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2 years ago

6

John is participating in a marathon that is 26.2 miles. His distance (d, in miles) depends on his time (t, in hours). Which is a

n appropriate range for this situation?

1 answer:

madreJ [45]2 years ago

6 0

The range of a function is representative of the values on the y-axis. In this case, the graph will contain distance on the y-axis at is the dependent variable, while the independent variable is time.

We know that the minimum value of the distance will be 0, given that there can be no negative distance. Moreover, the maximum value is 26.2 miles, since the marathon will then be over. Therefore, a good range for the situation will be 0-27 miles.

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The perimeter of a square is 56cm. What is the approximate length of its diagonal?

Nina [5.8K]

4. 19.8
56/4=14
Diagonal of a square is equal to one side multiplied by the square root of two.
Therefore, it is 19.8, being that square root is (in super simple rounding) 1.5.

8 0

2 years ago

Read 2 more answers

TravelEz sells dollars at a rate of ($1.40)/(1 euro) and buys dollars at a rate of ($1.80)/(1 euro). At the beginning of a trip,

Natalija [7]

Answer:

Sophie will get <u>$56</u> in exchange.

Step-by-step explanation:

Given:

TravelEz sells dollars at a rate of ($1.40)/(1 euro).

And dollars they buy at a rate of ($1.80)/(1 euro).

Sophie exchanged $540 to get 300 euros, at the beginning of trip.

And, she is left with 40 euros at the end of trip.

So exchanges the euros back to dollars.

Now, to find the dollars Sophie will get in exchange.

Let the dollars Sophie will get in exchange be $x.$

The rate at which TravelEz sells dollars = $\frac{\$1.40}{1\ euro}$

Number of euros Sophie is left with = $40.$

Now, to get the dollars she will get we set proportion:

<em>As, </em> $\$1.40$ <em> is equivalent </em> $1\ euro$ <em>.</em>

<em>So, </em> $x$ <em> is equivalent to </em> $40\ euros$ <em>.</em>

Thus,

$\frac{1.40}{1} =\frac{x}{40}$

By cross multiplying we get:

$56=x$

$x=\$56.$

Therefore, Sophie will get $56 in exchange.

5 0

2 years ago

Find the point (x,y) of x2+14xy+49y2=100 that is closest to the origin and lies in the first quadrant.

Gala2k [10]

Notice that

$x^2+14xy+49y^2=(x+7y)^2$

so the constraint is a set of two lines,

$(x+7y)^2=100\implies\begin{cases}x+7y=10\\x+7y=10\end{cases}$

and only the first line passes through the first quadrant.

The distance between any point $(x,y)$ in the plane is $\sqrt{x^2+y^2}$ , but we know that $\sqrt{f(x,y)}$ and $f(x,y)$ share the same critical points, so we need only worry about minimizing $x^2+y^2$ . The Lagrangian for this problem is then

$L(x,y,\lambda)=x^2+y^2+\lambda(x+7y-10)$

with partial derivatives (set equal to 0)

$L_x=2x+\lambda=0$

$L_y=2y+7\lambda=0$

$L_\lambda=x+7y-10=0$

We have

$L_y-7L_x=2y-14x=0\implies y=7x$

which tells us that

$x+7y-10=0\iff x+49x=10\implies x=\dfrac15\implies y=\dfrac75$

so that $\left(\dfrac15,\dfrac75\right)$ is a critical point. The Hessian for the target function $x^2+y^2$ is

$H(x,y)=\begin{bmatrix}2&0\\0&2\end{bmatrix}$

which is positive definite for all $x,y$ , so the critical point is the site of a minimum. The minimum distance itself (which we don't seem to care about for this problem, but we might as well state it) is $\sqrt{\left(\dfrac15\right)^2+\left(\dfrac75\right)^2}=2$ .

3 0

2 years ago

it is sixty-eight kilometres between venice and vicenza. every day the train does the journey four times. how far does the train

myrzilka [38]

68×4≈272. easy use ur calculator ii will help u more. have fun ejoy ur day

8 0

1 year ago

The value of good wine increases with age. Thus, if you are a wine dealer, you have the problem of deciding whether to sell your

Katyanochek1 [597]

Answer: 64 years

Step-by-step explanation:

Let assume the dealer sold the bottle now for $P, then invested that money at 5% interest. The return would be:

R1 = P(1.05)^t,

This means that after t years, the dealer would have the total amount of:

$P×1.05^t.

If the dealer prefer to wait for t years from now to sell the bottle of wine, then he will get the return of:

R2 = $P(1 + 20).

The value of t which will make both returns equal, will be;

R1 = R2.

P×1.05^t = P(1+20)

P will cancel out

1.05^t = 21

Log both sides

Log1.05^t = Log21

tLog1.05 = Log21

t = Log21/Log1.05

t = 64 years

The best time to sell the wine is therefore 64years from now.

7 0

2 years ago