The solution of derivative function is , [tex]\frac{d}{dx} (k(\frac{d}{dx} (t))[/tex] = 0
Given that,
d/dx(k dt/dx) = 0
Geometrically, the derivative of a function can be interpreted as the slope of the graph of the function or, more precisely, as the slope of the tangent line at a point. Its calculation, in fact, derives from the slope formula for a straight line, except that a limiting process must be used for curves.
[tex]\frac{d}{dx} (k(\frac{d}{dx} )t[/tex] = 0 (Equation-1)
Then,
[tex]\frac{d}{dx} (t)[/tex] = 0
The derivative of a function is defined as the instantaneous rate of change of a function at a specific point. The derivative gives the exact slope along the curve at a specific point. The derivative of the function is represented as d y d x , which means the derivative of with respect to the variable .
We can substitute equation-1,
So,
We can write,
[tex]\frac{d}{dx} (k*0)[/tex] = 0
[tex]\frac{d}{dx} (0)[/tex] = 0
0 = 0
Therefore,
The solution of derivative function is , [tex]\frac{d}{dx} (k(\frac{d}{dx} (t))[/tex] = 0
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Charlie wants to order lunch for his friends. He'll order 6 sandwiches and a $3 kid's meal for his little brother. Charlie has $27. How much can he spend on each sandwich if they are all the same price? Choose two answers: one for the inequality that models this situation and one for the correct answer.
A. Answer:$7 or less
B. Answer: $4 or less
C. Inequality: 3x+6>=27
D. Inequality: 3x+6<27
E. Inequality:6x+3<=27
F. Inequality:6x+3>=27
Answer:
then he'll get a bagel 2 pieced sanwich with a side of E
Step-by-step explanation:
the blue figure is a dilation image of the black figure. the labeled point is the center of dilation. tel whether the dilation is an enlargement or a reduction. then find the scale factor of the dilation.
The dilation is am enlargement or a reduction then the scale factor be 2.
What is meant by scale factor?The ratio of one object's scale to that of a new object, which has its representation but is larger, is known as a scale factor (bigger or smaller).
To scale shapes in various dimensions, utilize the scale factor. Different geometrical shapes, both in two- and three-dimensions, are covered in geometry classes. The scale factor is a way to compare figures that appear to be similar but actually have distinct scales or measurements.
A scale factor is the amount by which a thing is multiplied to produce a separate object that has the same appearance but is a different size. It creates a precise copy that is just bigger or smaller than the original. Scale Factor multiplies the image or object in the same way as a copy machine would enlarge or reduce it.
Taking two points and dividing them would yield the factor.
For instance, if the point was between x = 2 and x = 4, their division would be 4/2 = 2, as shown on the right side.
Now, if we split the points x = -1 and x = -2 on the left side, we get -2/-1 = 2.
Therefore, the scale factor be 2.
The complete question is;
22. the blue figure is a dilation image of the black figure. The center of the dilation is O. Tell whether the dilation is am enlargement or a reduction. Then find the scale factor
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if karen has a piece of fabric that is 1 187/240 yards long. if she needs a piece that is 5/6 yards long, many yards should she trim?
Karen that has a piece of fabric that is 1 187/240 yards long needs to trim 227/240 yards
What is a fraction?Is a number that expresses the portion of some number over a total. The number that expresses the portion is known as the numerator and the number that expresses the total is known as the denominator.
To solve this problem we must perform the corresponding algebraic operations with mixed fraction.
Data of the problem:
Total = 1 187/240Need = 5/6Trim = ?A mixed operation is solved as follows:
For the denominator: the same denominator is placed.
For the numerator:
The value of the denominator is multiplied by the integer component.
The result is added to the numerator of the fraction.
We transform the mixed fractions into improper fractions and we have:
1 187/240 =
[(240*1) + 187)] /240=
[240+ 187] /240=
427/240
Calculating how many yards should she trim:
Yards to trim: 427/240 - 5/6
Yards to trim: (427 - 200) / 240
Yards to trim: 227/240
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what is the maximum number of points on the convex hull of a set of 100 points inside a square?
The maximum number of points on the convex hull of a set of 100 points inside a square is 4.
A Convex Hull is defined as the smallest convex polygon which contains all the points in a set.
Since the points are inside a square, which means : the convex hull must be a subset of the square's boundary. The boundary of the square has 4 sides, so the maximum number of points on the convex hull is 4.
In Square , the number of points on the convex hull is a function of the distribution of the points and the shape of the region in which they are located.
Therefore , the maximum number of points on the convex hull of a set of 100 points inside a square is 4.
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Your scores on the last 3 bowling games are 99,92, and 115. Write and solve an inequality to find the score you need in the next game to have a mean score of at least 100.
Answer:
Score in 4th game = 94
Step-by-step explanation:
The mean is the average of all the data points, which means we divide the sum of all the points by the total number of points.
Letting s represent the score in the 4th game, we can use the following equation to find the score needed to end up with a mean score of 100:
[tex]\frac{99+92+115+s}{4}=100\\ \frac{306+s}{4}=100\\ 306+s=400\\s=94[/tex]
the physician orders heparin 1250units/hr. you have a solution of 50,000units/1000ml. how many gtt/min should the patient receive, using a 60gtt/ml set?
The patient should receive 50 gtt/min of heparin using a 60 gtt/ml set.
The unitary method is a useful tool in determining the amount of medication to be administered in a given time period.
The physician has ordered a medication called heparin, which is used to prevent blood clots.
The physician has ordered the patient to receive 1250 units of heparin per hour.
You have a solution of 50,000 units of heparin in 1000 ml.
To calculate the number of drops of heparin that the patient should receive per minute, we will use a method called the unitary method.
First, we need to determine the flow rate in ml/hr.
=> 50,000 units / 1000 ml = 50 ml/hr.
Now, we need to convert this to drops per minute.
=> 50 ml/hr x 60 gtt/ml = 3000 gtt/hr.
Finally, we divide the total number of drops per hour by 60 to get the number of drops per minute. So,
=> 3000 gtt/hr / 60 minutes = 50 gtt/min.
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Ms. Jackson wants to rent an oversized truck for a week. It will cost the weekly fee plus $0.20 per mile driven. Let m=the number of miles Ms. Jackson drives during the week.
Answer:
ms Jackson let m=the number of miles ms
Question Down below (PLS HELP FOR 50 BRAINLIST)
Answer:
there's nothing there. If you put the question there, I could help.
5 students are choose at random and there is 4 options (A, B, C and D)
1. What is the probability none choose option B
2. What is the probability all choose option A
3. What is the probability 3 students choose option C
The probability none choose option is [tex]\frac{243}{1024}[/tex] , the probability all choose option A is [tex]\frac{1}{1024}[/tex] , the probability 3 students choose option C is [tex]\frac{15}{256}[/tex]
What do you mean by Probability?Probability is a branch of mathematics that deals with the likelihood or chance of an event happening. It is a number between 0 and 1 that indicates the likelihood of an event occurring, with 0 meaning that an event is impossible and 1 meaning that an event is certain to occur.
Probability is used to model and make predictions about real-world situations such as the outcome of a coin flip, the results of a survey, or the success of a marketing campaign. It is also used in many fields including statistics, finance, engineering, and sciences to make decisions based on uncertain data.
Probabilities can be calculated using various methods, such as counting, Bayes' theorem, and simulation. In general, the probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
To find the probability that none of the 5 students choose option B, we need to find the probability that each student chooses one of the other 3 options (A, C, or D) and then multiply these probabilities. Since each student has the same choices, the probability that each student chooses one of the other options is 3/4. So, the probability that none of the 5 students choose option B is (3/4)^5 = 243/1024.To find the probability that all 5 students choose option A, we need to find the probability that each student chooses option A and then multiply these probabilities. The probability that each student chooses option A is 1/4. So, the probability that all 5 students choose option A is (1/4)^5 = 1/1024.To find the probability that 3 students choose option C, we can use combinations. There are C(5,3) = 10 ways to choose 3 students out of 5. For each of these combinations, the probability that the chosen 3 students choose option C is (1/4)^3, and the probability that the remaining 2 students choose options other than C is (3/4)^2. So, the total probability is 10 * (1/4)^3 * (3/4)^2 = 15/256.To know more about outcomes visit:
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Find the symmetric equations of the line that passes through the point P(−2,1,0) and is parallel to the vector v⃗ =⟨0,2,−3⟩ .
The symmetric equations of the line that passed through the given point and parallel to the given vector are x+2=0 , 3y=3-2z
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here: The co-ordinate P(-2,1,0) and parallel vector with components (0,2,-3)
The parametric equations of the line through the point P(-2,1,0) and parallel to the vector: u= (0,2,-3)are:
{x = -2
{y = 1+2t
{z = -3t
In order to get the symmetric form we derive t from the third and replace it into the second
t=-z/3⇒ y=1+2×(-z/3)
3y=3-2z
The symmetric form is
x+2=0 , 3y=3-2z
Hence, The symmetric equations of the line that passed through the given point and parallel to the given vector are x+2=0 , 3y=3-2z
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perform the indicated operations, given c = −4, a = 1 6 2 0 1 −1 , and b = 1 2 −1 6 . c(ba)
The value of give operation is =[[0,-4,-28][20.4.-32]]
A rectangular or square array of numbers or variables that are arranged in rows and columns is known as a matrix in mathematics. Elements or entries are the names for individual things in a matrix.
The application of matrix plays a major role in Mathematics, as well as in other fields. It helps in solving linear equations. Matrices are extremely valuable objects that can be found in a wide range of applications. The application of matrices in mathematics is used in a wide range of scientific fields as well as mathematical areas. Engineering mathematics is used in almost every aspect of our lives. In this article, we are going to learn what is a matrix, different matrix operations and the application of matrices in detail.
Some of the matrix's rows and columns define how big it is. A matrix of "m" rows and "n" columns is written as "m*n," where "m" and "n" are the dimensions of the matrix.
We have, c=-4
[tex]A=\left[\begin{array}{ccc}2&1&1\\-1&0&3\\\end{array}\right] \\\\and , B=\left[\begin{array}{ccc}-1&0\\3&1\\\end{array}\right][/tex]
first, compute the cA.
[tex]=(-4)\left[\begin{array}{ccc}2&1&1\\-1&0&3\\\end{array}\right] \\\\cA=\left[\begin{array}{ccc}-8&-4&-4\\4&0&-12\\\end{array}\right] \\\\Now, BcA=\left[\begin{array}{ccc}1&2\\-1&3\\\end{array}\right] \left[\begin{array}{ccc}-8&-4&-4\\4&0&-12\\\end{array}\right] \\\\\\=\left[\begin{array}{ccc}0&-4&-28\\20&4&-32\\\end{array}\right][/tex]
The complete question is-
Perform the indicated operation,c=-4,
[tex]A=\left[\begin{array}{ccc}2&1&1\\-1&0&3\\\end{array}\right] \\\\and , B=\left[\begin{array}{ccc}-1&0\\3&1\\\end{array}\right][/tex]
B(cA)=?
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use the definition for ai to answer the questions. for i ∈ z , ai is the set of all positive integer multiples of i. (a) describe the following set using set builder notation:
This set contains all positive integer multiples of 5, but does not include 0 or negative integers.
The set ⋂i=15Ai is the set of all positive integer multiples of the least common multiple (LCM) of 1, 5.
To find the LCM of 1 and 5, we multiply them together: LCM(1,5) = 1 * 5 = 5.
Therefore, the set ⋂i=15Ai is the set of all positive integer multiples of 5: {5, 10, 15, 20, ...}.
Using set builder notation, this set can be written as:
⋂i=15Ai = {x ∈ Z | x is a multiple of 5} = {5x | x ∈ Z and x > 0}.
Therefore, This set contains all positive integer multiples of 5, but does not include 0 or negative integers.
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3x^2+3y^2+12x-9y+12=0 what is the diameter of the circle
Which table of data could you collect by walking away from a motion detector.
In third table constant rate is not changed.
Hence the correct data table is option C.
What is word problem?
Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.
Here in given question, the constant rate is of motion detector is determined by difference between the distance by time. Now,
In option A) first table ,
=> constant rate = 10-10 =0
=> constant rate = 10-10=0
=> constant rate = 10-8 = 2
Here 0≠ 2. Then given table is not refer motion detector.
In option B) second table,
=> constant rate = 3-3=0
=> constant rate = 3-5 =-2
Here 0≠-2 then the given table is not refer motion detector.
In option C) third table,
=> constant rate = 9-7 =2
=> constant rate = 7-5 =2
=> constant rate = 5-3 =2
In this given table constant rate is not changed.
Hence the correct data table is option C.
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.A number increased by negative eight is equal to fourteen.Which equation could be used to find the number?
n + 8 = 14
n + (-8) = 14
8 - n = 14
Answer:
the second one. n + (-8) = 14.
Step-by-step explanation:
Trapezium ABCD is shown.
A
Work out the size of angle ADC.
Give your answer correct to 1 decimal place.
13 cm
12 cm-
Optional working
B
-9 cm-
-13 cm-
Answer: ADC=
C
D
Total marks: 5
In the given trapezium/trapezoid ABCD, the value for the measure of ∠ADC is obtained as 157.4°.
What is a trapezoid?
A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.
A trapezoid is also known as a trapezium.
A trapezium ABCD is given.
BE represents the height of the trapezium.
In Δ ABE use the trigonometric ratio since it is a right-angled triangle, to find the unknown ∠A.
cos θ = base / hypotenuse
Substitute the values in the equation -
cos θ = AE / AB
cos θ = 12 / 13
θ = 22.62°
The value of ∠A or ∠BAC is 22.62°.
Now ∠BAC and ∠ADC lie on the sample plane.
So according to the properties of a trapezium, the angles that lie on the plane have a sum of 180°.
The equation for the statement is -
∠BAC + ∠ADC = 180°
Substitute the values in the equation -
22.62° + ∠ADC = 180°
∠ADC = 180° - 22.62°
∠ADC = 157.38° ≈ 157.4°
Therefore, the measure of ∠ADC is 157.4°.
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How did you convert 3 feet into meters?
By multiplying the unit by 0.304, you can convert feet to meters.
How do you change feet to meters?In order to convert between feet and metres, basic math is needed. You can change the unit from feet to metres by multiplying by 0.304. As a result, you would need to multiply 5 by 0.304 in order to convert 5 feet to metres, for example.
Therefore, 5 feet is equal to 5 times 0.304, or 1.52 metres.
One can change measurement units from feet to metres by using the simple calculation Meter = Feet X 0.3048.
Below are some examples of feet-to-meter conversions.
Meter in feet
10 feet are equivalent to 10 * 0.305.
3.048 Meter
20 feet are equivalent to 20*0.305.
6.096 Meter
50 feet are equivalent to 50 * 0.305.
15.24 Meter
75 feet are equivalent to 75 * 0.305.
22.86 Meter
100 feet is equivalent to 100 * 0.305 30.48 meters.
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Solve for the given variable. 2m + 5m = 42
Answer:
m = 6
Step-by-step explanation:
first combine like terms
so 7m = 42
then isolate the variable by dividing both sides by 7
m = 42/7
m = 6
Find the unit digit of the product 91 92 93 …… 99
The unit digit of the product of 91, 92, 93, ... 99 is 0.
What is Unit digit?The digit that goes in the place of one in a number is known as the unit digit. i.e. It is the number's rightmost digit. As an illustration, the unit digit for 243 is 3, whereas the unit digit for 39 is 9.
It is easy to identify the unit place digit of the smaller number but when it comes to the numbers raised to the larger power it becomes difficult to identify the same by simple observation. It is when the concept of cyclicity comes into the picture.
The cyclicity concept is based on the fact that every digit in the number has its own repetitive pattern when raised to any specific power. This particular concept makes it easy for the students to find the unit place digit of the larger numbers and that too at much less time. So, let's learn about the cyclicity concept.
For example: - 2² = 4. Here, the unit digit is 4
2³ = 8. Here, the unit digit is 8.
Given:
91 × 92 × 93......×98 × 99
We want to find unit digit of the product of the numbers.
Here two digit is 92 and 95.
If we multiply 92 and 95, we will get zero as unit digit and if we multiply any digit by zero, unit digit always be zero.
So, the product of 92× 95 has zero in unit place.
So, in product of all numbers 91 × 92 × 93......×98 × 99 the unit will be zero. Because when we multiply any number by zero it become zero.
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PLEASE HELP MEEE!!! WILL GIVE BRAINLIEST!!
Describe exactly what type of transformation has been applied to triangle QRS to triangle Q'R'S'
a. if the price of kewpie dolls and the price of beanie babies are both $6, how many of each would lucinda buy if she were rational?
Lucinda will buy 2 kewpie dolls and 1 beanie baby if she were rational.
According to the question,
Given the table below compares the marginal benefit Lucinda gets from Kewpie dolls and Beanie Babies. The image of the table is attached.
If Lucinda has only $18 to spend and the price of kewpie dolls and the price of beanie babies are both $6,
Lucinda will buy the combination for which the marginal benefit is the same.
Therefore, Lucinda will buy 2 kewpie dolls and 1 beanie baby, if she were rational.
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The complete question is:
If Lucinda has only $18 to spend and the price of kewpie dolls and the price of beanie babies are both $6, how many of each would Lucinda buy if she were rational? 0 kewpie dolls and 3 beanie babies 3 kewpie dolls and 0 beanie babies 2 kewpie dolls and 1 beanie baby 1 kewpie doll and 2 beanie babies
In the figure below, AABC AYXZ.
Find sin X, tan X, and cosX.
Round your answers to the nearest hundredth.
B
12
17.4
12.6
Y
N
X
sin X = 0.72, cos X = 0.69, tan X = 1.05
What do you mean by Pythagorean Theorem?The Pythagorean Theorem is a fundamental mathematical principle named after the ancient Greek mathematician Pythagoras. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
The theorem can be expressed mathematically as c² = a² + b², where a and b are the lengths of the two shorter sides of the triangle and c is the length of the hypotenuse. The theorem can be used to find the length of a missing side of a right triangle if the lengths of the other two sides are known.
To find sin X, cos X, and tan X in triangle ABC, we need to first find the measures of the other angles in the triangle. Since angle C is a right angle, we can use the Pythagorean theorem to find the lengths of the sides adjacent to angle X (i.e., sides AC and BC).
AC² + BC² = AB²
(12.6)² + (12)² = (17.4)²
159.36 + 144 = 304.76
303.36 = 304.76
Since AC² + BC² = AB², we can conclude that triangle ABC is a right triangle, with angle X as the acute angle opposite side AC.
Using the definitions of sine, cosine, and tangent, we can find the values of sin X, cos X, and tan X:
sin X = [tex]\frac{AC}{AB}[/tex] = 12.6 / 17.4 = 0.72
cos X = [tex]\frac{BC}{AB}[/tex] = 12 / 17.4 = 0.69
tan X = [tex]\frac{AC}{BC}[/tex]= 12.6 / 12 = 1.05
Rounding to the nearest hundredth, the values are:
sin X = 0.72
cos X = 0.69
tan X = 1.05
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Which is the approximate measure of angle acb? 31.0° 36.9° 53.1° 59.0°
Answer: the answer is
53.1
38 divided 9=4 remalnder 2
The answer to 38 divided by 9 calculated using Long Division is 4 and remainder is 2
What is Algebraic expression ?
Algebraic expression can be defined as the combination of variables and constants.
Given expression ,
38 / 9 .
Step 1:
Start by setting it up with the divisor 9 on the left side and the dividend 38 on the right side like this:
Step 2:
The divisor (9) goes into the first digit of the dividend (3), 0 time(s). Therefore, put 0 on top:
Step 3:
Multiply the divisor by the result in the previous step (9 x 0 = 0) and write that answer below the dividend.
Step 4:
Subtract the result in the previous step from the first digit of the dividend (3 - 0 = 3) and write the answer below.
Step 5:
Move down the 2nd digit of the dividend (8) like this:
Step 6:
The divisor (9) goes into the bottom number (38), 4 time(s). Therefore, put 4 on top:
Step 7:
Multiply the divisor by the result in the previous step (9 x 4 = 36) and write that answer at the bottom:
Step 8:
Subtract the result in the previous step from the number written above it. (38 - 36 = 2) and write the answer at the bottom.
You are done, because there are no more digits to move down from the dividend.
The answer is the top number and the remainder is the bottom number.
Therefore, The answer to 38 divided by 9 calculated using Long Division is 4 and remainder is 2
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Given the arithmetic sequence 10, 15, 20, 25,... find the a15.
Answer
a15 is equal to 75
There are 14 sixth graders, 29 seventh graders,
and 37 eighth graders in the musical at
Canon Middle School. If 65% of the students
in the musical are girls, how many are girls?
Answer:
52 girls
Step-by-step explanation:
You have to find the total number of students first which is 80. Then you figure out 65% of 80. You can write a proportion which is 65/100 = x/80, you then solve for x by using the butterfly method.
So,
65/100 = x/80
5200 = 100x
divide by 100 to isolate x
52 out of the 80 students are girls
What is the slope of the linear relationship?
- 5/2
5/2
-2/5
2/5
The slope of the linear relationship is -5/2.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
Slope of a line with two points (x, y) and (x', y') on the line is,
Slope = (y' - y) / (x' - x)
Consider any two points from the line.
Let the points be (0, 3) and (2, -2).
Slope = (-2 - 3) / (2 - 0) = -5/2
Hence the slope of the given graphed line is -5/2.
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Find x and y.
PLEASE HELP
Answer:
Step-by-step explanation:
If a line is parallel to a side of a triangle, then the intersected sides are divided proportionally
4/2=y/3
2=y/3
y=2*3 = 6
next,
If the angles of one triangle are equal to the angles of another triangle, then the triangles are said to be equiangular.
(4+2)/4=6/x
6/4=6/x
x=4
if room temperature is 25 c and the coffee is originally at 80 c, how long will it take the coffee to cool to 45 c if the ratio ? provide your answer in minutes.
The time take for the object to cool down is 5 minutes.
The temperature of a substance is a measure of its thermal energy and it is important to know how it changes over time.
Heat transfer occurs from hot to cold, meaning that the coffee will transfer heat to the room until both reach thermal equilibrium. The temperature difference between the coffee and the room is
=> 80°C - 25°C = 55°C.
We will use this value to calculate the rate of heat transfer. We know that the final temperature of the coffee will be 45°C, so the temperature difference will become
=> 45°C - 25°C = 20°C.
The time it takes to cool from 80°C to 45°C will depend on the heat transfer rate, which is affected by factors such as the mass of the coffee, the material of the container, and the surrounding environment.
Let us consider that the average heat rate is 60 seconds that is one minute.
Then the time taken for it is calculated as,
=>20 x 60 = 300
So, in minutes 5 minutes.
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A bullet travelling at an average speed of 2 x 10³ kmh-¹ hits a target 500 m away. Find the time of the bullet's flight, in seconds.
Answer: 0.25 seconds.
Step-by-step explanation:
To find the time of flight of the bullet, we need to divide the distance the bullet travels by its velocity.
Average speed is distance over time. so
time = distance/speed
time = 500m / (2000 m/s)
time = 0.25 seconds
So, the bullet's flight time is 0.25 seconds.
