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Juli2301 [7.4K]
2 years ago
10

* Which expression means the same as the quotient of 10 and 5? *please help*

Mathematics
1 answer:
marta [7]2 years ago
4 0

Answer:

10 divided by 5

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A racecar travels 225 miles per hour. How far will it drive in 6 1/2 hours?
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Answer:

1462.5

Step-by-step explanation

225 mph means of course 225 miles per hour

225 x 6 is 1350 and then you have to do 225/2 which is 112.5 to find what half of 225 is then you add 1350+112.5 to get 1462.5

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What is 15 less than a number?​
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Answer:

x - 15

Step-by-step explanation:

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Please show step by step of working out the value of r for which is A minimum and calculate the minimum surface area of the cont
Genrish500 [490]

Answer:

A = 59.63cm^2

Step-by-step explanation:

You have the following function for the surface area of the container:

A=\pi r^2+\frac{100}{r}                (1)

where r is the radius of the cross sectional area of the container.

In order to find the minimum surface are you first calculate the derivative of A respect to r, to find the value of r that makes the surface area a minimum.

\frac{dA}{dr}=\frac{d}{dr}[\pi r^2+\frac{100}{r}]\\\\\frac{dA}{dr}=2\pi r-\frac{100}{r^2}         (2)

Next, you equal the expression (2) to zero and solve for r:

2\pi r-\frac{100}{r^2}=0\\\\2\pi r=\frac{100}{r^2}\\\\r^3=\frac{50}{\pi}\\\\r=(\frac{50}{\pi})^{1/3}

Finally, you replace the previous result in the equation (1):

A=\pi (\frac{50}{\pi})^{2/3}+\frac{100}{(\frac{50}{\pi})^{1/3}}}

A=59.63

The minimum total surface area is 59.63cm^2

3 0
3 years ago
The given line passes through the points (0, -3) and (2, 3).
puteri [66]

The equation, in point-slope form of the line that is  parallel to the given line and passes through the point  (-1, -1) is y + 1 = 3(x + 1).

<u>Solution:</u>

Given that, a line passes through (0, -3) and (2, 3).

We have to find the line equation which is parallel to above line and  passes through (-1, -1).

Now, let us find the slope of the given line.

\text { slope } m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}, \text { where }\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right) \text { are points on that line }

\text { Then, } m=\frac{3-(-3)}{2-0}=\frac{3+3}{2}=\frac{6}{2}=3

So, slope of given line is 3,  

Then, slope of required line is also 3, as slopes of parallel lines are equal.

Then, required line equation in point – slope form is given as:

\begin{array}{l}{y-y_{1}=m\left(x-x_{1}\right)} \\\\ {y-(-1)=3(x-(-1))} \\\\ {\rightarrow y+1=3(x+1)}\end{array}

Hence, the line equation is y + 1 = 3(x + 1).

6 0
3 years ago
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