#12 will mark as brainliest

Find the critical points of [tex]f(x,y)[/tex]:

[tex]\dfrac{\partial f}{\partial x}=-2x=0\implies x=0[/tex]

[tex]\dfrac{\partial f}{\partial y}=y-4y^3=y(1-4y^2)=0\implies y=0\text{ or }y=\pm\dfrac12[/tex]

All three points lie within [tex]D[/tex], and [tex]f[/tex] takes on values of

[tex]\begin{cases}f(0,0)=4\\f\left(0,-\frac12\right)=\frac{65}{16}\\f\left(0,\frac12\right)=\frac{65}{16}\end{cases}[/tex]

Now check for extrema on the boundary of [tex]D[/tex]. Convert to polar coordinates:

[tex]f(x,y)=f(\cos t,\sin t)=g(t)=4-\cos^2-\sin^4t+\dfrac12\sin^2t=3+\dfrac32\sin^2t-\sin^4t[/tex]

Find the critical points of [tex]g(t)[/tex]:

[tex]\dfrac{\mathrm dg}{\mathrm dt}=3\sin t\cos t-4\sin^3t\cos t=\sin t\cos t(3-4\sin^2t)=0[/tex]

[tex]\implies\sin t=0\text{ or }\cos t=0\text{ or }\sin t=\pm\dfrac{\sqrt3}2[/tex]

[tex]\implies t=n\pi\text{ or }t=\dfrac{(2n+1)\pi}2\text{ or }\pm\dfrac\pi3+2n\pi[/tex]

where [tex]n[/tex] is any integer. There are some redundant critical points, so we'll just consider [tex]0\le t< 2\pi[/tex], which gives

[tex]t=0\text{ or }t=\dfrac\pi3\text{ or }t=\dfrac\pi2\text{ or }t=\pi\text{ or }t=\dfrac{3\pi}2\text{ or }t=\dfrac{5\pi}3[/tex]

which gives values of

[tex]\begin{cases}g(0)=3\\g\left(\frac\pi3\right)=\frac{57}{16}\\g\left(\frac\pi2\right)=\frac72\\g(\pi)=3\\g\left(\frac{3\pi}2\right)=\frac72\\g\left(\frac{5\pi}3\right)=\frac{57}{16}\end{cases}[/tex]

So altogether, [tex]f(x,y)[/tex] has an absolute maximum of 65/16 at the points (0, -1/2) and (0, 1/2), and an absolute minimum of 3 at (-1, 0).

Answer:

$12 the hour

Step-by-step explanation:$360 divided by 30 is 12, meaning he will need to make a minimum of 12 an hour to support his family.

Answer: 12 dollars

Step-by-step explanation:

360 divided by 30 is 12

You intend to estimate a population mean μ from the following sample. 26.2 27.7 8.6 3.8 11.6 You believe the population is normally distributed. Find the 80% confidence interval.  Enter your answer as an open-interval (i.e., parentheses) accurate to twp decimal places.

Answer:

The  Confidence interval = (8.98 , 22.18)

Step-by-step explanation:

From the given information:

mean = [tex]\dfrac{ 26.2+ 27.7+ 8.6+ 3.8 +11.6 }{5}[/tex]

mean = 15.58

the standard deviation [tex]\sigma[/tex] = [tex]\sqrt{\dfrac{\sum(x_i - \mu)^2 }{n}}[/tex]

the standard deviation = [tex]\sqrt{\dfrac{(26.2 - 15.58)^2 +(27.7 - 15.58)^2 +(8.6 - 15.58)^2 + (3.8 - 15.58)^2 + (11.6 - 15.58)^2 }{5 } }[/tex]

standard deviation = 9.62297

Degrees of freedom df = n-1

Degrees of freedom df = 5 - 1

Degrees of freedom df = 4

For df  at 4 and 80% confidence level, the critical value t from t table  = 1.533

The Margin of Error M.O.E = [tex]t \times \dfrac{\sigma}{\sqrt{n}}[/tex]

The Margin of Error M.O.E = [tex]1.533 \times \dfrac{9.62297}{\sqrt{5}}[/tex]

The Margin of Error M.O.E = [tex]1.533 \times 4.3035[/tex]

The Margin of Error M.O.E = 6.60

The  Confidence interval = ( [tex]\mu \pm M.O.E[/tex] )

The  Confidence interval = ( [tex]\mu + M.O.E[/tex] , [tex]\mu - M.O.E[/tex] )

The  Confidence interval = ( 15.58 - 6.60 , 15.58 + 6.60)

The  Confidence interval = (8.98 , 22.18)

Answer:

-46 is your answer.

Step-by-step explanation:

=4-2(3+2)^2

=4-2(5)^2

=4-2(5✖️5)

=4-2(25)

Opening brackets to simplify

=4-50

=-46 is your answer.

Hope it will help you :)

Answer:

-46

Step-by-step explanation:

[tex]4 - 2(3 + 2)^{2} \\ [/tex]

PEDMAS

[tex]4 - 2(5)^{2} \\ 4 - 2(25) \\ 4 - 50 \\ = - 46[/tex]

Answer:

91

Step-by-step explanation: 7*13 = 91

91/7 = 13

Answer:

Our decision rule will be to reject The null hypothesis H0 if the test statistic is less than -1.645, or if it is greater than +1.645.

Step-by-step explanation:

The hypotheses would be;

Null hypothesis;H0: μ = 500

Alternative hypothesis;Ha: μ ≠ 500

Since it's two - tailed at 0.1 level of significance, then each tail will contain 5% or 0.05. From the z-table attached, the corresponding critical value of 0.05 is approximately 1.645 standard deviations from the mean.

Thus, our decision rule will be to reject The null hypothesis H0 if the test statistic is less than -1.645, or if it is greater than +1.645.

Answer:

b= {1,2,3,4} is the answer

Answer: 0.7 liters

Step-by-step explanation:

First convert 3 cups to Liters

3 cups = 0.709765

Now round 0.709765 to the nearest 10 which give you 0.7

Answer:

0.7 liters Hope this helps!

Step-by-step explanation:

Answer: 330 people

Step-by-step explanation:

added them all up

Answer:

-3x - 6 - 1

- 3x + 7

4x

Step-by-step explanation:

Answer:

Rational

Explanation: because it can be expressed in the quotient of two integers:67÷1

Acceleration = final speed - initial speed / time

Acceleration = 6 m/s  - 0 / 3s

Acceleration = 6m/s / 3s

Acceleration = 2 m/s^2

Answer:

[tex]\Huge \boxed{\mathrm{2 \ m/s^2 }}[/tex]

Step-by-step explanation:

[tex]\displaystyle acceleration = \frac{final \ velocity - initial \ velocity}{elapsed \ time}[/tex]

[tex]\displaystyle A = \frac{V_f - V_i}{t}[/tex]

The initial velocity is 0 m/s.

The final velocity is 6 m/s.

The elapsed time is 3 s.

[tex]\displaystyle A = \frac{6 - 0}{3}[/tex]

[tex]\displaystyle A = \frac{6}{3}=2[/tex]

The acceleration is 2 m/s².

Two ways of solving:

1. Convert the fractions to decimals:

3/7 = 0.42857

3/5 = 0.6

0.42857 < 0.6

So 3/7 < 3/5

Second way is to rewrite the fractions with a common denominator:

3/7 = 15/35

3/5 = 21/35

Now compare the numerators:

15 < 21 so 3/7 < 3/5

Answer:

(-3 ÷ 4)x^2 + 6x

Step-by-step explanation:

Data provided in the question

Maximum height = 12m

Number of seconds = 8

Height = 3m

Based on the above information, the quadratic equation is as follows

Since it took 8 seconds for reaching the maximum height and then it returned to the ground level so here the highest point is done after 4 seconds also this graph represents the motion in parabola so the a should be negative

Now it is mentioned that

a × x ^ 2 + bx + c =0

We can assume that

x = 0

x = 8

As these {0.8} are intercepts of x

When x = 0, then it would be

a × 0 ^ 2 + b(0)  + c = 0 .................... (i)

Therefore 0 = 0

Now x = 8, it would be

a × 8 ^ 2 + b(8)  + c = 0

Therefore a(8)^2 + b(8) + c =  0 ..................(ii)

As we can see  that in the first equation c should be zero

While the second equation would be

64a + 8b = 0

i.e.

8a = -b or a = -b ÷ 8

Now as per the quadratic function, it appears

(-b ÷8)x^2 + bx + 0

Now the parabola vertex is (4, 12)

Now put this in the place of a

(-b ÷ 8)(4)^2 + b(4) = 12

Now for solving this b, all terms should be multiplied by 8

That comes

-b(16) + 32b = 96

16b = 96

So, b = 6.  

As a = -b ÷8

a = -6 ÷ 8

a = -3 ÷4

Now the equation is

= (-3 ÷ 4)x^2 + 6x

Hence, this is the equation

Answer:

Step-by-step explanation:

Given the functions  z=(x+y)[tex]e^y\\[/tex] and x=u²+v² and y=u²−v²

Using the composite derivative formula;

∂z/∂u= ∂z/∂x*∂x/∂u+∂z/∂y*∂y/∂u

∂z/∂u = y[tex]e^y[/tex]*2u + [(x+y)[tex]e^y[/tex]+x[tex]e^y[/tex]]*2u

∂z/∂u =y[tex]e^y[/tex]*2u + 2u[x[tex]e^y[/tex]+y[tex]e^y[/tex]+x[tex]e^y[/tex]]

∂z/∂u = y[tex]e^y[/tex]*2u + 2u[2x[tex]e^y[/tex]+y[tex]e^y[/tex]]

∂z/∂u = 2u[u²−v²][tex]e^{u^2-v^2}[/tex]+ 2u[2(u²+v²)[tex]e^{u^2-v^2}[/tex]+y[tex]e^{u^2-v^2}[/tex]]]

∂z/∂v= ∂z/∂x*∂x/∂v+∂z/∂y*∂y/∂v

∂z/∂v = y[tex]e^y[/tex]*2v + [(x+y)[tex]e^y[/tex]+x[tex]e^y[/tex]]*-2v

∂z/∂v =y[tex]e^y[/tex]*2v -2v[x[tex]e^y[/tex]+y[tex]e^y[/tex]+x[tex]e^y[/tex]]

∂z/∂v = y[tex]e^y[/tex]*2v -2v[2x[tex]e^y[/tex]+y[tex]e^y[/tex]]

∂z/∂v = 2v[u²−v²][tex]e^{u^2-v^2}[/tex]-2v[2(u²+v²)[tex]e^{u^2-v^2}[/tex]+y[tex]e^{u^2-v^2}[/tex]]

Answer:

0.350

Step-by-step explanation:

Confidence interval = point estimate ± margin of error

Point estimate = Confidence interval - margin of error

To get the margin of error, we will take the average of the difference of the interval given. Given the confidence interval 0.325<p<0.375

Margin of error = 0.375-0.325/2

Margin of error = 0.050/2

Margin of error = 0.025

Using the interval of 0.375

Point estimate = 0.375 - 0.025

Point estimate = 0.350

Answer:

2804 cm²

Step-by-step explanation:

Total area comprises of 6 faces: 2 trapezoids and 4 rectangles

Total area:

552*2 + 544 + 238 + 408 + 510 =  2804 cm²

Answer: [tex]x(t)=-1[/tex]

[tex]y(t)=-4+4(t)[/tex]

[tex]z(t)=2-5(t)[/tex]

Step-by-step explanation:

To find: The vector parametric equations for the line through the points (−1,−4,2) and (−1,0,−3).

Let A (−1,−4,2) and B(−1,0,−3)

First we find direction vectors : [tex]\overrightarrow{AB}=<-1-(-1),0-(-4),-3-2>[/tex]

[tex]<0,4,-5>[/tex]

Now, the parametric equations of the line:

[tex]x(t)=-1+0(t)[/tex]

[tex]y(t)=-4+4(t)[/tex]

[tex]z(t)=2-5(t)[/tex]

Hence, the vector parametric equations for the line through the points (−1,−4,2) and (−1,0,−3):

[tex]x(t)=-1[/tex]

[tex]y(t)=-4+4(t)[/tex]

[tex]z(t)=2-5(t)[/tex]

Answer:

x ≥ -1/2

Step-by-step explanation:

We know that we cannot graph imaginary numbers. Therefore, our x value has to be greater than or equal to 0:

To find our domain, we need to set the square root equal to zero:

√(4x + 2) = 0

4x + 2 = 0

4x = -2

x = -1/2

We now know that no value below -1/2 can be used or we will get an imaginary number. Therefore, our answer is x ≥ -1/2

Alternatively, we can graph the function and analyze domain:

Answer:

The simple interest earned in one year is $10.5

Step-by-step explanation:

Simple interest = p × r × t

Where,

p = principal

r = interest rate

t = time

Principal= $350

Interest rate = 3%

=3/100

=0.03

Time= 1 year

Simple interest = p × r × t

= $350 × 0.03 × 1

= $10.5

The simple interest earned in one year is $10.5

Answer:

i think the answer is 0.3071

Step-by-step explanation:

But I might be wrong

Answer:

113°

Step-by-step explanation:

By remote interior angle theorem:

a + 35° = a - 30° + a - 48°

a + 35° = 2a - 78°

35° + 78° = 2a - a

113° = a

a = 113°

Answer:

2.6 ft

Step-by-step explanation:

8.3/sin 90 = MK/sin 18

MK = 8.3 sin 18 / sin 90

MK = 2.6 ft

Answer:

2.6

Step-by-step explanation:

Answer:

19v - 18

Step-by-step explanation:

Hello!

v - 6(-3v + 3)

Distribute the -6

-6 * -3v = 18v

-6 * 3 = -18

v + 18v -18

Combine like terms

19v - 18

The answer is 19v - 18

Hope this helps!

Answer:

V=6;v=1

Step-by-step explanation:

(V-6)(-3v+3)

-3v^2+3v+18v-18

-3v^2+21v-18

Multiple it by minus one we will get

3v^3-21v+18

Now breaking by midterm

3v^2-18v-3v+18

3v(v-6)-3(v-6)

(V-6)(3v-3)

V=6;v=1

Step-by-step explanation:

Let w be the speed of wind and v be speed of airplane without wind.

[tex]average \: speed = \frac{total \: distance }{total \: time} [/tex]

(A)

[tex]speed \: against \: wind( v - w) = \frac{2100}{6} = 350mph[/tex]

(B)

[tex]speed \: with \: wind(v + w) = \frac{2100}{4} = 525mph[/tex]

(C)

Adding equations A and B, we get :

(v - w) + (v + w) = 350 + 525

2v = 875

V = 437.5 mph

Answer:

Step-by-step explanation:

√2 + √3 + √3 - √7 + √7 - √ 2

by changing the position

√2 - √2 + √3 + √3 - √7 + √7

√2 and -√2 gets canceled

-√7 and √7 gets cancelled

we are left out with √3 + √3

√3 + √3 gives 2√3

so the answer is 2√3

hope this helps

plz mark as brainliest!!!!!!!!

Answer:

Interquartile range => 7

Third quartile => 22

Range => 13

First quartile => 15

Step-by-step explanation:

Order your data set, from the least amount to the highest amount:

$12, $14, $15, $15, $15, $15, $16, $22, $24, $25

Interquartile range (IQR) = third quartile (Q3) - first quartile (Q1)

Q1 = the middle value of the lower part of the data set, from the median to your left.

Q3 = the middle value of the upper part of the data set, from the median to your right.

The median lies between the 5th and 6th value that is enclosed in the parenthesis below:

$12, $14, ($15), $15, $15,[Median], $15, $16, ($22), $24, $25

The median divides the data set into upper and lower part.

Median = [tex] \frac{15 + 15}{2} = 15 [/tex]

First quartile: Q1 = $15

Third quartile: Q3 = $22

IQR = $22 - $15 = $7

Range = highest amount - least amount = 25 - 12 = $13

Answer: 0.07 calculatorsoup for significant rounding

10c^6d^-5×2c^-5d^4

20cd^-1

20c×1/d

20c/d

Answer:

No.

Step-by-step explanation:

Irrational numbers are numbers that you can't solve like 3 squared. See you can't find the end of 3 squared, the numbers will go on forever just like pi.

Answer:

No

Step-by-step explanation:

A rational number can be written as the ratio of integers

-4/-1 = -4

This is a rational number