The function f(x) = {2 - x if x ≤ 1, x if x > 1} is one-to-one but not onto.
To prove that a function f(x) is one-to-one but not onto, we need to show that it satisfies the following conditions:
One-to-one: For any two different values x1 and x2 in the domain, if f(x1) ≠ f(x2), then x1 ≠ x2.
Not onto: There exists at least one value y in the codomain that is not the image of any value x in the domain.
Let's analyze the function f(x) = {2 - x if x ≤ 1, x if x > 1}.
One-to-one:
To show that f(x) is one-to-one, we need to demonstrate that if f(x1) ≠ f(x2), then x1 ≠ x2.
Consider two different values x1 and x2 in the domain such that f(x1) ≠ f(x2).
If both x1 and x2 are less than or equal to 1, then f(x1) = 2 - x1 and f(x2) = 2 - x2. Since x1 and x2 are different, f(x1) and f(x2) will also be different. Therefore, x1 ≠ x2.
If both x1 and x2 are greater than 1, then f(x1) = x1 and f(x2) = x2. Since x1 and x2 are different, f(x1) and f(x2) will also be different. Therefore, x1 ≠ x2.
If one value is less than or equal to 1 and the other is greater than 1, then f(x1) = 2 - x1 and f(x2) = x2. In this case, f(x1) and f(x2) will always be different because 2 - x1 will never be equal to x2. Therefore, x1 ≠ x2.
In all cases, we have shown that if f(x1) ≠ f(x2), then x1 ≠ x2. Hence, f(x) is one-to-one.
Not onto:
To show that f(x) is not onto, we need to find at least one value y in the codomain that is not the image of any value x in the domain.
The codomain of f(x) is the set of all real numbers. Let's consider the value y = 3. No matter what value of x we choose from the domain, the function f(x) will never be equal to 3. Therefore, there is no x in the domain such that f(x) = 3.
Since we have found a value y (3) in the codomain that is not the image of any value x in the domain, we can conclude that f(x) is not onto.
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Find the sum: 5/8+3/10
Answer:
37/70
Step-by-step explanation:
5/8 + 3/10 = (5 × 5)/ (8 × 5) + (3 × 4)/ (10 × 4) =
25/40 + 12/40 = 37/40
Rhombus LMNO is shown with its diagonals.
Rhombus L M N O is shown. Diagonals are drawn from point M to point O and from point L to point N and intersect at point P. All sides are congruent.
Angle MLO measures 112°. What is the measure of angle MLP?
45°
56°
68°
90°
The angle m∠MLP in the rhombus is 56 degrees.
How to find the angle of a rhombus?A rhombus has all its sides equal to each other. The diagonals of a rhombus are angle bisectors.
Therefore,
m∠MLP = m∠MLO / 2
m∠MLO = 112°
m∠MLP = 112 / 2
Therefore,
m∠MLP = 56 degrees.
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Answer:
B. 56
Step-by-step explanation:
trust
In the figure pq is parallel to Ed the length of to is 4 cm the length of pt is 16 the length of qt is 20 what is the length of sq
By applying the basic proportionality theorem (BPT), the length of side SQ is equal to 5 cm.
How to calculate the length of side SQ?In order to determine the length of side SQ, we would apply basic proportionality theorem (BPT) as follows:
Since PQ ǁ RS, PT = 16
PT/RP = QT/SQ
16/4 = 20/SQ
Cross-multiplying, we have:
16SQ = 20 × 4
SQ = 80/16
SQ = 5 cm.
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Complete Question:
In the figure, PQ is parallel to RS. The length of RP is 4 cm; the length of PT is 16 cm; the length of QT is 20 cm. What is the length of SQ?
Which table shows a function that is decreasing only over the interval (–1, ∞)?
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 1, negative 3, negative 5, negative 2, negative 1, 2.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 3, negative 5, negative 7, negative 6, 1, negative 1.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 4, negative 3, negative 1, 2, 1, negative 6.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 5, negative 1, 1, 0, negative 4, negative 8.
The table that shows a function that is decreasing only over the interval (–1, ∞) is:
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 1, negative 3, negative 5, negative 2, negative 1, 2.
When a function is decreasing?A function is decreasing if when we increase the value of x, we decrease the value of y, and vice versa.
Decreasing on the (–1, ∞) means that as x increases on the interval, i.e. x = -100, then x = -10, then x = -2, the value of y decreases. The function that follows this pattern only on this interval is:
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 1, negative 3, negative 5, negative 2, negative 1, 2.
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Answer:
A
Step-by-step explanation:
A hyperbola centered at the origin has a vertex at (0, 36) and a focus at (0, 39). which are the equations of the directrices? x = ± y = ± x = ± y = ±
The equation of directrix is D. y=± 432/13.
Definition of hyperbola -
A plane curve generated by a point so moving that the difference of the distances from two fixed points is a constant . A curve formed by the intersection of a double right circular cone with a plane that cuts both halves of the cone.1. The vertex i at (0, 36) and a focus at (0, 39), then you have:
a=36
a²=1296
2. The equation of directrix is:
y = a² =c
c = 39
y = 1296/39
y = 432/13
Therefore, the answer is the option D, which is: D. y=± 432/13
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The complete question is -
A hyperbola centered at the origin has a vertex at (0, 36) and a focus at (0, 39)
Which are the equations of the directrices ?
A. x= ±12/13
B. y=±12/13
C. x=±432/13
D. y=± 432/13
Answer: Correct
Step-by-step explanation:
Rick received better results for his Maths test than for his English test. If the sum of his two marks is 163 and the difference is 31, find the mark for each subject.
Answer:
Math = 97
English = 66
Step-by-step explanation:
Let the score of the Math test be x, and the score of the English text be y
Then we have the two equations
[tex]x+y = 163\\x-y = 31[/tex]
To solve for x and y there are multiple ways, one of the easy ways is just to add the two equations together because that would cancel out the y:
[tex]x + x + y -y = 163 +31\\2x = 194\\x = 97\\[/tex]
Then using the x, we can find y by doing
[tex]x+y = 163\\97 + y = 163\\(97 + y) - 97 = (163) - 97\\y = 66[/tex]
Therefore, we have a math score of 97, and an English score of 66.
solve the equation below by factorising.
2x^2-8x=0
Hello,
2x² - 8x = 0
2x × x - 2x × 4 = 0
2x(x - 4) = 0
2x = 0 or x - 4 = 0
x = 0 or x = 4
On a certain math exam, $10\%$ of the students got 70 points, $25\%$ got 80 points, $20\%$ got 85 points, $15\%$ got 90 points, and the rest got 95 points. What is the difference between the mean and the median score on this exam
Joe needs to get to his house, which is 106 miles away in 2 hours. How fast does he need to drive? 48 mph 104 mph 0.019 mph 53 mph
Answer:53 mph
Step-by-step explanation:106 miles per hour would get him home in 1 hour but it takes 2 hours so you can divide 106 by 2 to 53 miles per hour.
Answer:
53 mphStep-by-step explanation:
Joe needs to get to his house, which is 106 miles away in 2 hours. How fast does he need to drive?
48 mph 104 mph 0.019 mph 53 mph106 miles is 2 hours = 53 miles in 1 hour (106 : 2)
so your answer is 53 mph
Martin is saving money to buy a new phone that costs $1,000 by selling trees. he is using an app to manage his sales, but it keeps a fraction of each sale. his net pay is modeled by the function p(x) = x2 20x – 196, where x represents the number of sales. how many sales does martin need to make to earn $1,000? 10 sales 26 sales 46 sales 1,296 sales
Answer:
26
Step-by-step explanation:
You want to know the value of x that makes y=1000. You can plug the equation in to your calculator or desmos. Look at the table for when y=1000. X is 26.
To check, plug in 26 for x. 26^2 + 20(26) - 196 = 1000.
Answer: 26 sales
Step-by-step explanation:
A maker of folding tables estimates that 1 in 40 tables is returned due to a manufacturer's defect.
for each table not returned, the manufacturer makes a profit of $4.50, but for each table
returned, it loses $48. what is the manufacturer's long-term average profit on this product?
Answer:
$127.50
Step-by-step explanation:
The average profit is found by adding up the profits from both scenarios.
39(4.5) + 1(-48)
= $127.50
Brainliest, please :)
Five possibilities are equally likely and have payoffs of $2, $4, $6, $8, and $10. the expected value is:____.
a. $4
b.$5
c. $6
d. $7
The expected value for the given Five possibilities is $6.
We have,
Payoffs of $2, $4, $6, $8, and $10.
Now,
We know that,
The expected value [tex]=\Sigma (x*P(x))[/tex]
i.e. The sum of product of possible outcome and each outcome.
Here, x = Each outcome
And
P(x) = Possible outcomes
So,
Probability of x (Px) [tex]=\frac{1}{5}[/tex],
Now,
According to the above mentioned formula,
i.e.
The expected value [tex]=\Sigma (x*P(x))[/tex]
We get,
[tex]=\Sigma\ (\frac{1}{5} * 2) + (\frac{1}{5} * 4) + (\frac{1}{5} * 6) +(\frac{1}{5} * 8) +(\frac{1}{5} * 10)[/tex]
On solving we get,
[tex]=\Sigma\ (0.4 + 0.8 + 1.2 + 1.6 + 2)[/tex]
i.e.
The expected value = $6
So,
The expected value for given possibilities is $6.
Hence we can say that the expected value for the given Five possibilities is $6.
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which of the following is equivalent to the logarithmic equation below?
Answer:
A
Step-by-step explanation:
using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex] , then
[tex]log_{2}[/tex] 8 = 3 ⇒ 2³ = 8
Answer:
A
Step-by-step explanation:
loga(b)=x
a^x=b
since the answer to log2(8)=3
a^3=8
b=8
a=2
so 2^3=8
I hope this helped!
the function, B (x), models the estimated tuition cost where x is the number
The expression that completes the function b(x) is b(x) = 33741 * (1.028)^x
How to determine the expression of b(x)?The given parameters are:
Initial value, a = 33741
Rate, r = 2.8%
The cost of tuition each year since 2015 is represented as
B(x) = a * (1 + r)^x
This gives
B(x) = 33741 * (1 + 2.8%)^x
Evaluate
b(x) = 33741 * (1.028)^x
Hence, the expression that completes the function b(x) is b(x) = 33741 * (1.028)^x
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Complete question
A study estimates that the cost of tuition at a university will increase by 2.8% each year. The cost of tuition at the University in 2015 was $33,741 the function b(x) , models the estimated tuition cost , where x is the number of years since 2015.
Find the expression that completes the function b(x)
Instructions: Find the circumference of the circle and round to the nearest tenth. 4 yrds
The circumference of the circle and round to the nearest tenth is 25.1 yds
Circumference of a circleThe formula for calculating the circumference of a circle is expressed as:
C = 2πr
Given the following
radius r = 4yds
Substitute
C = 2(3.14)(4)
C = 25.12 yds
Hence the circumference of the circle and round to the nearest tenth is 25.1 yds
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For 10-18, Determine whether the triangles can be proved
similar. If they are similar, write a similarity statement.
If they are not similar, explain why.
Answer:
180 - 92 - 41 = 47
There are not two similar congruent angle in the triangles.
Hope this helps!
Figure ABCD is a rhombus. Rhombus A B C D is shown. Angle A is (5 x 25) degrees and angle D is (7 x minus 1) degrees. What is the value of x
Answer: 18
Step-by-step explanation:
Opposite angles of a rhombus are congruent, so
[tex]5 \times 25=7x-1\\\\125=7x-1\\\\126=7x\\\\x=18[/tex]
An object has a kinectic energy of 25j and a mass of 34kg,how fast is the object moving
v = 1.21 m/s is the answer
Kinetic energy of object = 25 J
Mass of object = 34 kg
The formula for the kinetic energy of an object is given by
K.E. = 1/2 m v2.
25 = 1/2 *34* v2.
v2= 25/17
v2 = 1.47
v = 1.21 m/s
In physics, the kinetic energy of an object is the energy that the object has due to its motion. This is defined as the work required to accelerate an object of a given mass from a stationary state to a specified velocity. After the body gains this energy during acceleration, it retains this kinetic energy unless the velocity changes
Everything that moves at home is an example of kinetic energy. This could be a cue ball rolling on a pool table, a fan that circulates air on warm days, or a glass that shatters on the floor after falling off the counter. Electrical equipment that is turned on uses kinetic energy, much like people move around the house.
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Explain step by step please!! Find f’(x) for f(x)=sin^3(3x^2)
Answer:
Step-by-step explanation:
g(x) = [tan( 4x-1)]2
If the table of the function contains exactly two potential turning points, one with an input value of -1, which statement best describes all possible values of m?
The statement (inequality) which best describes all possible values of m is: -12 < m < 4.
What is an inequality?An inequality is a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following:
Less than (<).Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).The table indicates two local extremes or potential turning points at x = 1 and x = -1. Thus, the value of m can't exceed f(-3) = -12.
In conclusion, the statement (inequality) which best describes all possible values of m is: -12 < m < 4.
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Carmen is planning rail lines for a new train station. Help her find m1. Explain how you found that solution.
m<1 =163 degrees
163,17,163,17 (all in degrees)
163,17,163,17 (all in degrees)
I have reproduced and attached a diagram (in figure 1) of the problem.
For ease of understanding, I have attached a second diagram which is labelled.
On line a
17+<CBE=180 (Linear Pair Postulate)
m<2=<CBE=180-17=163 degrees
<ABG=<CBE=163 degrees (Vertically Opposite Angles)
<ABE=<GBC= 17 degrees(Vertically Opposite Angles)
On line b
m<1=<DEB=<ABG=163 degrees (Corresponding Angles)
<BEF=<GBC= 17 degrees (Corresponding Angles)
<HEF=<DEB=163 degrees (Vertically Opposite Angles)
<DEH=<BEF=17 degrees (Vertically Opposite Angles)
Therefore:
m<1 =163 degrees
Clockwise from top left, the angles formed with line a are: 163 degrees, 17 degrees, m<2=163 degrees and 17 degrees.
Clockwise from top left, the angles formed with line b are: m<1=163 degrees, 17 degrees, 163 degrees, and 17 degrees.
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7(x^2 y^2)dx 5xydyUse the method for solving homogeneous equations to solve the following differential equation.
I'm guessing the equation should read something like
[tex]7(x^2+y^2) \,dx + 5xy \, dy = 0[/tex]
or possibly with minus signs in place of +.
Multiply both sides by [tex]\frac1{x^2}[/tex] to get
[tex]7\left(1 + \dfrac{y^2}{x^2}\right) \, dx + \dfrac{5y}x \, dy = 0[/tex]
Now substitute
[tex]v = \dfrac yx \implies y = xv \implies dy = x\,dv + v\,dx[/tex]
to transform the equation to
[tex]7(1+v^2) \, dx + 5v (x\,dv + v\,dx) = 0[/tex]
which simplifies to
[tex](7 + 12v^2) \, dx + 5xv\,dv = 0[/tex]
The ODE is now separable.
[tex]\dfrac{5v}{7+12v^2} \, dv = -\dfrac{dx}x[/tex]
Integrate both sides. On the left, substitute
[tex]w = 7+12v^2 \implies dw = 24v\, dv[/tex]
[tex]\displaystyle \int \frac{5v}{7+12v^2} \, dv = -\int \frac{dx}x[/tex]
[tex]\displaystyle \dfrac5{24} \int \frac{dw}w = -\int \frac{dx}x[/tex]
[tex]\dfrac5{24} \ln|w| = -\ln|x| + C[/tex]
Solve for [tex]w[/tex].
[tex]\ln\left|w^{5/24}\right| = \ln\left|\dfrac1x\right| + C[/tex]
[tex]\exp\left(\ln\left|w^{5/24}\right|\right) = \exp\left(\ln\left|\dfrac1x\right| + C\right)[/tex]
[tex]w^{5/24} = \dfrac Cx[/tex]
Put this back in terms of [tex]v[/tex].
[tex](7+12v^2)^{5/24} = \dfrac Cx[/tex]
Put this back in terms of [tex]y[/tex].
[tex]\left(7+12\dfrac{y^2}{x^2}\right)^{5/24} = \dfrac Cx[/tex]
Solve for [tex]y[/tex].
[tex]7+12\dfrac{y^2}{x^2} = \dfrac C{x^{24/5}}[/tex]
[tex]\dfrac{y^2}{x^2} = \dfrac C{x^{24/5}} - \dfrac7{12}[/tex]
[tex]y^2= \dfrac C{x^{14/5}} - \dfrac{7x^2}{12}[/tex]
[tex]y = \pm \sqrt{\dfrac C{x^{14/5}} - \dfrac{7x^2}{12}}[/tex]
In his first month of training,Landon biked 3.1 miles and ran 0.75 miles each workout. He completed 18 workouts that month. What is the total distance that he biked in his first month of training?
Taking into account the change of units, the total distance that he biked in his first month of training is 55.8 miles.
Rule of threeIn first place, the rule of three is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.
That is, what is intended with it is to find the fourth term of a proportion knowing the other three.
If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other) , the direct rule of three must be applied.
To solve a direct rule of three, the following formula must be followed, being a, b and c known data and x the variable to be calculated:
a ⇒ b
c ⇒ x
So: [tex]x=\frac{cxb}{a}[/tex]
Total distance that he biked in his first month of trainingIn his first month of training,Landon biked 3.1 miles and ran 0.75 miles each workout. He completed 18 workouts that month.
So you can apply the following rule of three: if for each workout Landon biked 3.1 miles, in 18 workouts he biked how far?
1 workout ⇒ 3.1 miles
18 workouts ⇒ total distance
So: [tex]total distance=\frac{18 workoutsx3.1 miles}{1 workout}[/tex]
Solving:
total distance= 55.8 miles
In summary, the total distance that he biked in his first month of training is 55.8 miles.
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The student council is hosting a homecoming event for past graduates and current students. The treasurer determines that the event revenue from the event can be represented by R (z) = 0.05x³75, where x is the number of tickets sold. The cost to put on the event is represented by the function C(z) = 30x + 12,500. Which function describes the funds raised, F(x), as a function of the number of tickets sold? O F(z) F(x) F(x) 0.05³ +30 - 12, 425 F(x) 0.05z³ 30x - 12,425 O = 0.05³ +30 - = 12,575 = 0.05³ 30 - 12,575
The function that describes the fund that was raised is 0.05³ - 30x - 12425
How to solve for the functionThe revenue is R (z) = 0.05x³ + 75
the cost = C(z) = 30x + 12,500.
Please note that the equation for revenue missed a sign in the question so I made use of the plus sign
We would have revenue - cost
Hence ( 0.05x³ + 75) - (30x + 12,500)
We would open the bracket
0.05x³ + 75 -30x -12500
We would take the like term to
0.05³ - 30x -12500 + 75
0.05³ - 30x - 12425
The function that describes the fund that was raised is 0.05³ - 30x - 12425
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Answer: F(x)=0.05x^3-30x-12,575
Step-by-step explanation:
Correct on test.
Determine whether side-side-angle (SSA) is a valid means for establishing triangle congruence. In this case, you know the measure of two adjacent sides and the angle opposite to one of them. If it is a valid criterion, explain why. If it is not valid, use GeoGebra to create a counterexample demonstrating that it doesn’t work and give an explanation. (Hint: Try constructing a triangle where the known angle is opposite to the shortest known side.) If you construct a counterexample, take a screenshot of your work, save it, and insert the image in the space below.
The illustration to determine whether side-side-angle (SSA) is a valid means for establishing triangle congruence is given below.
How to illustrate the information?Congruence of triangles means that two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
In this case, these triangles can be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with each other.
To illustrate the question, this will be:
Step 1: Draw a line segment AB
Step 2:Draw an acute angle (let's say 45° ) at A as AX
Step 3: From B draw an altitude on AX BY ⊥ AX
Step 4 Using suitable compass width and taking Y as center cut AX on both sides at C and D
Now BC = BD as BY is perpendicular bisector
Now compare ΔABC and ΔABD. Using suitable compass width and taking B as center cut AX at 2 points C & D directly so BC = BD.
This can illustrate that SSA is not a valid means for establishing triangle congruence.
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Answer:
Below is an example to show whether side-side-angle (SSA) is a legitimate method for proving triangle congruence. How should the information be illustrated? Triangle congruence refers to the property that two triangles are congruent if their three corresponding sides and their three corresponding angles are both equal in size. In this instance, the triangles can be moved around, rotated, flipped, and turned to have a same appearance. They are in alignment with one another when moved. This can serve as an example of why SSA cannot be used to prove triangle congruence.
Step-by-step explanation:
The airspeed of an airplane is 850 km/hr, and there is a wind blowing southwest at 30 km/hr.
If the airplane needs to head due south, at what angle does the pilot need to fly the plane?
Answer:
α = αG − αZL
thos is the equation for the absoulute angle of attack
The numbers 7, 11, 12, 13, 14, 18, 21, 23, 27, and 29 are written on separate cards, and the cards are placed on a table with the numbers facing down.
The probability of picking a card with an even number is [tex]\frac{3}{10}[/tex].
What is probability?Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.To find the probability of picking a card with an even number:
There are 10 cards on which numbers are written 7, 11, 12, 13, 14, 18, 21, 23, 27, and 29.These cards are placed on a table with the numbers facing down.To find the probability of picking a card with an even number, first, we count all the even numbers written on the cards.12, 14, and 18 out of 10 cards there are 3 even numbers written on the cards.So, the probability of picking a card with an even number is [tex]\frac{3}{10}[/tex].Therefore, the probability of picking a card with an even number is [tex]\frac{3}{10}[/tex].
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COMPLETE QUESTION:
The numbers 7, 11, 12, 13, 14, 18, 21, 23, 27, and 29 are written on separate cards, and the cards are placed on a table with the numbers facing down. The probability of picking a card with an even number is _____.
It has been determined that 15% of all cars tested emit excessive hydrocarbons, 12% emit excessive CO, and 8% emit excessive amounts of both. Find the probability that emissions of both hydrocarbons and CO are excessive. Round your answer to 2 decimal places.
The probability that emission of both CO and hydrocarbon is in excess is 0.8.
What is probability?The proportion of favorable cases to all possible cases used to determine how likely an event is to occur.
Let, A be the event in which cars are emitting excess CO:
P(A) = 0.12
Let, B be the event in which cars are emitting excess hydrocarbons:
P(B) = 0.15
The cars which emit both CO and Hydrocarbons in:
P(A∩B) = 0.8
The probability that emission of both CO and hydrocarbon is in excess is 0.8.
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Which equation can be used to solve for xxx in the following diagram?
Answer: D. 2x + 4x = 150
Step-by-step explanation:
We know that the section of 2x and 4x together equal 150 degrees because they are vertical angles. The 150 degrees is vertical to the section with 2x and 4x. So you would use equation D to solve for x.
In order to create the reverse of the 150 angle, when two angles meet, 2x and 4x are combined.
Thus, the angles formed by 2x, 4x, and 150 are vertical. We know that vertical angles are equivalent, .Therefore, the labeled angles are equivalent.
Answer :-
[tex]\bf D. \: 2 {x}^{o} + 4 {x}^{o} = 15 {0}^{o} [/tex]
HELP ASAP THANK YOU!)
In order to hang a block of gold from a chain necklace, a jeweler drilled a hole in the center, 5 mm in diameter the original block of gold.
If the original block of gold was 27 mm long, 8 mm wide, and 12 mm high, find the volume of the remaining piece of gold to the nearest tenth cubic millimeter.
(The answer choices are below)
Answer:
2061.9[tex]mm^{3}[/tex]
Step-by-step explanation:
We can see the original shape of the gold block is a cuboid.
Volume of Cuboid = Length x Width x Height
Volume of Original Gold Block = 27mm x 8mm x 12mm = [tex]2592mm^{3}[/tex]
Next, we can see the shape of the cut-out hole is a cylinder.
Volume of Cylinder = [tex]\pi r^{2} h[/tex]
We know that r = 0.5 x diameter = 0.5 x 5 = 2.5mm
Volume of cut-out hole = [tex]\pi (2.5)^{2} (27)\\[/tex] = [tex]168.75\pi mm^{3}[/tex]
Volume of Remaining Gold Block = Volume of Original Gold block - Volume of cut-out hole
= [tex]2592mm^{3} -168.75\pi mm^{3}[/tex]
= 2061.9[tex]mm^{3}[/tex]