Need some help with these 2 math questions, They are related so best to finish one then work on the bisect. Thank you.

a. Parameterize C₁ by

[tex](x(t),y(t)) = (1-t)(-13,-7) + t(0,6) = (-13+13t,-7+13t)[/tex]

with 0 ≤ t ≤ 1. Then both dx = 13 dt and dy = 13 dt, so that the line integral along C₁ is

[tex]\displaystyle \int_C y^2\,dx + x\,dy = \int_0^1 (-7+13t)^2(13\, dt) + (-13+13t)(13\,dt)[/tex]

[tex]\displaystyle \int_C y^2\,dx + x\,dy = 13 \int_0^1 (169t^2 - 169t + 36) \, dt[/tex]

[tex]\displaystyle \int_C y^2\,dx + x\,dy = 13 \left(\frac{169}3-\frac{169}2+36\right) = \boxed{\frac{611}6}[/tex]

b. Parameterize C₂ by

[tex](x(t),y(t)) = (36-t^2,t)[/tex]

with -7 ≤ t ≤ 6. Then dx = -2t dt and dy = dt, so the line integral is

[tex]\displaystyle \int_C y^2\,dx + x\,dy = \int_{-7}^6 t^2(-2t\,dt) + (36-t^2)\,dt[/tex]

[tex]\displaystyle \int_C y^2\,dx + x\,dy = \int_{-7}^6 (36-t^2-2t^3) \, dt[/tex]

[tex]\displaystyle \int_C y^2\,dx + x\,dy = \left(36\cdot6-\frac{6^3}3-\frac{6^4}2\right) - \left(36\cdot(-7)-\frac{(-7)^3}3-\frac{(-7)^4}2\right) = \boxed{\frac{5005}6}[/tex]

Answer:

[tex]\huge\boxed{z=6;\ x=12.5}[/tex]

Step-by-step explanation:

If two figures are similar, then corresponding sides are in proportion.

Therefore:

[tex]\dfrac{z}{15}=\dfrac{4}{10}\qquad|\text{cross multiply}\\\\10z=(15)(4)\\\\10z=60\qquad|\text{divide both sides by 10}\\\\\boxed{z=6}[/tex]

[tex]\dfrac{x}{5}=\dfrac{10}{4}\qquad|\text{cross multiply}\\\\4x=(5)(10)\\\\4x=50\qquad|\text{divide both sides by 4}\\\\x=\dfrac{50}{4}\\\\\boxed{x=12.5}[/tex]

Answer:

250 girls

Step-by-step explanation:

Add the ratio together (2+5=7), then do 350÷7=50

50 is one part of the ratio so to find how many girls, you would do 50x5=250

Answer:

In point-slope form the equation is:

[tex]y - 2 = \binom{1}{3} \times (x - 1)[/tex]

El carro de mercancía experimenta una aceleración neta de 0.333 metros por segundo al cuadrado al soltarse.

En esta situación se requiere una fuerza de 30 N para alcanzar la fuerza estática máxima ([tex]f_{s}[/tex]), entonces la fuerza de fricción ([tex]f_{k}[/tex]) se reduce a 20 N mientras se encuentre en movimiento. Si consideramos que la fuerza externa de 30 N se mantiene durante el fenómeno físico, entonces tenemos que la aceleración neta ([tex]a[/tex]), en metros por segundo al cuadrado, experimentada por el carrito de mercancía es determinada a partir de las leyes de Newton:

[tex]a = \frac{F-f_{k}}{m}[/tex] (1)

Donde [tex]m[/tex] es la masa del carrito de mercancía, en kilogramos.

Si sabemos que [tex]F = 30\,N[/tex], [tex]f_{k} = 20\,N[/tex] and [tex]m = 30\,kg[/tex], entonces la aceleración neta del carro de mercancías es:

[tex]a = \frac{30\,N-20\,N}{30\,kg}[/tex]

[tex]a = 0.333\,\frac{m}{s^{2}}[/tex]

El carro de mercancía experimenta una aceleración neta de 0.333 metros por segundo al cuadrado al soltarse.

Invitamos a consultar esta pregunta sobre la fricción seca: https://brainly.com/question/19115001

Answer:

The trick for these is finding out what makes the largest known value into the corresponding lower value. Then we use that number to find the missing side length based on the value we know.

1. The missing side length is 40.

We can find this by dividing 70 by 56 to get 1.25. We then multiply this by 32 to get our missing side length.

2. The missing side length is 91.

We can find this by dividing 130 by 30 to get 4.333(repeating decimal). We then multiply this by our known value (21) to get our answer of 91.

3. The missing side length is 21.

We can fid this by dividing 36 by 12 to get 3. Then we multiply this by 7 (our known value) to get our answer.

Step-by-step explanation:

hope this helps. . .<3

good luck!       UwU

Answer:

remainder = 21

Step-by-step explanation:

If f(x) is divided by (x - h) then the remainder is f(h)

Here f(x) is divided by (x - 2) with h = 2 , then remainder is

f(2) = 4(2) + 3(2)² + 1 = 8 + 3(4) + 1 = 8 + 12 + 1 = 21

Answer & Step-by-step explanation:

A = 60 ft

C = 12

D = 1/2 of C

1/2 of 12 = 6

Part A:

e = 6ft

Part B:

It's positive because it is above sea level

Answer:

Step-by-step explanation:

gg I got the points

Answer:

24.0

Step-by-step explanation:

do 34sin(45) to solve for x

Answer:

2/3

Step-by-step explanation:

-5/3 + 2 1/3 =

= 2 1/3 - 5/3

= 2 1/3 - 1 2/3

= 1 4/3 - 1 2/3

= 2/3

Answer:

2/3

Step-by-step explanation:

First, change 2 1/3 into an improper fraction.

2 1/3 --> 7/3

Substitute that value back into the equation

-5/3 + 7/3

At this point, you can rewrite the equation into:

7/3 - 5/3

Since they have the same denominator, just subtract the numerator's values.

2/3

Answer:

8000

Step-by-step explanation:

anwers: is 15 because I did 30 percent of 50

Answer:

B

Step-by-step explanation:

HOPE IT HELPS <3

MARK as brainliest

Answer:

Expression: -7 + 8f - 2b - f + 3b + 6

# of Terms: 6

Like Terms: 8f and f, -2b and 3b, and -7 and 6

Coefficients: 8, 1, -2, and 3

Constants: -7 and 6

Expression: -11x + 4 + 8x - 4 + 3x

# of Terms: 5

Like Terms: -11x, 8x, and 3x & 4 and -4

Coefficients: -11, 8, and 3

Constants: 4 and -4

Step-by-step explanation:

The coefficient is the number in front of the variable.

The variable is any letter that you may see in an expression.

Terms are the numbers and variables, that are separated by the different signs.

Like terms are the terms that share the same variable/exponent.

Constants are the terms without variables.

Hope this helps you :)

Sorry if it's somehow wrong.

Take the first partial derivatives of f(x, y):

∂f/∂x = -2 (x - 5) = 10 - 2x

∂f/∂y = -2y

The critical points occur where both derivatives are zero:

10 - 2x = 0   ===>   x = 5

-2y = 0   ===>   y = 0

So there is only critical point at (5, 0), which takes on a value of f(5, 0) = 25.

Compute the Hessian matrix for f :

[tex]H(x, y) = \begin{bmatrix}\frac{\partial^2f}{\partial x^2} & \frac{\partial^2f}{\partial x\partial y} \\ \frac{\partial^2f}{\partial y\partial x} & \frac{\partial^2f}{\partial y^2}\end{bmatrix} = \begin{bmatrix}-2&0\\0&-2\end{bmatrix}[/tex]

Since det(H(x, y)) = 4 > 0 for all x, y, the critical point (5, 0) is a relative minimum.

f has no saddle points.

Answer:

Half-Life uses the formula N () = Noe # No = Initial Amount time h = length of half-life. Ifyou start with 65 milligrams of Chromium 51,used to track red blood cells, which has half-life of 27.7 days: How long will it take for 80% ofthe material to decay? t= (27.7) h5 (65) (h3) 4= (27.7) h; (05)

Step-by-step explanation:

For the given data it will take 8.69 days for 80% of the material to decay.

A radioactive substance's half-life is typically described as the amount of time it takes for one-half of its atoms to disintegrate or change into another substance.

It is given that, If you start with 65 milligrams of Chromium 51, used to track red blood cells, which has a half-life of 27.7 days.

N₀ = 65 milligrams

t1/2=27.7 days

N(t)=0.8(65 milligrams)=52 milligrams

[tex]N(t) = N_0(1/2)^ {\frac{t}{t_{1/2}} }[/tex]

Here,

N(t) is the amount of the substance remaining

N₀ is the initial substance amount

t is the time elapsed

t1/2 is the half-life

Substitute the given values,

[tex]N(t) = N_0(1/2)^ {\frac{t}{t_{1/2}} } \\\\ 52 = 65(1/2)^\frac{t}{27.7} \\\\ 52=65\left(\frac{1}{2}\right)^{\frac{t}{27.7}} \\\\ \frac{65\left(\frac{1}{2}\right)^{\frac{t}{27.7}}}{65}=\frac{52}{65} \\\\ \left(\frac{1}{2}\right)^{\frac{t}{27.7}}=\frac{4}{5} \\\\ \frac{t}{27.7}\ln \left(\frac{1}{2}\right)=\ln \left(\frac{4}{5}\right) \\\\ t =-\frac{27.7\ln \left(\frac{4}{5}\right)}{\ln \left(2\right)}[/tex]

[tex]t = 8.69 \ days[/tex]

Thus, for the given data it will take 8.69 days for 80% of the material to decay.

Learn more about half-life here,

https://brainly.com/question/24710827

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Step-by-step explanation:

-9x + 1 = -x + 17

collect like terms

-9x + x = 17-1

-8x = 16

divide both sides by -8

-8x/-8 = 16/8

x = 2

Using the multiplication operation, the population of the species in 30 years would be 8 times the current population. Hence, the population at the time would be [tex] 5.44 \times 10^{10}[/tex]

Therefore, 8 times the current population can be calculated thus :

[tex] 6.8 \times 10^{9} \times (8) = 54.4 \times 10^{9}[/tex]

Therefore, the population at the time would be [tex] 5.44 \times 10^{10}[/tex]

Learn more : https://brainly.com/question/25411212

Hello!

0.85b-0.2b

0.65b

0.65b=0.65b

So these expressions are equivalent.

Hope it helps!

~Just a determined gal

#CarryOnLearning

[tex]MysteriousNature[/tex]

Answer:

$30 on CDs

$20 on Makeup

hope it helps

Step-by-step explanation:

The money spent on each product is $20 and $30 respectively.

A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.

Given that,

The money spent by Lauren on make up and CDs is $50.

Suppose the money spent on CDs be x.

Then, the money spent on make up is  x + 10.

As per the question the following equation can be formed,

x + x + 10 = 50

=> 2x + 10 = 50

=> 2x = 40

=> x = 20

Thus, money spent on make up is 20 + 10 = 30 dollars.

Hence, the money spent on CDs and make up is $20 and $30 respectively.

To know more about linear equation click on,

https://brainly.com/question/11897796

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Answer:

Step-by-step explanation:

14 out of 70 given as percentage:

Lets see

cyclist a speed is d = v × t

so you can find velocity of a and b.

then compare them both.

Answer:

no

Step-by-step explanation:

the ratios shown in this table are not proportionate. You will also never get (0,0) in this table.

Enter a problem...

Calculus Examples

Popular Problems Calculus Find the Domain and Range f(x)=5x-3

f

(

x

)

=

5

x

−

3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

(

−

∞

,

∞

)

Set-Builder Notation:

{

x

|

x

∈

R

}

The range is the set of all valid

y

values. Use the graph to find the range.

Interval Notation:

(

−

∞

,

∞

)

Set-Builder Notation:

{

y

|

y

∈

R

}

Determine the domain and range.

Domain:

(

−

∞

,

∞

)

,

{

x

|

x

∈

R

}

Range:

(

−

∞

,

∞

)

,

{

y

|

y

∈

R

}

Answer:

32.5

Step-by-step explanation:

order the numbers) 30, 31, 32, 32, 33, 34, 36, 37

cancel the numbers from each side to the middle) 32 and 33

add the values together and divide by two) [32+33] divide by 2=65/2=32.5

Answer:

7/100

Step-by-step explanation:

:)

Applying the percentages, and considering that 70% of the first group drinks at least 2 glasses of water a day, it is found that 0.725 = 72.5% of the team drinks at least 2 glasses of water a day.

The team is divided into two equal groups, hence, each represents 50%.

The percentages associated with drinking at least 2 glasses of water a day is:

Hence, applying the weighed percentage, the total percentage is:

[tex]T = 0.7(0.5) + 0.75(0.5) = 0.725[/tex]

0.725 = 72.5% of the team drinks at least 2 glasses of water a day.

A similar problem is given at https://brainly.com/question/1517088

Answer: 48

Step-by-step explanation:

l = w + 7

2w + 2l = 178

2w + 2(w + 7) = 178

2w + 2w + 14 = 178

4w = 164

w = 41

l = w + 7

l = 41 + 7

l = 48