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3 years ago

Find the unit rate for 420 miles on 10 gallons of gas

Mathematics

1 answer:

Mars2501 [29]3 years ago

8 0

Answer:

42 miles per gallon

Step-by-step explanation:

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Find the average value of f over region

SVETLANKA909090 [29]

$D$ is a right triangle with base length 1 and height 8, so the area of $D$ is $\dfrac12(1)(8)=4$ .

The average value of $f(x,y)$ over $D$ is given by the ratio

$\dfrac{\displaystyle\iint_Df(x,y)\,\mathrm dA}{\displaystyle\iint_D\mathrm dA}$

The denominator is just the area of $D$ , which we already know. The average value is then simplified to

$\displaystyle\frac74\iint_Dxy\,\mathrm dA$

In the $x,y$ -plane, we can describe the region $D$ as all points $(x,y)$ that lie between the lines $y=0$ and $y=8x$ (the lines which coincide with the triangle's base and hypotenuse, respectively), taking $0\le x\le1$ . So, the integral is given by, and evaluates to,

$\displaystyle\frac74\int_{x=0}^{x=1}\int_{y=0}^{y=8x}xy\,\mathrm dy\,\mathrm dx=\frac78\int_{x=0}^{x=1}xy^2\bigg|_{y=0}^{y=8x}\,\mathrm dx$
$=\displaystyle56\int_{x=0}^{x=1}x^3\,\mathrm dx$
$=14x^4\bigg|_{x=0}^{x=1}$
$=14$

3 0

2 years ago

Help please explain

MatroZZZ [7]

Given:

$\sin^{-1}\left(\dfrac{5}{8}\right)=A$

To find:

The correct equivalent equation.

Solution:

We have,

$\sin^{-1}\left(\dfrac{5}{8}\right)=A$

Taking sin on both sides, we get

$\sin \sin^{-1}\left(\dfrac{5}{8}\right)=\sin A$

$\dfrac{5}{8}=\sin A$ $[\because \sin (\sin^{-1}\theta )=\theta]$

Interchanging the sides, we get

$\sin A=\dfrac{5}{8}$

Therefore, the correct option is 4.

8 0

3 years ago

Can someone tell me what x equals!

Zinaida [17]

Answer:

Step-by-step explanation:

hope u find this helpfull

5 0

2 years ago

Read 2 more answers

PLEASEEE HELPP MEEE ASAP!!!!!!! WITH NUMBER 6!!!! PLEASEE HELPP MEE NO GUESSING PLEASEEE!!!! ANSWER IT CORRECTLYYY!!!!!!!

Kisachek [45]

Answer:

A stem and leaf plot is not suitable in this data because this data is not kind of data for a stem and leaf plot.

Step-by-step explanation:

If you're finding out the mean for this plot You could use a stem and leaf plot.

7 0

3 years ago

cos theta = 4/5, 0˚< theta < 90˚ use the information given to find sin2theta, cos2theta, and tan 2theta

NikAS [45]

First calculate $\sin\theta$ .

$\sin^2\theta+\cos^2\theta=1\\\\\sin^2\theta=1-\cos^2\theta\\\\\sin^2\theta=1-\left(\dfrac{4}{5}\right)^2\\\\\\\sin^2\theta=1-\dfrac{16}{25}\\\\\\\sin^2\theta=\dfrac{9}{25}\quad|\sqrt{(\dots)}\\\\\\\sin\theta=\sqrt{\dfrac{9}{25}}\\\\\\\boxed{\sin\theta=\dfrac{3}{5}}$

We take positive value of sinθ because 0° < θ < 90°
Now we could calculate sin2θ, cos2θ and tan2θ:

$\sin2\theta=2\sin\theta\cos\theta=2\cdot\dfrac{3}{5}\cdot\dfrac{4}{5}=\dfrac{2\cdot3\cdot4}{5\cdot5}=\dfrac{24}{25}\\\\\\\cos2\theta=\cos^2\theta-\sin^2\theta=\left(\dfrac{4}{5}\right)^2-\left(\dfrac{3}{5}\right)^2=\dfrac{16}{25}-\dfrac{9}{25}=\dfrac{7}{25}\\\\\\
\tan2\theta=\dfrac{\sin2\theta}{\cos2\theta}=\dfrac{\frac{24}{25}}{\frac{7}{25}}=\dfrac{24\cdot25}{7\cdot25}=\dfrac{24}{7}=3\dfrac{3}{7}$

5 0

2 years ago

Read 2 more answers