Answer:
210, 150
Step-by-step explanation:
Answer:
-510, 210 and 570.
Step-by-step explanation:
I'm on the same assignment right now! If you draw them you will see that those are the answers.
Please Help!!!
a. Write in words, a two-step sequence of transformations, that maps ΔABC to ΔA’B’C’.
b. Write a two-step ordered-pair rule, for the transformation sequence.
Answer:
a) Δ ABC is rotated around the origin by angle 180° and then translated 1
unite to the right and 3 units up
b) R (O , 180°) and T (x + 1 , y + 3)
Step-by-step explanation:
* Lets revise some transformation
- If point (x , y) rotated about the origin by angle 180° then its image
is (-x , -y)
- If the point (x , y) translated horizontally to the right by h units
then its image is (x + h , y)
- If the point (x , y) translated horizontally to the left by h units
then its image is (x - h , y)
- If the point (x , y) translated vertically up by k units
then its image is = (x , y + k)
- If the point (x , y) translated vertically down by k units
then its image is (x , y - k)
* Lets solve the problem
∵ Δ ABC change its place from 2nd quadrant to the 4th quadrant
and reverse its direction Point A up and its image A" down
∵ No change in its size
∴ Triangle ABC rotates 180° clockwise around the origin
# Remember : There is no difference between rotating 180° clockwise
or anti-clockwise around the origin
∵ The vertices of Δ ABC are:
# A = (-3 , 5)
# B = (-3 , 2)
# C = (-1 , 2)
∵ If point (x , y) rotated about the origin by angle 180° then its image
is (-x , -y)
∴ A'' = (3 , -5)
∴ B'' = (3 , -2)
∴ C'' = (1 , -2)
∴ Triangle ABC rotates 180° around the origin to form ΔA"B"C"
∵ The vertices of Δ A'B'C are:
# A' = (4 , -2)
# B' = (4 , 1)
# C' = (2 , 1)
- By comparing the x-coordinates and y-coordinates of points of
Δ A''B''C'' and Δ A'B'C' we will find that every x-coordinate add by 1
and every y-coordinate add by 3
∵ 4 - 3 = 1 and 2 - 1 = 1 ⇒ x- coordinates
∵ -2 - (-5) = -2 + 5 = 3 and 1 - (-2) = 1 + 2 = 3 ⇒ y-coordinates
∴ ΔA''B''C'' translates to the right 1 unite and up 3 units to form
Δ A'B'C'
a) Δ ABC is rotated around the origin by angle 180° and then
translated 1 unite to the right and 3 units up
b) R (O , 180°) and T (x + 1 , y + 3)
Alex purchased a calling card for $32. He has used t minutes of access time at 15 cents per minute. To write an algebraic expression to represent how many dollars Alex has left on his card, fill in the boxes.
Answer:
The answer to your question is: T = 32 - 0.15t
Step-by-step explanation:
calling card cost = $32
t = minutes used
cost = 15 c / min
Equation = ?
T = money left on his card
T = 32 - 0.15t
URGENT!
Each day we purchase 1.7 thousand ice cream cones per minute. Use the fact that there are approximately 5.3 times 10^5 minutes in a year to approximate how many ice cream cones are purchased in one year. Write your answer in scientific notation.
Approximately [tex]\(8.51 \times 10^8\)[/tex] ice cream cones are purchased in one year, given a rate of 1.7 thousand cones per minute over [tex]\(5.3 \times 10^5\)[/tex] minutes.
To find the total number of ice cream cones purchased in one year, we can multiply the rate of purchase per minute by the total number of minutes in a year.
Given: Purchase rate = 1.7 thousand ice cream cones per minute, and there are [tex]\(5.3 \times 10^5\)[/tex] minutes in a year.
[tex]\[ \text{Total cones in one year} = \text{Rate per minute} \times \text{Minutes in a year} \][/tex]
[tex]\[ \text{Total cones} = 1.7 \times 10^3 \, \text{cones/minute} \times 5.3 \times 10^5 \, \text{minutes} \][/tex]
Now, multiply the coefficients and add the exponents:
[tex]\[ \text{Total cones} = 8.51 \times 10^8 \, \text{ice cream cones} \][/tex]
Therefore, approximately [tex]\(8.51 \times 10^8\)[/tex] ice cream cones are purchased in one year.
Final answer:
By multiplying 1.7 × 10³ cones per minute by 5.3 × 10⁵ minutes per year, the total number of cones purchased in one year is approximately 9.01 × 10⁸ cones.
Explanation:
To calculate the total number of ice cream cones purchased in one year, we can use scientific notation and multiplication. First, convert the number of ice cream cones bought per minute into scientific notation:
1.7 thousand cones per minute = 1.7 × 10³ cones/minute
Next, multiply this by the total number of minutes in a year, also given in scientific notation:
5.3 × 10⁵ minutes/year
The calculation will look like this:
(1.7 × 10³ cones/minute) × (5.3 × 10⁵ minutes/year) = (1.7 × 5.3) × (10³× 10⁵) = 9.01 × 10⁸ cones/year
The approximation for the number of cones purchased in one year is 9.01 × 10⁸ cones.
Are there any clusters or outliers in the scatter plot?
Answer:
A) There is one cluster and one outlier.
Step-by-step explanation:
We are given the following information in the question:
We are given a scatter plot.
Sometimes the data points in a scatter plot form distinct groups. These groups are called clusters. A cluster is formed when several data points lie in a small interval. An outlier is defined as a data point that can be differentiated from the rest of the data. It is an observation that lies an abnormal distance from other values in a random sample from a population.When observed, the given scatter plot has one cluster and one outlier.
Hence, option A) is the correct answer.
A certain stock exchange designates each stock with a one-, two-, or three-letter code, where each letter is selected from the 26 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes?
Answer:
There are 16276 different stocks which are possible to uniquely designate with these codes
Step-by-step explanation:
The information we have is that
1. There are 26 different letters.
2. The stock can be designated with a one, two or three letter code and the letters may be repeated (We always have 26 options for the first, second and third letter)
3. Order matters (different order constitute a different code), which means we're talking about permutations.
The total codes we can make would be:
[tex]P_{26|1} + P_{26|2}+ P_{26|3} \\26+650+15600= 16276[/tex]
How can you express 20 percent as a fraction?
Answer:
20/100
Step-by-step explanation:
20 over 100 due to 100 percent is a whole and you are taking 20 percent so 20 will be ur numerator and 100 for you dominator
A crop scientist is conducting research with a drought resistant corn hybrid. She is interested in determining if using fertilizer X will increase plant height. She prepares 20 single acre plots and randomly assigns 10 to have normal soil while the other 10 are planted with fertilizer X. The resulting average height for each group of 10 plots was recorded. Select all that apply.
a. This is best described as an observational study.
b. The response variable is whether or not fertilizer X was used.
c. The explanatory variable is the average height for each group of 10 plots
d. This study is best described as an experiment.
e. The explanatory variable is whether or not fertilizer X was used.
f. The response variable is the average height for each group of 10 plots
Answer: d. This study is best described as an experiment.
e. The explanatory variable is whether or not fertilizer X was used.
f. The response variable is the average height for each group of 10 plots.
Step-by-step explanation:
Given : A crop scientist is conducting research with a drought resistant corn hybrid.
She is interested in determining if using fertilizer X will increase plant height.
She prepares 20 single acre plots and randomly assigns 10 to have normal soil while the other 10 are planted with fertilizer X.
This study is best describe as an experiment because the scientist is experimenting about the increase in plant height with an generation of 20 single acre plots not like an observational study where the observer just observe the study without any influence.
Here the fertilizer is used to see the change in the plant height.
So, the explanatory variable is whether or not fertilizer X was used and the response variable is the average height for each group of 10 plots.
A candy bowl contains 723 candies. Some of the candies are red, and the rest are green. There are twice as many green candies as red candies. How many red candies are in the candy bowl ?
Answer: There are 241 red candies in the bowl. 482 Green candies in bowl.
Step-by-step explanation:
241 (is the answer) x2= 482. There's TWICE as many green as there is red, since there is 241 red candies, we multply that by two (482). Now let's add to check if it is correct. 241+482= is indeed 723.
Answer:
red = 241
green = 482
Step-by-step explanation:
The total = 723
red candies = x
green candies = y
⇒ x + y =723
There are twice as many green candies as red candies.
this means: y = 2x
x + y = 723
x +2x = 723
3x = 723
x = 241
y = 723 - 241 = 482
To control this y = 2x ⇒ 482 = 2 * 241
This means that there 241 red candies and 482 green candies.
Madison has a goal of saving more than $1,000 she has $300 saved now and each month she adds $40 to that amount the inequality 40m + 300 > 1,000 can be solved to find the number of months, m, it will take Madison to reach her goal which statement about the number of months it will take Madison to reach her goal is true
Answer:
Step-by-step explanation:
[tex]40m + 300 > 1000[/tex]
[tex]40m > 700[/tex]
[tex]m > 17.5[/tex]
Rounding up to the nearest whole number, it will take Madison at least 18 months to reach her goal.
She will need 18 months to reach her goal.
What is an inequality?
The word inequality means a mathematical expression in which the sides are not equal to each other. Basically, an inequality compares any two values and shows that one value is less than, greater than, or equal to the value on the other side of the equation.
An inequality may be expressed by a mathematical sentence that uses the following symbols:
< is less than
> is greater than
≤ is less than or equal to
≥ is greater than or equal to
≠ is not equal to
Given, inequality is
40m +300 > 1000
40m > 1000-300
40m > 700
m > 700/40
m > 17.5
Hence, she will take more than 17 months and on 18th month she will achieve her goal.
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A 12-oz can of soda pop costs eighty-nine cents. A 2.00 L bottle of the same variety of soda pop costs $2.29. How many times more expensive it is to buy the 12-oz can of pop compared to buying it in a 2.00 L bottle? (1.00 L = 1.057 quart and 1 quart contains 32 oz)
Answer: It's 2.2 times more expensive to buy the 12-oz can of pop compared to buying it in a 2.00 L bottle
Step-by-step explanation:
You know that:
[tex]1.00\ L = 1.057\ quarts[/tex]
[tex]1.00\ quart=32\ oz[/tex]
Then, you can make the conversion from liters to quarts:
[tex](2.00\ L)(\frac{1.057\ quarts}{1.00\ L})=2.114\ quarts[/tex]
Now, you need to make the conversion from quarts to ounces:
[tex](2.114\ quarts)(\frac{32\ 0z}{1.00\ quart})=67.648\ oz[/tex]
You know that a 12-oz can of soda pop costs 89 cents (which is $0.89). Then, the cost per ounce is:
[tex]\frac{\$0.89}{12}=\$0.074[/tex]
And a 2.00 L bottle (67.648 oz) of the same variety of soda pop costs $2.29. The cost per ounce is:
[tex]\frac{\$2.29}{67.648}=\$0.033[/tex]
Finally, you must divide $0.074 by $$0.033:
[tex]\frac{\$0.074}\$0.033}=2.2[/tex]
Therefore, It's 2.2 times more expensive to buy the 12-oz can of pop compared to buying it in a 2.00 L bottle.
Buying soda pop in a 12-oz can is about 2.19 times more expensive per ounce than buying it in a 2.00 L bottle.
To compare the cost effectiveness of buying soda pop in different quantities, we first need to convert the volume measurements consistently:
1. Convert 2.00 L to ounces:
Since 1.00 L = 33.8 oz (using the conversion factor 1.00 L = 1.057 quart and 1 quart = 32 oz),
[tex]\[ 2.00 \text{ L} = 2.00 \times 33.8 \text{ oz} = 67.6 \text{ oz} \][/tex]
2. Calculate the cost per ounce for the 2.00 L bottle:
[tex]\[ \text{Cost per ounce} = \frac{\$2.29}{67.6 \text{ oz}} \approx \$0.0339 \text{ per ounce} \][/tex]
3. Calculate the cost for the 12-oz can:
[tex]\[ \text{Cost of 12-oz can} = \$0.89 \][/tex]
4. Compare the costs:
[tex]\[ \text{Cost per ounce for the can} = \frac{\$0.89}{12 \text{ oz}} = \$0.0742 \text{ per ounce} \][/tex]
5. Calculate how many times more expensive the can is compared to the bottle:
[tex]\[ \text{Times more expensive} = \frac{\$0.0742}{\$0.0339} \approx 2.19 \][/tex]
Buying a 12-oz can of soda pop costs approximately $0.0742 per ounce, while buying a 2.00 L bottle costs approximately $0.0339 per ounce. This makes the can approximately 2.19 times more expensive per ounce compared to the bottle.
Let's say A keep tossing a fair coin, until he get 2 consecutive heads, define X to be the number of tosses for this process; B keep tossing another fair coin, until he get 3 consecutive heads, define Y to be the number of the tosses for this process. 1) Calculate P{X>Y}
A=Tossing a fair coin, until getting 2 consecutive heads,
Minimum Number of tosses
=(SF)(FS)(FF)(SS)
X =8 tosses
S=Success
F=Failure
B=Tossing a fair coin, until getting 3 consecutive heads.
Minimum Number of tosses
=(SFS)(FSS)(SSF)(SFF)(FSF)(FFS)(FFF)(SSS)
Y =24 Tosses
Probability of an event
[tex]=\frac{\text{Total favorable Outcome}}{\text{Total Possible Outcome}}\\\\P(X)=\frac{SS}{8}\\\\P(X)=\frac{2}{8}\\\\P(X)=\frac{1}{4}\\\\P(Y)=\frac{SSS}{24}\\\\P(Y)=\frac{3}{24}\\\\P(Y)=\frac{1}{8}\\\\\frac{1}{4}> \frac{1}{8}\\\\P(X)>P(Y)[/tex]
How many times greater is 8.4 x 10-^5 than 2.1 x 10^-6?
a.
0.04
b.
0.4
c. 4
d. 40
Answer:
40
Step-by-step explanation:
[tex]\dfrac{8.4\cdot 10^{-5}}{2.1\cdot 10^{-6}}=\dfrac{8.4}{2.1}\cdot 10^{-5-(-6)}=4\cdot 10^1=40[/tex]
8.4×10^-5 is 40 times the value of 2.1×10^-6
You are choosing between two health clubs. Club A offers membership for a fee of $ 19plus a monthly fee of $ 21.  Club B offers membership for a fee of $ 23plus a monthly fee of $ 20.  After how many months will the total cost of each health club be the​ same
Answer:
For 2 months
Step-by-step explanation:
Let after x months the cost of each health club is same,
Now, In club A,
Membership fees = $ 19,
Monthly fees = $ 21,
So, the total fees for x months = membership fees + total monthly fees for x months
= 19 + 21x
In Club B,
Membership fees = $ 23,
Monthly fees = $ 20,
So, the total fees for x months = membership fees + total monthly fees for x months
= 23 + 20x
Thus, we can write,
19 + 21x = 23 + 20x
21x - 20x = 23 - 21
x = 2
Hence, for 2 months the total cost of each health club would be same.
Solve for x: 2 over 3 equals the quantity x minus 1 end quantity over 5
Question 6 options:
7 over 3
11 over 3
13 over 3
3
Answer:
13 over 3
Step-by-step explanation:
Hi Jakeyriabryant! I hope you’re fine!
I hope I have understood the problem well.
If so, what the exercise raises is the following equality:
(x-1) / 5 = 2/3
From this equation you must clear the "x".
First, we pass the 5 that is dividing on the side of the x, to the other side and passes multiplying
(X – 1) / 5 = 2/3
(X – 1) = (2/3)*5
X – 1 = 10/3
Then we pass the one that is subtracting from the side of the x, to the other side and passes adding
X = 10/3 + 1
Remember that to add or subtract fractions they must have the same denominator or a common denominator (in this case we can write 1 as fraction 3/3). Then,
X = 10/3 + 3/3
X = 13/3
I hope I've been helpful!
Regards!
The solution to the equation 2/3 = (x-1)/5 is x = 13/3. This is achieved by cross-multiplying, then isolating x.
Explanation:To solve for x in the equation 2/3 = (x-1)/5, you will need to isolate the variable 'x'. This requires you to perform the same mathematical operation on both sides of the equation in order to maintain balance. Here we have a situation that involves proportions. Solve it by cross-multiplying:
Multiply 2 by 5, the denominator on the right side of the equation; and 3, the denominator on the left, by (x-1). So, 2*5 = 3*(x-1).This simplifies to 10 = 3x -3.Add 3 to both sides to get '3x=13', then divide both sides by 3 to get x= 13/3.Learn more about Algebraic Equation here:https://brainly.com/question/32183344
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A restaurant chef ordered product to make a stew. He ordered 4 pounds of beef at 9.25 per pound, 6 pounds of potatoes at $6.75 a pound, and 5 pounds of carrots at $9.80 per pound. If the stew serves 30 people and he charges $12.50 per serving, how much profit will he make?
ok so. A restaurant chef ordered product to make a stew. He ordered 4 pounds of beef at 9.25 per pound, 6 pounds of potatoes at $6.75 a pound, and 5 pounds of carrots at $9.80 per pound. If the stew serves 30 people and he charges $12.50 per serving, how much profit will he make?
Answer:
Step-by-step explanation:
248.50 your welcome
The 1992 world speed record for a bicycle (human powered vehicle) was set by Chris Huber. His time through the measured 200 m stretch was a sizzling 6.509 s, at which he commented, "Cogito ergo zoom!" (I think, therefore I go fast!) In 2001, Sam Whittingham beat Huber's record by 19.0 km/h. What was Whittingham's time through the 200 m?
Answer:
Whittingham's time through the 200 m was 5.55 seconds.
Step-by-step explanation:
Huber's peed = 200m / 6.509s = 30.72m/s
1 meter per second = 3.6 km per hour
30.72 m/s = [tex]30.72\times36.=110.6[/tex] km/hr
Sam's speed is 110.6 + 19 = 129.6 km/hr
1 km per hour = 0.2778 meter per second.
So, 129.6 km/hr = [tex]129.6\times0.2778[/tex]= 36m/s
So, Sam Whittingham's time through the 200 m was =
[tex]\frac{200}{36}= 5.55[/tex] seconds.
Final answer:
Chris Huber's average speed was 30.73 m/s. Sam Whittingham beat this by 19.0 km/h, or 5.28 m/s, totaling to an average speed of 35.01 m/s. Whittingham's time for the 200m stretch was thus approximately 5.71 seconds.
Explanation:
To calculate Sam Whittingham's time through the 200 m stretch, we first need to find Chris Huber's average speed during his record-setting ride. Huber's time was 6.509 seconds for a 200 meter stretch, giving us an average speed of 200 m / 6.509 s ≈ 30.73 m/s. Whittingham beat Huber's record by 19.0 km/h. Since 1 km/h is approximately 0.27778 m/s, a 19.0 km/h increase translates to 19.0 km/h * 0.27778 m/s/km/h ≈ 5.28 m/s. Therefore, Whittingham's average speed was 30.73 m/s + 5.28 m/s = 35.01 m/s.
To find Whittingham's time for the 200 m stretch, we divide the distance by his average speed.
Time = Distance / Speed
Time = 200 m / 35.01 m/s ≈ 5.71 seconds.
Therefore, Sam Whittingham's record-breaking time through the 200-meter distance was approximately 5.71 seconds.
Find the coordinates of point G
Answer:
G = (2, 9)
Step-by-step explanation:
The midpoint is the average of the endpoints, so we have ...
M = (G+H)/2
Solving for G gives ...
G = 2M -H = 2(5, 9) -(8, 9) = (10-8, 18-9)
G = (2, 9)
Dara ran on a treadmill that had a readout indicating the time remaining in her exercise session. When the readout indicated 24 min 18 sec, she had completed 10% of her exercise session. The readout indicated which of the following when she had completed 40% of her exercise session?A. 10 min 48 secB. 14 min 52 secC. 14 min 58 secD. 16 min 6 secE. 16 min 12 sec
Answer:
E. 16 min 12 sec
Step-by-step explanation:
See it in the pic.
At arraignment, Jackson accepts a plea deal that will shorten his sentence in return for naming one of his marijuana dealer. About what percentage of cases every year end in plea bargains instead of a criminal trial?
a) 60 percent
b) 80 percent
c) 70 percent
d) 90 percent
Answer:
d) 90 percent
Step-by-step explanation:
A plea bargain is an arrangement made between the prosecutor and the defendant.
Here the defendant pleads guilty to a lesser charge in exchange for a more lenient sentence like here Jackson says he will name one of the dealer, in return for a lesser sentence.
This arrangement takes place in almost 90 percent cases.
A professor computing the sample average exam score of 20 students and using it to estimate the average exam score for the 1,500 students taking the exam is an example of inferential statistics.
True / False.
Answer:
True, It is a example of inferential statistics.
Step-by-step explanation:
There are two types of statistics which are:
Inferential StatisticsDescriptive StatisticsIn Inferential Statistics we describe the valuable characteristic of the population using a sample of data.
Here, Since the professor is estimating the average score of 1,500 students using an average score of 20 students. So it is Inferential Statistics.
Gabriel wants to make five banners for the parade. He has 75 feet of material. The size of four of the banners are: 12 1/3 ft., 16 1/6 ft., 11 3/4 ft., and 14 1/2 ft. How much material is left for the fifth banner?
Answer:
20 1/4 ft
Step-by-step explanation:
Subtracting the four given lengths from 75 feet will tell you how much is left.
75 - (12 1/3 +16 1/6 +11 3/4 +14 1/2) = 75 -54 3/4 = 20 1/4
Gabriel has 20 1/4 ft of material left for his 5th banner.
After adding the lengths of the first four banners, we subtract that number from the total material Gabriel originally had. Gabriel has 20 13/24 feet of material left for the fifth banner.
Explanation:To determine the amount of material left for the fifth banner, we first have to add the lengths of the four banners that Gabriel has already made. These lengths are 12 1/3 ft., 16 1/6 ft., 11 3/4 ft., and 14 1/2 ft. We add these four values together:
12 1/3 + 16 1/6 + 11 3/4 + 14 1/2 = 54 11/24 ft.
Gabriel originally had 75 feet of material, so to find out how much is left for the fifth banner, we subtract the total length of the first four banners from the original amount:
75 - 54 11/24 = 20 13/24 ft.
So, Gabriel has 20 13/24 ft. of material left for the fifth banner.
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A professional baseball team won 84 games this season.The team won 14 more games than it lost.There was no ties.How many games did the team lose? How many games did it play?
Answer:
The answer to your question is: lost 70 games; played 154 games
Step-by-step explanation:
Data
Won 84 games
Won 14 more games than it lost
There was no toes.
# of games did the team lose?
# of games did it play?
Process
games lost = games won - 14
games lost = 84 - 14
games lost = 70
# of games played = games won + games lost
# games played = 84 + 70
= 154
Which equation is the equation of the line, in point-slope form, that has a slope of 2 and passes through the point (−8, 1) ?
Answer:
Step-by-step explanation:
y - 1 = 2(x + 8)
y - 1 = 2x + 16
y = 2x + 17
An equation of the line, in point-slope form, that has a slope of 2 and passes through the point (−8, 1) is: B. y - 1 = 2(x + 8).
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.At data point (-8, 1) and a slope of 2, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 1 = 2(x - (-8))
y - 1 = 2(x + 8)
In slope-intercept form, the equation of the line is given by;
y - 1 = 2x + 16
y = 2x + 16 + 1
y = 2x + 17
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Complete Question:
Which equation is the equation of the line, in point-slope form, that has a slope of 2 and passes through the point (−8, 1)?
A. y - 1 = 2(x - 8)
B. y - 1 = 2(x + 8)
C. y - 8 = 2(x + 1)
D. y - 8 = 2(x - 1)
Consider a metal bar of initial length L and cross-sectional area A. The Young's modulus of the material of the bar is Y. Find the "spring constant" k of such a bar for low values of tensile strain. Express your answer in terms of Y, L, and A.
Answer:
k = Y*A/L
Step-by-step explanation:
We can apply the Law of Hooke in order to explain the problem.
If we define k = F / ΔL and the Y = S / δ
Where S is the uniaxial stress: S = F / A (i)
and δ is the strain: δ = ΔL / L (ii)
ΔL is the change in length
we can combine the equations i and ii as follows
Y = (F / A) / (ΔL / L) = (F * L) / (A * ΔL) (iii)
if k = F / ΔL the equation iii results
Y = k * (L / A) ⇒ k = Y*(A / L)
The spring constant of a metal bar for low values of tensile strain can be determined using Hooke's Law. It is given by the formula k = (A * Y) / L, where A is the cross-sectional area, Y is the Young's modulus of the material, and L is the initial length of the bar.
Explanation:The 'spring constant' of a metal bar for low values of tensile strain can be determined using Hooke's Law, which relates the applied force to the resulting elongation. In this case, the elongation is equivalent to the tensile strain.
Start by writing Hooke's Law: F = k * x, where F is the applied force, k is the spring constant, and x is the elongation.For a metal bar, the elongation is given by the formula x = (L * ΔL) / L, where ΔL is the change in length. Using Young's modulus (Y), the change in length can be expressed as ΔL = (F * L) / (A * Y).Substituting the value of ΔL in the elongation formula, we get x = (L * (F * L) / (A * Y)) / L.Simplifying the equation gives x = (F * L) / (A * Y).Substituting the formula for elongation into Hooke's Law, we get F = (k * L * F) / (A * Y).Dividing both sides by F gives 1 = (k * L) / (A * Y).Multiplying both sides by (A * Y) and rearranging the equation, we find that the spring constant (k) is given by k = (A * Y) / L.Therefore, the spring constant of a metal bar for low values of tensile strain is
k = (A * Y) / L
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Functions f(x) and g(x) are defined below. Determine where f(x) = g(x) by graphing.
f(x)=1/x-3+1
g(x)=2rootx-3
A. x = 1 B. x = 3 C. x = 2 D. x = 4
Answer:
Option D. x = 4
Step-by-step explanation:
we have
[tex]f(x)=\frac{1}{x-3}+1[/tex]
[tex]g(x)=2\sqrt{x-3}[/tex]
we know that
The solution of the system
f(x)=g(x)
is the x-coordinate of the intersection point both graphs
using a graphing tool
The intersection point is (4,2)
see the attached figure
therefore
The solution is x=4
Answer:
for plato its d
Step-by-step explanation:
i got it
which equation is the equation of the line, in point-slope form, that has a slope of -4 and passes through the point (7, -1) ?
Answer:
y - 1 = -4(x - 7).
Step-by-step explanation:
Point-slope equation is:
y - y1 = m(x - x1) where m = the slope and (x1, y1) is a point on the line.
Here m = -4 , x1 = 7 and y2 = 1, so:
y - 1 = -4(x - 7).
An equation of the line in point-slope form is: D. y - 1 = -4(x - 7).
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.
m represent the slope.
At data point (7, 1) and a slope of -4, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 1 = -4(x - 7)
Read more on point-slope here: brainly.com/question/24907633
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Suppose that you are swimming in a river while a friend watches from the shore. In calm water, you swim at a speed of 1.25 m/s . The river has a current that runs at a speed of 1.00 m/s.Note that speed is the magnitude of the velocity vector. The velocity vector tells you both how fast something is moving and in which direction it is moving.Part AIf you are swimming upstream (i.e., against the current), at what speed does your friend on the shore see you moving?Express your answer in meters per second.
Answer:
Your friend sees you moving at 0.25 m/s upstream.
Step-by-step explanation:
Remember that relative velocity is the velocity of an object in relation to another object. In this example, your friend sees you moving with respect to the river with a relative velocity (Vr) of:
Vr = Yor Velocity (Vy) - The river Velocity (Vriver) =
Vr = 1.25 m/s - 1 m/s = 0.25 m/s
I hope my answer helped you.
What is the best solution for the equation -5/2=3/4+n
Answer:-13/4
Step-by-step explanation:
Move 3/4 to the left:
-2/5-3/4=-20/8-6/8
-26/8=n
-13/4=n
The first one is the answer
A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average speed of 3 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?A. 0.5< t < 0.75B. 1.75< t < 2.0C. 2.0 < t < 2.5D. 2.5 < t < 3.0E. 3 < t < 3.5
Answer:
Option C is the answer.
Step-by-step explanation:
Given diameter is = 2 miles
So, radius will be = 1 mile
Let t represents the number of hours it took Johanna to walk completely around the lake.
Now, the circumference is given as: [tex]2\pi r[/tex]
So, circumference = [tex]2(3.14)(1)[/tex] = 6.28 miles
Johanna's speed = 3 miles/ hour
We know the formula [tex]Time=Distance / Speed[/tex]
t = [tex]6.28/3[/tex]
t = 2.09 hours
This is greater than 2, but less than 2.5, therefore, 2.0 < t < 2.5 is the answer.
Demarcus and Fabian live 23 miles apart and play soccer at a park between their homes Demarcus rode his bike for 3/4 of an hour and Fabian rode his bike for 1/2 of an hour to get to the park Fabian speed of 60 mph faster than the demarcus's speed find the speed of the soccer players
Answer:
Step-by-step explanation:
3/4r + 1/2(r+6)=23
3/4r + 1/2r +3=23
5/4r =20
Multiplying by 45 yields r=16
DaMarcus's speed is r=16 miles per hour & Fabian's speed is r+6=22 miles per hour.
Speed of demarcus is 16 mph & speed of fabian is 22 mph.
What is speed of a particle ?The rate of change of position of a particle with respect to time is called speed of that particle.
Distance = Speed × time
What are the speeds of soccer players ?Let, Demarcus rides x mph for 3/4th of an hour i.e. 0.75 hour
So, he rode 0.75x miles
Given that, Fabian's speed is 6 mph more than Demarcus's speed.
Fabian rides (x+6) mph for half an hour, i.e. 0.5 hour
So, he rode 0.5(x+6) miles
According to the question,
0.75x+0.5(x+6) = 23
⇒ 0.75x+0.5x+3=23
⇒ 1.25x = 20
⇒ x = 20/1.25
⇒ x = 16 mph
So, Demarcus's speed is 16 mph
Hence, Fabian's speed is 16+6 = 22 mph
Learn more about speed here :
https://brainly.com/question/23421880
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