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3 years ago

A stone dropped from a bridge strikes the water 2.2 s later. How high is the bridge above thewater

2 answers:

8 0

Distance = ut+1/2gt^2
u is initial velocity g acceleration due to gravity t is time in seconds

u=0, t=2.2 g=9.8
distance = 0.5(9.8)(2.2)^2=23.716

vivado [14]3 years ago

3 0

Let the only force acting on the ball is the gravity (free-failing) and the ball was initially stationary
vo = 0

s = vot + 1/2 gt^2

s = 1/2 x 10 x (2.2) ^2 = 24.2 m

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Pam has 90 m of fencing to enclose an area in a petting zoo with two dividers to separate three types of young animals. The thre

andrew-mc [135]

Answer:

The area function is

$A=\frac{135}{2}x-\frac{9}{2}x^2$ .

The domain and range of A is $(0,15m)$ and $(0, 253.125 m^2]$ .

Step-by-step explanation:

The given length of fencing is $90 m$ .

Let the length and width of each pen be $x$ and $y$ respectively as shown in the figure.

As there are 3 pens, so, the total area,

$A= 3 xy \;\cdots (i)$

From the figure the total length of fencing is $6x+4y$ .

Here, for a significant area for the animals, $x>0$ as well as $y>0$ as $x$ and $y$ are the sides of ben.

From the given value:

$6x+4y=90\;\cdots (ii)$

$\Rightarrow y=\frac {45}{2}-\frac{3x}{2}$

Now, from equation (i)

$A=3x\left(\frac {45}{2}-\frac{3x}{2}\right)$

$\Rightarrow A=\frac{135}{2}x-\frac{9}{2}x^2\;\cdots (iii)$

This is the required area function in the terms of variable $x$ .

For the domain of area function, from equation (ii)

$x=15-\frac{2y}{3}$

$\Rightarrow x$ [as y>0]

So, the domain of area function is $(0,15m)$ .

For the range of area function:

As $x \rightarrow 0$ or $y\rightarrow 0$ , then $A\rightarrow 0$ [from equation (i)]

$\Rightarrow A>0$

Now, differentiate the area function with respect to $x$ .

$\frac {dA}{dx}=\frac{135}{2}-9x$

Equate $\frac {dA}{dx}$ to zero to get the extremum point.

$\frac {dA}{dx}=0$

$\Rightarrow \frac{135}{2}-9x=0$

$\Rightarrow x=\frac{15}{2}$

Check this point by double differentiation

$\frac {d^2A}{dx^2}=-9$

As, $\frac {d^2A}{dx^2}$ , so, point $x=\frac{15}{2}$ is corresponding to maxima.

Put this value back to equation (iii) to get the maximum value of area function. We have

$A=\frac{135}{2}\times \frac {15}{2}-\frac{9}{2}\times \left(\frac {15}{2}\right)^2$

$\Rightarrow A=253.125 m^2$

Hence, the range of area function is $(0, 253.125 m^2]$ .

4 0

4 years ago

A fast food restaurant executive wishes to know how many fast food meals adults eat each week. They want to construct a 98% conf

adelina 88 [10]

Answer:

$n=(\frac{2.326(1.1)}{0.07})^2 =1336.006 \approx 1337$

So the answer for this case would be n=1337 rounded up to the nearest integer

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=1.1$ represent the population standard deviation

n represent the sample size

Solution to the problem

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =0.07 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 98% of confidence interval now can be founded using the normal distribution. And in excel we can use this formula to find it:"=-NORM.INV(0.01;0;1)", and we got $z_{\alpha/2}=2.326$ , replacing into formula (b) we got:

$n=(\frac{2.326(1.1)}{0.07})^2 =1336.006 \approx 1337$

So the answer for this case would be n=1337 rounded up to the nearest integer

3 0

4 years ago

Please help I will give out brainliest

Nitella [24]

Answer:

i)x=0,x=1

ii)

$\frac{2}3} + \frac{\sqrt{40} }{6} \\\frac{2}3}-\frac{\sqrt{40} }{6}$

Step-by-step explanation:

so I did not use the graphs actually.

for the answer to question i), i wrote out the equation as given:

3x^2-3x+2=2

then, i subtracted the two from the right side of the equation to make the equation set equal to 0, and I got:

3x^2-3x+2-2=+2-2, which becomes 3x^2-3x=0

then, I used the quadratic method of taking out the greatest common factor, which in this case is 3x, and the equation becomes:

3x(x-1)=0

finally, for this equation, I set 3x=0 and x-1 =0 to get the solutions to this equation, as shown below

3x=0(divide both sides by 3 to get)x=0

x-1=0(add 1 to both sides to get)x=1

now for the second equation, I had no other choice but to use the quadratic formula to find the solutions.

so I set up the quadratic formula as shown:

$\frac{-(-4)+ or -\sqrt{(9-4)^2)-4(-2)(3)} }{2(3)}$

from there the equation gets simplified down to:

$\frac{4+ or -\sqrt{16-4(-6)} }{6}$

simplifying the formula even further gives us:

$\frac{4+ or -\sqrt{40} }{6}$

if we simplify the equation one last time, we get:

$\frac{2}{3} + or -\frac{\sqrt{40} }{6}$

therefore, the solutions to this equation are:

$\frac{2}{3} +\frac{\sqrt{40} }{6}\\ \frac{2}{3} - \frac{\sqrt{40} }{6}$

8 0

3 years ago

Consider the following polynomial expression: 4x^5-16x^2+13x^8. Part A: Write the polynomial expression in standard form.

zavuch27 [327]

Answer:

13x^8 + 4x^5 - 16x^2

Step-by-step explanation:

Standard form is just rearranging each group of numbers so that the group with the most exponents on the variables is at the beginning. So it's basically least to greatest but with exponents. Hope this helped!

7 0

4 years ago

Identify like terms of 8a b2 b3 4b2 4 5a

ipn [44]

Like terms are any terms that have the same variable value.

In the sequence 8a, b^2, b^3, 4b^2, 4, and 5a, the like terms are the ones that have the same variable to the same power.

8a and 5a are like terms, as well as b^2 and 4b^2, because both sets of terms have the same variable.
Hope that helped =)

7 0

4 years ago

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