All categories

3 years ago

A boat can travel 105 miles on 15 gallons of gasoline. How much gasoline will it need to go 140 miles?

2 answers:

7 0

20 gallons
First you have to find the ratio or unit rate so 105/15= 140/x x is the gasoline needed so when you cross multiply you get 2100/105x divide both sides by x and you get 20

Mrac [35]3 years ago

4 0

Answer:

20 gallons

Step-by-step explanation:

105/15=7

7*20=140

You might be interested in

In the standard (x,y) coordinate plane, what is the slope of the line 4x+7y=9?

o-na [289]

Answer: -4/7

Step-by-step explanation:

To find the slope, let's change the equation to slope-intercept form.

$4x+7y=9$ [subtract both sides by 4x]

$7y=-4x+9$ [divide both sides by 7]

$y=-\frac{4}{7}x+\frac{9}{7}$

Now, we know the slope is -4/7.

5 0

3 years ago

Break the numbers 0-9 into 3 groups. Each group needs to equal the same number when added! Write out the groupsand the sum of ea

Burka [1]

we must do the following:

select the major, the minor and the half and add, like this:

$9+0+5+1=15$

therefore:

$7+6+2=15$

also:

$\begin{gathered} 8+4+3=15 \\ \end{gathered}$

the groups are:

(9,0,1,5); (7,6,2); (8,4,3)

8 0

1 year ago

Can someone check whether its correct or no? this is supposed to be the steps in integration by parts

Gwar [14]

Answer:

$\displaystyle - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}$

Step-by-step explanation:

$\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}$

Given integral:

$\displaystyle -\int \dfrac{\sin(2x)}{e^{2x}}\:\text{d}x$

$\textsf{Rewrite }\dfrac{1}{e^{2x}} \textsf{ as }e^{-2x} \textsf{ and bring the negative inside the integral}:$

$\implies \displaystyle \int -e^{-2x}\sin(2x)\:\text{d}x$

Using <u>integration by parts</u>:

$\textsf{Let }\:u=\sin (2x) \implies \dfrac{\text{d}u}{\text{d}x}=2 \cos (2x)$

$\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}$

Therefore:

$\begin{aligned}\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\sin (2x)- \int \dfrac{1}{2}e^{-2x} \cdot 2 \cos (2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\sin (2x)- \int e^{-2x} \cos (2x)\:\text{d}x\end{aligned}$

$\displaystyle \textsf{For }\:-\int e^{-2x} \cos (2x)\:\text{d}x \quad \textsf{integrate by parts}:$

$\textsf{Let }\:u=\cos(2x) \implies \dfrac{\text{d}u}{\text{d}x}=-2 \sin(2x)$

$\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}$

$\begin{aligned}\implies \displaystyle -\int e^{-2x}\cos(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\cos(2x)- \int \dfrac{1}{2}e^{-2x} \cdot -2 \sin(2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x\end{aligned}$

Therefore:

$\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x$

$\textsf{Subtract }\: \displaystyle \int e^{-2x}\sin(2x)\:\text{d}x \quad \textsf{from both sides and add the constant C}:$

$\implies \displaystyle -2\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+\text{C}$

Divide both sides by 2:

$\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{4}e^{-2x}\sin (2x) +\dfrac{1}{4}e^{-2x}\cos(2x)+\text{C}$

Rewrite in the same format as the given integral:

$\displaystyle \implies - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}$

5 0

2 years ago

Can someone help me with this it's making no sense to me

Dafna11 [192]

Answer:

The most reasonable is 2 h

Step-by-step explanation:

If you see the graph is decreasing in hours while is increasing in years. When a person is 45 years the amount of daily physical activity is 3 hours, so a person that is 50 years needs to do less than 3 hours a day and the only option less than 3 hours is 2 hours.

7 0

3 years ago

Help me please, thank you.

Ivan

The correct answer is -2

4 0

3 years ago