A part of a line that has 1 endpoint and extends indefinitely in only one direction is called a ray.
A ray is named using its endpoint first, and then any other point on the ray
Properties of ray:
A line is a series of points placed together that continue infinitely.When this line is restricted from one direction and is extended in the other direction indefinitely, it forms a ray.It has just one starting point and does not have an opposite end and goes through and cuts many points and lines and is often used to draw angles, and we cannot measure the length of a ray.To know more about ray:
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The derivative of f is given by f ' (x) = e^x(-x3 +3x) - 3 for 0 ≤ x ≤ 5 . At what value of x is f(x) anabsolute minimum?
The value of x is 6, f(x) an absolute minimum is (5, -16, 328.4475).
The derivative of f is [tex]$& f(x)=e^x\left(-x^3+3 x\right)-3[/tex]
[tex]& f(x)=-e^x x^3+3 x e^x-3\end{aligned}$$[/tex]
Domain for: [tex]$0 \leq x \leq 5$[/tex] is [0,5]
[tex]$& \frac{d}{d x}[f(x)]=\frac{d}{d x}\left[-e^x x^3\right]+\frac{d}{d x}\left[3 x e^x\right]+\frac{d}{d x}[-3] \\$$[/tex]
[tex]\\& f^{\prime}(x)=\left(-e^x\right)\left(3 x^2\right)+\left(x^3\right)\left(-e^x\right) \\& +(3 x)\left(e^x\right)+\left(e^x\right)(3)+0 \\\\[/tex]
[tex]& f^{\prime}(x)=-3 x^2 e^x-x^3 e^x+3 x e^x+3 e^x \\[/tex]
[tex]& f^{\prime}(x)=e^x\left[-x^3-3 x^2+3 x+3\right]\end{aligned}$$[/tex]
Set the first derivative equal to zero and
solve for x to find the critical number.
[tex]$$-x^3-3 x^2+3 x+3=0$$[/tex]
x=-3.601679 (outside of the domain) not valid here
x=-0.6601231 (outside of the domain) not valid here
x=1.2618022 ... TEST this one
Now to find the absolute extremes, test the critical numbers and the endpoints by plugging their x-values back into the f (x) function to find their y - value.
Testing x = 0
x = 1.2618022
x = 5
Finding their y-values:
[tex]& f(0)=e^0\left[-(0)^3+3(0)\right]-3=0-3=-3 \\\\& f(1.2618022)=e^{1.2618022} \cdot\left[-(1.2618022)^3+3(1.2618\right. \\\\& f(1.2618022)=3.273978192[/tex]...Highest y-value.
absolute maximum: (1.2618022,3.273978192)
Where x==1.2618022
[tex]& f(5)=-e^5(5)^3+3(5) e^5-3 \\\\ f(5)=-125 e^5+15 e^5-3 \\\\& f(5)=-110 e^5-3=-16,328.4475 \\[/tex]
absolute minimum: (5, -16, 328.4475)
where x = 5.
Therefore, the absolute minimum of F(x) is (5, -16, 328.4475) and x is 5.
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18
What is the perimeter of this shape?
7 cm
7 cm
7 cm
cm
7 cm
7 cm
7 cm
Answer:
[tex]\huge\boxed{\sf Perimeter = 42\ cm}[/tex]
Step-by-step explanation:
Perimeter:The sum of all sides of a shape is known as its perimeter.Here,
Perimeter = 7 cm + 7 cm + 7 cm + 7 cm + 7 cm + 7 cm
Perimeter = 42 cm[tex]\rule[225]{225}{2}[/tex]
Observe the table. How many times greater must the acceleration of Object B be than the acceleration of Object A to make the table true? Enter your answer as a whole number, like this: 4 Mass Acceleration Force Object A 20 kg 9 m/s2 180 N Object B 40 kg 1800 N
The acceleration of Object B should be 5 times the acceleration of Object A in order to make the table true.
What is Acceleration?We have a table that gives the values of mass, acceleration and force of object A and object B.
We have to find by how many times greater must the acceleration of Object B be than the acceleration of Object A to make the table true.
The formula to calculate the force is -
F = m x a
From the table,
Mass = 40 Kg
Force = 1800 N
By substitution
a =F/m = 1800/40 = 45 m/s²
The acceleration of Object A is 9m/s² . On comparing the acceleration of both the objects, we can see that the acceleration of Object B is 5 times the acceleration of Object A.
Hence, the acceleration of Object B should be 5 times the acceleration of Object A in order to make the table true.
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write least to greatsest plsssssssssssssssssssssss i give 100 points
Answer:
-3.5,-3,-2[tex]\frac{1}{2}[/tex], -2,2.5
Step-by-step explanation:
For numbers that are negative, the larger the number is the lesser the value is. For numbers that are positive, the larger the number is the larger is value is. Positive numbers are always greater than negative numbers.
Answer:
-3.5 | -3 | -2[tex]\frac{1}{2}[/tex] | -2 | 2.5 |
Step-by-step explanation:
Negative number are smaller than positive numbers so 2.5 is the largest number. Negative numbers are kind of opposite of positive numbers. The larger the negative number is, the smaller it is. With positive numbers, the larger the number, the larger the value is.
someone please please help.
Answer:
The slope is 4.
Step-by-step explanation:
y=mx+b says that m is the slope and b is the y intercept. So this means slope=4 and int = 8.
Answer: 4
Step-by-step explanation:
This question is given to us in slope-intercept form. This is written as y = mx + b. The slope is the m variable, y = mx + b.
Using the equation given, the slope is;
y = 4x + 8 ➜ m = 4
If c(x)=x^3-2x and d(x)=4x^2-6x+8,
find the value of 3c(a-4)+3d(a+5)
By evaluating the quadratic equations we will get:
3c(a-4)+3d(a+5) = 3*(a^3 - 8a^2 + 102a + 22)
How to find the value of the expression?Here we have two quadratic functions:
c(x)=x^3-2x and d(x)=4x^2-6x+8
And we want to find the value of the expression:
3c(a-4)+3d(a+5)
First, let's evaluate the functions in these values:
3*c(a - 4) = 3*[ (a - 4)^3 - 2*(a - 4)] = 3*(a - 4)*[ (a - 4)^2 - 2]
= 3*(a -4)*(a^2 - 8a + 16 - 2)
= 3*(a - 4)*(a^2 - 8a + 14)
= 3*(a^3 - 12a^2 + 46a - 56)
3*d(a + 5) = 3*[ 4*(a + 5)^2 - 6*(a + 5) + 8]
= 3*[ 4a^2 + 40a + 100 -6a - 30 + 8]
= 3*[4a^2 + 36a + 78]
Then the expression is:
3c(a-4)+3d(a+5) = 3*(a^3 - 12a^2 + 46a - 56) + 3*[4a^2 + 36a + 78]
= 3*(a^3 - 12a^2 + 46a - 56 + 4a^2 + 36a + 78)
= 3*(a^3 - 8a^2 + 102a + 22)
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Use the following box plot on TV Time per night (in minutes) to answer the
following question:
0 15
60
110
225
Use the outlier rule to determine if the 225 minutes of TV watching time is
an outlier.
O Yes, because 225 minutes is greater than 205 minutes.
O No, because 225 is not greater than 252.5 minutes.
O Yes, because it is more than twice as much time as the 110 minutes.
O Yes, because it is more than 95 minutes away from the upper quartile.
Yes, because 225 minutes is greater than 205 minutes.
what is outlier rule?Outlier rules, also known as outlier detection algorithms, are algorithms designed to detect the presence of outliers in a dataset. Outliers are data points that are significantly different from the rest of the data, and can be caused by measurement error, experimental error, or some other anomaly. Outlier rules are used to identify and remove outliers from data sets in order to improve the accuracy of data analysis and modeling. Outlier rules typically use some combination of statistical measures, such as mean, median, and standard deviation, to detect the presence of outliers in the data.In this question answer is
Yes, because 225 minutes is greater than 205 minutes.
This can be determined by using the outlier rule
which states that any data point that is more than 1.5 times the interquartile range (IQR) away from the upper quartile (Q3) is considered an outlier.
The IQR is calculated as Q3 - Q1,
which in this case is
110 - 15 = 95. Therefore,
1.5 times the IQR is 95 x 1.5 = 142.5.
The upper quartile (Q3) is 110,
so any data point more than 205 (110 + 142.5) is considered an outlier, including 225.
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Yes, because 225 minutes is greater than 205 minutes.
what is outlier rule?Outlier rules, also known as outlier detection algorithms, are algorithms designed to detect the presence of outliers in a dataset.
Outliers are data points that are significantly different from the rest of the data, and can be caused by measurement error, experimental error, or some other anomaly.
Outlier rules are used to identify and remove outliers from data sets in order to improve the accuracy of data analysis and modeling.
Outlier rules typically use some combination of statistical measures, such as mean, median, and standard deviation, to detect the presence of outliers in the data.
In this question answer is
Yes, because 225 minutes is greater than 205 minutes.
This can be determined by using the outlier rule
which states that any data point that is more than 1.5 times the interquartile range (IQR) away from the upper quartile (Q3) is considered an outlier.
The IQR is calculated as Q3 - Q1,
which in this case is
110 - 15 = 95. Therefore,
1.5 times the IQR is 95 x 1.5 = 142.5.
The upper quartile (Q3) is 110,
so any data point more than 205 (110 + 142.5) is considered an outlier, including 225.
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Jaquan passed a checkpoint jogging at a constant speed of 9\,\dfrac{\text{km}}{\text{h}}9 h km 9, start fraction, start text, k, m, end text, divided by, start text, h, end text, end fraction. then, 222 minutes later, odalis passed the same checkpoint. if odalis runs at a constant speed of 12\,\dfrac{\text{km}}{\text{h}}12 h km 12, start fraction, start text, k, m, end text, divided by, start text, h, end text, end fraction, then how far past the checkpoint will odalis be when they catch up to jaquan?
The checkpoint Odalis will be when they catch up to Jaquan is 0.1 km.
Given that, Jaquan passed a checkpoint jogging at a constant speed of 9 km/hr.
2 minutes later Odalis passed the same checkpoint.
Odalis runs at a constant speed of 12 km/hr.
We know that, 1 hour = 60 minutes
So, 2 minutes = [tex]\frac{2}{60}[/tex] hour
= [tex]\frac{1}{30}[/tex] hour
So, the distance = [tex]9\times\frac{1}{30}[/tex]
= [tex]\frac{3}{10}[/tex] km
When the speed is 12 km/hr, we get
Distance = [tex]12\times\frac{1}{30}[/tex]
= [tex]\frac{2}{5}[/tex] km
Now, [tex]\frac{2}{5} - \frac{3}{10}[/tex]
= [tex]\frac{4}{10} - \frac{3}{10}[/tex]
= [tex]\frac{1}{10}[/tex] km
= 0.1 km
Therefore, the checkpoint Odalis will be when they catch up to Jaquan is 0.1 km.
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Answer:
1.2
Step-by-step explanation:
none
the sides of a rectangle are 6.2cm and 4.8cm each measured to 2.s.f and to 3.s.f.
find the minimum percentage error in the area 29.76.
Percentage error in the area is 79.84 %
what is percentage error?Percentage error is defined by the difference between actual value and estimated value while comparing to the actual value and expressed in percentage.
What is the minimum percentage error?
given, sides of a rectangle are 6.2 cm and 4.8 cm.
actual length = 6.2 cm
actual width = 4.8 cm
hence, area of rectangle = length × width
= 6.2 cm x 4.8 cm
actual area = 29. 76 square centimeters.
measured length = 2 cm
measured width = 3 cm
measured area = 2 x 3 = 6 square cm
percentage error in the area = (actual area - measured area) / actual area ×100
=(29.76 - 6) / 29.76 × 100
percentage error = 79.84 %
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A store sells boxes of juice in equal-sized packs.Garth bought 18 boxes, Rico bought 36 boxes, and Mia bought 45 boxes. What was the greatest number of boxes in each pack? How many packs did each person buy if each box contained the greatest number posible?
The maximum number of boxes in each pack is 9, and:
Garth bought 2 packs.Rico bought 4 packs.Mia bought 5 packs.What was the greatest number of boxes in each pack?To find the greatest number of boxes in each pack, we need to find the largest common factor between the given numbers.
We know that:
Ghart bought 18 boxes.Rico bought 36 boxes.Mia bought 45 boxes.We can decompose these numbers as a product between their prime factors, we will get:
18 = 2*3*3
36 = 2*2*3*3
45 = 5*3*3
You can see that the largest common factor is 3*3 = 9
So the maximum number of boxes that each pack can have is 9 boxes.
In that case:
Garth bought 18/9 = 2 packs.
Rico bougth 36/9 = 4 packs.
Mia bought 45/9 = 5 packs.
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What are the coordinates of D' when the quadrilateral is reflected across the line Y=X?
6
5
4
3
2
A
B
(1, 3)
O (2,4)
O (3.4)
Mark this and return
D
3
4
6
X
4
Save and Exit
Next
Submit
The Coordinates of point D(3,1) ,after reflection along, line, y=x, will be=(1,3).
What are coordinates?
coordinates can be defined as the pair of numbers which are used to determine the position of a given point.
Rule of reflection along line, y=x.
Suppose a point (a,b) is reflected along line, y=x,the coordinates of point after reflection along the line will be (b,a),that is abscissa and ordinate interchange their place, after reflection.
Coordinates of point D =(3,1)
→→Coordinates of point D(3,1) ,after reflection along, line, y=x, will be=(1,3).
Hence, The Coordinates of point D(3,1) ,after reflection along, line, y=x, will be=(1,3).
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You fill a swimming pool with water at a rate of 17 gallons per minute.
a. Is the amount of water in the pool a function
of the number of minutes? Explain.
b. Find the domain of the function. Is the domain
discrete or continuous? Explain.
c. Graph the function using its domain.
a. Yes, the amount of water in the pool is a function of the number of minutes. b. The domain of the function is 0 < x ≤ 588. The domain is continuous c. The required graph has been attached below.
What are the domain and range of the function?The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.
a. Yes, the amount of water in the pool is a function of the number of minutes. This is because, for each input value of the number of minutes, there is a unique output value of the amount of water in the pool.
Where the function is y = 17x
b. The domain of the function is the set of all possible values of the input, which in this case is the number of minutes. The domain is continuous because it includes all possible values within a range (in this case, all possible values of the number of minutes), rather than only a set of specific, discrete values.
Assume that the capacity of the swimming pool with water is 10000 gallons.
So it completed fully fills with water in 588.2 (=10000/17) minutes
Thus, the domain of the functin is 0 < x ≤ 588.
c. Here is a graph of the function using its domain:
Where the vertical axis represents the amount of water in the pool and the horizontal axis represents the number of minutes.
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Question 3(Multiple Choice Worth 3 points)
(Compound Interest and Geometric Sequences MC)
A saving account that earns 3.2% interest compounded bi-annually has a balance of $6,049.15 after 6 years. Determine the total amount of interest earned on the
account
O$1,049.15
O$1,409.15
O$4,145 24
O $5,000.00
Answer:
(a) $1049.15
Step-by-step explanation:
You want to know the interest earned by an account that pays 3.2% interest compounded semiannually if the balance is $6049.15 after 6 years.
Compound interestThe formula for the balance of an account earning compound interest is ...
A = P(1 +r/n)^(nt)
where P is the principal invested, r is the annual interest rate, n is the number of times per year interest is compounded, and t is the number of years.
ApplicationWe have ...
6049.15 = P(1 +0.032/2)^(2·6) = P(1.016^12)
The amount of interest earned is the difference between the account balance and the principal:
interest = 6049.15 -(6049.15/1.016^12) ≈ 1049.15
The total amount of interest earned is $1049.15.
<95141404393>
If TV and WY are parallel lines and m
Answer:
53
Step-by-step explanation:
They're vertical angles so they equal the
Answer:
∠ VUX = 53°
Step-by-step explanation:
∠ VUX and ∠ TUS are vertically opposite angles and are congruent, so
∠ VUX = 53°
Identify the y-intercept. Write as an ordered pair.
Answer: Its y-intercept is obtained when the x coordinate is 0, so that the function crosses the y-axis. Therefore, it means that x=0 . Note that the y value that corresponds to this intercept is y=f(0) y = f ( 0 ) . Thus, an ordered pair that represents the y-intercept is (0,f(0)) ( 0 , f ( 0 ) )
Step-by-step explanation:
Tom owes his dad $12. He mowed the neighbors grass and earned $55. He stopped at the store on the way home to get a drink and a snack for $7. How much money does Tom have?
Answer:
Tom has $36 after paying his dad and buying the drink.
Answer:
36
Step-by-step explanation:
because if you take away 12 from 55 you would have 43 and if you take away 7 you would have 36
PLEASE HELP!!!! IN A RUSH!!!!
Which equations represent linear functions?
Select all that apply.
y=x(2x+4)
x=2y+4
y=x2−19
y=3x2
x=y
Answer:
the second one and the last one
a) 3.2 ÷ 0.8 b) 7.5 +0.5
Answer:
a) 4
b) 8
Step-by-step expla nation:
a) 3.2 ÷ 0.8 = 4
b) 7.5 + 0.5 = 8
can someone explain this please
Answer:
X =56
Step-by-step explanation:
Total angles of a triangle = 180
Since it's the total, we add these three angles
[tex](x - 31) + (x) + (x + 43) = 180[/tex]
Next, we combine like terms
[tex]3x + 12 = 180[/tex]
Next, you can subtract 12 from both sides to get numbers on one side
[tex]3x = 168[/tex]
Last step is to divide by 3 to get the X alone
[tex]x = 56[/tex]
Answer:
x = 56
F = 25
R = 99
O = 56
Step-by-step explanation:
all triangles equal 180 degrees
that means that when you add angle F, O, + R, you will get 180
create the formula based on this info:
F + R + O = 180
x - 31 + x + 43 + x = 180
solve:
-31+43+x+x+x = 180
12 + 3x = 180
3x = 168
x = 56
now plug in x and find each angle
F = x - 31
F = 56 - 31
F = 25
R = x + 43
R = 56 + 43
R = 99
O = x
O = 56
Jerry is presently twice as old as his brother and six years older than his sister. How many years from now will Jerry's age be $\frac{2}{3}$ of the combined ages of his brother and sister at that time
Using leaner equation we find that After 12 years from now will Jerry's age be (2/3) of the combined ages of his brother and sister at that time.
What is leaner equation?A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
Let Jerry's brother present age be X years,
Then Jerry's present age will be 2x
And his sister's present age will be 2X - 6
And let y be the number of years from now when Jerry's age = (2/3) of combined age of his brother and sister.
So we have that,
(2X + y) = (2/3) [(X + y) + (2X - 6 + x)]
simplify the above equation
2X + y = (2/3) [3X + 2y - 6]
multiply through by 3/2
3X + (3/2)y = 3X + 2y - 6
subtract 3X from both sides
(3/2)y = 2y - 6
subtract 2y from both sides
-1/2y = -6
divide both sides by -1/2
y = 12 years
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"Find the value of each missing variable.
Note: Write your answer in simplest radical form. In the first blank put the coefficient in front of the √. And in the second blank, put the coefficient that is inside the √. ** If there is no coefficient in front of the √, enter a 1 in the blank **"
The value of the hypotenuse y = 9, and the value of the opposite side of the right angle triangle x = 4.5
Trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
Considering the angle 30° in the right angle triangle, the hypotenuse is y, the opposite side is x and the adjacent side is 9√3
cos 30° = √3 = adjacent/hypotenuse
sin 30° = 1/2 = opposite/hypotenuse
√3 = 9√3/y {cross multiply}
y = 9√3/√3 {cancel out √3}
y = 9
1/2 = x/9 {cross multiply}
x = 9/2
x = 4.5
Therefore, by proper application of trigonometric ratios for the right angle triangle, the hypotenuse y is equal to 9 and the opposite side x is equal to 4.5.
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How do you add mixed fractions?
Answer:
You have to first convert them to improper fractions, by multiplying the whole with the denominator (bottom number). And then you add the answer with the numerator (top number). This answer is then the numerator of the improper fraction, and the denominator remains the same. Then you add the two improper fractions. If the denominators are different, you find the lowest common multiple (LCM) of the denominators and multiply both the numerator and denominator so that the new denominator is the lowest common multiple. Then you add the numerators and keep the denominator the same
Example:
5[tex]\frac{3}{6}[/tex] + 3[tex]\frac{3}{4}[/tex]
5[tex]\frac{3}{6}[/tex]
= 5 x 6 = 30
= 30 + 3 = 33
= [tex]\frac{33}{6}[/tex]
3[tex]\frac{3}{4}[/tex]
= 3 x 4 = 12
= 12 + 3 = 15
= [tex]\frac{15}{4}[/tex]
[tex]\frac{33}{6}[/tex] + [tex]\frac{15}{4}[/tex]
LCM of 6 and 4 is 12
[tex]\frac{33}{6}[/tex]
= 33 x 2 and 6 x 2
= 66 and 12
= [tex]\frac{66}{12}[/tex]
[tex]\frac{15}{4}[/tex]
= 15 x 3 and 4 x 3
= 45 and 12
= [tex]\frac{45}{12}[/tex]
[tex]\frac{66}{12}[/tex] + [tex]\frac{45}{12}[/tex] = [tex]\frac{111}{12}[/tex]
Given that cos in the triangle below, show that
y² = ax² +bx+c
where a, b and c are numbers.
What are the values of a, b and c?
x+3
0
4x
Y
The values of a, b and c are a= 2, b = 3, c = -10
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We have been given an Cos Ф = 1/8
Cos Ф = 4x/y
Cos Ф = 4x/y = 1/8
x/y = 1/32
We need to write given expression in the form y² = ax² +bx+c, where a, b and c are numbers.
2x² + 12x + 8
= 2x² + 12x + 18 - 18 + 8
= (√2x + 3√2)² - 10
= (√2)² (x + 3)² - 10
= 2(x + 3)² - 10
Comparing with expression where a, b and c are numbers.
a = 2, b = 3 and c = -10
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Please help me with this, it doesn't make sense to me!
Answer: Jacob will be 16 (16.5) years old, which is half of Todd's age, in 4 years.
I respect the Todoroki profile pic :)
Step-by-step explanation:
33 ÷ 2 = 16.5
1/2 of Todd's age = 16.5 (16)
16 - 12 = 4 years (4.5 years to be specific)
You need a 60% alcohol solution. On hand, you have a 455 mL of a 30% alcohol mixture. You also have 95% alcohol mixture. How much of the 95% mixture will you need to add to obtain the desired solution?
The volume of the 95% solution that we need is 390 mL.
What is the amount of the volume required?We are told that we have in the solution that we have;
455 mL of a 30% alcohol mixture95% alcohol mixture.We have also been told that we are trying to make a solution that would contain a known volume of 60% alcohol solution
Given the mixture of the solutions that we have, we can write;
(455 * 0.3) + (0.95 * x) = (0.60 * x)
x is the unknown volume that we are looking for
136.5 + 0.95x = 0.6x
x = 390 mL
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A 10 cm thick grindstone is initially 200 cm in diameter, and it is wearing away at a rate of. At what rate is it's diameter decreasing?.
The diameter is twice the radius, so it is decreasing at a rate of [tex]$2(1.26 \times 10^{-2} \ \text{cm}/\text{hr}) = \boxed{2.52 \times 10^{-2} \ \text{cm}/\text{hr}}$[/tex]
The volume of the grindstone is [tex]$\pi r^2 h = \pi \cdot 100^2 \cdot 10 = 3141600 \ \text{cm}^3$[/tex], so the rate at which it is wearing away is [tex]$\frac{50}{3141600} = 1.59 \times 10^{-4} \ \text{cm}^3/\text{hr}$[/tex]
The grindstone is a cylinder, so its volume is proportional to its radius squared. Therefore, the radius is decreasing at a rate proportional to [tex]$\sqrt{1.59 \times 10^{-4}} = 1.26 \times 10^{-2} \ \text{cm}/\text{hr}$[/tex].
The diameter is twice the radius, so it is decreasing at a rate of [tex]$\sqrt{1.59 \times 10^{-4}} = 1.26 \times 10^{-2} \ \text{cm}/\text{hr}$[/tex].
A diameter is a line segment that passes through the centre of a circle or other curved shape and has its ends at the circumference. The length of a diameter is twice the length of the radius of the circle. A radius is a line segment joining the centre of a circle or other curved shape to any point on its circumference. The length of a radius is half the length of the diameter of the circle. Both the diameter and radius are fundamental measurements in determining the size and shape of a circle or other curved shape.
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The diameter of the grindstone is decreasing at a rate of 5/(πr) cm/hr.
Therefore the answer is b) 5/ (πr) cm/hr.
The grindstone is losing material at a rate of 50 cm³/hr, and since it is a cylinder, we can use the formula for the volume of a cylinder to find the rate at which its diameter is decreasing.
The volume of a cylinder is given by:
[tex]V= \frac{ \pi D^{2} h}{4}[/tex]
where V is the volume, d is the diameter and h is the height (in this case the thickness of the grindstone).
We know that the grindstone is losing material at a rate of 50 cm³/hr, and that the grindstone's thickness is 10 cm. To find the rate at which the diameter is decreasing, we need to find the rate at which the radius is decreasing, which we can find by differentiating the volume equation with respect to time.
So
[tex]\frac{dV}{dt} = -50\ cm^{3}/hr[/tex]
[tex]\frac{d(\frac{\pi\\D^{2}h }{4}) }{dt} = -50\ cm^{3}/hr[/tex]
[tex]\frac{2}{4}\pi Dh\frac{dD}{dt} = -50\ cm^{3}/hr[/tex]
Substitute the known values,
[tex]\frac{2}{4}\pi *(D)*(10cm)\frac{dD}{dt} = -50\ cm^{3}/hr[/tex]
[tex]\frac{dD}{dt}= (-50 cm^3/hr)*\frac{4}{2\pi *(D cm)*(10 cm)}[/tex]
[tex]\frac{dD}{dt}= \frac{-10}{\pi D}cm/hr[/tex]
We know D = 2r
[tex]\frac{dD}{dt}= \frac{-10}{\pi*(2r)}cm/hr[/tex]
[tex]\frac{dD}{dt}= \frac{-5}{\pi r}cm/hr[/tex]
--The question is incomplete, answering to the question below--
"A 10 cm thick grindstone is initially 200 cm in diameter, and it is wearing away at a rate of 50 cm³/hr. At what rate is it's diameter decreasing?
a. 5/ (2πr) cm/hr
b. 5/ (πr) cm/hr
c. 5/ (2π) cm/hr
d. 5/ π cm/hr"
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if you're given a true equation and you multiply each side by the same number the resulting equation is also a true equation if you're given a false equation and you multiply each side by the same number will the resulting equation be a true equation or a false equation
Give an example to explain
If you're given a false equation and you multiply both sides by the same non-zero number, the resulting equation will also be a false equation.
What will be the resulting equation if you multiply each side of a false equation by the same number?If you're given a false equation and you multiply both sides by the same non-zero number, the resulting equation will also be a false equation.
This is because the equation was already unbalanced, and multiplying both sides by the same non-zero number does not change that.
For example, consider the equation 2 + 3 = 6. This is a false equation. If we multiply both sides by 2, we get:
(2 + 3) × 2 = 6 × 2
4 + 6 = 12
The resulting equation 4 + 6 = 12 is also a false equation.
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Let [tex]f(x)=9-2^x[/tex]
Calculate the area that approximates [tex]A(f,1\leq x\leq 3)[/tex]
Write (2,4) (4,8) in slope-intercept form.
Answer: y = 2x
Step-by-step explanation:
Write in slope-intercept form,
y = mx + b.
y = 2x
On a graph, the coordinates will be:
(2,4);(4,8) Just like you had said above.
Hope this helped!
your chocolate chip cookie recipe will make 36 cookies. As you were cooling the first batch out of the oven, your dad came by and took 3. Of the remaining cookies, 2/3 will be gifted to your teachers. How many cookies does that leave you wiith for yourself. Write an equation and solve
I will have 11 cookies remaining.
The expression will be; Y = 33 - X
What is Linear Equation?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. A linear equation can have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on.
For the first batch
Total = 36 - 33 (collected by dad)
Total = 33
Second batch
Let remainder = Y
Y = 33 - X
where X = teachers part
To find the remainder, X = 2/3 x Total
X = 2/3 x 33
X = 22
Therefore;
Y = 33 - 22
Y = 11
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