Find the missing length indicated. Pls show ur work. Thank you.

Time taken by Adam to complete his seventh lap of the circular track as per given data is equal to 1minute 28seconds.

As given in the question,

Time taken by Adam to complete hi first lap of circular track = 1 min 58 sec

First term t₁ = 1 minute 58seconds

Time taken by each successive lap is 5seconds less then the previous lap

Common difference 'd' = -5seconds

let time taken to complete the seventh lap be t₇

t₇ = t₁ + ( 7 - 1 ) d

⇒ t₇ = 1 minute 58 seconds + ( 6 ) (- 5seconds)

       =  1 minute 58 seconds - 30seconds

      = 1 minute 28 seconds

Therefore, the time taken by Adam to complete his seventh lap is equal to

1 minute 28 seconds.

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Answer:

because if u divide the top and bottom by 5, you'll get 2/5

Step-by-step explanation:

Answer: Porque dividir ambos por 5 y eso es lo más bajo que pueden ir

Step-by-step explanation:

10 / 5 = 2

25 / 5 = 5

The lines KL and MN perpendicular to each other.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

here, we have,

If a line passes through two points, then the slope of the line is

m = y2-y1/x2-x1

From the given graph it is clear that coordinates of points on line KL are K(-8,2) and L(6,2).

The slope of line KL is

m = 0

The slope of line KL is 0, it means it is a horizontal line.

From the given graph it is clear that coordinates of points on line MN are M(-4,8) and N(-4,-6).

The slope of line MN is

m = 1/0

The slope of line MN is 1/0 or undefined, it means it is a vertical line.

We know that vertical and horizontal lines are perpendicular to each other.

Therefore the lines KL and MN perpendicular to each other.

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Answer:

16 is the range

Step-by-step explanation:

First, arrange the numbers from least to greatest.

21, 25, 25, 26, 28, 37

Then, subtract 21 (smallest number) from the 37 (biggest number).

37 - 21 = 16

So, the range is 16

Have a wonderful day!

Answer:

6.48

Step-by-step explanation:

you have to use the sin rule

Answer:

6.48

Step-by-step explanation:

The point where all the three medians of a triangle intersect is known as the centroid or the center of gravity of the triangle.

It divides each median in the ratio 2:1, with the larger portion being on the side of the vertex away from the midpoint of the opposite side. The centroid of a triangle is always inside the triangle, and it is the point of intersection of the three medians.

The centroid is an important point in the study of geometry because it can be used to define the center of mass of a triangle. It is also used to find the area of the triangle and to calculate the centroid of other figures.

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The numbers of new CDs is 30 and the old CDs is 21.

To solve this problem, we have to write a system of equations in which we would know the numbers of each types of CD she bought.

This is used to solve a series or complex of word problems in which we can represent in a mathematical statements;

The equations can be represented as

\(n + u = 51 ...equation(i)\\15n + 6u = 576 ... equation(ii)\)

Let's take equation (i)

Making n the subject of formula

\(n + u = 51\\n = 51 - u...equation(iii)\)

we can put equation (iii) into equation (ii)

\(15n + 6u =576\\n = 51 - u\\15(51 - u) + 6u = 576\\765-15u + 6u = 576\\collect like terms\\765-576=15u - 6u\\189=9u\\9u/9 = 189/9\\u = 21\)

Let's put the value of u into equation (i)

\(n + u = 51\\u = 21\\n + 21 = 51\\n = 51 - 21\\n = 30\)

From the calculations above, the numbers of new CDs is 30 and the old CDs is 21.

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To approximate the area under the curve y = x³ from x = 3 to x = 7 using a right endpoint approximation with 6 subdivisions, the formula for Right Endpoint Approximation is:

RIEMANN SUM = ∑ f(xi)Δx

The interval is divided into n equal parts which can be expressed as:

Δx = (b - a) / n

where a and b are the lower and upper bounds respectively, n is the number of subdivisions.

Δx = (7 - 3) / 6 = 4 / 6 = 0.6666666667

Then, we can calculate the values of xi:

xi = a + iΔx

x0 = 3

x1 = 3.6666666667

x2 = 4.3333333333

x3 = 5

x4 = 5.6666666667

x5 = 6.3333333333

x6 = 7

We can now substitute the values of xi into the function, f(x) = x³ and obtain the values of f(xi).

f(x0) = 3³ = 27

f(x1) = 3.6666666667³ = 50.847221820371

f(x2) = 4.3333333333³ = 84.703703672997

f(x3) = 5³ = 125

f(x4) = 5.6666666667³ = 189.58271616609

f(x5) = 6.3333333333³ = 273.96296293926

f(x6) = 7³ = 343

Now, the Riemann sum can be obtained using the formula above.

RIEMANN SUM = ∑ f(xi)Δx

= [f(x0) + f(x1) + f(x2) + f(x3) + f(x4) + f(x5) + f(x6)]Δx

= [27 + 50.847221820371 + 84.703703672997 + 125 + 189.58271616609 + 273.96296293926 + 343] × 0.6666666667

= 1598.5479336901

Therefore, the approximate area under the curve y = x³ from x = 3 to x = 7 using a right endpoint approximation with 6 subdivisions is 1598.5479336901.

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Answer:

130

Step-by-step explanation:

Hello There!

An included angle is equal to half the measure of its included arc

So more specifically for this circle

∠mABC = \(\frac{1}{2}\) arc(mAB)

So in order to find the value of x we are going to want an equation

Because angle ABC is equal to 1/2 of arc AB we are going to want to multiply angle ABC's expression by two

So 2(3x+32) = 10x+20

now we solve for x

step 1 distribute the 2

2 * 3x = 6x

2 * 32 = 64

now we have

6x + 64 = 10x + 20

step 2 subtract 20 from each side

64 - 20 = 44

20 - 20 cancels out

now we have 6x + 44 = 10x

step 3 subtract 6 x from each side

10x - 6x = 4x

6x - 6x cancels out

now we have 44 = 4x

step 4 divide each side by 4x

44/4=11

4x/4=x

we're left with x = 11

finally we want to plug in 11 to x for (10x+20)

10(11)+20

10*11=110

110+20=130

so arc ab = 130

Answer:

AB = 130

Step-by-step explanation:

So, according to a certain theorem to do with arcs and their angles, If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc.

In this case, the ARC is AB, and the angle is CBA.

CBA = 3x+32

AB = 10x+20

And,

\(CBA = \frac{1}{2} AB\)

Now,

\(3x+32=\frac{1}{2} (10x+20)\)

\(3x+32=5x+10\\32=2x+10\\22=2x\\11=x\)

Now we can substitute x into the equation that equals AB

\(10(11)+20 \\=110+20\\=130\)

So, the answer is 130, sorry I took a while, the explanation takes a long time to do lol.

Have a nice day fam. Spread The Love.

Answer:

yes.

Step-by-step explanation:

The amount you could save per month would be 25% of your discretionary money.

Discretionary income is the money you have left over after paying taxes and necessary cost-of-living expenses.

The formula for discretionary money is: Discretionary money = Realized income - Fixed expenses. Inputting data, we have: Discretionary money = $3,543.22 - Fixed expenses

Amount to be saved = 25% of discretionary money

Amount to be saved = 0.25 * (Realized income - Fixed expenses)

Therefore, the amount savable is calculated as 0.25 times the difference between your realized income and fixed expenses.

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commas and capital letters

To find the coordinates of points Q and R where the normal to the curve intersects the curve again, we need to follow these steps:

Find the derivative of the given curve y = 2x³ - 12x² + 23x - 11.

dy/dx = 6x² - 24x + 23

Substitute x = 2 into the derivative to find the slope of the tangent line at that point.

dy/dx = 6(2)² - 24(2) + 23

= 24 - 48 + 23

= -1

The normal to the curve is perpendicular to the tangent line, so the slope of the normal is the negative reciprocal of the tangent's slope.

Slope of the normal = -1/(-1) = 1

Find the equation of the line with a slope of 1 passing through the point (2, y(2)).

Using the point-slope form: y - y₁ = m(x - x₁)

y - y(2) = 1(x - 2)

y - (2(2)³ - 12(2)² + 23(2) - 11) = x - 2

y - (16 - 48 + 46 - 11) = x - 2

y - (-3) = x - 2

y + 3 = x - 2

y = x - 5

Set the equation of the line equal to the original curve and solve for x.

x - 5 = 2x³ - 12x² + 23x - 11

Rearranging the equation:

2x³ - 12x² + 22x - x = 16

Simplifying further:

2x³ - 12x² + 21x - 16 = 0

Solve the equation for x to find the x-coordinates of points Q and R. This can be done using numerical methods or factoring techniques. In this case, we will use numerical approximation.

Using a numerical method or calculator, we find the approximate solutions:

x ≈ 0.486 and x ≈ 5.274

Substitute the values of x back into the original curve equation to find the y-coordinates of points Q and R.

For x ≈ 0.486:

y ≈ 2(0.486)³ - 12(0.486)² + 23(0.486) - 11

≈ -6.091

For x ≈ 5.274:

y ≈ 2(5.274)³ - 12(5.274)² + 23(5.274) - 11

≈ 51.811

Therefore, the coordinates of point Q are approximately (0.486, -6.091), and the coordinates of point R are approximately (5.274, 51.811).

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Answer:

As this triangle is being transformed by rotation, the angles will stay same as well as the  sides and other details, if you are doing this on a coordinate plane, then the points of the triangle would be changed and nothing else

If my answer helped, please mark me as the brainliest!!

Thank You!

The point (x, y) = (7, - 1) lies on the line whose equation is y + 4 = (3 / 5) · (x - 2). (Correct choice: E)

In this problem we find five different points of the form (x, y), each of which has to be checked in the linear equation given in the statement. A point is a solution of the linear equation if and only an equality exists, that is, the reflexive property of equalities is guaranteed by evaluating the expression.

Now we proceed to check the expression for each case:

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

- 5 + 4 = (3 / 5) · (1 - 2)

- 1 = (3 / 5) · (- 1)

- 1 = - 3 / 5     (FALSE)

(x, y) = (- 8, - 12)

- 12 + 4 = (3 / 5) · (- 8 - 2)

- 8 = (3 / 5) · (- 10)

- 8 = - 30 / 5

- 8 = - 6    (FALSE)

(x, y) = (- 3, - 8)

- 8 + 4 = (3 / 5) · (- 3 - 2)

- 4 = (3 / 5) · (- 5)

- 4 = - 3    (FALSE)

(x, y) = (12, 10)

10 + 4 = (3 / 5) · (12 - 2)

14 = (3 / 5) · 10

14 = 30 / 5

14 = 6     (FALSE)

(x, y) = (7, - 1)

- 1 + 4 = (3 / 5) · (7 - 2)

3 = (3 / 5) · (5)

3 = 3    (TRUE)

The point (x, y) = (7, - 1) lies on the line whose equation is y + 4 = (3 / 5) · (x - 2).

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Answer: did you make that up ??

Step-by-step explanation:

Answer:

A. Alternate interior

B. Transitive property

C. Converse alternate interior angles theorem.

The function f(x) = |x^2 - 4| is differentiable for x in the intervals (-∞, 2] and [2, ∞).

To determine for what values of x the function f(x) = |x^2 - 4| is differentiable, we need to consider the following,

1. Define the function f(x) in two separate cases:
  a) When x^2 - 4 ≥ 0, f(x) = x^2 - 4
  b) When x^2 - 4 < 0, f(x) = -(x^2 - 4)

2. Find the critical points of f(x) where the function changes from one case to another:
  x^2 - 4 = 0 => x^2 = 4 => x = ±2

3. Analyze the differentiability of each case:
  a) For x^2 - 4 ≥ 0, f'(x) = 2x
  b) For x^2 - 4 < 0, f'(x) = -2x

4. Check the differentiability at the critical points x = ±2:
  - As f'(x) exists in both cases and the left and right limits are equal, the function is differentiable at x = ±2.

5. Combine the results using interval notation:
  The function f(x) = |x^2 - 4| is differentiable for x in the intervals (-∞, 2] and [2, ∞).

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Given: Radius of the wheel = 30 inches, Revolutions per minute = 401 rpmThe linear speed of the car in miles per hour can be calculated as follows:

Step 1: Convert the radius from inches to miles by multiplying it by 1/63360 (1 mile = 63360 inches).30 inches × 1/63360 miles/inch = 0.0004734848 milesStep 2: Calculate the distance traveled in one minute by the wheel using the circumference formula.Circumference = 2πr = 2 × π × 30 inches = 188.496 inchesDistance traveled in one minute = 188.496 inches/rev × 401 rev/min = 75507.696 inches/minStep 3: Convert the distance traveled in one minute from inches to miles by multiplying by 1/63360.75507.696 inches/min × 1/63360 miles/inch = 1.18786732 miles/minStep

4: Convert the distance traveled in one minute to miles per hour by multiplying by 60 (there are 60 minutes in one hour).1.18786732 miles/min × 60 min/hour = 71.2720392 miles/hour Therefore, the linear speed of the car is 71.3 miles per hour (rounded to the nearest tenth).Answer: 71.3

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The radius of the wheel on a car is 30 inches. If the wheel is revolving at 401 revolutions per minute, The linear speed of the car is approximately 19.2 miles per hour.

To find the linear speed of the car in miles per hour, we need to calculate the distance traveled in one minute and then convert it to miles per hour. Here's how we can do it step by step:

Calculate the circumference of the wheel:

The circumference of a circle is given by the formula

C = 2πr

where r is the radius of the wheel.

In this case, the radius is 30 inches, so the circumference is

C = 2π(30)

   = 60π inches.

Calculate the distance traveled in one revolution:

Since the circumference represents the distance traveled in one revolution, the distance traveled in inches per revolution is 60π inches.

Calculate the distance traveled in one minute:

Multiply the distance traveled in one revolution by the number of revolutions per minute.

In this case, it is 60π inches/rev * 401 rev/min = 24060π inches/min.

Convert the distance to miles per hour:

There are 12 inches in a foot, 5280 feet in a mile, and 60 minutes in an hour.

Divide the distance traveled in inches per minute by (12 * 5280) to convert it to miles per hour.

The final calculation is (24060π inches/min) / (12 * 5280) = (401π/66) miles/hour.

Approximating π to 3.14, the linear speed of the car is approximately (401 * 3.14 / 66) miles per hour, which is approximately 19.2 miles per hour.

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The SI units of the proportionality constant G is Newton \(Kg^{-2} m^2\)

Gravitational force is given by Newton's law of gravitation which states that every particle of matter in the cosmos is drawn to every other particle by a force of attraction that varies directly with the product of their masses and is inversely proportional to the square of the distance or degree of separation from each other.

F = G \($ \frac{m_1 m_2}{r^2}\)

Upon rearranging the terms we get,

G = \($\frac{F r^2}{m_1 m_2}\)

Where F is the gravitational force, \(m_{1}\) and \(m_{2}\) are masses, and r is the length.

Force has the SI units kg · m/s2

The SI units of the proportionality constant G

SI Unit of G = \($\frac{(\text { Newton })\left(\mathrm{m}^2\right)}{\mathrm{kg} ^2}\)

= Newton \(Kg^{-2} m^2\)

Therefore the units are Newton \(Kg^{-2} m^2\)

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Newton's law of universal gravitation is represented by F = G \($ \frac{m_1 m_2}{r^2}\) where F is the gravitational force, \(m_{1}\) and \(m_{2}\) are masses, and r is a length. force has the SI units kg· m/s2. what are the SI units of the proportionality constant G?

According to the question the fraction of the bigger square that is shaded is 50%.

Fraction is a numerical representation of a part of a whole or a ratio between two numbers. It is written in the form of a/b where a is the numerator and b is the denominator. A fraction can refer to a part of a whole number, a part of a set, or a part of a unit. Fractions are commonly used in mathematics, cooking, science, and many other areas.

This is because the ratio of the area of the smaller square to the area of the bigger square to the area of the triangle is 1:3:2. Therefore, the ratio of the area of the shaded parts of the squares to the area of the shaded triangle is 25%: 25%:50%. Since the area of the bigger square is three times that of the smaller square, then 50% of the bigger square must be shaded to maintain the given ratio.

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Answer:

32.7 degress

Step-by-step explanation:

In this question we are to find the value of the angle

The best way to do with the information given is the cosine rule

Mathematically that would be;

y^2 = x^2 + z^2 -2xzCosY

where x = 90 ft , y = 55ft and z = 50 ft

Plugging the values we have;

55^2 = 90^2 + 50^2-2(90)(50)CosY

-7575 = -9000cosY

cosY = 7575/9000

cosY = 0.841666666667

Y = cos^-1 0.841666666667

Y = 32.68 degrees which is 32.7 to the nearest tenth

Answer:

32.7

Step-by-step explanation:

Answer: wavelength or frequency

Step-by-step explanation:

The reflectance curve is a plot of the light reflected off a surface as a function of wavelength or frequency. It shows how much light is reflected at each specific wavelength or frequency and can be used to analyze the optical properties of a material.

Answer: 7

Step-by-step explanation: This is an equalateral triangle. You can tell by the marks on each angle, marking that they are equal.

This means that the two sides that aren't the hypotenuse are the same.

Therefore,

\(4(x+2) = 36\)

Multiply out the 4

\(4x + 8 = 36\)

Subtract 8

\(4x = 28\)

Divide by 4

\(x = 7\)

Answer:

When the coefficient of the variable is negative, as shown below,

Step-by-step explanation:

2-4y>14

-4y>14-2

-4y>12, divde through by - 4

y>-3

We find that it takes approximately 47 months to recover the initial investment.

To calculate the time it takes to recover the initial investment on a monthly basis, we need to consider the savings in fuel costs and the cost of funds over time.

First, let's calculate the monthly savings in fuel costs by subtracting the average natural gas cost from the fuel oil cost:

Savings in fuel costs = Fuel oil cost - Natural gas cost

= $145 - $60

= $85

Next, let's calculate the present value of the savings in fuel costs over the recovery period. Since the savings occur monthly, we can use the formula for the present value of an annuity:

Present value of savings = Savings in fuel costs * (1 - (1 + interest rate)^(-n)) / interest rate

Where:

Savings in fuel costs is $85 per month

Interest rate is 9% per year, which is 0.75% per month

n is the number of months it takes to recover the initial investment

Now, let's calculate the present value of the savings using the given values:

Present value of savings = $85 * (1 - (1 + 0.0075)^(-n)) / 0.0075

Next, let's calculate the present value of the initial investment using the formula for present value:

Present value of initial investment = Initial investment / (1 + interest rate)^n

Where:

Initial investment is $2500

Interest rate is 9% per year, which is 0.75% per month

n is the number of months it takes to recover the initial investment

Now, let's calculate the present value of the initial investment using the given values:

Present value of initial investment = $2500 / (1 + 0.0075)^n

To recover the initial investment, the present value of savings must equal the present value of the initial investment:

$85 * (1 - (1 + 0.0075)^(-n)) / 0.0075 = $2500 / (1 + 0.0075)^n

To solve for n, we can rearrange the equation and solve for n using trial and error or by using numerical methods.

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To find the derivative of f(x) = 5x^4 - 6x^2 + 4x - 2, we can differentiate each term separately using the power rule.

f'(x) = d/dx (5x^4) - d/dx (6x^2) + d/dx (4x) - d/dx (2)

Applying the power rule, we get:

f'(x) = 20x^3 - 12x + 4

To find f'(2), we substitute x = 2 into the derivative:

f'(2) = 20(2)^3 - 12(2) + 4
      = 160 - 24 + 4
      = 140

Therefore, f'(2) = 140.

2. To find the derivative of f(x) = x^2e^x, we use the product rule.

Let u = x^2 and v = e^x. Then,

f'(x) = u'v + uv'

Differentiating u = x^2 with respect to x gives u' = 2x.

Differentiating v = e^x with respect to x gives v' = e^x.

Substituting these values back into the product rule, we have:

f'(x) = 2x * e^x + x^2 * e^x
     = (2x + x^2) * e^x

To find f'(1), we substitute x = 1 into the derivative:

f'(1) = (2(1) + (1)^2) * e^1
     = (2 + 1) * e
     = 3e

Therefore, f'(1) = 3e.

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To find the x and y components of the total force exerted on the third charge, as well as the magnitude and direction of this force, we need to calculate the individual forces due to each pair of charges and then find their vector sum.

The force between two charges can be calculated using Coulomb's law:

F = (k * |q1 * q2|) / r^2,

where F is the force, k is Coulomb's constant (k = 8.99 × 10^9 N m^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.

Let's calculate the forces between the third charge (5.00 nC) and the two other charges:

Force between the third charge and the charge at the origin:

F1 = (k * |(-2.50 × 10^(-9) C) * (5.00 × 10^(-9) C)|) / r1^2,

where r1 is the distance between the third charge and the charge at the origin.

Force between the third charge and the charge on the y-axis:

F2 = (k * |(1.70 × 10^(-9) C) * (5.00 × 10^(-9) C)|) / r2^2,

where r2 is the distance between the third charge and the charge on the y-axis.

To calculate the x and y components of the total force, we can resolve each force into its x and y components:

F1x = F1 * cos(θ1),

F1y = F1 * sin(θ1),

where θ1 is the angle between F1 and the x-axis.

F2x = 0 (since the charge on the y-axis is along the y-axis),

F2y = F2.

The x and y components of the total force are then:

Fx = F1x + F2x,

Fy = F1y + F2y.

To find the magnitude of the total force, we can use the Pythagorean theorem:

|F| = √(Fx^2 + Fy^2).

Finally, to determine the direction of the force, we can use trigonometry:

θ = arctan(Fy/Fx).

By plugging in the given values and performing the calculations, the x and y components of the total force, the magnitude of the force, and the direction of the force can be determined.

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Answer:

A) 3

Step-by-step explanation:

divide 77 by 11

you get 7

divide 21 by 7 to find x

x=3

The total number of arrangements, we can simply add up the results from each case:

C(21,8) + C(5,1) C(21,7) 8 + C(5,2) C(21,6) 2

Now, We can solve this problem, we can break it down into three cases, based on the number of vowels included in the arrangement.

Hence, Here are the three cases:

Case 1: No vowels included: In this case, we need to select 8 letters from the 21 consonants in the alphabet.

This can be done with C(21,8) ways.

Case 2: One vowel included:

Here, we need to select one of the five vowels and then select 7 letters from the 21 consonants.

The vowel can be placed in any of the 8 positions, but once it is placed, the other vowels must be placed in alphabetical order.

Therefore, the number of arrangements in this case is, C(5,1) C(21,7) 8.

Case 3: Two vowels included: In this case, we need to select two of the five vowels, and then select 6 letters from the 21 consonants.

Again, the vowels must be placed in alphabetical order once they are selected.

However, we have two possible orders to place the vowels - either at the start or in the middle of the 8-letter arrangement.

Therefore, the number of arrangements in this case is C(5,2) C(21,6) 2.

So, The total number of arrangements, we can simply add up the results from each case:

C(21,8) + C(5,1) C(21,7) 8 + C(5,2) C(21,6) 2

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