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Gre4nikov [31]
3 years ago
6

Michael ran 3 miles in 24 minutes. What is his average running speed in miles per hour?

Mathematics
2 answers:
givi [52]3 years ago
7 0

Answer:

7.5 miles / hour

Step-by-step explanation:

See the step-by-step solution in the picture attached below.

I hope this answer will help you. Have a nice day !

sergij07 [2.7K]3 years ago
4 0

Answer: 7.5

Step-by-step explanation:

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Mean Value theorem help! BRAINLIEST if you can explain it clearly!!!
Korolek [52]
\bf f(x)=ln(x-5)\qquad [6,8]\qquad \cfrac{df}{dx}=\cfrac{1}{x-5}\\\\
-----------------------------\\\\
\textit{mean value theorem}\qquad f'(c)=\cfrac{f(b)-f(a)}{b-a}\\\\
-----------------------------\\\\
f'(c)=\cfrac{1}{c-5}\qquad thus\quad \cfrac{1}{c-5}=\cfrac{f(8)-f(6)}{8-6}
\\\\\\
\cfrac{1}{c-5}=\cfrac{ln(3)-ln(1)}{2}\implies \cfrac{1}{c-5}=\cfrac{ln(3)-0}{2}
\\\\\\
\cfrac{2}{ln(3)}=c-5\implies \boxed{\cfrac{2}{ln(3)}+5=c}
7 0
3 years ago
A projectile is launched from the ground at an angle of theta above the horizontal with an initial speed of v in​ ft/s. The rang
VARVARA [1.3K]

Answer:

\theta=24.4^\circ

Step-by-step explanation:

The formula you wrote has the fraction the other way around. You can find that the range​ of a projectile is in reality approximated by the equation x=\frac{v^2}{g} sin(2\theta)=\frac{v^2}{32ft/s^2} sin(2\theta), where we will use ft for distances.

From the given equation we have then \frac{x32ft/s^2}{v^2} =sin(2\theta), which means \theta=\frac{Arcsin(\frac{x32ft/s^2}{v^2})}{2} since the arcsin is the inverse function of the sin.

Since we have x = 170 ft and  v = 85 ft/s, we can substitute these values from the equation written, and we will have \theta=\frac{Arcsin(\frac{(170ft)(32ft/s^2)}{(85ft/s)^2})}{2}, and from now on we have just to use a calculator, obtaining \theta=\frac{Arcsin(0.75294117647)}{2}=\frac{48.84579804^\circ}{2}=24.4^\circ

3 0
3 years ago
What is the first step in the construction of a line perpendicular to `stackrel(harr)(AB)` and passing through an external point
melisa1 [442]

take your compass on a point on your line. then draw a circle. take the 2 points in which the circle hit the line and draw 2 circles larger than half the distance between he 2 points. take the point that they intersect and and connect it to the line and you point M and it is purpendicular. does that make sense?

6 0
3 years ago
In this exercise, we estimate the rate at which the total personal income is rising in the Richmond-Petersburg, Virginia, metrop
babymother [125]

Answer:

The rate at which the total income is increasing is$1627415600

Step-by-step explanation:

From the given data

Population in the area=P=961400

The rate of increase in population=dP/dt=9200

The Average Income=I=$30593

The rate of increase in Average Income=dI/dt=$1400

Now the total income is given as

Total Income=TI=PI

So the rate of increase of total personal income is given as \frac{d}{dt}(PI)

From the product rule of derivatives

\frac{d}{dt}(P*I)=I*\frac{dP}{dt}+P*\frac{dI}{dt}

Here

I is the Average Income which is given as $30593

dI/dt is the rate of increase of income which is given as $1400.

P is the population of the area which is given as 961400

dP/dt=9200 is the rate of increase of population which is given as 9200

By substituting the values,

\frac{d}{dt}(P*I)=I*\frac{dP}{dt}+P*\frac{dI}{dt}\\\frac{d}{dt}(P*I)=30593*9200+961400*1400\\\frac{d}{dt}(P*I)=\$1627415600

So the rate at which the total income is increasing is$1627415600

8 0
3 years ago
Six less than the product of 12 translate to algebraic expressions
Y_Kistochka [10]

Answer:

12 multiply 6 or 12*6.

Step-by-step explanation:

5 0
3 years ago
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