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Ludmilka [50]
3 years ago
6

A Sum of $14 is made of 92 coins consisting of dimes and quarters. How Many are there of each kind of coin

Mathematics
2 answers:
steposvetlana [31]3 years ago
7 0
So first I would say, what if all of them were dimes, how far away would it be from $14?

So 92 coins * 10 cents = $9.20

So it's 4.80 dollars away from 14 dollars.

So if we were to switch one to a quarter, it would increase by 0.15 cents.

So we want to see how many increases we need to reach 4.80 dollars more.

4.80/0.15 = 32

So there are 32 quarters and 60 dimes.
boyakko [2]3 years ago
7 0

Answer:

30 quarters and 60 dimes

hope this helps :)

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A pumpkin is thrown horizontally off of a building at a speed of 2.5\,\dfrac{\text m}{\text s}2.5 s m ​ 2, point, 5, start fract
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Answer:−47.0

​

​

Step-by-step explanation:Step 1. List horizontal (xxx) and vertical (yyy) variables

xxx-direction yyy-direction

t=\text?t=?t, equals, start text, question mark, end text t=\text?t=?t, equals, start text, question mark, end text

a_x=0a

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​

=0a, start subscript, x, end subscript, equals, 0 a_y=-9.8\,\dfrac{\text m}{\text s^2}a

y

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s

2

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a, start subscript, y, end subscript, equals, minus, 9, point, 8, start fraction, start text, m, end text, divided by, start text, s, end text, squared, end fraction

\Delta x=12\,\text mΔx=12mdelta, x, equals, 12, start text, m, end text \Delta y=\text ?Δy=?delta, y, equals, start text, question mark, end text

v_x=v_{0x}v

x

​

=v

0x

​

v, start subscript, x, end subscript, equals, v, start subscript, 0, x, end subscript v_y=\text ?v

y

​

=?v, start subscript, y, end subscript, equals, start text, question mark, end text

v_{0x}=2.5\,\dfrac{\text m}{\text s}v

0x

​

=2.5

s

m

​

v, start subscript, 0, x, end subscript, equals, 2, point, 5, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction v_{0y}=0v

0y

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=0v, start subscript, 0, y, end subscript, equals, 0

Note that there is no horizontal acceleration, and the time is the same for the xxx- and yyy-directions.

Also, the pumpkin has no initial vertical velocity.

Our yyy-direction variable list has too many unknowns to solve for v_yv

y

​

v, start subscript, y, end subscript directly. Since both the yyy and xxx directions have the same time ttt and horizontal acceleration is zero, we can solve for ttt from the xxx-direction motion by using equation:

\Delta x=v_xtΔx=v

x

​

tdelta, x, equals, v, start subscript, x, end subscript, t

Once we know ttt, we can solve for v_yv

y

​

v, start subscript, y, end subscript using the kinematic equation that does not include the unknown variable \Delta yΔydelta, y:

v_y=v_{0y}+a_ytv

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=v

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+a

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tv, start subscript, y, end subscript, equals, v, start subscript, 0, y, end subscript, plus, a, start subscript, y, end subscript, t

Hint #22 / 4

Step 2. Find ttt from horizontal variables

\begin{aligned}\Delta x&=v_{0x}t \\\\ t&=\dfrac{\Delta x}{v_{0x}} \\\\ &=\dfrac{12\,\text m}{2.5\,\dfrac{\text m}{\text s}} \\\\ &=4.8\,\text s \end{aligned}

Δx

t

​

 

=v

0x

​

t

=

v

0x

​

Δx

​

=

2.5

s

m

​

12m

​

=4.8s

​

Hint #33 / 4

Step 3. Find v_yv

y

​

v, start subscript, y, end subscript using ttt

Using ttt to solve for v_yv

y

​

v, start subscript, y, end subscript gives:

\begin{aligned}v_y&=v_{0y}+a_yt \\\\ &=\cancel{0\,\dfrac{\text m}{\text s}}+\left(-9.8\,\dfrac{\text m}{\text s}\right)(4.8\,\text s) \\\\ &=-47.0\,\dfrac{\text m}{\text s} \end{aligned}

v

y

​

​

 

=v

0y

​

+a

y

​

t

=

0

s

m

​

​

+(−9.8

s

m​

)(4.8s)

=−47.0

s

m

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