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Y_Kistochka [10]
2 years ago
9

How to work this out

Mathematics
1 answer:
Burka [1]2 years ago
8 0

Answer:

2x^2+x^2

=3x

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In 2005, a Nevada silver mine exported 200 tons of silver. In 2008, as the silver supply became exhausted, it only exported 25 t
yulyashka [42]
To obtain the rate of change of mine's silver output, subtract the number of silver exported on 2005 from that on 2008. From the given, from 2005 to 2008, which is a span of 3 years, the exported silver decreased by 175 tons. Thus, the rate of change is equal to -175 tons per 3 years. 
7 0
3 years ago
A toy cannon ball is launched from a cannon on top of a platform. The equation h(t) =- 5<img src="https://tex.z-dn.net/?f=t%5E%7
DanielleElmas [232]

Answer:

Part A)

No

Part B)

About 2.9362 seconds.

Step-by-step explanation:

The equation  \displaystyle h(t)=-5t^2+14t+2  models the height h in meters of the ball t seconds after its launch.

Part A)

To determine whether or not the ball reaches a height of 14 meters, we can find the vertex of our function.

Remember that the vertex marks the maximum value of the quadratic (since our quadratic curves down).

If our vertex is greater than 14, then, at some time t, the ball will definitely reach a height of 14 meters.

However, if our vertex is less than 14, then the ball doesn’t reach a height of 14 meters since it can’t go higher than the vertex.

So, let’s find our vertex. The formula for vertex is given by:

\displaystyle (-\frac{b}{2a},h(-\frac{b}{2a}))

Our quadratic is:

\displaystyle h(t)=-5t^2+14t+2

Hence: a=-5, b=14, and c=2.

Therefore, the x-coordinate of our vertex is:

\displaystyle x=-\frac{14}{2(-5)}=\frac{14}{10}=\frac{7}{5}

To find the y-coordinate and the maximum height, we will substitute this value back in for x and evaluate. Hence:

\displaystyle h(\frac{7}{5})=-5(\frac{7}{5})^2+14(\frac{7}{5})+2

Evaluate:

\displaystyle \begin{aligned} h(\frac{7}{2})&=-5(\frac{49}{25})+\frac{98}{5}+2 \\ &=\frac{-245}{25}+\frac{98}{5}+2\\ &=\frac{-245}{25}+\frac{490}{25}+\frac{50}{25}\\&=\frac{-245+490+50}{25}\\&=\frac{295}{25}=\frac{59}{5}=11.8\end{aligned}

So, our maximum value is 11.8 meters.

Therefore, the ball doesn’t reach a height of 14 meters.

Part B)

To find out how long the ball is in the air, we can simply solve for our t when h=0.

When the ball stops being in the air, this will be the point at which it is at the ground. So, h=0. Therefore:

0=-5t^2+14t+2

A quick check of factors will reveal that is it not factorable. Hence, we can use the quadratic formula:

\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

Again, a=-5, b=14, and c=2. Substitute appropriately:

\displaystyle x=\frac{-(14)\pm\sqrt{(14)^2-4(-5)(2)}}{2(-5)}

Evaluate:

\displaystyle x=\frac{-14\pm\sqrt{236}}{-10}

We can factor the square root:

\sqrt{236}=\sqrt{4}\cdot\sqrt{59}=2\sqrt{59}

Hence:

\displaystyle x=\frac{-14\pm2\sqrt{59}}{-10}

Divide everything by -2:

\displaystyle x=\frac{7\pm\sqrt{59}}{5}

Hence, our two solutions are:

\displaystyle x=\frac{7+\sqrt{59}}{5}\approx2.9362\text{ or } x=\frac{7-\sqrt{59}}{5}\approx-0.1362

Since our variable indicates time, we can reject the negative solution since time cannot be negative.

Hence, our zero is approximately 2.9362.

Therefore, the ball is in the air for approximately 2.9362 seconds.

5 0
3 years ago
Read 2 more answers
Find the lateral area of this cone.
tatyana61 [14]

Given:

Radius of the base of the cone = 12 in.

The slant height of the cone = 15 in.

To find:

The lateral surface area of the given cone.

Solution:

The lateral surface area of the cone is:

LA=\pi rl

Where, r is the radius of the base of the cone and h is the slant height of the cone.

Putting r=12,h=15, we get

LA=\pi (12)(15)

LA=180\pi

The lateral surface area of the cone is 180π in ² and the missing value for the blank is 180.

7 0
3 years ago
Read 2 more answers
Megan has a pen for her dog. The dimensions of the pen are in meters (m) as shown below.
adoni [48]

Answer:

22 m²

Step-by-step explanation:

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4 0
3 years ago
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A sociologist develops a test to measure attitudes towards public transportation, and 27 randomly selected subjects are given th
taurus [48]

Answer:

The margin of error for the 95% confidence interval for the mean score of all such subjects is of 8.45.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 27 - 1 = 26

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 26 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.95}{2} = 0.975. So we have T = 2.0518

The margin of error is:

M = T\frac{s}{\sqrt{n}}

In which s is the standard deviation of the sample and n is the size of the sample.

In this question:

n = 27, s = 21.4. So

M = 2.0518\frac{21.4}{\sqrt{27}}

M = 8.45

The margin of error for the 95% confidence interval for the mean score of all such subjects is of 8.45.

5 0
3 years ago
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