What is your hfavorite distance between Points A and B?

A parabolic arch sculpture is on top of a city bank. A model of the arch is y = −0.005x2 + 0.3x where x and y are in feet.

o-na [289]

Answer:

A. a. 34.5 feet

b. 60 feet

Step-by-step explanation:

Parabola equation

$y=-0.005x^2+0.3x$

Differentiating with respect to x we get

$\dfrac{dy}{dx}=-0.01x+0.3$

Equating with zero

$-0.01x+0.3=0\\\Rightarrow -0.01x=-0.3\\\Rightarrow x=\dfrac{0.3}{0.01}\\\Rightarrow x=30$

Double derivative of the parabolic equation

$\dfrac{d^2y}{dx^2}=-0.01$

So, $x=30$ is maximum.

$y=-0.005\times 30^2+0.3\times 30\\\Rightarrow y=4.5$

So, the maximum height of the arch will be 4.5 feet.

From the ground the highest point of the arch will be $30+4.5=34.5\ \text{ft}$

We are taking the x axis as the width of the bank.

$0=-0.005x^2+0.3x\\\Rightarrow 0.005x^2=0.3x\\\Rightarrow x=\dfrac{0.3}{0.005}\\\Rightarrow x=60$

So, the width of the bank will be 60 feet.

7 0

3 years ago

What is the the area to this

Zina [86]

Answer:

164 sq. meters

Step-by-step explanation:

8 0

3 years ago

Brown tree snakes are an invasive species causing huge environmental and financial damage in Guam. Researchers captured brown tr

storchak [24]

Answer:

Null Hypothesis, $H_0$ : $\mu$ $\leq$ 120 grams

Alternate Hypothesis, $H_A$ : $\mu$ > 120 grams

Step-by-step explanation:

We are given that researchers captured brown tree snakes on Guam's Andersen Air Force Base, and a random sample of 250 of these snakes were weighed.

The researchers want to perform a hypothesis test to see if the mean weight of a brown tree snake in Guam is significantly greater than 120 grams.

Let $\mu$ = mean weight of a brown tree snake in Guam.

So, Null Hypothesis, $H_0$ : $\mu$ $\leq$ 120 grams

Alternate Hypothesis, $H_A$ : $\mu$ > 120 grams

Here, null hypothesis states that the mean weight of a brown tree snake in Guam is smaller than or equal to 120 grams.

On the other hand, alternate hypothesis states that the mean weight of a brown tree snake in Guam is significantly greater than 120 grams.

So, this would be the appropriate null and the alternative hypothesis to test this claim.

8 0

3 years ago

Find the distance (-4, 6) and (3 - 7)

Sergio [31]

Exact form: 218
decimal form: 14.764

5 0

3 years ago

Read 2 more answers

Use the Change of Base Formula to evaluate log3 58. Then convert log3 58 to a logarithm in base 4. Round to the nearest thousand

Natali5045456 [20]

Hello,

$log_3(58)= \dfrac{ln(58)}{ln(3)}=3,69597450... \\

log_3(58)=log_4(x)\\

 \dfrac{ln(58)}{ln(3)} = \dfrac{ln(x)}{4}==\textgreater\ x=e^{ \frac{ln(58)*ln(4)}{ln(3)}}\\

 =167,957104437222249066099...

$

≈167.96

5 0

3 years ago

Read 2 more answers