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AleksandrR [38]

3 years ago

9

Each paper clip can be traded for three matches. Each pencil can be traded for six paper clips. two pencils and two paper clips

are worth ______ 38 matches

1 answer:

Dima020 [189]3 years ago

6 0

They're worth 42 matches

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1 7/3 in simplest form

MrMuchimi

It is already in simplest form, since 17 is a prime number.

8 0

4 years ago

1. The mechanics at Lincoln Automotive are reborning a 6 in deep cylinder to fit a new piston. The machine they are using increa

Firdavs [7]

Answer:

$0.0239\frac{in^{3}}{min}$

Step-by-step explanation:

In order to solve this problem, we must start by drawing a diagram of the cylinder. (See attached picture)

This diagram will help us visualize the problem better.

So we start by determining what data we already know:

Height=6in

Diameter=3.8in

Radius = 1.9 in (because the radius is half the length of the diameter)

The problem also states that the radius will increase on thousandth of an inch every 3 minutes. We can find the velocity at which the radius is increasing with this data:

$r'=\frac{1/1000in}{3min}$

which yields:

$r'=\frac{1}{3000}\frac{in}{min}$

with this information we can start solving the problem.

First, the problem wants us to know how fast the volume is increasing, so in order to find that we need to start with the volume formula for a cylinder, which is:

$V=\pi r^{2}h$

where V is the volumen, r is the radius, h is the height and π is a mathematical constant equal approximately to 3.1416.

Now, the height of the cylinder will not change at any time during the reborning, so we can directly substitute the provided height, so we get:

$V=\pi r^{2}(6)$

or

$V=6 \pi r^{2}$

We can now take the derivative to this formula so we get:

$\frac{dV}{dt}=2(6)\pi r \frac{dr}{dt}$

Which simplifies to:

$\frac{dV}{dt}=12\pi r \frac{dr}{dt}$

We can now substitute the data provided by the problem to get:

$\frac{dV}{dt}=12\pi (1.9) (\frac{1}{3000})$

which yields:

$\frac{dV}{dt}=0.0239\frac{in^{3}}{min}$

3 0

4 years ago

Solve the following quadratic equation by using the quadratic formula.

Bas_tet [7]

Answer:

B. $\frac{-3}{4}$ ± $\frac{\sqrt{41} }{4}$

Step-by-step explanation:

First, substitute the equation into the quadratic formula.

$x=\frac{b+-\sqrt{(b^{2} )-4(a)(c)} }{2a}$

x= $\frac{-3+-\sqrt{(3)^2-4(-2)(4)} }{4}$

Solve for x.

x= $\frac{-3+-\sqrt{9+32} }{4}$

x= $\frac{-3+-\sqrt{41} }{4}$

The answer is x= $-\frac{3}{4}$ ± $\frac{\sqrt{41} }{4}$

6 0

3 years ago

A plane takes off at an angle of elevation of 15° and travels in a straight line for 3,000 meters. What is the height of the pla

vampirchik [111]

check the picture below.

make sure your calculator is in Degree mode.

3 0

3 years ago

Read 2 more answers

Solve x^2-8x+5=0 using the completing-the-square method

eduard

Answer:

x = 4 ± $\sqrt{11}$

Step-by-step explanation:

To complete the square

add (half the coefficient of the x- term)² to both sides

x² + 2(- 4)x + 16 + 5 = 16

(x - 4)² + 5 = 16 ( subtract 5 from both sides )

(x - 4)² = 11 ( take the square root of both sides )

x - 4 = ± $\sqrt{11}$ ( add 4 to both sides )

x = 4 ± $\sqrt{11}$ ← exact values

4 0

3 years ago