HELP PLZ WILL MARK U BRAINLIEST
9x2 - 4x + 2
2x2 + 9x - 3

The derivative function for equations 1 and 2 will be

y' = -1/ [2√(1-x²)] and y' = 3/[2(1 + x²)] respectively

Here we need to find the derivative of

\(y = tan^{-1}\sqrt{\frac{1-x}{1+x} }\)

Let x = cos2z

Hence we get

\(y = tan^{-1}\sqrt{\frac{1-cos2z}{1+cos2z} }\)

\(or, y = tan^{-1}\sqrt{\frac{2sin^{2}z}{2cos^{2}z} }\)

\(or, y = tan^{-1}(tanz)\)

or, y = z

Hence dy/dx = dz/dx

We know that

x = cos2z

or, 2z = cos⁻¹x

or, 2 dz/dx = -1/√(1-x²)

Hence dy/dx = -1/ [2√(1-x²)]

The second equation is

\(y = 3tan^{-1}[x-\sqrt{1+x^{2}} ]\)

Let x = cotz

Hence we get

\(y = 3tan^{-1}[cotz-\sqrt{1+cot^{2}z} ]\)

\(y = 3tan^{-1}[cotz-\sqrt{cosec^{2}z} ]\)

or, y = 3tan⁻¹ [cotz - cosecz]

or, y = 3tan⁻¹ [cosz/sinx - 1/sinz]

or, y = 3tan⁻¹ [(cosz - 1)/sinz]

or, y = 3tan⁻¹ [-2sin²(z/2)/{2sin(z/2) cos(z/2)}]

or, y = 3tan⁻¹ [-sin(z/2)/cos(z/2)]

or, y = 3tan⁻¹ [-tan{z/2)]

or, y = 3tan⁻¹ [tan{-z/2)]

or, y = -3z/2

or, dy/dz = -3/2 dz/dx

We have

x = cotz

or, z = cot⁻¹z

or, dz/dx = -1/(1 + x²)

Hence we get

dy/dx = 3/[2(1 + x²)]

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Answer:

acute

Step-by-step explanation:

the angles are all less than 90°

they are not equal so not equialteral

has to be acute

Answer:

Exact Form:

1/256

Decimal Form:

0.00390625

Step-by-step explanation:

The solution to the equation 2(t - 5) = 48 is t = 29.

To solve the equation 2(t - 5) = 48, we can use the following steps:

Distribute the 2 to the terms inside the parentheses:

2t - 10 = 48

Add 10 to both sides of the equation to isolate the variable term:

2t = 58

Divide both sides of the equation by 2 to solve for t:

t = 29

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Answer:

logb(x y) = y ∙ logb(x)

Step-by-step explanation:

Answer:

Thus, train speed = 70 mph while wind speed is. y = 14 mph

Step-by-step explanation:

Let x = speed of the plane in mph.

Let y = speed of wind in mph.

We are told that The trip there was with the wind. It took 4 hours. The trip back was into the wind. The trip back took 6 hours.

Formula for distance is;

Distance = speed × time

Thus;

(x + y)4 = 336

(x + y) = 84 - - - - (1)

Also;

(x - y)6 = 336

Divide both sides by 6

(x - y) = 56 - - - (eq 2)

Add eq 1 and 2 to give;

2x = 84 + 56

2x = 140

x = 140/2

x = 70 mph

Plug in 70 mAh for x in eq 1.

(70 - y) = 56

y = 70 - 56

y = 14 mph

Thus, train speed = 70 mAh while wind speed is. y = 14 mph

Answer:

g(x) =1

x-1

it's either g(x) or f(x)

Answer:

negation

Step-by-step explanation:

Other options include: opposite, sign change

Answer:

2

a=-3 , b=-7 , c=2

a=quadratic term

b=linear term

c=constant term

Answer:

y = x² + 11x + 24

Step-by-step explanation:

y = (x + 3)(x + 8)

Expand

y = x² + 8x + 3x + 24

Combine like terms

y = x² + 11x + 24

The value of the car in 2000 is expected to be $3800, given a starting value of $7700 in 1990 and a decrease of $390 per year for 10 years.

To find the value of the car in each subsequent year, we can subtract $390 from the previous year's value. Let's calculate the value of the car for each year from 1990 to 2000.

Year 1990: $7700

Year 1991: $7700 - $390 = $7310

Year 1992: $7310 - $390 = $6920

Year 1993: $6920 - $390 = $6530

Year 1994: $6530 - $390 = $6140

Year 1995: $6140 - $390 = $5750

Year 1996: $5750 - $390 = $5360

Year 1997: $5360 - $390 = $4970

Year 1998: $4970 - $390 = $4580

Year 1999: $4580 - $390 = $4190

Year 2000: $4190 - $390 = $3800

Therefore, the value of the car is expected to be $3800 in the year 2000.

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Answer: y = 5x + 26

Step-by-step explanation:

To find the equation of a line that is perpendicular to the given line y = -1/5x + 1 and passes through the point (-5, 1), we need to determine the slope of the perpendicular line. The given line has a slope of -1/5. Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of -1/5, which is 5/1 or simply 5. Now, we have the slope (m = 5) and a point (-5, 1) that the perpendicular line passes through.

We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Substituting the values, we get:

y - 1 = 5(x - (-5))

Simplifying further:

y - 1 = 5(x + 5)

Expanding the brackets:

y - 1 = 5x + 25

Rearranging the equation to the slope-intercept form (y = mx + b):

y = 5x + 26

Therefore, the equation of the perpendicular line that passes through the point (-5, 1) is y = 5x + 26.

Answer:

See Explanation

Step-by-step explanation:

The expression and the dimension of the prism are not given.

So, I will just give a general expression.

The volume of a prism is:

\(Volume = Length * Width * Height\)

Assume that:

\(Length = 2\)

\(Width = 2\)

\(Height = 1\frac{2}{3}\)

See attachment

Monica's expression should be:

\(Volume = 2 * 2 * 1\frac{2}{3}\)

And the solution will be:

\(Volume = 2 * 2 * \frac{5}{3}\)

\(Volume = \frac{20}{3}\)

Answer:

b and c

Step-by-step explanation:

i took the test <3

Answer:

63°

Step-by-step explanation:

Triangle= 180°

=180°-90°-27°

=90°-27°

=63°

Answer:

63°

Step-by-step explanation:

90° + 27°= 117°

180°- 117°= 63°

Answer:

String

2.

4

6

Percussion

5

10

15

Step-by-step explanation:

Answer:

noo

because we know that (x,y) is the situation

nd the solution in yr question here y is( -)

hope it helps

Answer:

no

Step-by-step explanation:

( x, y ) = ( 4, - 4 )

Here,

x = 4

y = - 4

y ≠ - x

Answer: The 2nd and 3rd one are correct

Step-by-step explanation:

After reflecting it, the square itself would not change, only the position of the square. Therefore, the same line segments from the beginning which were given would be parallel.

False, True, True.

PQ and PS cannot be parallel, because there is two P's in the first one.

Answer:

20 : 50

Step-by-step explanation:

sum the parts of the ratio , 2 + 5 = 7 parts

divide 70 by 7 to find the value of one part of the ratio

70 ÷ 7 = 10 ← value of 1 part of the ratio , then

2 parts = 2 × 10 = 20

5 parts = 5 × 10 = 50

then

50 divided in the ratio 2 : 5 is 20 : 50

Answer:

use the line segment instead

The probability that five cars will arrive during the next thirty minute interval is 0.0361

What is probability?

Probability is a way of calculating how likely something is to happen. Numerous things are difficult to forecast with absolute confidence.

Main Body:

Let X = number of cars arriving at Sami Schmitt's Scrub and Shine Car Wash.

The average number of cars arriving in 15 minutes is 6.

The average number of cars arriving in 1 minute is = 6/15 = 2/5

The average number of cars arriving in 5 minutes is, (2/5)*5 = 2

The random variable X follows a Poisson distribution with parameter λ = 2.

The probability mass function of X is:

P(X=\(x\)) = \((e^{-2} 2^{x} )/x!\)  , x = 0,1 ,2 ,3...

Compute the probability that 5 cars will arrive in 5 minutes as follows:

P(X=5) =\((e^{-2} 2^{5} )/5!\)

P (X= 5) = 0.0361

Hence probability is 0.0361

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Answer:

because they mirror eachother, they both have two acute angles and an obtuse angle. they are both obtuse triangles

Answer:

b, sas

Step-by-step explanation:

i don't understand this one very well, but i believe it to be b, side-angle-side.

Therefore, The differential of the function z = e−9x cos(6t) with respect to both x and t is given by dz = (∂z/∂x)dx + (∂z/∂t)dt.

The differential of the function z = e−9x cos(6t) with respect to both x and t is given by dz = (∂z/∂x)dx + (∂z/∂t)dt.
Using the chain rule, we find that ∂z/∂x = -9e^(-9x)cos(6t) and ∂z/∂t = -6e^(-9x)sin(6t).
Substituting these values, we get dz = (-9e^(-9x)cos(6t)dx) + (-6e^(-9x)sin(6t)dt).
The differential of a function is a measure of the sensitivity of the function to small changes in its inputs. In this case, we are asked to find the differential of the function z = e^-9x cos(6t) with respect to both x and t. To do this, we use the chain rule to find the partial derivatives of z with respect to x and t, and then substitute them into the formula for the total differential. The resulting differential dz represents the change in z due to small changes in both x and t.

Therefore, The differential of the function z = e−9x cos(6t) with respect to both x and t is given by dz = (∂z/∂x)dx + (∂z/∂t)dt.

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The conditional expected number of heads in the 10 flips, given that exactly two of the first three flips landed heads, can be calculated by taking the weighted average of the expected number of heads for each coin. Using the probabilities of choosing each coin and the conditional probabilities of obtaining two heads in three flips for each coin, the conditional expected number of heads can be determined.

To solve this problem, we need to use conditional probability and expected value concepts. Let's denote the event of choosing the 0.4 probability coin as A and the event of choosing the 0.7 probability coin as B. We need to calculate the conditional expected number of heads in the 10 flips given that exactly two of the first three flips landed heads.

First, we calculate the probability of choosing each coin. Since there are two coins in the box and they are equally likely to be chosen, the probability of choosing each coin is 0.5.

Next, we calculate the conditional probability of obtaining exactly two heads in the first three flips given that coin A is chosen. The probability of getting exactly two heads in three flips with a 0.4 probability coin is given by the binomial distribution formula: P(2 heads in 3 flips | A) = (3 choose 2) * (0.4)² * (1 - 0.4).

Similarly, we calculate the conditional probability of obtaining exactly two heads in the first three flips given that coin B is chosen. The probability of getting exactly two heads in three flips with a 0.7 probability coin is:

P(2 heads in 3 flips | B) = (3 choose 2) * (0.7)² * (1 - 0.7).

Using these probabilities, we can calculate the conditional expected number of heads in the 10 flips by taking the weighted average of the expected number of heads for each coin. The conditional expected number of heads in the 10 flips is given by: (0.5 * P(2 heads in 3 flips | A) * 10) + (0.5 * P(2 heads in 3 flips | B) * 10).

By substituting the calculated values into this formula, we can find the conditional expected number of heads in the 10 flips given that exactly two of the first three flips landed heads.

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The solution to the given system of equations, with the given values of E, L, R, C, 17(0), and 12(0), is i(t) = (E/R) + A exp(-(R/L)t)sin(ωt), and v(t) = Ecos(ωt) - (Li(t))/R - (Q(0)/C)exp(-(1/RC)t), where A = -((E/R) + 11(0)) and ω = sqrt(1/(LC) - (R/(2L))^2).

Using Kirchhoff's laws, we can derive the following system of equations:

dii L + Ri2 = E(t) ...(1)

diz RC + 12 - 11 = 0 ...(2)

dt 11(t) iz(t)

Substituting the given values of E, L, R, and C, we get:

dii 2 + 100i2 = 60 ...(3)

diz 10-4 + 12 - 11 = 0 ...(4)

dt 11(t) iz(t)

We can solve equation (3) by first finding the general solution to the homogeneous equation (i.e., the equation without the right-hand side):

dii 2 + 100i2 = 0

The characteristic equation is λ^2 + 100 = 0, which has roots ±10i. Therefore, the general solution to the homogeneous equation is:

i(t) = A exp(-(R/L)t)sin(ωt)

where A is a constant and ω = sqrt(1/(LC) - (R/(2L))^2).

To find the particular solution to equation (3), we can use the method of undetermined coefficients. We assume that the particular solution has the form i(t) = (E/R) + B, where B is a constant. Substituting this into equation (3), we get:

dB/dt = 0

Integrating both sides, we get B = (E/R) + 11(0).

Therefore, the general solution to equation (1) is:

i(t) = (E/R) + A exp(-(R/L)t)sin(ωt) - (E/R) - 11(0)

i(t) = A exp(-(R/L)t)sin(ωt) - 11(0)

To solve equation (2), we first rearrange it as:

diz/dt = -(1/RC)iz(t) - 12/RC

This is a first-order linear homogeneous differential equation, which has the general solution:

iz(t) = Q(0)exp(-(1/RC)t)

where Q(0) is the initial charge on the capacitor.

Finally, we can find the voltage across the capacitor using Ohm's law:

v(t) = E - Li(t) - iz(t)/C

Substituting the values of i(t) and iz(t), we get:

v(t) = Ecos(ωt) - (Li(t))/R - (Q(0)/C)exp(-(1/RC)t)

Therefore, the solution to the given system of equations, with the given values of E, L, R, C, 17(0), and 12(0), is i(t) = (E/R) + A exp(-(R/L)t)sin(ωt), and v(t) = Ecos(ωt) - (Li(t))/R - (Q(0)/C)exp(-(1/RC)t), where A = -((E/R) +

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1/7 of the animals in the zoo are male monkeys.

To find the fraction of animals in the zoo that are male monkeys, we have to calculate the product of the fractions representing the proportion of monkeys and the proportion of male monkeys among them.

Given that 1/5 of the animals in the zoo are monkeys, we will then represent this as:

= 1/5

= 5/25.

And 5/7 of the monkeys are male which is written as 5/7.

To get fraction of male monkeys, we will multiply these two fractions:

= (5/25) * (5/7)

= 25/175

= 1/7.

Full question:

1/5 of the animals in the zoo are monkeys 5/7 of the monkeys are male. What fraction of the animals in the zoo are male monkeys?

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The coordinate of the vertex is; (h, k) = (3, -5)

The final equation of the parabola is; y = 5(x - 3)² - 5

The vertex is the coordinate of the crest or trough of the curve. Now, in the given graph, we only have a Trough which is the lowest point of the graph.

The coordinate of the vertex is; (h, k) = (3, -5)

2) Since the general equation is;

y = a(x - h)² + k

We will have;

y = a(x - 3)² - 5

At x = 2, y = 0. Thus;

0 = a(2 - 3)² - 5

a - 5 = 0

a = 5

3) The final equation of the parabola is;

y = 5(x - 3)² - 5

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The partial derivatives of \(fx\)= x / (√(x² + y²)) , \(fy\) = y / (√(x² + y²)),

\(fx(4, 1)\)= 4 / (√17) and \(fy(-1, -3)\) =  -3 / (√10).

Let's calculate the partial derivatives of \(f(x, y)\) = √(√(x² + y²)).

To find \(fx\), we differentiate \(f(x, y)\) with respect to x while treating y as a constant. Using the chain rule, we have:

\(fx\) = (∂f/∂x) = (∂/∂x) √(√(x² + y²)).

Using the chain rule, we obtain:

\(fx\) = (∂/∂x) (√(x² + y²))^(1/2).

Applying the power rule, we have:

\(fx\) = (1/2) (√(x² + y²))^(-1/2) (2x).

Simplifying further, we get:

\(fx\) = x / (√(x² + y²)).

Next, let's calculate \(fy\) by differentiating \(f(x, y)\) with respect to y while treating x as a constant.

Using the chain rule, we have:

\(fy\) = (∂f/∂y) = (∂/∂y) √(√(x² + y²)).

Using the chain rule and the power rule, we obtain:

\(fy\) = (1/2) (√(x² + y²))^(-1/2) (2y).

Simplifying, we get:

\(fy\) = y / (√(x² + y²)).

To evaluate \(fx(4, 1)\), we substitute x = 4 into the expression for \(fx\):

\(fx(4, 1)\) = 4 / (√(4² + 1²)) = 4 / (√17).

To evaluate \(fx(4, 1)\) we substitute y = -3 into the expression for \(fy\):

\(fy(-1, -3)\)= -3 / (√((-1)² + (-3)²)) = -3 / (√10).

Therefore, the exact values are \(fx(4, 1)\)= 4 / (√17) and \(fy(-1, -3)\)= -3 / (√10).

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Answer:

couch

Step-by-step explanation: