Answer:
24p8 - 36p6 + 36p2 = 48p
Step-by-step explanation:
I hope this helps!
y = x + 2y = -2x + 2y = -3x + 2y = -5x + 2y = -
3
2
x + 2y = -
5
2
x + 2y = -x + 2y = 2x + 2y = 5x + 2y =
5
2
x + 2
0
Answer:
i need more context
Step-by-step explanation:
Which graph below uses the correct number A. B. C. D.
Hence correct option is b with 4 colors.
Step by-step explanation:
We are given a graph in which we need to color every vertex or node such that no adjacent vertex or node should have the same color, ex:- If color of node B is blue than it's adjacent vertex A and D must not have the same blue color. Now, Let's start coloring of graph :
Color vertex A as red : Now, it's adjacent vertex as B,C,D,E must not have red color we know this!.
Color vertex B as blue: Now, it's adjacent vertex A and D must not have blue color!
Color vertex C as blue: Now, it's adjacent vertex A,E and D must not have blue color!
Color vertex D as green: Now, it's adjacent vertex A,B,C and E must not have green color!
Color vertex E as purple: Now, it's adjacent vertex C and D must not have purple color!
Hence correct option is b with 4 colors.
A bag contains 88 red, 66 orange, and 99 green jellybeans. What is the probability of reaching into the bag and randomly withdrawing 1212 jellybeans such that the number of red ones is 22, the number of orange ones is 44, and the number of green ones is 66? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer:
P ( 2 R , 4 O , 6 G ) = 0.0261
Step-by-step explanation:
Given:
- Red beans = 8
- Orange beans = 6
- Green beans = 9
Find:
What is the probability of reaching into the bag and randomly withdrawing 12 jellybeans such that the number of red ones is 2, the number of orange ones is 4, and the number of green ones is 6?
Solution:
- The question requires the number of selection of 12 jellybeans we can make from total available such that out of those 12 we choose 2 Red, 4 Orange and 6 Green.
- For selection we will use the combinations. So to choose 2 Red from 8; Choose 4 Orange from 6 and 6 green from 9 available. The number of possible outcomes with such condition is:
Outcomes ( 2 R , 4 O , 6 G ) = 8C2 * 6C4 * 9C6
= 28*15*84
= 35280
- The total number of outcomes if we randomly select 12 beans irrespective how many of each color we select from available 23 we have:
Outcomes ( Select 12 from 23 ) = 23C12
= 1352078
- Hence, the probability for the case is given by:
P ( 2 R , 4 O , 6 G ) = Outcomes ( 2 R , 4 O , 6 G ) / Outcomes ( Select 12 from 23 )
P ( 2 R , 4 O , 6 G ) = 35280 / 1352078 = 0.0261
Tara bought Three boxes of dog treats with 40 truth in each box two boxes of cat treats with 20 trees in each box simplify the expression below to find the total number of trees are bought
Answer:
Tara bought a total of 160 treats.
Step-by-step explanation:
We are given the following in the question:
Number of boxes of dog treats = 3
Number of treats in each dog box = 40
Total number of treats in dog box =
[tex]40 \times 3 = 120[/tex]
Number of boxes of cat treats = 2
Number of treats in each cat box = 20
Total number of treats in cat box =
[tex]20\times 2 = 40[/tex]
Total number of treats Tara brought =
Total number of treats in dog box + Total number of treats in cat box
[tex](40\times 3)+(20\times 2)\\= 120 + 40\\=160[/tex]
Thus, Tara bought a total of 160 treats.
PLZ HELPPPPPPPPPPPPPPPP
Statuary Hall is an elliptical room in the United States Capitol in Washington, D.C. The room is also called the Whispering Gallery because a person standing at one focus of the room can hear even a whisper spoken by a person standing at the other focus. The dimensions of Statuary Hall are 46 feet wide by 97 feet long. A) Find an equation that models the shape of the room.B) How far apart are the two foci?C) What is the area of the floor of the room?
Answer:
a) [tex]\frac{x^{2}}{2352.25} + \frac{y^{2}}{529} = 1[/tex], b) [tex]c = 42.7 ft[/tex], c) [tex]A \approx 3504.447 ft^{2}[/tex]
Step-by-step explanation:
a) An Ellipse centered at origin is modelled by using this formula:
[tex]\frac{x^{2}}{a^2} +\frac{y^2}{b^2}=1[/tex]
Where [tex]a, b[/tex] represents the lengths of horizontal and vertical axis, respectively. Let consider that horizontal axis is parallel and coincident with width of Statuary Hall. So, the measures of each axis are, respectively:
[tex]a = 48.5 ft, b = 23 ft[/tex]
By substituting known variables, the equation that models the hall is:
[tex]\frac{x^{2}}{2352.25} + \frac{y^{2}}{529} = 1[/tex]
b) The distance between origin and any of the foci is:
[tex]c = \sqrt{a^{2} - b^{2}} \\c = 42.7 ft[/tex]
c) The area of ellipse can determined by applying this formula:
[tex]A = \pi \cdot a \cdot b[/tex]
[tex]A \approx 3504.447 ft^{2}[/tex]
What do you know about the solution(s) to the system of equations?
A. There is no solution.
B. The solution is (2,0).
C. The solution is (0,−1).
D. There are infinitely many solutions.
Answer:
A because the linesnever cross.
Step-by-step explanation:
Answer:
There is no solution
Step-by-step explanation:
To anticipate the dip and hump in the road, the driver of a car applies her brakes to produce a uniform deceleration. Her speed is 100 km/h at the bottom A of the dip and 50 km/h at the top C of the hump, which is 120 m along the road from A. If the passengers experience a total acceleration of 3 m/s2 at A and if the radius of curvature of the hump at C is 150 m, calculate the radius of curvature rho at A.
Answer:
Therefore the radius of curvature at A is 432.03 m.
Step-by-step explanation:
Radius of curvature : If an object moves in curvilinear motion, then any point of the motion, the radius of circular arc path which best approximates the curve at that point is called radius of curvature.
Radius of curvature =[tex]\rho = \frac{V^2_p}{a}[/tex]
[tex]V_p[/tex]= velocity
a = acceleration perpendicular to velocity.
Velocity at the point A = [tex]V_A= 100 \ km/h[/tex] [tex]=\frac{100 \ km}{1 \ h}= \frac{100\times 1000 \ m}{3600 \ s}=\frac{250}{9}[/tex] m/s
Velocity at the point C [tex]=V_C=50 \ km/ h=\frac{125}{9} \ m/s[/tex]
The distance between A and B is 120 m.
To find the declaration between the point A and C we use the following formula
[tex]V^2_C=V^2_A+2a_ts[/tex]
[tex]\Rightarrow( \frac{125}{9})^2=(\frac{250}9})^2+2a_t.120[/tex]
⇒[tex]a_t[/tex] = -2.41 m/s²
[tex]a_t[/tex]= tangential acceleration
Given the passengers experience a total acceleration of 3 m/s².
Total acceleration= 3 m/s².
[tex]a = \sqrt{a^2_t+a^2_n[/tex]
[tex]\Rightarrow a^2_n= a^2- a^2_t[/tex]
[tex]\Rightarrow a_n=\sqrt{3^2-(-2.41)^2}[/tex]
= 1.786 m/s²
Radius of curvature [tex]\rho_A=\frac{V^2_A}{a_n}[/tex]
[tex]=\frac{(\frac{250}{9})^2}{1.786}[/tex]
= 432.03 m
Therefore the radius of curvature at A is 432.03 m.
The population pyramid of a city in southern Florida, Arizona, or even northern Japan may have a visual appearance of ________ because the city's population is dominated by elderly people.
Answer:
A. upside down
Explanation:
Pyramid population, sometimes called afe-gender population is an illustration showing showing various age group distribution. The illustration usually forms the shape of a pyramid, hence its name as the age group increases. It's assumed there are more younger people than older people in a region or country. In this case, the pyramid population is said to be Upside down, because in those regions listed, the number of elderly people is greater than those of the younger people. Population pyramid usually represents the distribution or breakdown of ages and gender of a region at a given point in time.
For a given data set, the equation of For a given data set, the equation of the least squares regression line will always pass throughthe least squares regression line will always pass through
For a given data set, the equation of the least squares regression line will always pass through the point [tex]\((\bar{x}, \bar{y})\),[/tex] where [tex]\(\bar{x}\)[/tex] is the mean of the x-values and[tex]\(\bar{y}\)[/tex] is the mean of the y-values.
Explanation:The least squares regression line minimizes the sum of squared differences between the observed y-values and the values predicted by the line. The equation of the line is given byy = mx + b, where m is the slope and bis the y-intercept. The slopem and y-intercept b are determined by formulas involving the means[tex](\(\bar{x}\)[/tex] and [tex]\(\bar{y}\))[/tex]and other statistical measures from the data set.
The specific formulas for the least squares regression line are:
[tex]\[ m = \frac{\sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y})}{\sum_{i=1}^{n} (x_i - \bar{x})^2} \]\[ b = \bar{y} - m\bar{x} \][/tex]
It can be observed from the formulas that when [tex]\(x = \bar{x}\)[/tex], the corresponding y value is[tex]\(\bar{y}\)[/tex]. Therefore, the least squares regression line passes through the point[tex]\((\bar{x}, \bar{y})\)[/tex]. This point represents the centroid of the data set and ensures that the line adequately represents the overall trend of the data.
Question:
It seems there might be some repetition or an incomplete question in your request. Could you please provide more details or clarify your question so that I can assist you accurately? If you have a specific question related to the least squares regression line or any other topic, feel free to provide more context, and I'll do my best to help you.
Jerry manages a local car dealership. At the beginning of the month, his lot had m vehicles. During the month his salesman sold n vehicles, and he purchased p vehicles more. How many vehicles did the dealership have at the end of the month?
Answer:
m+p-n
Step-by-step explanation:
given that Jerry manages a local car dealership. At the beginning of the month, his lot had m vehicles. During the month his salesman sold n vehicles, and he purchased p vehicles more
We are to find the number of vehicles did the dealership have at the end of the month
At the end of the month the dealer would have
no of vehicles at the start of the month- sales of the vehicle in that month+Purchase of vechicles during that month
No of vehicles at the start of the month = m
Purchase during month =p
Total vehicles including purchase = m+p
LESS: Vehicles sold in the month = n
No of vehicles at the end = m+p-n
sin= 5/13, and cos b= 3/5, evaluate cos(a-b).
cos (a - b) is 56/65
Step-by-step explanation:
Step 1:Given sin a = 5/13, find cos a.
sin a = opposite side/hypotenuse = 5/13
The adjacent side can be found using Pythagoras Theorem.
Hypotenuse² = Opposite Side² + Adjacent Side²
⇒ Adjacent side² = Hypotenuse² - Opposite Side²
= 13² - 5² = 169 - 25 = 144
∴ Adjacent Side = 12
⇒ cos a = adjacent side/hypotenuse = 12/13
Step 2:Given cos b = 3/5, find sin b.
cos b = adjacent side/hypotenuse = 3/5
The opposite side can be found using Pythagoras Theorem.
Hypotenuse² = Opposite Side² + Adjacent Side²
⇒ Opposite side² = Hypotenuse² - Adjacent Side²
= 5² - 3² = 25 - 9 = 16
∴ Opposite Side = 4
⇒ sin b = opposite side/hypotenuse = 4/5
Step 3:Find cos(a - b).
cos(a - b) = cos a cos b + sin a sin b
= 12/13 × 3/5 + 5/13 × 4/5
= 36/65 + 20/65 = 56/65
Find the volume of a right circular cone that has a height of 17 ft and a base with a circumference of 5 ft. Round your answer to the nearest tenth of a cubic foot.
Answer:
V = 11.3 ft^3
Step-by-step explanation:
The volume of a cone is given by one third of its base area multiplied by its height:
V = (1/3)*A*h
This cone have a circular base, so the base area is given by
A = pi*r^2, where r is the base radius
The length of a circumference is given by L = 2*pi*r
the base circumference is 5 ft, so we can calculate the base radius:
5 = 2*pi*r -> r = 5/(2*pi)
Using this value, we can calculate A:
A = pi*r^2 = pi * [5/(2*pi)]^2 = pi * 25/(4*pi^2) = 25/(4*pi) = 1.9894
Now, we use the formula to calculate the volume:
V = (1/3)*A*h = (1/3) * 1.9894 * 17 = 11.2735 ft^3
rounding it, we have V = 11.3 ft^3
Having trouble with these two. Please help!!
Answer:
[tex]3\frac{3}{10} = \frac{33}{10}[/tex]
Step-by-step explanation:
a bowl contains 6 blue and four red marbles. Three random picks are to be made from the bowl in the following fashion: for each pick, a marble is selected and its color is recorded. It is then returned to the jar along with an additional marble of the same color. Determine the probability that a red marble is selected on each of the three picks?
The probability of picking a red marble 3 times in a row = [tex](\frac{8}{125})[/tex]
Step-by-step explanation:
Here, the total number of red marbles = 4
The total number of blue marbles = 6
Now, as the Repetition is allowed.
Let E: The event of picking a red marble
[tex]P(E) = \frac{\textrm{The total number of red marbles}}{\textrm{Total marbles}}[/tex]
So, [tex]P(E) = \frac{4}{10} = \frac{2}{5}[/tex]
Now, as we know after first picking, the chosen red marble is REPLACED in the bowl.
So, again the bowl has 4 red marbles and 10 in total.
⇒P(picking a red marble again) = 2/5
And similarly for the third time.
So, the probability of picking a red marble 3 times in a row = [tex](\frac{2}{5}) \times (\frac{2}{5})\times (\frac{2}{5}) = \frac{8}{125}[/tex]
The probability of selecting a red marble on each of the three picks is 2/55.
Explanation:To determine the probability of selecting a red marble on each of the three picks, we need to consider the number of red and blue marbles in the bowl and the fact that a marble is replaced after each pick.
First, there are 4 red marbles and 6 blue marbles in the bowl. For the first pick, the probability of selecting a red marble is 4/10. After the pick, the bowl will have 5 red marbles and 6 blue marbles.
For the second pick, the probability of selecting a red marble is 5/11. After the pick, the bowl will have 6 red marbles and 6 blue marbles. Finally, for the third pick, the probability of selecting a red marble is 6/12, which simplifies to 1/2.
To find the probability of all three picks being red, we multiply the probabilities of each pick: (4/10) * (5/11) * (1/2) = 2/55.
Therefore, the probability of selecting a red marble on each of the three picks is 2/55.
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In a survey of 248 people, 156 are married, 70 are self-employed, and 25 percent of those who are married are self-employed. If a person is to be randomly selected from those surveyed, what is the probability that the person selected will be self-employed but not married?
Answer:
The probability of selecting a person which is self-employed but not married equals 1/8.
Step-by-step explanation:
Here, the given survey says:
Total number of people surveyed = 248
Number of people married = 156
The number of people are self employed = 70
Now, 25% of people who are married are SELF EMPLOYED.
Now, calculating 25% of 156 , we get:
[tex]\frac{25}{100} \times 156 = 39[/tex]
⇒ out of total 156 married people, 39 are self employed.
So, number of self employed people but not married
= Self employed people - Self employed people PLUS married
= 70 - 39 = 31.
So, the probability that the person selected will be self-employed but not married = [tex]\frac{\textrm{The total number of people self-employed but not married}}{\textrm{Total Number of people}}[/tex] = [tex]\frac{31}{248} = \frac{1}{8}[/tex]
Hence The probability of selecting a person which is self-employed but not married equals 1/8.
In order to develop a more appealing cheeseburger, a franchise uses taste tests with 15 different buns, 8 different cheeses, 3 types of lettuce, and 4 types of tomatoes. If the taste tests were done at one restaurant by one tester who takes 10 minutes to eat each cheeseburger, approximately how long would it take the tester to eat all possible cheeseburgers?
Answer:
There would be
13 x 8 x 4 x 3 = 3,276 different cheeseburger combinations
If the taste tester takes 10 minutes to eat a cheeseburger, then it would take him
3276 x 10 = 32760 minutes
Eating round the clock, it would take him
32760 / 60 = 546 hours
546 / 24 = 22 days 18 hours
Now these are the numbers I'm seeing
1313 buns
88 cheese
44 lettuces
33 tomatoes
There would be
1313 x 88 x 44 x 33 = 167,769,888 different cheeseburger combinations
If the taste tester takes 10 minutes to eat a cheeseburger, then it would take him
167769888 x 10 = 1,677,698,880 minutes
1677698880 / 60 = 27,961,647 hours
27961647 / 24 = 1,165,068.62 days
1165068.62 / 365 = 3,191.97 years
Step-by-step explanation:
A factory received a shipment of 38 sprockets, and the vendor who sold the items knows there are 5 sprockets in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the sprockets in the sample are defective, he will refuse the shipment.
a) If a sample of 5 sockets is selected, find the probabilty that all in the sample are defective.
b) If a sample of 5 sprockets is selected, find the probability that none in the sample are defective.
Answer:
a) 0.00019923%
b) 47.28%
Step-by-step explanation:
a) To find the probability of all sockets in the sample being defective, we can do the following:
The first socket will be in a group where 5 of the 38 sockets are defective, so the probability is 5/38
The second socket will be in a group where 4 of the 37 sockets are defective, as the first one picked is already defective, so the probability is 4/37
Expanding this, we have that the probability of having all 5 sockets defective is: (5/38)*(4/37)*(3/36)*(2/35)*(1/34) = 0.0000019923 = 0.00019923%
b) Following the same logic of (a), the first socket have a chance of 33/38 of not being defective, as we will pick it from a group where 33 of the 38 sockets are not defective. The second socket will have a chance of 32/37, and so on.
The probability will be (33/38)*(32/37)*(31/36)*(30/35)*(29/34) = 0.4728 = 47.28%
The caldwells are moving across the country. Mr Caldwell leaves 3 hours before Mrs Caldwell. If he averages 45 mph and she averages 65 mph, how many hours will it take Mrs Caldwell to catch mr. Caldwell
Mrs. Caldwell will travel 135 miles at an additional 20 mph to catch up to Mr. Caldwell. Therefore, it will take Mrs. Caldwell 6.75 hours to catch up to Mr. Caldwell.
Explanation:This is a rate time distance problem in mathematics, typically learned in middle school. To calculate how long it will take Mrs. Caldwell to catch up with Mr. Caldwell, we need to compare the distance traveled by each person in the same time. Because rate equals distance over time (r=d/t), we know that the distance each person traveled is rate x time.
Mr. Caldwell left 3 hours before Mrs. Caldwell, so he traveled at 45 mph for 3 hours, or 135 miles. Once Mrs. Caldwell leaves, she needs to cover these 135 miles at a faster speed to catch up. Her speed is 20 mph greater than Mr. Caldwell’s. We divide the distance that Mr. Caldwell has covered (135 miles) by the difference in their speeds (20 mph) to find it will take Mrs. Caldwell 6.75 hours to catch up to him.
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The vertex of this parabola is at (4, -3). Which of the following could be its equation?
A.x = -3(y + 4)2 - 3
B.x = -3(y - 4)2 - 3
C.x = -3(y + 3)2 + 4
D.x = -3(y - 3)2 + 4
Answer:
B) x=-3(y+3)^2+4
Step-by-step explanation:
Plug quadratic in for proof
Answer:
The answer to your question is Letter C
Step-by-step explanation:
Data
Vertex (4, -3)
Process
From the image, we notice that it is a horizontal parabola that opens to the left.
So, it formula must be (y - k)² = 4p(x - h)
-Substitute the vertex
(y + 3)² = 4p(x - 4)
Consider 4p = 1
(y + 3)² = x - 4
Solve for x
x = (y + 3)² + 4
Solution
Letter C
In a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 147,000, how many red beads were removed?
A) 5
B) 4
C) 3
D) 2
E) 0
Answer: Option 'D' is true.
Step-by-step explanation:
Since we have given that
Number of points are 7,5,3, and 2 each.
Product of the point values of the removed beads = 147000
So, the possible way is given by
[tex]2^3\times 3\times 5^3\times 7^2=147000[/tex]
Since no other beads is a multiple of 7.
So, there must be two red beads removed.
Hence, Option 'D' is true.
One number is 20 times another number. The product of the two numbers is 180. Write an equation and use it to find all pairs of numbers that satisfy the
Answer: the Smaller number is 3
The larger number is 60
Step-by-step explanation:
Let x represent the smaller of the numbers.
Let y represent the larger number.
One number is 20 times another number. This means that
y = 20x
The product of the two numbers is 180. This means that
xy = 180- - - - - - - - - -1
Substituting y = 2x into equation 1, it becomes.
x × 20x = 180
20x² = 180
x² = 180/20 = 9
x = √9
x = 3
y = 20x = 20 × 3
y = 60
At 9:00, Paula has x cups of food in a container. Pamula pours 2 1/2 cups of food into the container. Then she removes 3/4 cups of food to feed her dog. Now there are 5 1/4 of food in the container. What is the equation?
Answer:
The equation representing the scenario is [tex]x+\frac{5}{4}-\frac{3}{4} = \frac{21}{4}[/tex].
Step-by-step explanation:
Given:
Amount of food in the container = [tex]x \ cups[/tex]
Amount of food added in the container = [tex]2\frac12\ cups[/tex]
We will now convert the mixed fraction into Improper fraction by Multiplying the whole number part by the fraction's denominator and then add that to the numerator and then write the result on top of the denominator.
[tex]2\frac12\ cups[/tex] can be rewritten as [tex]\frac{5}{4}\ cups[/tex]
Amount of food added in the container = [tex]\frac{5}{4}\ cups[/tex]
Amount of food removed from container to feed dog = [tex]\frac34 \ cups[/tex]
Amount of food remaining = [tex]5\frac{1}{4} \ cups[/tex]
[tex]5\frac{1}{4} \ cups[/tex] can be Rewritten as = [tex]\frac{21}{4}\ cups[/tex]
Amount of food remaining = [tex]\frac{21}{4}\ cups[/tex]
We need to write the equation for above scenario.
Solution:
Now we can say that;
Amount of food remaining is equal to Amount of food in the container plus Amount of food added in the container minus Amount of food removed from container to feed dog.
framing in equation form we get;
[tex]x+\frac{5}{4}-\frac{3}{4} = \frac{21}{4}[/tex]
Hence the equation representing the scenario is [tex]x+\frac{5}{4}-\frac{3}{4} = \frac{21}{4}[/tex].
A car travels along a straight road for 30 seconds starting at time t = 0. Its acceleration in ft/sec2 is given by the linear graph below for the time interval [0, 30]. At t = 0, the velocity of the car is 0 and its position is 10.
What is the total distance the car travels in this 30 second interval? Your must show your work but you may use your calculator to evaluate. Give 3 decimal places in your answer and include units.
Im not really sure how to go about this? Would I use the trapezoidal rule i dont know please help.
Answer:
666.667 feet
Step-by-step explanation:
Slope = -1
Intercept = 10
y = -t + 10
y is the acceleration
Integrate y fornv
v = -t²/2 + 10t + c
At t=0, v=0 so c = 0
v = -t²/2 + 10t
Turns when v = 0,
-t²/2 + 10t = 0
t = 0, 20
Integrate v for s
s = -t³/6 + 5t² + c
At t = 0, s = 10
10 = c
s = -t³/6 + 5t² + 10
s at t=30,
-(30³)/6 + 5(30)² + 10
= 10m
(Back to starting point)
At t = 20,
Displacement in
-(20³)/6 + 5(20)² + 10
= 343.333
Total distance = 2(343.333-10)
= 666.6667
The total distance the car travels in this 30 second interval is 1333.34 units
From the graph, we have the following points
(0, 10) and (10, 0).
Start by calculating the slope (m) of the graph
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{0 - 10}{10-0}[/tex]
[tex]m =- \frac{10}{10}[/tex]
[tex]m =- 1[/tex]
The equation is then calculated as:
[tex]y = m(x -x_1) + y_1[/tex]
This gives
[tex]y = -1(x -0) + 10[/tex]
[tex]y = -1x+ 10[/tex]
[tex]y = -x+ 10[/tex]
The above equation represents the acceleration (y) as a function of time (x).
Integrate to get the velocity (v)
[tex]v = -\frac{x\²}{2} + 10x + c[/tex]
From the question, we have:
The velocity (v) of the car is 0, when the time (x) is 0.
So, we have:
[tex]0 = -\frac{0\²}{2} + 10(0) + c[/tex]
This gives
[tex]c = 0[/tex]
So, the equation becomes
[tex]v = -\frac{x\²}{2} + 10x + 0[/tex]
[tex]v = -\frac{x\²}{2} + 10x[/tex]
Set v = 0.
So, we have:
[tex]-\frac{x\²}{2} + 10x = 0[/tex]
Multiply through by -2
[tex]x^2 -20x = 0[/tex]
Factorize
[tex]x(x -20) = 0[/tex]
Split
[tex]x = 0\ or\ x -20 = 0[/tex]
Solve for x
[tex]x = 0[/tex] or [tex]x = 20[/tex]
Integrate velocity (v) to get the displacement (d)
[tex]v = -\frac{x\²}{2} + 10x[/tex]
[tex]d = -\frac{t\³}{6} + 5t\² + c[/tex]
From the question, we have:
The position (d) of the car is 10, when the time (x) is 0.
So, we have:
[tex]-\frac{(0)\³}{6} + 5(0)\² + c = 10[/tex]
[tex]c = 10[/tex]
So, the equation becomes
[tex]d = -\frac{t\³}{6} + 5t\² + 10[/tex]
The position at 30 seconds is:
[tex]d = -\frac{(30)\³}{6} + 5(30)\² + 10[/tex]
[tex]d = 10[/tex]
The position at 20 seconds is:
[tex]d = -\frac{(20)\³}{6} + 5(20)\² + 10[/tex]
[tex]d = 676.667[/tex]
The total distance is then calculated as:
[tex]Total = 2 \times (d_2 -d_1)[/tex]
This gives
[tex]Total = 2 \times (676.667 -10)[/tex]
[tex]Total = 2 \times 666.667[/tex]
[tex]Total = 1333.34[/tex]
Hence, the total distance is 1333.34 units
Read more about distance at:
https://brainly.com/question/2239252
Chase measured a line to be 8.9 inches long. If the actual length of the line is 9.5 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
Answer:
10%
Step-by-step explanation:
In this question, we are asked to calculate the percentage error in a measurement.
This can be obtained by first getting the error involved. That is calculated by Subtracting the value calculated from the actual value. That is 9.5 - 8.9 = 0.6
The percentage error is thus 0.6/9.5 * 100 = 6%
The value is actually 10% to the nearest tenth of a percent
Answer:
6.3%
Step-by-step explanation:
A scientist measured the exact distance between two points on a map and came up with the following number: 0.04000 km.
Which digits are the significant figures in this measurement?
Explain your answer.
Answer:
The first zero after decimal point and 4 only
Step-by-step explanation:
Despite having 5 decimal points, the rules of significant figures dictate that unless there is a digit other than zero after, the only significant numbers are those that come before zero. For this case, the significant digits are only 0.04 but if it was 0.0400005 then all the other zeros would have also be considered significant.
Simply Find the derivative. I would do it, but I don't want to. lol
Differentiate
f(x)=(x^4-6x^10)^23
f'(x)=[](x^4-6x^10)^[]([]x^[]+[]x^9)
FILL IN THE BLANKS
Answer:
23, 22, 4, 3, -60
Step-by-step explanation:
f(x)=(x⁴ - 6x¹⁰)²³
f'(x)= 23(x⁴ - 6x¹⁰)²²(4x³ - 60x⁹)
Dont skip plzzzzzzzzzzzzzzzzzzzzzzzz
Answer:
B
Step-by-step explanation:
The slope is rise over run, meaning it is 3/4. The y-intercept is 2, making the equation y = (3/4)x + 2
WILL MARK BRAINLIEST
Which of the following equations is written in the slope-intercept form?
y = -2x + 4
9 + y = m - b
y + 3/2 = m - x
b = 1/5x + y
Answer:
y = -2x + 4
Step-by-step explanation:
Slope: -2
Intercept: +4
PLZ HELP WILL MARK BRAINLIEST
Using the distance formula, d = √(x2 - x1)2 + (y2 - y1)2, what is the distance between point (3, 2) and point (5, 4) rounded to the nearest tenth?
5.3 units
1 unit
10 units
2.8 units
Answer:
2.8 units
You should get 2√(2) or √(8) which is less than 3 and greater than 2.
Answer: 2.8 units
Step-by-step explanation:
The formula for determining the distance between two points on a straight line is expressed as
Distance = √(x2 - x1)² + (y2 - y1)²
Where
x2 represents final value of x on the horizontal axis
x1 represents initial value of x on the horizontal axis.
y2 represents final value of y on the vertical axis.
y1 represents initial value of y on the vertical axis.
From the given points
x2 = 5
x1 = 3
y2 = 4
y1 = 2
Therefore,
Distance = √(5 - 3)² + (4 - 2)²
Distance = √2² + 2² = √4 + 4 = √8
Distance = 2.8 units