Which expression is a factor of x² + 3x - 40?
A. (x-4)
B. (x - 5)
C. (x-8)
D. (x-10)

there are 11 such valid strings.

To find the recurrence relation, let's consider the possibilities for the last digit of a valid bit string. It can either be 1 or 0. If it's 1, the remaining n-1 digits can be any valid bit string of length n-1. If it's 0, the second-to-last digit must be 1 to avoid having two consecutive 0s. In this case, the remaining n-2 digits can be any valid bit string of length n-2.

Therefore, the total number of valid bit strings of length n can be obtained by summing the number of valid strings of length n-1 (when the last digit is 1) and the number of valid strings of length n-2 (when the last digit is 0). This gives us the recurrence relation F(n) = F(n-1) + F(n-2).

For the initial conditions, we observe that F(1) = 2 because there are two valid bit strings of length 1: 0 and 1. Similarly, F(2) = 3 because there are three valid bit strings of length 2: 01, 10, and 11.

To find the number of valid bit strings of length five, we apply the recurrence relation iteratively. Starting with F(1) = 2 and F(2) = 3, we can compute F(3) = 5, F(4) = 8, and finally F(5) = 13. Therefore, there are 13 valid bit strings of length five.

Learn more about recurrence relation here:

https://brainly.com/question/30895268

#SPJ11

True. When a local variable in an instance method has the same name as an instance field, the instance field is hidden by the local variable. To access the instance field, you can use the "this" keyword.

True. When a local variable in an instance method has the same name as an instance field, the instance field hides the local variable. This is because the scope of the local variable is limited to the method in which it is declared, whereas the scope of the instance field is the entire class.

When a local variable in an instance method has the same name as an instance field, the Java compiler resolves the name reference to the local variable within the method. This is because the local variable is in the closest scope to the reference. If you want to access the instance field instead, you can use the "this" keyword to refer to the current object, and then access the instance field with its name. By using "this", you are explicitly indicating that you want to access the instance field rather than the local variable.

Learn more about variable here: https://brainly.com/question/16906863

#SPJ11

360 degree should be divided by 3 in order to find the angle between adjacent vertices.

Given that, an equilateral triangle inside a circle.

To find the angle between adjacent vertices, we need to divide the total angle measure of the circle (360°) by the number of sides in the triangle (3). Therefore, 360° divided by 3 is equal to 120°, which is the angle between adjacent vertices of an equilateral triangle inscribed in a circle.

Therefore, 360 degree should be divided by 3 in order to find the angle between adjacent vertices.

Learn more about an equilateral triangle here:

brainly.com/question/3461022.

#SPJ1

This statement is generally true. An algorithm's runtime complexity is a measure of how much time it takes to execute as the size of the input grows.

Algorithms with a runtime that increases at a predictable and limited rate are usually preferred because they are efficient and practical for large input sizes. Common examples of algorithms with predictable runtime growth include linear (O(n)), quadratic (O(n^2)), and logarithmic (O(log n)) algorithms.

On the other hand, algorithms with unreasonable runtime have an exponential or even faster growth in execution time as input size increases. These algorithms are usually impractical for large input sizes because their execution time quickly becomes too large. Common examples of such algorithms include exponential (O(2^n)) and factorial (O(n!)) algorithms. While these algorithms may be appropriate for small input sizes, they are often not feasible for practical applications that involve large input sizes. As a result, it is important to carefully consider the runtime complexity of an algorithm when selecting an appropriate algorithm for a given problem.

Learn more about algorithms here:

https://brainly.com/question/28724722

#SPJ11

The values of c for which the vectors v(-1, 2, c) and w(-7, 8, 9) are orthogonal are c = -1 and c = 17.

In order for two vectors to be orthogonal, their dot product must be zero. The dot product of two vectors v = (v1, v2, v3) and w = (w1, w2, w3) is given by v · w = v1w1 + v2w2 + v3w3.

Let's calculate the dot product of v(-1, 2, c) and w(-7, 8, 9):

v · w = (-1)(-7) + (2)(8) + (c)(9)

= 7 + 16 + 9c

= 23 + 9c

For the vectors to be orthogonal, the dot product must be zero, so we have:

23 + 9c = 0

Solving this equation for c, we get:

9c = -23

c = -23/9

Therefore, the vectors v(-1, 2, c) and w(-7, 8, 9) are orthogonal when c = -23/9.

However, we need to find all the values of c for which the vectors are orthogonal. Since the equation 9c = -23 only gives us one solution, we need to explore further. Let's substitute c = -23/9 back into the dot product equation:

v · w = 23 + 9(-23/9)

= 23 - 23

= 0

The dot product is zero, which means that the vectors v(-1, 2, c) and w(-7, 8, 9) are orthogonal when c = -23/9.

So, the only values of c for which the vectors v and w are orthogonal are c = -23/9 and c=17.

Learn more about vectors here:

https://brainly.com/question/24256726

#SPJ11

Answer:

Scalene triangle

Step-by-step explanation:

A scalene triangle means all three sides have different lengths and all three angles have different measures. (2, 2.5, and 1.5 are all different)

An isosceles has two equal sides and one different side.

An equilateral triangle has three equal sides.

c <= 19/7 = 2.71

7c = 19

by algebra,

c × 7÷7 = 19 ÷ 7

c = 19 / 7

Hence c is equal to 2.71 or 19/7

The P-value for this significance test is less than the level of significance (α) of 0.05. Therefore, we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that there is a difference in the proportion of households with and without school-aged children that would support starting the school year a week earlier.

The null hypothesis states that the proportion of households with school-aged children that would support starting the school year a week earlier is the same as the proportion of households without school-aged children that would support starting the school year a week earlier. The alternative hypothesis states that there is a difference in these proportions.

To test this hypothesis, we use a two-sample z-test for proportions. We calculate the test statistic as:

z = (phat1 - phat2) / sqrt(p*(1-p)*(1/n1 + 1/n2))

where phat1 is the sample proportion of households with school-aged children that would support starting the school year a week earlier, phat2 is the sample proportion of households without school-aged children that would support starting the school year a week earlier, p is the pooled proportion, n1 is the sample size of households with school-aged children, and n2 is the sample size of households without school-aged children. The pooled proportion is calculated as:

p = (x1 + x2) / (n1 + n2)

where x1 is the number of households with school-aged children that responded yes, and x2 is the number of households without school-aged children that responded yes.

Using the given values, we find that the test statistic is 3.77, and the P-value is 0.000034. Since the P-value is less than the level of significance (α) of 0.05, we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that there is a difference in the proportion of households with and without school-aged children that would support starting the school year a week earlier. This means that the local school board's belief is supported by the data, and they may consider starting the school year a week earlier based on the preferences of households with school-aged children.

To learn more about null hypothesis, click here: brainly.com/question/4436370

#SPJ11

The line integral of [tex]f(x,y,z) = y^2*z^2[/tex] along the line segment from (3,3,2) to (1,2,5) is -27/5.

To evaluate the line integral, we first need to parameterize the line segment from (3,3,2) to (1,2,5). One way to do this is to let x = 3-t, y = 3-t/2, and z = 2+3t/2, where [tex]0 \leq t \leq 1[/tex]. Then, the line integral can be written as:

[tex]\int\limits^c {y^2*z^2 ds} \, = \int\limits^0_1 {f(x(t),y(t),z(t)) ||r'(t)|| dt} \,[/tex]

where r(t) = <x(t), y(t), z(t)> is the parameterization of the line segment, ||r'(t)|| is the magnitude of the derivative of r(t), and [tex]f(x,y,z) = y^2*z^2[/tex] is the function that we are integrating.

We can calculate r'(t) using the parameterization we chose:

r'(t) = <-1, -1/2, 3/2>

and ||r'(t)|| = sqrt(11)/2. Substituting everything into the line integral, we get:

[tex]\int\limits^c {y^2*z^2 ds} \, = \int\limits^0_1 {(2+3t/2)^2 (3-t/2)^2 ||r'(t)|| dt} \,[/tex]

Simplifying this expression, we get:

[tex]\int\limits^c {y^2*z^2 ds} \, = \int\limits^0_1 {(27/4 t^4 - 39/2 t^3 + 41/2 t^2 - 27/4 t + 4) sqrt(11)/2 dt} \,[/tex]

Evaluating this integral using the limits of integration 0 and 1, we get:

[tex]\int\limits^c {y^2*z^2 ds} \, = -27/5[/tex]

Therefore, the line integral of [tex]f(x,y,z) = y^2*z^2[/tex] along the line segment from (3,3,2) to (1,2,5) is -27/5.

Learn more about integration here:

https://brainly.com/question/31744185

#SPJ11

Low Earth Orbit (LEO) is a term used to describe the orbit of a spacecraft or satellite that is relatively close to Earth. The altitude range considered typical for LEO is between b) 60 to 1000 miles.

Within this range, most LEO satellites orbit at an altitude of approximately 250 to 300 miles above the Earth's surface.
LEO is an important orbit for a variety of space missions, including Earth observation, communications, and scientific research. Satellites in LEO typically have a shorter orbital period than those in higher orbits, which allows them to provide more frequent observations of the Earth's surface. Additionally, the closer proximity to Earth allows for stronger signals and faster data transfer rates for communications.
The altitude range of LEO is important because it affects the satellite's speed and the amount of time it takes to complete an orbit. Satellites in lower altitudes, such as below 60 miles, have a faster orbital velocity and complete more orbits per day than those at higher altitudes. On the other hand, satellites at higher altitudes, such as 700 to 1000 miles, have a slower orbital velocity and complete fewer orbits per day.
In summary, the typical altitude range for Low Earth Orbit is between 60 to 1000 miles, with most LEO satellites orbiting at an altitude of approximately 250 to 300 miles.

To learn more about Low Earth Orbit, refer:-

https://brainly.com/question/30175028

#SPJ11

The midpoint M of the line segment AB is (1,6).

The midpoint formula is expressed as:

[tex]M = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

Where (x₁, y₁) and (x₂, y₂) are the coordinates of the two endpoints of the line segment.

Given the coordinates of the endpoints AB:

Point A (-3,4)

Point B (5,8)

Plug the values into the above midpoint formula and simplify.

[tex]M = (\frac{-3+5}{2},\frac{4+8}{2})\\\\M = (\frac{2}{2},\frac{12}{2})\\\\M = (1,6)[/tex]

Therefore, the midpoint of the line is (1,6).

Learn more about midpoint here: brainly.com/question/29164764

#SPJ1

The average rate of change of the function r(x) = x² + 2x - 5 over the interval [0,3] is given as follows:

r = 5.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function.

The function for this problem is defined as follows:

r(x) = x² + 2x - 5.

The numeric values of the function are given as follows:

Hence the average rate of change is given as follows:

r = (10 - (-5))/(3 - 0)

r = 5.

More can be learned about the average rate of change of a function at brainly.com/question/11627203

#SPJ1

The sample space provided represents the possible outcomes of rolling a blue die and a gray die together. Each die has six sides, numbered one to six. The sample space consists of 36 possible outcomes, which are the different combinations of numbers that can be rolled on both dice.

The first die has six possible outcomes (1, 2, 3, 4, 5, and 6), and for each outcome of the first die, there are six possible outcomes for the second die. Therefore, the sample space consists of 6 × 6 = 36 possible outcomes. Each outcome is represented by a pair of numbers, where the first number represents the number on the blue die and the second number represents the number on the gray die.

The sample space is an important concept in probability theory as it represents all the possible outcomes of an experiment. In this case, the experiment is rolling two dice together, and the sample space provides a complete list of all the possible outcomes. This can be used to calculate probabilities for different events, such as the probability of rolling a certain combination of numbers or the probability of rolling a certain sum of numbers. The sample space is also useful for visualizing the different outcomes and understanding the structure of the experiment.

Learn more about Sample space:

brainly.com/question/30206035

#SPJ11

The correct answer is:  OC. True. The zeros of f' are the local extrema of f.

By the first derivative test, if f'(x) changes sign from positive to negative at a critical point, then there is a local maximum at that point. If f'(x) changes sign from negative to positive at a critical point, then there is a local minimum at that point.

In this case, the zeros of f' are -3, 1, and 4, which are the critical points of f. Therefore, by the first derivative test, there are local extrema of f at these points.

Option A is incorrect because the denominator of f' is not relevant in determining the local extrema of f. Option B is incorrect because the zeros of f' are not necessarily inflection points. Option D is incorrect because a zero of f' is not necessarily a local extremum unless f'(x) changes sign at that point.

Learn more about zeros here:

https://brainly.com/question/29120033

#SPJ11

The required polynomial having the given zeroes is x³ - 8x² + 22x - 20.

The given zeroes are

3 + i, 2

Now let,

x = 3+i or x = 2

If 3 + i is a zero then its conjugate must be a zero of polynomial

Then x = 3-i

therefore, we can write is as

x - 3 - i = 0 or  x - 3+i = 0 or x - 2 =0

The its product must be zero,

(x - 3)+i)  (x - 3)-i) (x - 2) =0

⇒  ((x - 3)² - i²)(x-2) = 0

⇒  (x² - 6x + 10)(x-2)                              (since i² = -1)

⇒  x³ - 6x² + 10x - 2x² + 12x - 20

⇒  x³ - 8x² + 22x - 20

Thus, the polynomial be,

x³ - 8x² + 22x - 20

To learn more about equation visit:

https://brainly.com/question/29174899

#SPJ1

We have a sample of 10 randomly selected children with Tourette syndrome, and we need to find a 95% confidence interval for the tics per hour exhibited by children with Tourette syndrome. Tourette syndrome is between 3.094 and 9.106.

To calculate the confidence interval, we first calculate the sample mean and standard deviation, which are 6.1 and 3.69, respectively. Then we calculate the margin of error, which is the product of the t-score (with 9 degrees of freedom and a 0.025 tail probability) and the standard error (which is the sample standard deviation divided by the square root of the sample size). The margin of error is 2.241. Finally, we construct the confidence interval by adding and subtracting the margin of error from the sample mean. Therefore, the 95% confidence interval is (6.1 - 2.241, 6.1 + 2.241), which simplifies to (3.059, 8.541).

This means we can be 95% confident that the true mean tics per hour exhibited by all children with Tourette syndrome is between 3.059 and 8.541. This interval provides a range of plausible values for the population mean, based on the observed sample.

The 95% confidence interval for the tics per hour exhibited by children with Tourette syndrome is (3.059, 8.541) based on the given data.

Learn more about margin here:

https://brainly.com/question/28481234

#SPJ11

The doubling time of a population can be computed by using the exponential growth formula: dt = ln(2)/r.

Exponential growth refers to a situation where the value keeps on increasing at a constant rate relative to the initial value.

The exponential growth function represents this situation and is given as

f(x) =a(1+r)ˣ

f(x) = exponential growth function

a = initial amount or value

r = growth rate

x = period of time

To find the population's doubling time, we can apply the exponential formula for time: dt = ln(2)/r

Where:

dt = the doubling time,

r = the growth rate (expressed as a decimal fraction)

ln(2) = the natural logarithm of 2 (about 0.693)

For instance, when a population has a growth rate of 0.05 (5%) per year, its doubling time is about ln(2)/0.05 = 13.9 years.

Thus, one can calculate the exact doubling time of a population by using the exponential growth equation above, solving for time.

Learn more about exponential growth equations at https://brainly.com/question/13223520.

#SPJ1

Answer:

We need to know the rate constant (k), which can be determined experimentally or given in the reaction's rate equation to calculate the half-life of a reaction or decay process.

Once you have the rate constant, you can use the following formula:

[tex]\bold{t_{\frac{1}{2}}=\frac{ln 2}{k}}[/tex]

Where:

[tex]t_{\frac{1}{2}}[/tex]

represents the half-life of the reaction or decay process.

ln represents the natural logarithm.

k is the rate constant.

By plugging in the appropriate rate constant into the formula, you can calculate the half-life for a specific chemical reaction or decay process.

Answer:

Orthocenter

Step-by-step explanation:

The orthocenter is the intersection point of the altitudes drawn from the vertices of the triangle to the opposite sides. For an acute triangle, it lies inside the triangle. For an obtuse triangle, it lies outside of the triangle. For a right-angled triangle, it lies on the vertex of the right angle.

The solutions of the system of equations are:

(2, -9) and (1, -8)

Here we want to solve the system of equations:

y = x² - 4x - 5

y = -x - 7

To solve this we can write:

-x - 7 = x² - 4x - 5

We can rewrite this as:

x² - 4x - 5 + x + 7 = 0

x² - 3x + 2 = 0

Using the quadratic formula we will get the solutions:

[tex]x = \frac{3 \pm \sqrt{(-3)^2 - 4*1*2} }{2*1}\\ \\x = \frac{3 \pm 1}{2}[/tex]

Then the two solutions are:

x = (3 + 1)/2 = 2

x = (3 - 1)/2 = 1

Evaluating the line in these values:

when x = 2

y = -2 - 7 = -9

when x = 1

y = -1 - 7 = -8

Then the solutions are (2, -9) and (1, -8)

Learn more about systems of equations:

https://brainly.com/question/13729904

#SPJ1

The area of the shaded region shown is 84.81 cm².

The area of the shaded region shown is calculated as follows;

Area of shaded region = area of hexagon - area of the parallelogram;

Area of the hexagon = ¹/₂ (a) x (P)

where;

Area of the hexagon = ¹/₂ x (5√3) x (6 x 10)

Area of the hexagon = 259.81  cm²

The side length of the parallelogram is calculated as;

s² = (5√3)² + 10²

s² = 75 + 100

s = √ (175)

s = 13.229

Area = s² = 175 cm²

Area of shaded region = 259.81 cm² - 175 cm² = 84.81 cm²

Learn more about area of shaded region here: https://brainly.com/question/14989383

#SPJ1

The Minimum  Surface area of paper required to wrap each box is 4470 square centimeters.

To determine the minimum area of paper required to wrap each box produced by Edward Boxmakers, we need to find the surface area of the box. The surface area of a rectangular box can be found by adding the areas of all six sides. In this case, the box has three pairs of sides, each with the same area, so we can simplify the formula to:

Surface Area = 2lw + 2lh + 2wh

where l = 40 cm, w = 25 cm, and h = 19 cm

Substituting these values into the formula, we get:

Surface Area = 2(40)(25) + 2(40)(19) + 2(25)(19)

Surface Area = 2000 + 1520 + 950

Surface Area = 4470 cm²

Therefore, the minimum area of paper required to wrap each box is 4470 square centimeters.

To know more about Surface area.

https://brainly.com/question/16519513

#SPJ11

The correct statements regarding the quadratic function are given as follows:

The quadratic function in the context of this problem is defined as follows:

y = 2x(x - 11).

Using the factor theorem, the roots are given as follows:

Hence the x-intercepts are given as follows:

The standard format of the function is given as follows:

y = 2x² - 22x.

Hence the coefficients are:

a = 2, b = -22.

Hence the x-coordinate of the vertex is given as follows:

x = -b/2a

x = 22/4

x = 5.5.

More can be learned about quadratic functions at https://brainly.com/question/4061870

#SPJ1

Answer:

Step-by-step explanation:

You want the lengths of the baselines in a right triangle figure with hypotenuse 34, and angles marked 42° and 63°.

The mnemonic SOH CAH TOA reminds you of the trig relations:

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

  Tan = Opposite/Adjacent

The side given as 34 is the hypotenuse of the larger triangle, and the side marked 'b' is adjacent to the given angle 42°. This tells us we can use the cosine relation:

  cos(42°) = b/34

  b = 34·cos(42°) ≈ 25.2669 ≈ 25.27

Once we find 'a', we can find 'c' by subtraction. To find 'a', we need to know the measure of the vertical side opposite the angle 42°.

  sin(42°) = (vertical side)/34

  vertical side = 34·sin(42°) ≈ 22.7504

We now have the side opposite angle 63°, so we can find the side adjacent (a) using the tangent relation:

  tan(63°) = (vertical side)/a = 22.7504/a

  a = 22.7504/tan(63°) ≈ 11.5919 ≈ 11.59

Now the length c can be found from ...

  c = b -a

  c = 25.2669 -11.5919 ≈ 13.67

The lengths are ...

  a ≈ 11.59, b ≈ 25.27, c ≈ 13.67

__

Additional comment

As is often the case with rounded numbers, the sum of the rounded numbers is not the same as the rounded value that represents their total. You need more significant digits than shown above to see why. The calculator image in the attachment shows values with more significant digits.

The calculator expression uses 34·sin(42°)/tan(42°) for 34·cos(42°). These are equivalent, and we know the calculator has sufficient precision that the result is the same either way. This lets us find both 'a' and 'b' in one calculator entry. The final result is [a | b | c].

<95141404393>

To solve these probability questions, we'll use the standard normal distribution since the per capita consumption of soft drinks is assumed to be approximately normally distributed.

a) To find the probability that someone in the United States consumed more than 750 eight-ounce servings, we need to calculate the area under the standard normal curve to the right of the z-score corresponding to 750 servings.

We'll use the formula:

P(X > 750) = 1 - P(X ≤ 750)

First, we need to standardize the value 750 using the z-score formula:

z = (x - μ) / σ

where x is the value (750), μ is the mean (642), and σ is the standard deviation (100).

z = (750 - 642) / 100

z = 1.08

Using a standard normal distribution table or a calculator, we can find the cumulative probability for z = 1.08. The area to the left of z = 1.08 is approximately 0.8599.

P(X > 750) = 1 - 0.8599

P(X > 750) ≈ 0.1401

Therefore, the probability that someone in the United States consumed more than 750 eight-ounce servings is approximately 0.1401.

b) To find the probability that someone in the United States consumed between 450 and 500 eight-ounce servings, we need to calculate the area under the standard normal curve between the z-scores corresponding to 450 and 500 servings.

First, we standardize the values 450 and 500:

z1 = (450 - 642) / 100

z1 = -1.92

z2 = (500 - 642) / 100

z2 = -1.42

Using the standard normal distribution table or a calculator, we can find the cumulative probabilities for z = -1.92 and z = -1.42. The area to the left of z = -1.92 is approximately 0.0274, and the area to the left of z = -1.42 is approximately 0.0778.

P(450 ≤ X ≤ 500) = P(X ≤ 500) - P(X ≤ 450)

P(450 ≤ X ≤ 500) = 0.0778 - 0.0274

P(450 ≤ X ≤ 500) ≈ 0.0504

Therefore, the probability that someone in the United States consumed between 450 and 500 eight-ounce servings is approximately 0.0504.

c) To find the probability that someone in the United States consumed less than 450 eight-ounce servings, we need to calculate the area under the standard normal curve to the left of the z-score corresponding to 450 servings.

Using the z-score formula:

z = (450 - 642) / 100

z = -1.92

Using the standard normal distribution table or a calculator, we can find the cumulative probability for z = -1.92. The area to the left of z = -1.92 is approximately 0.0274.

P(X < 450) ≈ 0.0274

Therefore, the probability that someone in the United States consumed less than 450 eight-ounce servings is approximately 0.0274.

d) To find the value where 99% of the people in the United States consumed less, we need to find the z-score that corresponds to a cumulative probability of 0.99. This value will be the number of standard deviations from the mean.

Using the standard normal distribution table or a calculator, we can find the z-score that corresponds to a cumulative probability of 0.99. This z-score represents the number of standard deviations from the mean.

The z-score corresponding to a cumulative probability of 0.99 is approximately 2.33.

Now, we can use the z-score formula to find the corresponding value of soft drink consumption:

z = (x - μ) / σ

We rearrange the formula to solve for x:

x = z * σ + μ

Substituting the values:

x = 2.33 * 100 + 642

x = 233 + 642

x = 875

Therefore, 99% of the people in the United States consumed less than 875 eight-ounce servings of soft drinks in 2016.

Learn more about standard normal distribution here : brainly.com/question/15103234

#SPJ11    

Answer:

k = 5

Step-by-step explanation:

Answer

If a 95% confidence interval includes the null value, then there is no statistically meaningful or statistically significant difference between the groups. If the confidence interval does not include the null value, then we conclude that there is a statistically significant difference between the groups. [ (n - 1)s2] / B < σ2 < [ (n - 1)s2] / A. Here n is the sample size, s2 is the sample variance. The number A is the point of the chi-square distribution with n -1 degrees of freedom at which exactly α/2 of the area under the curve is to the left of A.

The measure of angle 3, 4 and 5 from the given figure are 36°, 72° and 72° respectively.

From the given figure,

50°+65°+x=180° (By angle sum of property of a triangle)

115°+x=180°

x=180°-115°

x=65°

∠2=65° (Vertically opposite angles)

140°+y=180° (Sum of adjacent angles is 180°)

y=40°

Now, 40°+68°+∠5=180°

108°+∠5=180°

∠5=180°-108°

∠5=72°

∠4=∠5=72° (Vertically opposite angles)

∠3+∠4+∠5=180°

∠3+72°+72°=180°

∠3+144°=180°

∠3=36°

Therefore, the measure of angle 3, 4 and 5 from the given figure are 36°, 72° and 72° respectively.

To learn more about the vertical angle theorem visit:

brainly.com/question/8119520.

#SPJ1

a)   The arclength of the curve x = 2t^2, y = t^3, where 2 ≤ t ≤ 23, is approximately 73.11 units.

b)   The arclength of the curve x = 2cos(θ), y = 2sin(θ), where 0 ≤ θ ≤ π, is 2π units.

(a) To find the arclength of the curve x = 2t^2, y = t^3, where 2 ≤ t ≤ 23, we use the formula for arclength:

L = ∫(a to b) √[dx/dt]^2 + [dy/dt]^2 dt

First, we find the derivatives dx/dt and dy/dt:

dx/dt = 4t

dy/dt = 3t^2

Then, we plug them into the arclength formula and integrate:

L = ∫(2 to 23) √[(4t)^2 + (3t^2)^2] dt

L = ∫(2 to 23) √(16t^2 + 9t^4) dt

L = ∫(2 to 23) t√(16 + 9t^2) dt

To solve this integral, we can use the substitution u = 16 + 9t^2, du/dt = 18t, dt = du/18t. Substituting this into the integral, we get:

L = (1/18) ∫(52 to 8134) u^(1/2) du

L = (1/27) [u^(3/2)](52 to 8134)

L = (1/27) [(8164^(3/2) - 640) - (168^(3/2) - 640)]

L = (1/27) [1520√168 - 2004√2]

L ≈ 73.11

Therefore, the arclength of the curve x = 2t^2, y = t^3, where 2 ≤ t ≤ 23, is approximately 73.11 units.

(b) To find the arclength of the curve x = 2cos(θ), y = 2sin(θ), where 0 ≤ θ ≤ π, we use the formula for arclength:

L = ∫(a to b) √[dx/dθ]^2 + [dy/dθ]^2 dθ

First, we find the derivatives dx/dθ and dy/dθ:

dx/dθ = -2sin(θ)

dy/dθ = 2cos(θ)

Then, we plug them into the arclength formula and integrate:

L = ∫(0 to π) √[(-2sin(θ))^2 + (2cos(θ))^2] dθ

L = ∫(0 to π) 2 dθ

L = 2π

Therefore, the arclength of the curve x = 2cos(θ), y = 2sin(θ), where 0 ≤ θ ≤ π, is 2π units.

Learn more about arclength here:

https://brainly.com/question/24251184

#SPJ11

After polygon STUV is reflected across the y-axis, the coordinates of point S' are (-2, 3).

Reflecting a polygon across the y-axis is a type of transformation in geometry that involves flipping the shape over the y-axis. When reflecting a polygon across the y-axis, the x-coordinates of all the points in the shape are multiplied by -1, while the y-coordinates remain the same.

In the case of polygon STUV, point S has coordinates (2, 3). When reflected across the y-axis, the x-coordinate becomes -2, while the y-coordinate remains 3. Therefore, the image of point S after the transformation, denoted as S', has coordinates (-2, 3).

It's important to note that reflecting a polygon across the y-axis is just one of many possible transformations in geometry. Other common transformations include translations, rotations, and dilations. These transformations can be used to explore the properties of shapes and to solve problems in geometry.

Learn more about polygon here:

https://brainly.com/question/23846997

#SPJ11