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3 years ago

Mario ran 24 miles in 3 hours. what was his average speed in miles per hour

Mathematics

2 answers:

kumpel [21]3 years ago

8 0

Answer:

8 miles per hour (mph)

Step-by-step explanation:

24/3 = 8

Check:

8mph x 3 hours = 24 miles

stira [4]3 years ago

4 0

<u>Answer:</u>

Mario’s average speed is 8 miles per hour.

<u>Solution:</u>

It is given that Mario runs 24 miles in 3 hours. We have to find what is Mario’s average speed in miles per hour.

In other words we have to find how much mile did Mario run in 1 hour. To find his average speed in miles will use the unitary method.

Using Unitary method,

In 3 hours Mario can run 24 miles.

In 1 hour Mario can run $\frac{24}{3}$ miles.

On dividing we get,

Thus, in 1 hour Mario runs 8 miles.

This means Mario’s average speed is 8 miles per hour.

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Find dy/dx by implicit differentiation for ysin(y) = xcos(x)

tatyana61 [14]

Answer:

$\frac{dy}{dx}=\frac{\cos(x)-x\sin(x)}{\sin(y)+y\cos(y)}$

Step-by-step explanation:

So we have:

$y\sin(y)=x\cos(x)$

And we want to find dy/dx.

So, let's take the derivative of both sides with respect to x:

$\frac{d}{dx}[y\sin(y)]=\frac{d}{dx}[x\cos(x)]$

Let's do each side individually.

Left Side:

We have:

$\frac{d}{dx}[y\sin(y)]$

We can use the product rule:

$(uv)'=u'v+uv'$

So, our derivative is:

$=\frac{d}{dx}[y]\sin(y)+y\frac{d}{dx}[\sin(y)]$

We must implicitly differentiate for y. This gives us:

$=\frac{dy}{dx}\sin(y)+y\frac{d}{dx}[\sin(y)]$

For the sin(y), we need to use the chain rule:

$u(v(x))'=u'(v(x))\cdot v'(x)$

Our u(x) is sin(x) and our v(x) is y. So, u'(x) is cos(x) and v'(x) is dy/dx.

So, our derivative is:

$=\frac{dy}{dx}\sin(y)+y(\cos(y)\cdot\frac{dy}{dx}})$

Simplify:

$=\frac{dy}{dx}\sin(y)+y\cos(y)\cdot\frac{dy}{dx}}$

And we are done for the right.

Right Side:

We have:

$\frac{d}{dx}[x\cos(x)]$

This will be significantly easier since it's just x like normal.

Again, let's use the product rule:

$=\frac{d}{dx}[x]\cos(x)+x\frac{d}{dx}[\cos(x)]$

Differentiate:

$=\cos(x)-x\sin(x)$

So, our entire equation is:

$=\frac{dy}{dx}\sin(y)+y\cos(y)\cdot\frac{dy}{dx}}=\cos(x)-x\sin(x)$

To find our derivative, we need to solve for dy/dx. So, let's factor out a dy/dx from the left. This yields:

$\frac{dy}{dx}(\sin(y)+y\cos(y))=\cos(x)-x\sin(x)$

Finally, divide everything by the expression inside the parentheses to obtain our derivative:

$\frac{dy}{dx}=\frac{\cos(x)-x\sin(x)}{\sin(y)+y\cos(y)}$

And we're done!

5 0

3 years ago

Carter hikes from the top of a hill that is 120 2/3 feet above sea level down

egoroff_w [7]

Answer:

77 feet

Step-by-step explanation:

Difference is asking for subtraction. The equation would look like:

Top of Hill - Valley = X

(P.S.- 2/3 is equal to . 67)

120.67 - 43.67 = 77

Marking as Brainliest is much appreciated.

5 0

3 years ago

Find the value of x if a linear function goes through the following points and has the following slope: (x,2), (-4,6), m=3

Anastasy [175]

The slope is defined as

$m=\dfrac{\Delta y}{\Delta x}=\dfrac{6-2}{-4-x}$

So, we have the follwing equation:

$\dfrac{6-2}{-4-x} = 3 \iff 4 = 3(-4-x) \\\iff 4=-12-3x \iff16=-3x \iff x = -\dfrac{16}{3}$

6 0

3 years ago

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mr_godi [17]

<h2>Answer:</h2>

$-3(x + 4) + 5x = 24\\\\-3x - 12 + 5x = 24\\\\2x - 12 = 24\\\\2x = 36\\\\x = 18$

The solution for x in this equation is <em>18</em>.<em> </em>

6 0

3 years ago

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Determine the equation for the given line in

Tema [17]

Answer:

Y= -3/5 - 1

Step-by-step explanation:

if you start on the y intercept an go down once (-1)

then go down three times (-3)

positive 5 so go right 5 times it lands on the point :)

im not a teacher and i took this last year so sorry if my explanation isn't the best

6 0

3 years ago

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