Let a function f (x) = x² + 1
Find f (4):​

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:

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:

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: 0.07 calculatorsoup for significant rounding

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:

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:  $6,144

Step-by-step explanation:

In March her commission was;

= 3% * 20,000 + 8% ( 54,500 - 20,000)

= $3,360

In April;

= 3% * 20,000 + 8% ( 47,300 - 20,000)

= $2,784‬

Total commission

= 3,360 + 2,784

= $6,144

Answer:

[tex]\alpha = 35º[/tex]

Step-by-step explanation:

Primeiro, vamos dizer que essa folha tem extremidades nos pontos [tex]A, B, C, D[/tex].

E vamos chamar os vértices do triângulo que contém o ângulo [tex]\alpha[/tex] de [tex]E, F, G[/tex].

Na semireta de baixo, formada por [tex]DC[/tex], a gente tem um ângulo de [tex]70º[/tex] e um outro ângulo de [tex]90º[/tex] (porque ele indica um ângulo reto).

Vamos dizer que estes dois ângulos se encontram no ponto [tex]E[/tex], que combinamos antes, como vértice (extremidade) do triângulo de cima.

Como os dois ângulos, estão num mesmo ponto, [tex]E[/tex], podemos dizer que existe um terceiro ângulo para o qual sua soma seja [tex]180º[/tex]. E tem, seria o ângulo à esquerda de

Vamos chamar este ângulo de [tex]\beta _{I}[/tex]. Portanto:

[tex]\beta _{I} + 90º + 70º = 180º\\\beta _{I} = 180º - 160º\\\beta _{I} = 20º[/tex]

Agora, temos um outro triângulo no canto inferior esquerdo da folha, cujos ângulos são [tex]\beta x_{I}[/tex], [tex]90º[/tex] e um outro ângulo, que vamos chamar de [tex]\beta x_{II}[/tex]

Esse último vai ser o ângulo superior deste triângulo, tá legal?

Então, vamos ter que:

[tex]\beta _{I} + 90º + \beta _{II} = 180º\\\beta _{I} + \beta _{II} = 90º\\[/tex]

Como [tex]\beta _{I} = 20º[/tex],

[tex]\beta _{I} + \beta _{II} =20º + \beta _{II}[/tex]

[tex]20º + \beta _{II} = 90º\\\beta _{II} = 90º - 20º\\\beta _{II} = 70º[/tex]

Ou seja, o ângulo superior do triângulo no canto inferior esquerdo, é 70º.

Vamos concordar, que este mesmo triângulo tem vértices nos pontos [tex]F, D, E[/tex]. Onde [tex]F[/tex] é o ponto superior, [tex]D[/tex] é a extremidade inferior esquerda do retângulo e [tex]E[/tex] é aquele mesmo ponto em que se encontram os ângulos de [tex]90º[/tex]e [tex]70º[/tex].

Mais à frente, você vai entender o porquê é importante nomear estes pontos, eu fiquei 40 minutos tentando fazer essa questão sem fazer isso e  não conseguia porque empacava numa parte da resolução.

Então, agora, sabemos que o ângulo [tex]\beta _{II}[/tex], que é o encontro dos seguimentos [tex]FD[/tex] e [tex]EF[/tex] vale [tex]70º[/tex].

Até aqui, foi só aplicar propriedades. Mas, a partir desse ponto, você vai precisar usar a criatividade.

Então, você entende que o ângulo [tex]\beta _{II}[/tex] está inserido numa reta com outros dois ângulos concentrados no ponto [tex]F[/tex].

Então, pode dizer que esse ângulo externo é o suplemento de [tex]\beta _{II}[/tex].

Vamos chamar todo ele de [tex]\beta _{III}[/tex]

[tex]\beta _{II} + \beta _{III} = 180º\\70º + \beta _{III} = 180º\\\beta _{III} = 180º - 70º\\\beta _{III} = 110º[/tex]

Agora, vamos elevar o nível de criatividade no raciocínio e ver também que temos um quadrilátero formado pelos pontos [tex]A, G, F, E[/tex]

A soma dos ângulos de qualquer quadrilátero é 360º.

E temos que esse mesmo quadrilátero é formado por dois ângulos retos, além do ângulo de 110º que calculamos.

A última extremidade que falta é um ângulo formado pela soma de [tex]\alpha[/tex] a um outro ângulo, que vamos chamar de [tex]\beta _{IV}[/tex].

Então, temos que:

[tex]90º + 110º + 90º + \alpha + \beta _{IV} = 360º\\\alpha + \beta _{IV} +290º = 360º\\\alpha + \beta _{IV} = 360º + 290º\\\alpha + \beta _{IV} = 70º\\[/tex]

De todas, as etapas dessa resolução essa é a mais importante de entendermos os pontos que definimos. Eu refiz ela várias vezes porque não fiz isso antes.

Mas, veja, quando a gente dobra a folha, pegamos um formato qualquer e destacamos do resto dela.

Isso quer dizer que o formato que ficou dobrado é o mesmo que falta na folha. Do contrário, estaríamos criando folha ou excluindo matéria, o que não é possível no caso de uma simples dobra.

Em outras palavras, os triângulos [tex]AGF[/tex] e [tex]EFG[/tex] são os mesmos. (Eu recomendo que você construa esse desenho e coloque as letras em cada ponto, pra visualizar melhor.)

Isso é o mesmo que dizer que os ângulos de um vão ser os ângulos do outro.

Portanto, os ângulos são equivalentes. (Mesmos ângulos para ambos os triângulos, mudando só de posição.)

Assim, você pode afirmar que [tex]\alpha[/tex] = [tex]\beta _{IV}[/tex]

Se subirmos um pouco a resolução, vamos lembrar que encontramos que [tex]\alpha + \beta _{IV} = 70º\\[/tex]

Se [tex]\alpha = \beta _{IV}[/tex]

Temos:

[tex]\alpha + \alpha = 70º\\2\alpha = 70º\\\alpha = \frac{70º}{2} \\[/tex]

e TCHARAAN!

[tex]\alpha = 35º[/tex]

-------------------------

Força, guerreiro(a). Sucesso e que Deus te abençoe nos estudos.

10c^6d^-5×2c^-5d^4

20cd^-1

20c×1/d

20c/d

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:

$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:

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:

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:

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:

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: 4:3

eats out : not eating out

Step-by-step explanation:

so theres 7 days in a week so you do simple subtraction and do 7-4=3

then you get the remaining days of the week that you dont eat out.

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: First solve the parentheses using order of operations. Then add and subtract from left to right.

Demo:

(3 * 11) = 33

Equation now looks like:

63 - 21 + 33

63 - 21 = 42

Equation now looks like:

42 + 33

42 + 33 = 75

The value of this expression is 75.

Answer:

Step-by-step explanation:

Answer:

Rational

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

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

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

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.

Answer:

91

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

91/7 = 13

Answer:

2972.5

Step-by-step explanation:

3500*7/8 - 90 = 2972.5

Answer:

-3x - 6 - 1

- 3x + 7

4x

Step-by-step explanation:

Answer:

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

Answer:

Graph the two struts on the model of the roller coaster. Take a screenshot of your graph and paste the image below, or sketch a graph by hand. (5 points)

Recall that a reinforcement beam will extend from one strut to the other when the two struts are 2 feet apart.

•

• Algebraically determine the x -value of where the beam should be placed. (15 points)

root(x + 8) = 2 + rootx − 4)

x + 8 = 4 + 4root(x − 4) + x − 4

8 = 4root(x − 4)

2 = root(x − 4)

x − 4 = 4

x = 8

• Explain where to place the beam.  (10 points)

The beam should be places 8 feet apart.

Step-by-step explanation:

I don't have a graph. Correct on E2020

Hope that this helps. If someone finds a graph i have a question on my page that needs it

Peace and love

Answer:

Here is the missing graph.

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: 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: