Geometry Help Please!!

\(R_2\)  is 3 ohms

In a circuit containing two resistors \(R_1\) and \(R_2\) connected together in parallel, the total resistance \(R_T\) is given by;

\(\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2}\)              ---------(i)

Make \(R_2\) subject of the formula;

=> \(\frac{1}{R_2} = \frac{1}{R_T} - \frac{1}{R_1}\)  

=> \(\frac{1}{R_2} = \frac{R_1 - R_T}{R_TR_1}\)

=>   \({R_2} = \frac{R_TR_1}{R_1 - R_T}\)       ---------------(ii)

From the question,

\(R_1\) = 6Ω

\(R_T\) = 2Ω

Substitute these values into equation (ii) as follows;

=> \({R_2} = \frac{2*6}{6 - 2}\)

\({R_2} = \frac{12}{4}\)

\(R_2\) = 3Ω

Therefore, the value of \(R_2\) = 3 ohms or \(R_2\) = 3Ω

Answer: is 3 ohms.

Explanation: edmentum/plato :)

Answer:

C

Step-by-step explanation:

To prove that two triangles are congruent using the SSS Congruence criterion, we must establish that all three sides of one triangle are equal to all the corresponding sides of the other.

Thus,

Side AD in ∆ADB is congruent to side AD in ∆ADC.

Side BD in ∆ADB is congruent to side CD in ∆ADC.

Side AB in ∆ADB is congruent to side AC in ∆ADC.

Therefore, based on the SSS congruence criterion, it is concluded that both triangles are congruent.

The statements necessary to prove that they are congruent by SSS is:

C.

If the random variable z has a standard normal distribution, then we can use a standard normal distribution table or a calculator to find the probability of a range of values for z. In this case, we want to find the probability that z falls between 1.17 and 2.26.

Using a standard normal distribution table, we can look up the probabilities for each of these values individually:

- The probability that z is less than or equal to 1.17 is 0.8790.
- The probability that z is less than or equal to 2.26 is 0.9886.

To find the probability that z falls between these two values, we can subtract the probability of the lower value from the probability of the higher value:

- P(1.17 ≤ z ≤ 2.26) = P(z ≤ 2.26) - P(z ≤ 1.17)
- P(1.17 ≤ z ≤ 2.26) = 0.9886 - 0.8790
- P(1.17 ≤ z ≤ 2.26) = 0.1096

Therefore, the probability that z falls between 1.17 and 2.26 is 0.1096, or approximately 11%.

Know more about standard normal distribution, here:

https://brainly.com/app/ask?q=32096479

#SPJ11

Answer: 38 students

Step-by-step explanation:

     To answer this question we will find 95% of 40. Keep in mind that a percent divided by 100 becomes a decimal.

95% / 100 = 0.95

0.95 * 40 = 38

         38 students passed their test.

The general solution for the given differential equation is the sum of the complementary function and the particular solution:

\(y = y_h + y_p\\\\= C_1e^{6x} + C_2e^{-6x} + (-1/70)e^{3x} + (-1/70)e^{-3x}\)

where C₁ and C₂ are arbitrary constants determined by the initial or boundary conditions of the problem.

We are given the differential equation: d²y/dx - 36y = cosh(3x).

In this case, the homogeneous equation is d²y/dx - 36y = 0.

The characteristic equation associated with the homogeneous equation is obtained by replacing the derivatives with their corresponding algebraic expressions. In our case, we have r² - 36 = 0. Solving this quadratic equation, we find the roots to be r = ±6.

Since the roots are distinct and real, the general solution for the homogeneous equation is given by:

\(y_h = C_1e^{6x} + C_2e^{-6x}\)

where C₁ and C₂ are arbitrary constants determined by the initial or boundary conditions of the problem.

The term cosh(3x) can be written as a linear combination of exponential functions using the identities:

\(cosh(ax) = (e^{ax} + e^{-ax})/2, \\\\sinh(ax) = (e^{ax} - e^{-ax})/2.\)

Therefore, \(cosh(3x) = (e^{3x} + e^{-3x})/2.\)

Now, we assume the particular solution has the form:

\(y_p = A_1e^{3x} + A_2e^{-3x}\)

where A₁ and A₂ are undetermined coefficients.

Substituting these derivatives into the original differential equation, we get:

\((9A_1e^{3x} + 9A_2e^{-3x}) - 36(A_1e^{3x} + A_2e^{-3x}) = (e^{3x} + e^{-3x})/2.\)

To satisfy this equation, the coefficients of the exponential terms on both sides must be equal. Therefore, we have the following system of equations:

9A₁ - 36A₁ = 1/2,

9A₂ - 36A₂ = 1/2.

Solving these equations, we find A₁ = -1/70 and A₂ = -1/70.

Thus, the particular solution is:

\(y_p = (-1/70)e^{3x} + (-1/70)e^{-3x}\)

Finally, the general solution for the given differential equation is the sum of the complementary function and the particular solution:

\(y = y_h + y_p\\\\= C_1e^{6x} + C_2e^{-6x} + (-1/70)e^{3x} + (-1/70)e^{-3x}\)

where C₁ and C₂ are arbitrary constants determined by the initial or boundary conditions of the problem.

To know more about differential equation here

https://brainly.com/question/30074964

#SPJ4

Answer:

\(2³ + 3²-3 \times 4 - 5² ÷ 5 + (7 \times 4) = 28\)

Answer:

Everybody's laughing in my mind

Rumors spreading 'bout this other guy

Do you do what you did when you did with me

Does he love you the way I can

Did you forget all the plans that you made with me?

'Cause baby I didn't

That should be me, holding your hand

That should be me, making you laugh

That should be me, this is so sad

That should be me

That should be me

That should be me, feeling your kiss

That should be me, buying you gifts

This is so wrong

I can't go on

Till you believe

That should be me

That should be me

Answer: (x +-1)3 (x + 1)3 = (x + 1)(x + 1)2

= (x + 1)(x2 + 2x + 1)

= x3 + 3 x2 + 3x + 1

Step-by-step explanation:

Multiplication is a method of finding the product of two or more numbers

when we multiply  (x + - 1)3 (x + 1)3  we get (x³-3x²+3x-1)( x³+ 3 x² + 3x + 1)

Multiplication is a method of finding the product of two or more numbers

We need to multiply

(x + - 1)³ (x + 1)³

(x - 1)³=(x-1)(x - 1)²

=(x-1)(x² - 2x + 1)

=x³-2x²+x-x²+2x-1

=x³-3x²+3x-1

(x + 1)³ = (x + 1)(x + 1)²

= (x + 1)(x² + 2x + 1)

= x³+ 3 x² + 3x + 1

So (x³-3x²+3x-1)( x³+ 3 x² + 3x + 1)

Hence when we multiply  (x + - 1)3 (x + 1)3  we get (x³-3x²+3x-1)( x³+ 3 x² + 3x + 1)

To learn more on Multiplication click:

https://brainly.com/question/5992872

#SPJ2

Based on the provided information, there is evidence to suggest that the marble floor is unsafe on rainy days since the sample mean coefficient of static friction exceeds the accepted standard of 0.5.

The coefficient of static friction is a measure of how easily an object can move across the surface of another object without slipping. In the context of a marble floor, a higher coefficient of static friction indicates a greater resistance to slipping, thus indicating a safer floor. The accepted standard for a safe marble floor is a coefficient of static friction no greater than 0.5.

In this scenario, a random sample of 50 rainy days was selected, and the coefficient of static friction was measured on each day. The resulting sample mean coefficient of static friction was found to be 0.6. Since the sample mean exceeds the accepted standard of 0.5, it suggests that, on average, the marble floor is unsafe on rainy days.

To draw a more definitive conclusion, statistical analysis can be performed to assess the significance of the difference between the sample mean and the accepted standard. This analysis typically involves hypothesis testing, where the null hypothesis assumes that the population mean is equal to or less than the accepted standard (0.5 in this case). If the statistical analysis yields a p-value below a predetermined significance level (e.g., 0.05), it provides evidence to reject the null hypothesis and conclude that the marble floor is indeed unsafe on rainy days.

Therefore, based on the provided information, there is evidence to suggest that the marble floor is unsafe on rainy days due to the sample mean coefficient of static friction exceeding the accepted standard of 0.5. Further statistical analysis can provide a more precise evaluation of the evidence.

Learn more about mean coefficient here:

brainly.com/question/30901831

#SPJ11

Answer:

D

Step-by-step explanation:

The match of solutions with the exponential expressions is

1) \(\frac{(2(3^{-2}) )^{3} (5(3^{2}) )^{2} }{(3^{-2})((5)(2))^{2}}=2\)

2) \((3^3) (4^0)^2 (3(2))^{-3} (2^2)=1/2\)

3) \(\frac{(3^74^7) (2(5))^{-3} (5)^2}{(12^7) (5^{-1}) (2^{-4})} =2\)

4) \(\frac{(2(3))^{-1} (2^0)}{(2(3))^{-1}}=1\)

The base will be multiplied by itself a certain number of times, as indicated by the exponent (also known as a power or degree).

Formulae for solving exponents are referred to as exponents formulas. The exponent of a number is written as \(x^{n}\), which means that x has been multiplied by itself n times.

\(x^{n}(x^{m})=x^{n+m} \\\frac{x^{n} }{x^{m} }=x^{n-m} \\(x^{n} )^{m} =x^{nm} \\((x)(y))^{n}=x^{n}(y^{n} \\x^{0}=1\)

1) the solution of the first expression will be

\(\frac{(2(3^{-2}) )^{3} (5(3^{2}) )^{2} }{(3^{-2})((5)(2))^{2}}\)

\((2^3) (3^{-6} ) (5^2) (3^4) / (3^{-2}) (10^2)= (2.2^2.5^2) (3^{-6}.3^4) / (3{^-2}) (10^2)= (2)(10^2) (3^{-2}) / (3^{-2}) (10^2)\\=2\)

2)The solution of the second expression will be

\((3^3) (4^0)^2 (3(2))^{-3} (2^2)\)

Any  number with power zero is 1.

So,

\((3^3) (1^2) (3^{-3}) (2^{-3}) (2^2)= (2^{(-3+2)})=2^-1\\= 1/2\)

3) The solution of third expression will be

\(\frac{(3^74^7) (2(5))^{-3} (5)^2}{(12^7) (5^{-1}) (2^{-4})} \\= \frac{(12^7) (2^{-3}) (5^{-3}) (5^2)}{(12^7) (5^{-1}) (2^{-4})} =\frac{(2^-3) (5^{(-3+2)})}{(5^{-1}) (2^{-4})} = \frac{(2^{-3}) (5^{-1})}{(5^{-1}) (2^{-}4)} = \frac{1}{(2^{-1})} = 2\)

4) The solution to the forth expression will be

\(\frac{(2(3))^{-1} (2^0)}{(2(3))^{-1}}\\=2^{0}\\ =1\)

To learn more about properties of exponents, visit: https://brainly.com/question/17318340

#SPJ4

Answer:

The person above litteraly gave you the answer just reread the first equations and then you will figure it out

Step-by-step explanation:

Answer:

x=17 degrees

Step-by-step explanation:

All 3 angles = 180 degrees

So 90 + 54 + (x+19) = 180

Combine like terms

163 + x = 180

Subtract 163 from both sides

x = 180-163

x = 17

The metric unit that would be best to measure the capacity of a cereal bowl is milliliters (ml).

Capacity is a measure of the amount of fluid that a container can hold. Cereal bowls are typically used to hold liquids such as milk or yogurt along with cereal. Milliliters are a commonly used metric unit of volume that would be appropriate for measuring the capacity of a cereal bowl. Other metric units of volume such as liters or cubic centimeters could also be used, but milliliters would provide a more precise measurement for a smaller container such as a cereal bowl. To measure the capacity of a cereal bowl in milliliters, one would simply pour a known amount of water into the bowl and measure the volume of the water using a measuring cup or a graduated cylinder.

Learn more about metric unit here

https://brainly.com/question/28896549

#SPJ11

Explanation

the length of an arc is given by:

where r is the radius and theta is the angle

then

Step 1

Let

radius=13

angle=68

replace

I hope this helps you

(a) The equation 7x² + 3x + 7y² + z² = 3 in cylindrical coordinates is expressed as 7r² cos²θ + 3r cosθ + 7r² sin²θ + z² = 3.

(b) The equation z = 9x² - 9y² in cylindrical coordinates is expressed as z = 9r² cos²θ - 9r² sin²θ.

To convert the given equations from Cartesian coordinates to cylindrical coordinates, we use the following substitutions: x = r cosθ, y = r sinθ, and z remains unchanged.

For equation (a), substituting x = r cosθ and y = r sinθ into 7x² + 3x + 7y² + z² = 3 gives us 7(r cosθ)² + 3(r cosθ) + 7(r sinθ)² + z² = 3. Simplifying further yields 7r² cos²θ + 3r cosθ + 7r² sin²θ + z² = 3.

For equation (b), substituting x = r cosθ and y = r sinθ into z = 9x² - 9y² gives us z = 9(r cosθ)² - 9(r sinθ)². Simplifying further results in z = 9r² cos²θ - 9r² sin²θ.

Thus, the equations in cylindrical coordinates are:

(a) 7r² cos²θ + 3r cosθ + 7r² sin²θ + z² = 3

(b) z = 9r² cos²θ - 9r² sin²θ.

Learn more about Cartesian coordinates here:

https://brainly.com/question/8190956

#SPJ11

The value of \(\iint_S\) curl F. dS using Stokes' Theorem is 0.

Let the double integral is,

I = \(\iint_S\) curl F. dS

where F(x,y,z) = x²z² i + y²z² j + xyz k

and S is the part of the paraboloid z = x² + y² that lies inside the cylinder x² + y² = 1 oriented upward.

Using Stokes' Theorem we get,  

\(\iint_S\)  curl F. dS = \(\int_C\) F .dr

where C is the boundary of the surface oriented counter clockwise.

So, C: x² + y² = 1, z = 1

Parametrizing the boundary we get,

r(t) = < cos t, sin t, 1 >

dr =  < -sin t, cos t, 0 > dt

So, f(r(t)) = cos² t i + sin² t j + cos t sin t k

Now evaluating the given we get,

\(\iint_S\)  curl F. dS = \(\int_C\) F .dr = \(\int_0^{2\pi}\) <cos² t + sin² t + cos t sin t>< -sin t, cos t, 0 > dt = \(\int_0^{2\pi}\) (sin t cos² t + cos t sin² t)dt = \([\frac{\cos^3t}{3}+\frac{\sin^3t}{3}]_0^{2\pi}\) = 0.

To know more about Stokes' Theorem here

https://brainly.com/question/13067929

#SPJ4

Answer:

It would be negative 13 because if add a positive nine to a negative 22 you get negative 13.

Step-by-step explanation:

Answer:

8 minutes

Step-by-step explanation:

Step one:

given

A submarine is 105 feet below the surface of the water

depth of submarine= 105 feet

let the time of ascending be x

Required

The time taken to ascend up to 81 ft

Step two:

the expression for the situation is

81=105-3x

solve for x

3x=105-81

3x=24

divide both sides by 3

x= 24/3

x=8 minutes

The first term of the infinite geometric series is 625.Let's dive deeper into the explanation.

We are given that the sum of the infinite geometric series is \(\( \frac{15625}{24} \)\)and the common ratio is\(\( \frac{1}{25} \).\)The formula for the sum of an infinite geometric series is \(\( S = \frac{a}{1 - r} \)\), where \( a \) is the first term and \( r \) is the common ratio.
Substituting the given values into the formula, we have \(\( \frac{15625}{24} = \frac{a}{1 - \frac{1}{25}} \).\)To find the value of \( a \), we need to isolate it on one side of the equation.
To do this, we can simplify the denominator on the right-hand side.\(\( 1 - \frac{1}{25} = \frac{25}{25} - \frac{1}{25} = \frac{24}{25} \).\)
Now, we have \(\( \frac{15625}{24} = \frac{a}{\frac{24}{25}} \).\) To divide by a fraction, we multiply by its reciprocal. So, we can rewrite the equation as \( \frac{15625}{24} \times\(\frac{25}{24} = a \).\)
Simplifying the right-hand side of the equation, we get \(\( \frac{625}{1} = a \).\)Therefore, the first term of the infinite geometric series is 625.
In conclusion, the first term of the given infinite geometric series is 625, which corresponds to option (a).



learn more about geometric series here here

https://brainly.com/question/30264021



#SPJ11

Answer:

38

Step-by-step explanation:

76*4= 304

304/8= 38

Hope this helps!! Can I get a brainlist pls?? :))

All three components of the fire triangle are usually present whenever and wherever surgery is performed. The fire triangle consists of three elements: fuel, heat, and oxygen.

In the context of surgery, nitrous oxide can be considered as a source of the fuel component of the fire triangle. Nitrous oxide is commonly used as an anesthetic in surgery, and it is highly flammable. It can act as a fuel for fire if it comes into contact with a source of ignition, such as sparks or open flames.

Therefore, it is important for healthcare professionals to be aware of the potential fire hazards associated with the use of nitrous oxide in surgical settings and take appropriate safety precautions to prevent fires.

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ11

If the length of each side of a cube is tripled, the volume of the cube will increase by a factor of 27.

The volume of a cube is given by the formula V = s^3, where s represents the length of each side.

Let's consider the initial volume of the cube as V1 and the new volume after tripling the side length as V2.

If we triple the side length, the new side length becomes 3s.

So, the new volume V2 can be calculated as V2 = (3s)^3 = 27s^3.

Comparing V2 to V1, we can see that V2 is 27 times greater than V1.

Therefore, the volume of the cube increases by a factor of 27 when the length of each side is tripled.

Learn more about the volume of the cube :

brainly.com/question/29275443

#SPJ11

Answer:

Step-by-step explanation:

The explicit rule for determining the nth term of a geometric sequence is expressed as Tₙ = arⁿ⁻¹ where;

a is the first term of the geometric sequence

r is the common ratio

n is the number of terms

If a geometric sequence has a common ratio of 2 and the 12th term is −12,288, then;

T₁₂ = ar¹²⁻¹

T₁₂ = ar¹¹

Given T₁₂ = -12,288 and r = 2, we can calculate the first term a

-12,288 = a2¹¹

a = -12,288/2¹¹

a =  -12,288/2048

a = -6

Since the explicit rule for determining the nth term of a geometric sequence is expressed as Tₙ = arⁿ⁻¹, then for the sequence given, the explicit rule will be;

Tₙ = -6(2)ⁿ⁻¹

Tₙ = -6 * 2ⁿ * 2⁻¹

Tₙ = -6 * 2ⁿ * 1/2

Tₙ = -3(2)ⁿ

Hence the explicit rule that describes this sequence is Tₙ = -3(2)ⁿ

Polynomials are expressions. The solution of the division can be written as \(4x^2-27x+167-\dfrac{996}{x+6}\).

Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.

The division of the polynomial  (4x³-3x²+5x+6) when divided by (x+6), can be done in the following manner,

\(\dfrac{4x^3-3x^2+5x+6}{x+6}\)

\(=4x^2+\dfrac{-27x^2+5x+6}{x+6}\)

\(=4x^2-27x+\dfrac{167x+6}{x+6}\)

\(=4x^2-27x+167+\dfrac{-996}{x+6}\\\\\\=4x^2-27x+167-\dfrac{996}{x+6}\)

Hence, the solution of the division can be written as \(4x^2-27x+167-\dfrac{996}{x+6}\).

Learn more about Polynomial:

https://brainly.com/question/17822016

Answer:

Step-by-step explanation:

OPT D ON EDG 2023

The type of sampling the student used is known as convenience sampling.

Convenience sampling involves selecting individuals who are easily accessible or readily available for the study. In this case, the student surveyed members of his own class, which was likely a convenient and easily accessible group for him to gather data from.

However, convenience sampling may introduce bias and may not provide a representative sample of the entire student population.

Learn more about sampling  at https://brainly.com/question/24466382

#SPJ1

The graph of the quadratic function y = 0.75x² is given by the image at the end of the answer.

The notation y = 0.75x² is already in vertex form, meaning that the function was vertically compressed by a factor of 3/4 from the original graph.

The definition of a quadratic equation with vertex (h,k) is given as follows:

y = a(x - h)² + k.

In which a represents the leading coefficient of the quadratic function.

In this problem the coordinates of the vertex are:

(0,0).

Hence the parameters are:

h = 0, k = 0.

Thus the equation is:

y = ax².

When x = -2, y = 3, hence the leading coefficient is given as follows:

3 = a(-2)²

4a = 3

a = 3/4

a = 0.75.

Hence the equation is:

y = 0.75x².

The multiplication by 0.75 means that the parent function y = x² is vertically compressed by a factor of 0.75.

More can be learned about quadratic functions at https://brainly.com/question/24737967

#SPJ1

Answer:The total cost is $41.04

Step-by-step explanation:

Answer:

area = length * width

1,500 = 50 m * width

width = 1,500 / 50

width = 30 meters

Step-by-step explanation:

The probability of getting heads is 3/8.

Probability:

Probability is a branch of mathematics that quantifies the likelihood of an event occurring or the likelihood of a statement being true. Probability is a number between 0 and 1, with 0 generally indicating impossibility and 1 indicating certainty. that an event will occur. A simple example is tossing a fair (unbiased) coin. Since the coin is fair, the two outcomes (heads and tails) are equally likely. The probability of heads is the same as the probability of tails. Since no other outcome is possible, the probability of heads or tails is 1/2 (also written as 0.5 or 50%).

Since 3 is a small number, let's list out all possible combinations.

H represents a head while T represents a tail.

3 Heads

HHH

2 Heads

HHT

HTH

THH

1 Head

HTT

THT

TTH

0 Head

TTT

The answer is

3/1+3+3+1=3/8

                                            OR

In general, we will find that the list resembles a particular row of the pascal's triangle.

If you want to know the probability of getting r heads (or tails) from n flips, it is the sum of the rth  elements in the n + 1 line. All elements of the series n+1.

\(\left[\begin{array}{ccc}N\\\\R\end{array}\right]\)/ 2ⁿ = \(\frac{n!}{r! * (n - r)!* 2^{n} }\)

n this case,

N =3andR= 2

   3!/ 2!×1! × 2³

= 6/ 2× 1 × 8

= 3/8

Learn more about Probability:

https://brainly.com/question/11234923

#SPJ4