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-Dominant- [34]

1 year ago

10

The cost for renting a truck for one day is $19.95 and has a rate of$0.50 per mile. Write a function rule to model the cost of r

enting atruck for one day. Then evaluate the function for traveling 73 miles.

1 answer:

jeyben [28]1 year ago

4 0

The cost of renting a truck for one day is $19.95 and has a rate of $0.50 per mile.

We can write a function rule to model the cost of renting a truck for one day.

$y=0.50x+19.95$

Where x is the number of miles and y is the corresponding cost of renting.

Now we can find the cost of renting for traveling 73 miles.

Substitute x = 73 into the function.

$\begin{gathered} y=0.50(73)+19.95 \\ y=36.5+19.95 \\ y=\$56.45 \end{gathered}$

Therefore, the cost of renting the truck for one day and 73 miles will be $56.45

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The combined height of one for tree and one pine tree is 21 meters. The height of 4 for trees stacked on top of each other is 24

slamgirl [31]

Answer:

The height of the fir tree is <u>9 meters</u> tall and the pine tree is <u>12 meters</u>.

Step-by-step explanation:

Given:

Note :→ there is a mistake it is <u>fir tree</u> not for tree.

The combined height of one fir tree and one pine tree is 21 meters.

The height of 4 fir trees stacked on top of each other is 24 meters taller than one pine tree.

Now, to find how tall are the types of trees.

Let the height of one fir tree be $x$ .

And the height of one pine tree be $y$ .

So, the combined height of one fir tree and one pine tree:

$x+y=21.$

$y=21-x.$ .........( 1 )

Now, as given the height of 4 for trees stacked on top of each other is 24 meters taller than one pine tree:

$4x=y+24.$

Putting the value of equation (1) in the place of $y$ :

$4x=21-x+24$

<em>Adding both the sides $x$ we get:</em>

$5x=21+24.$

$5x=45.$

<em>Dividing both the sides by 5 we get:</em>

$x=9\ meters.$

<em>So, the height of one fir tree = 9 meters.</em>

Now, putting the value of $x$ in equation (1) we get:

$y=21-9$

$y=12\ meters.$

<em>Thus, the height of one pine tree = 12 meters.</em>

Therefore, the fir tree is 9 meters tall and the pine tree is 12 meters tall.

6 0

2 years ago

What is the areas of triangle

SashulF [63]

135 is the answer hope this helps

6 0

2 years ago

I don’t know how to do this one.

serious [3.7K]

Answer:

(a) The unit circle is centered at (0,0) with a radius of 1.

(b) The equation of a circle of radius <em>r</em>, with a center located at (0,0):

<em>x</em>²<em>+ y</em>² <em>= r</em>².

(c) (i) P(1,0)

(ii) P(0,1)

(iii) P(-1,0)

(iv) P(0,-1)

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

Eve is making a bird house. To make the walls she takes a piece of wood and cuts it into 4 pieces in the ratio 5:6:6:7. The long

allsm [11]

Answer:

The original piece of wood is 108 cm

Step-by-step explanation:

From the given ratio, the shortest is of the ratio 5 and the longest is of the ratio 7

Let the original piece of wood be x

so the sum of the ratios will be;

5 + 6 + 6 + 7 = 24

the shortest length would be 5/24 * x

= 5x/24

the longest will be 7/24 * x = 7x/24

From the question;

7x/24 -5x/24 = 9

(7x-5x) = 24(9)

2x = 24(9)

x = (24 * 9)/2

x = 108 cm

4 0

2 years ago

Find the general solution of the differential equation and check the result by differentiation. (Use C for the constant of integ

atroni [7]

Answer: $y=Ce^(^3^t^{^9}^)$

Step-by-step explanation:

Beginning with the first differential equation:

$\frac{dy}{dt} =27t^8y$

This differential equation is denoted as a separable differential equation due to us having the ability to separate the variables. Divide both sides by 'y' to get:

$\frac{1}{y} \frac{dy}{dt} =27t^8$

Multiply both sides by 'dt' to get:

$\frac{1}{y}dy =27t^8dt$

Integrate both sides. Both sides will produce an integration constant, but I will merge them together into a single integration constant on the right side:

$\int\limits {\frac{1}{y} } \, dy=\int\limits {27t^8} \, dt$

$ln(y)=27(\frac{1}{9} t^9)+C$

$ln(y)=3t^9+C$

We want to cancel the natural log in order to isolate our function 'y'. We can do this by using 'e' since it is the inverse of the natural log:

$e^l^n^(^y^)=e^(^3^t^{^9} ^+^C^)$

$y=e^(^3^t^{^9} ^+^C^)$

We can take out the 'C' of the exponential using a rule of exponents. Addition in an exponent can be broken up into a product of their bases:

$y=e^(^3^t^{^9}^)e^C$

The term e^C is just another constant, so with impunity, I can absorb everything into a single constant:

$y=Ce^(^3^t^{^9}^)$

To check the answer by differentiation, you require the chain rule. Differentiating an exponential gives back the exponential, but you must multiply by the derivative of the inside. We get:

$\frac{d}{dx} (y)=\frac{d}{dx}(Ce^(^3^t^{^9}^))$

$\frac{dy}{dx} =(Ce^(^3^t^{^9}^))*\frac{d}{dx}(3t^9)$

$\frac{dy}{dx} =(Ce^(^3^t^{^9}^))*27t^8$

Now check if the derivative equals the right side of the original differential equation:

$(Ce^(^3^t^{^9}^))*27t^8=27t^8*y(t)$

$Ce^(^3^t^{^9}^)*27t^8=27t^8*Ce^(^3^t^{^9}^)$

QED

I unfortunately do not have enough room for your second question. It is the exact same type of differential equation as the one solved above. The only difference is the fractional exponent, which would make the problem slightly more involved. If you ask your second question again on a different problem, I'd be glad to help you solve it.

7 0

2 years ago