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2 years ago

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In Exercises 1–6, find the gradient of the function at the given point. Then sketch the gradient together with the level curve t

hat passes through the point.
f(x,y)=y-x, (2,1)

1 answer:

kirill115 [55]2 years ago

4 0

Answer:

Step-by-step explanation:

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An artist cuts 4 squares with sides of length x ft from the corners of a 12 ft-by-18 ft rectangular piece of sheet metal. She be

ehidna [41]

Answer:

$V = 216x - 60x^2 + 4x^3$

Step-by-step explanation:

The volume V of the fountain is equal to:

V = L*W*h

Where L is the lenght of the fountain, W is the width of the fountain and h is the high of the fountain

We already know that h is equal to x. On the other hand, if we cut a square with side of length x, L and W are calculated as:

L = 18 - 2x

W = 12 - 2x

So, replacing L, W and h on the equation of the volume, we get:

V = (18-2x)*(12-2x)*x

Finally, simplifying the function we get:

$V = ((18*12)+(18*(-2x))+(-2x*12)+((-2x)*(-2x)))*x$

$V = (216-36x-24x+4x^2)*x\\V = (216-60x+4x^2)*x\\V = 216x - 60x^2 + 4x^3$

6 0

2 years ago

The Ignorance Survey: United Kingdom A survey was conducted in the United Kingdom, where respondents were asked if they had a un

lukranit [14]

Answer:

Here we have given two catogaries as degree holder and non degree holder.

So here we have to test the hypothesis that,

H0 : p1 = p2 Vs H1 : p1 not= p2

where p1 is population proportion of degree holder.

p2 is population proportion of non degree holder.

Assume alpha = level of significance = 5% = 0.05

The test is two tailed.

Here test statistic follows standard normal distribution.

The test statistic is,

Z = (p1^ - p2^) / SE

where SE = sqrt[(p^*q^)/n1 + (p^*q^)/n2]

p1^ = x1/n1

p2^ = x2/n2

p^ = (x1+x2) / (n1+n2)

This we can done in TI_83 calculator.

steps :

STAT --> TESTS --> 6:2-PropZTest --> ENTER --> Input all the values --> select alternative "not= P2" --> ENTER --> Calculate --> ENTER

Test statistic Z = 1.60

P-value = 0.1090

P-value > alpha

Fail to reject H0 or accept H0 at 5% level of significance.

Conclusion : There is not sufficient evidence to say that the percent of correct answers is significantly different between degree holders and non-degree holders.

7 0

2 years ago

A basketball player makes 39% of her shots from the free throw line. Suppose that each of her shots can be considered independen

myrzilka [38]

68 is the correct answer. Thank you for your help! Love doing this!

4 0

2 years ago

The average blood alcohol concentration (bac) of eight male subjects was measured after consumption of 15 ml of ethanol (corresp

Neporo4naja [7]

Answer:

After 5 minutes, the BAC was increasing at the rate of 0.0137 mg/mL a minute.

Step-by-step explanation:

The average blood alcohol concentration (bac) is modeled by the following function.

$c(t) = 0.0225te^{-0.0467t}$

In which t is measured in minuted.

How rapidly was the BAC increasing after 5 minutes?

This is c'(t) when t = 5.

Using the derivative of the product.

Derivative of the product:

$c(t) = f(t)*g(t)$

$c'(t) = f'(t)*g(t) + f(t)*g'(t)$

In which problem:

$f(t) = 0.0225t$

$g(t) = e^{-0.0467t}$

So

$c'(t) = 0.0225e^{-0.0467t} - 0.0225*0.0467*te^{-0.0467t}$

$c'(5) = 0.0225e^{-0.0467*5} - 0.0225*0.0467*5e^{-0.0467*5} = 0.0137$

After 5 minutes, the BAC was increasing at the rate of 0.0137 mg/mL a minute.

3 0

2 years ago

Marissa ate six slices of pizza from the 16-piece large pizza. What percent of the pizza did she eat?

olya-2409 [2.1K]

Answer:

0.96%

Step-by-step explanation:

look on google and search dollar times it helps with problems like this

hope this helps

7 0

2 years ago