e

umka21 [38]

Answer:

$F(t,y)=(2+7e^t)y+3(1-t)e^t +C$

Step-by-step explanation:

You have the following differential equation:

$e^t(7y-3t)dt+(2+7e^t)dy=0$

This equation can be written as:

$Mdt+Ndy=0$

where

$M=e^t(7y-3t)\\\\N=(2+7e^t)$

If the differential equation is exact, it is necessary the following:

$\frac{\partial M}{\partial y}=\frac{\partial N}{\partial t}$

Then, you evaluate the partial derivatives:

$\frac{\partial M}{\partial y}=\frac{\partial}{\partial t}e^t(7y-3t)\\\\\frac{\partial M}{\partial t}=7e^t\\\\\frac{\partial N}{\partial t}=\frac{\partial}{\partial t}(2+7e^t)\\\\\frac{\partial N}{\partial t}=7e^t\\\\\frac{\partial M}{\partial t} = \frac{\partial N}{\partial t}$

The partial derivatives are equal, then, the differential equation is exact.

In order to obtain the solution of the equation you first integrate M or N:

$F(t,y)=\int N \partial y = (2 +7e^t)y+g(t)$ (1)

Next, you derive the last equation respect to t:

$\frac{\partial F(t,y)}{\partial t}=7ye^t+g'(t)$

however, the last derivative must be equal to M. From there you can calculate g(t):

$\frac{\partial F(t,y)}{\partial t}=M=(7y-3t)e^t=7ye^t+g'(t)\\\\g'(t)=-3te^t\\\\g(t)=-3\int te^tdt=-3[te^t-\int e^tdt]=-3[te^t-e^t]$

Hence, by replacing g(t) in the expression (1) for F(t,y) you obtain:

$F(t,y)=(2+7e^t)y+3(1-t)e^t +C$

where C is the constant of integration

8 0

4 years ago

You synthetic division to find P(3) for p(x)=x^4-6x^3-4x^2-6x-2

klio [65]

By the polynomial remainder theorem, the remainder upon dividing $p(x)$ by $x-3$ will be the value of $p(3)$ .

... | 1 ... -6 ... -4 ... -6 .... -2
3. | .. ... 3 ... -9 ... -39 .. -135
--------------------------------------
... | 1 ... -3 ... -13 . -45 .. -137

So you have

$\dfrac{x^4-6x^3-4x^2-6x-2}{x-3}=x^3-3x^2-13x-45-\dfrac{137}{x-3}$

which means $p(3)=-137$ .

5 0

3 years ago