Find the difference: 77/8-31/4

Write an expression that sho how to use the halving and doubling strategy to find 28×50

swat32

28x50
14x100
7x200=14,000

8 0

3 years ago

A number exceeds its four-sevenths by 18. Find the number.

Andru [333]

Answer:

42

Step-by-step explanation:

let the number be x

4/7 of x

(4/7) × x

4x/7

As stated in the question:

x=4x/7+18

=x-4x/7=18

=(7x-4x)/7=18

=3x/7=18

3x= 18×17

3x= 126

x=126/3

x=42

5 0

1 year ago

Mind lending a hand here?

elixir [45]

Answer:

C

Step-by-step explanation:

8 0

1 year ago

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A metal beam was brought from the outside cold into a machine shop where the temperature was held at 65degreesF. After 5 min, t

ivolga24 [154]

Answer:

The beam initial temperature is 5 °F.

Step-by-step explanation:

If T(t) is the temperature of the beam after t minutes, then we know, by Newton’s Law of Cooling, that

$T(t)=T_a+(T_0-T_a)e^{-kt}$

where $T_a$ is the ambient temperature, $T_0$ is the initial temperature, $t$ is the time and $k$ is a constant yet to be determined.

The goal is to determine the initial temperature of the beam, which is to say $T_0$

We know that the ambient temperature is $T_a=65$ , so

$T(t)=65+(T_0-65)e^{-kt}$

We also know that when $t=5 \:min$ the temperature is $T(5)=35$ and when $t=10 \:min$ the temperature is $T(10)=50$ which gives:

$T(5)=65+(T_0-65)e^{k5}\\35=65+(T_0-65)e^{-k5}$

$T(10)=65+(T_0-65)e^{k10}\\50=65+(T_0-65)e^{-k10}$

Rearranging,

$35=65+(T_0-65)e^{-k5}\\35-65=(T_0-65)e^{-k5}\\-30=(T_0-65)e^{-k5}$

$50=65+(T_0-65)e^{-k10}\\50-65=(T_0-65)e^{-k10}\\-15=(T_0-65)e^{-k10}$

If we divide these two equations we get

$\frac{-30}{-15}=\frac{(T_0-65)e^{-k5}}{(T_0-65)e^{-k10}}$

$\frac{-30}{-15}=\frac{e^{-k5}}{e^{-k10}}\\2=e^{5k}\\\ln \left(2\right)=\ln \left(e^{5k}\right)\\\ln \left(2\right)=5k\ln \left(e\right)\\\ln \left(2\right)=5k\\k=\frac{\ln \left(2\right)}{5}$

Now, that we know the value of $k$ we can use it to find the initial temperature of the beam,

$35=65+(T_0-65)e^{-(\frac{\ln \left(2\right)}{5})5}\\\\65+\left(T_0-65\right)e^{-\left(\frac{\ln \left(2\right)}{5}\right)\cdot \:5}=35\\\\65+\frac{T_0-65}{e^{\ln \left(2\right)}}=35\\\\\frac{T_0-65}{e^{\ln \left(2\right)}}=-30\\\\\frac{\left(T_0-65\right)e^{\ln \left(2\right)}}{e^{\ln \left(2\right)}}=\left(-30\right)e^{\ln \left(2\right)}\\\\T_0=5$

so the beam started out at 5 °F.

6 0

3 years ago

In complete sentences, explain how to draw a double number line representing a 1:4 ratio.

Yuri [45]

Answer:

ratios equivalent to 1/3=2/6,3/9

Step-by-step explanation:

Double number line is a diagram used when. quantities have different units.

It shows each of the quantities on its own number line with corresponding pairs of values lined up.The values of each number line are not the same unless there is a 1:1 ratio between them.

some ratios equivalent to 1:3 are;

2:6,3:9,4:12,5:15,6:18,7:21,etc

6 0

2 years ago

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