The change in electric potential energy of an alpha particle is:
1.3V/cm
"Information available from the question"
In a region where there is a uniform electric field, the potential, v1, is 1. 3 v at position y1=26 cm.
At position y2=28 cm , the potential, v2, is 3. 9 v.
Now, According to the question:
Calculation of magnitude:
Since V1 is 1.3 V at position y1=26 cm. At position y2=28 cm, the potential, V2, is 3.9 V
So, We know that
[tex]E =\frac{V_2-V_1}{Y_2-Y_1}[/tex]
[tex]E=\frac{3.9-1.3}{28-26}[/tex]
[tex]E=\frac{2.6}{2}[/tex]
E = 1.3V/cm
Learn more about Magnitude at:
https://brainly.com/question/14452091
#SPJ4
HELP ASAP !!!!!!!PLEASE
Due to the fact that they are both increased to the same power, the two functions are exponential. Both functions have distinct constants and rates.
What is a function?A unit of code known as a function carries out a particular task. A function in mathematics is a relationship between a set of allowable inputs and outputs, having the condition that each input is connected to exactly one output.
As illustrated in the graphic that represents the posed question, the two functions that we are considering are all such that we can see that they are exponential in nature.
Learn more about function:https://brainly.com/question/12431044?
#SPJ1
Find the measure of the indicated angle in each triangle?
The measure of ∠U= 80°, ∠B=44°, ∠Q= 93° respectively which indicates the angle of each triangle.
First take the Triangle TUV:
⇒∠T+∠U+∠V=180°
⇒37°+∠U+63°=180°
⇒∠U+100°=180°
⇒∠U=80°
Now, take triangle ABC:
⇒∠A+∠B+∠C=180°
⇒46°+∠B+90°=180°
⇒∠B+136°=180°
⇒∠B=44°
Finally take triangle PQR:
⇒∠P+∠Q+∠R=180°
⇒51°+∠Q+36°=180°
⇒∠Q+87°=180°
⇒∠Q=93°
Therefore, measure of the indicated angle in each triangle are 80°, 44 and 93° respectively.
Learn more about Triangles:
https://brainly.com/question/14366937
#SPJ4
Solve for lengths of the missing sides in each pair of similar triangles. Round to nearest tenth if if necessary jk kl
For the given similar triangles, the length of the missing side in the second triangle is 20.
To solve for the length of the missing side in the pair of similar triangles, we can use the SSS similarity theorem. The theorem states that 'if all three pairs of corresponding sides of two triangles are proportional, then the two triangles are similar'. Since the triangles are similar, the ratio of their corresponding sides will be equal.
The given measurements of the first triangle are 12, 18, and 24, and the measurements of the second triangle are 10, 15, and x. To solve for x, you can use the ratio of corresponding sides of similar triangles. The ratio for the sides of the first triangle are 12:18:24 and for the second triangle are 10:15:x. The ratio of the corresponding sides is 10:12, 15:18, and x:24.
We can set up a proportion using the given dimensions and solve for x.
The proportion will look like this:
12/10 = 18/15 = 24/x
Cross-multiplying and simplifying, we get:
12x = 240
x = 20
Therefore, the length of the missing side in the second triangle is 20.
Note: The question is incomplete. The complete question probably is: Solve for length of the missing side in the pair of similar triangles. The dimensions of one triangle are 12, 18, and 24, and the dimensions of the second triangle is 10, 15, and x. (These are corresponding measurements).
Learn more about Similar triangles:
https://brainly.com/question/29782809
#SPJ11
Male and female high school students reported how many hours they worked each week in
summer jobs. The data is represented in the following box plots.
0
Males
Females
4.
10
20
30
40
50
Identify any values of data that might affect the statistical measures of spread and center. (1
point)
The value of data that might affect the statistical measures of spread and center is B. There is a high data value that causes the data set to be asymmetrical for the males.
How can spread and center be affected ?Outliers stretch out the data further, resulting in a wider range and a higher standard deviation. On the other hand, eliminating outliers reduces data spread, resulting in a lower range and standard deviation.
When an outlier is present, it might change the way the graph looks since it raises the mean. From the chart, there is a high data value in the males which will therefore make the data to be asymmetrical for the males as the larger spread for the males means the data set tilts towards them.
Find out more on spread and center at https://brainly.com/question/28660799
#SPJ1
Question in the picture.
The domain and range of the function for the given graph is -
Domain : (-∞, + ∞)Range: [3, ∞)Define the term domain and range of the function?The range of values which we're permitted to enter into our function is known also as domain of a function.
The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.The collection of all potential inputs for a function is its domain.The collection of potential output values for a function is known as its range. For instance, the range seems to be the non-negative real numbers for the function f(x)=x2 here on domain among all real numbers (xR), which may be represented as f(x)≥0 (or [0,∞) using interval notation).Thus, the domain and range of the function for the given graph is -
Domain : (-∞, + ∞)Range: [3, ∞)To know more about the function, here
https://brainly.com/question/11624077
#SPJ1
Write an exponential function for a graph that passes through the points (3, 2.8) and (4, 5.6) . Write the function in the form y=a(b)x.
The formula of the given exponential function whose graph passes through the points (3, 2.8) and (4, 5.6) is :
y = 0.35* (2)ˣ
What is an exponential function?
When the input variable x appears as an exponent in the formula
f(x) = aˣ, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x. It is mostly used to determine exponential growth or decay.
When there is exponential growth, the quantity grows initially extremely slowly and subsequently quickly. Over time, the rate of change quickens. As time goes on, the rate of increase accelerates. In exponential decay, the quantity initially falls very quickly and then gradually. Over time, the rate of change slows. As time goes on, change happens at a slower rate.
The general formula of an exponential function is:
y = abˣ
It is said that points (3, 2.8) and (4, 5.6) are present on the graph of the given exponential function.
W can substitute these value values in the above formula.
2.8 = ab³
5.6 = ab⁴
Dividing the above equations,
2.8 /5.6 = b³/b⁴
1/2 = 1/b
b = 2
Now substituting this value in one of the equations to find the value of a.
2.8 = a. (2)³
a = 2.8/8 = 0.35
Therefore the formula of the given exponential function is :
y = 0.35* (2)ˣ
To learn more about exponential function, follow the link.
https://brainly.com/question/2456547
#SPJ1
What is the difference between positive and negative z-score table?
Z-scores can be either positive or negative, with a positive number signifying a score above the mean and a negative value signifying a score below the mean according to the z-score table.
The statistical measurement known as the Z-score describes the relationship between a value and the mean of a group of values. Z-score is quantified by the standard deviations from the mean. The mean score and the data point's score are equal when the Z-score is 0. The Z-score for a value that deviates by one standard deviation is 1.0. Z-scores are binary, with a positive value denoting a score above the mean and a negative value denoting a score below the mean.
Equation of the z-score: z = ( x - μ ) / σ
Get the value corresponding to one decimal place of the z-score by first looking at the left side column of the z-table.
Learn more about Z-Score:
https://brainly.com/question/15016913
#SPJ4
A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.
Number of hours Total number of students
0 1
1 3
2 2
3 5
4 9
5 7
6 3
Determine the probability that a student studied for 1 hour.
1.0
0.9
0.3
0.1
hellppppppp ASAP
The probability that a student studied for 1 hour will be 0.10. Then the correct option is D.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
The table is given below.
Number of hours Total number of students
0 1
1 3
2 2
3 5
4 9
5 7
6 3
The total number of students is given as,
Total = 1 + 3 + 2 + 5 + 9 + 7 + 3
Total = 30
Then the probability that a student studied for 1 hour is given as,
P = 3 / 30
P = 0.10
The probability that a student studied for 1 hour will be 0.10. Then the correct option is D.
More about the probability link is given below.
https://brainly.com/question/30034780
#SPJ9
Translation: 2 units left and 1 unit down. Q(0,-1), D(-2,2), V (2,4), J(3,-3)
Translation: 2 units left and 1 unit down. Q(0,-1), D(-2,2), V (2,4), J(3,-3)
New coordinates are respectively, (-2, -2), (-4, 1), (0, 3), (1, -4)
What is the point?A point is a location of an object by taking reference of origin, In general case we consider it at (0,0), At the origin value of both the coordinate position is considered as Zero, In simple words point indicates how much it is above or below from the coordinate axes.
Vertical distance from the x axis is known as y coordinate and horizontal distance from the y axis is known as x coordinate.
Given the points Q(0,-1), D(-2,2), V (2,4), and J(3,-3),
we can see that each point has been translated 2 units to the left and 1 unit down.
This is because each x-coordinate has decreased by 2 and each y-coordinate has decreased by 1.
So, the translation of 2 units left and 1 unit down has moved each point along the plane in the negative x-direction and the negative y-direction.
the points are respectively (-2, -2), (-4, 1), (0, 3), (1, -4)
To know more about Point check:
https://brainly.com/question/2168690
#SPJ9
Use the triangles to answer the question. Triangle A B C with A B = square root of 13, B C = 2, A C = 3, and angle C is labeled as a right angle. Also shown is triangle D E F with E F = 4, D F = 6, and angle F is labeled as a right angle. © 2016 StrongMind. Created using GeoGebra. If △ABC∼△DEF, what is the scale factor for the dilation that maps △ABC to △DEF? Enter your answer as a number.
The scale factor for the dilation that maps △ABC to △DEF is 0.75.
What is triangle?A triangle is a geometric shape that consists of three line segments that connect to form three angles. These angles always add up to 180 degrees. A triangle has three sides and three vertices (corners). Triangles can have different shapes and sizes, and they are often classified based on the length of their sides or the size of their angles. Some common types of triangles include equilateral triangles (where all sides are equal in length and all angles are equal to 60 degrees), isosceles triangles (where two sides are equal in length), and right triangles (where one angle is a right angle, or 90 degrees). Triangles have many properties and are an important part of geometry and mathematics.
Here,
To determine the scale factor for the dilation that maps △ABC to △DEF, we need to find the ratio of the corresponding side lengths of the two triangles.
Since △ABC ∼ △DEF, we know that the corresponding angles of the two triangles are congruent. Therefore, angle B in △ABC corresponds to angle E in △DEF, and angle A in △ABC corresponds to angle D in △DEF.
Using the Pythagorean theorem, we can find the length of the missing side of △DEF:
DF² = DE² + EF²
6² =DE² + 4²
DE=√20
DE=2√5 units
3/4=2/2√5=√13/6=0.75
To know more about triangle,
https://brainly.com/question/28600396
#SPJ1
Is it possible to form a triangle with side lengths 3.5, 3.5, and 9? If so, will it be scalene, isosceles, or equilateral? A. Yes; scalene O B. Yes; isosceles O C. Yes; equilateral O D. No
No , it is not possible to form a triangle with side lengths 3.5, 3.5, and 9 , because of the rule that sum of any two sides must be greater than other side. So, Option D is correct.
A triangle is a two-dimensional shape formed by three line segments connecting three points. In order to form a triangle, a necessary and sufficient condition is that the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the triangle inequality theorem.
If the sum of the lengths of any two sides is less than or equal to the length of the third side, then the three line segments will not be able to form a closed shape, and therefore cannot form a triangle.
In the case of the triangle with side lengths 3.5, 3.5, and 9, the sum of the lengths of the first two sides is 7, which is less than the length of the third side, 9. Hence, these three side lengths do not satisfy the triangle inequality theorem, and therefore cannot form a triangle.
In general, to determine the type of triangle that can be formed with three given side lengths, it is necessary to compare the lengths of the sides and check if any two sides are equal in length (isosceles), or if all three sides are equal in length (equilateral). If none of the sides are equal, then the triangle is called scalene.
In this case, since it is not possible to form a triangle with the given side lengths, it is not possible to determine the type of triangle that would be formed.
To learn more about triangle click on,
https://brainly.com/question/21228157
#SPJ4
what is the solution to the system
line 1: y= -2x-4
line 2: y=2/5x + 16/5
The solution of system of equation y= -2x-4 and y=2/5x + 16/5 is (-3, 2).
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The system of equations are y= -2x-4
and y=2/5x + 16/5
By substitution method let us find the solution.
2/5x + 16/5=-2x-4
2/5x+2x=-4-16/5
12x/5=-20-16/5
12x=-36
Divide both sides by 12
x=-3
Now plug in x value in any of the equation
y=-2(-3)-4
y=6-4
y=2
Hence, the solution of system of equation y= -2x-4 and y=2/5x + 16/5 is (-3, 2).
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ9
What is the equation of the line that passes through the point (5,0) and has a slope of 6/5?
The solution is, the equation of the line that passes through the point (5,0) and has a slope of 6/5 is , y=6/5*x - 6
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
here, we have,
the line that passes through the point (5,0) and has a slope of 6/5
now, w know, the point slope form of straight line is,
y-y1=m(x-x1)
so, putting the values , we get,
y-0=6/5(x-(5))
y-0=6/5(x-5)
y=6/5*x- 30/5
y=6/5*x- 6
Hence, The solution is, the equation of the line that passes through the point (5,0) and has a slope of 6/5 is , y=6/5*x - 6
To learn more on Equation 0f Straight-Line click:
brainly.com/question/11116168
#SPJ1
Can someone help me answer this question??? LOL :)
For the exponential function:
g(x) = 14*(2)^x
We can see that:
a = 14, and b = 2.
How to identify the parts of the exponential function?A general exponential function is written as:
y = a*(b)^x
Where a is the inital value of the exponential function and b is the base.
Here we have the exponential function:
g(x) = 14*(2)^x
Comparing that to the general one, we can see that the initial value is 14 and the base is 2.
Then:
a = 14
b = 2
The correct option is the second one.
Learn more about exponential functions at.
https://brainly.com/question/11464095
#SPJ1
Help. This is 2 parts
Answer:can u take a picture that is a bit more closer
Step-by-step explanation:
please submit a closer picture
What does 500x235 equal?
Answer:
[tex]117500[/tex]
Step-by-step explanation:
[tex]500 \times 235=100\times (5\times 235)=1175 \times 100=117500[/tex]
Answer: 117,500
Step-by-step explanation: 500 x 235 = 117,500
if a residual is negative, then that data point lies _________________ the regression line.
A residual is the difference between an observed value and the predicted value from a regression line.
A negative residual indicates that the observed value lies below the regression line. This can be expressed mathematically using the formula [tex]y = mx + b[/tex], where y is the observed value, m is the slope, x is the independent value, and b is the y-intercept of the line.
For example, if the observed value is y = 3, the predicted value is y = 5, and the slope and intercept of the line are m = 2 and b = 1, respectively, then the residual can be calculated as [tex]y = 3 - (2*1 + 1) = -1.[/tex] Since the residual is negative, this indicates that the observed value lies below the regression line.
Learn more about regression line here:
https://brainly.com/question/17731558
#SPJ4
Based on the t-test assuming equal variances on the T-Test Equal worksheet, is it reasonable to assume that the variances are equal? O Examining the ratio of the variances, it is reasonable to conclude that the variances are unequal. O Whether the variances are equal or not is not relevant for this situation.O Examining the ratio of the variances, it is reasonable to conclude that the variances are equal. O It is impossible to determine if the variances are equal given the data we have.
Based on the t-test assuming equal variances "Examining the ratio of the variances, it is reasonable to conclude that the variances are unequal."
When conducting a t-test assuming equal variances, it is necessary to determine whether or not the variances of the two groups being compared are actually equal. This is important because the calculation of the t-statistic depends on the assumption of equal variances.
To assess the assumption of equal variances, one can examine the ratio of the variances of the two groups. Typically, if the ratio of the variances is greater than 2 or less than 1/2, then it is reasonable to conclude that the variances are unequal. In the absence of such evidence, one can assume that the variances are equal.
Therefore, it is not reasonable to assume that the variances are equal.
To learn more about Variances :
https://brainly.com/question/13708253
#SPJ4
The result of a number, when decreased by 66 2/3%, is 432. Find the number
Answer:
1298/3 is the answer
Step-by-step explanation:
Answer:
1296
Step-by-step explanation:
Let the unknown number be x.
If 432 is the result of x being decreased by 66²/₃%, then 432 is 33¹/₃% of x since 100% - 66²/₃% = 33¹/₃%.
Therefore:
[tex]\implies 33\frac{1}{3}\%\;\textsf{of}\;x=432[/tex]
[tex]\implies \dfrac{33\frac{1}{3}}{100} \cdot x=432[/tex]
[tex]\implies \dfrac{33\frac{1}{3}x}{100} =432[/tex]
Multiply both sides of the equation by 100:
[tex]\implies 33\frac{1}{3}x =43200[/tex]
Rewrite 33¹/₃ as an improper fraction:
[tex]\implies \dfrac{100}{3}x =43200[/tex]
Multiply both sides by 3:
[tex]\implies 100x=129600[/tex]
Divide both sides by 100:
[tex]\implies x=1296[/tex]
Therefore, the number that when decreased by 66²/₃% is 432, is 1296.
Mrs. Gregory, the golf course superintendent at a country club, plans to reseed the putting green of the first hole. The circular putting green has a diameter of 38 ft.
People on golf course, aerial view.
What is the area of the putting green?
Use π=3.14.
Question 1 options:
------------------------
ANSWERS:
1133.54 ft²
119.32 ft²
1133 ft²
1314.14 ft²
Answer:
Step-by-step explanation: 1133.5.
How many milliliter in 1 microliter?
From the given information provided, by converting the units there are 0.001 milliliters in 1 microliter.
This means that if you have 1 microliter of liquid, it is equal to 0.001 milliliters of liquid.
The conversion factor between milliliters (mL) and microliters (μL) is:
1 mL = 1000 μL
Therefore, to convert microliters to milliliters, you divide the number of microliters by 1000.
For example, if you have 500 μL of liquid, you can convert it to milliliters by dividing 500 by 1000:
500 μL / 1000 = 0.5 mL
So, 500 microliters of liquid is equal to 0.5 milliliters of liquid.
Learn more about unit conversion here: brainly.com/question/13016491
#SPJ4
1. A solid metal cuboid has a volume of 600cm3.
(a) The base of the cuboid is 10cm by 12cm. Calculate the height of the cuboid.
(b) The solid metal cuboid is melted and made into 1120 spheres, each with radius 0.45cm. Find the volume of metal not used in making these spheres.
Answer:
(a) The height of the cubiod is 5cm.
(b) The volume of metal not used in making these spheres is 172cm^3.
Step-by-step explanation:
(a) 12*10= 120
600/120= 5cm
(b) volume of 1120 spheres= (4/3*π*0.45^3)(1120)
= 428cm^3 (to 3 s.f.)
600-428= 172cm^3
How many inches are there in 150 meters?
1 m≈39.37 in.
Responses
3.8 in.
3.8 in.
1554.1 in.
1554.1 in.
4355.5 in.
4355.5 in.
5905.5 in.
5905.5 in.
Solve each system by graphing
x-y=3
7x-y=-3
Consider the equation pT=kVN, where k is a constant. Select all of the correct
answers that describe the variation between variables.
p varies [inversely or directly]with V
N varies [inversely or directly]with V
p varies [ inversely or directly]With T
T varies [ inversely or directly] with N
The correct answer is P and T directly varies with V and N, and P and N inversely varies with T and V respectively.
What is direct variation?It is the mathematical relationship between two variables which can be expressed by an equation in which one variable is equal to a constant times the other.
Given that, the equation pT = kVN, where k is a constant.
pT = kVN
If we remove constant, then,
pT ∝ VN
or
p 1/∝ T
V 1/∝ N
Hence, the correct answer is P and T directly varies with V and N, and P and N inversely varies with T and V respectively.
Learn more about direct variation, click;
https://brainly.com/question/13977805
#SPJ1
Use technology to find points and then graph the function y = log₂ (x − 1) — 5,
following the instructions below.
done plotting points
Plot at least four points that fit on the axes below. Click a point to delete it.
10 9 8
10
8
N
9
4
3
10
The (x,y) coordinate points of the logarithmic function are as follows. (2, -5), (3, -4), (5, -3), (9, -2), (1, - 10).
The graph of a logarithmic function
The exponential function is thought of as the inverse of the logarithmic function because of its close relationship. The logarithmic function logaN = x is derived from the exponential function ax = N.
When seen as an exponential form, the logarithm of any integer N is the exponent to which the base of the logarithm needs to be raised in order to reach the value of N.
The fundamental logarithmic function has the notation f(x) = log_ax(r) y = log_a(x), where a > 0. Natural logarithm (ln) and common logarithm are examples of log functions (log).
From the given information, the logarithmic function y = log₂ (x − 1)- 5 is plotted on the graph and the following x,y points are obtained.
(x, y)(2, -5), (3, -4), (5, -3), (9, -2), (1, - 10).Learn more about the graph of a logarithmic function.
https://brainly.com/question/13473114
#SPJ1
You pick a card at random.
1 2 3 4
What is P(factor of 10)?
Write your answer as a fraction or whole number.
The probability of picking a factor of 10 is 1/4 or 0.25 as a decimal.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
To calculate the probability of picking a factor of 10, we need to count the number of cards that are factors of 10 and divide that by the total number of cards.
The factors of 10 are 1, 2, 5, and 10. Out of the given cards, only 2 is a factor of 10.
Therefore, the probability of picking a factor of 10 is 1/4 or 0.25 as a decimal.
Learn more about probability here:
brainly.com/question/14290572
#SPJ1
a wildlife biologist is doing research on chronic wasting disease and its impact on the deer populations in northern colorado. to estimate the difference between the proportions of deer with chronic wasting disease in two different regions, a random sample of 200 deer was obtained from one region and a random sample of 197 deer was obtained from the other region. the biologist checked for the following.
The biologist was checking the condition for inference that (d) the observations within each sample are close to independent.
This is concluded from the fact that the biologist was checking if the product of sample size and the proportion of deer with chronic wasting disease in each sample was greater than or equal to 10. This is a commonly used rule of thumb to ensure that each sample has enough data to provide meaningful information about the population, and it is based on the idea that the sample size should be large enough such that the expected number of success (deer with chronic wasting disease) is at least 10 and the expected number of failures (deer without chronic wasting disease) is at least 10.
This helps to ensure that the observations within each sample are close to independent, as the sample proportions are unlikely to be greatly influenced by any individual deer in the sample.
Correct Question :
A wildlife biologist is doing research on chronic wasting disease and its impact on the deer populations in northern colorado. to estimate the difference between the proportions of deer with chronic wasting disease in two different regions, a random sample of 200 deer was obtained from one region and a random sample of 197 deer was obtained from the other region. the biologist checked for the following:
(200)(0.06)≥10
(200)(0.94)≥10
(197)(0.086)≥10
(197)(0.914)≥10
Which of the following conditions for inference was the biologist checking?
a. The population of deer within each region is approximately normal.
b. It is reasonable to generalize from the samples to the populations.
c. The samples are independent of each other.
d. The observations within each sample are close to independent.
e. The sampling distribution of the difference in sample proportions is approximately normal.
To learn more about inference here:
https://brainly.com/question/30026731
#SPJ4
20,−10,5,___ what comes next
The next term is -25.
What is the number pattern?A number pattern is a pattern in a series of numbers that represents the common relationship between the numbers. In Maths, number patterns are the patterns in which a list number that follows a certain sequence. usaually, the patterns establish the relationship between two numbers. It is known as the sequences of series in numbers.
Given;
The pattern20,−10,5,___
Here, first term is 20, second is -10
Difference=20+10
=30
Now,
=5-30
=-25
Therefore, the answer of the given pattern will be -25.
Learn more about a number pattern:
https://brainly.com/question/11659133
#SPJ9
At what points does the helix r(t) = sin(t), cos(t), t intersect the sphere x2 + y2 + z2 = 26? (round your answers to three decimal places. If an answer does not exist, enter dne. ).
At (0.958, 0.287, 5) and (0.958, -0.287, -5) points, the helix r(t) = sin(t), cos(t), t intersect the sphere x^2 + y^2 + z^2 = 26.
The sphere x^2 + y^2 + z^2 = 26 is a sphere with center at the origin and radius sqrt(26).
The helix r(t) = sin(t), cos(t), t is parameterized by sine and cosine functions, which oscillate between -1 and 1.
To find the points at which the helix intersects the sphere, we need to find the values of t such that the distance between r(t) and the origin is equal to sqrt(26).
The distance between a point (x, y, z) and the origin is given by the formula:
d = sqrt(x^2 + y^2 + z^2)
So, substituting the values from r(t), we have:
d = sqrt(sin^2(t) + cos^2(t) + t^2)
Setting d equal to sqrt(26), we have:
sqrt(sin^2(t) + cos^2(t) + t^2) = sqrt(26)
Squaring both sides, we have:
sin^2(t) + cos^2(t) + t^2 = 26
Recall that sin^2(t) + cos^2(t) = 1, so we have:
1 + t^2 = 26
Subtracting 1 from both sides, we have:
t^2 = 25
Taking the square root of both sides, we have:
t = ±5
So, the two points of intersection are (sin(5), cos(5), 5) and (sin(-5), cos(-5), -5).
Rounding the results to three decimal places, we have:
(sin(5), cos(5), 5) = (0.958, 0.287, 5)
(sin(-5), cos(-5), -5) = (0.958, -0.287, -5)
To know more on helix
https://brainly.com/question/16911869
#SPJ4