what is the rate of change of the cube’s surface area when its edges are 50 mm long?
Answers
The first thing we are going to do is identify the volume and surface of the cube and their respective derivatives or rate of change
[tex]\begin{gathered} V\to\text{volume} \\ S\to\text{surface} \\ l=\text{side of a square} \end{gathered}[/tex][tex]\begin{gathered} V=l^3\to(1) \\ \frac{dV}{dt}=3l^2\frac{dl}{dt}\to(2) \end{gathered}[/tex][tex]\begin{gathered} S=6l^2\to(3) \\ \frac{dS}{dt}=12\cdot l\cdot\frac{dl}{dt}\to(4) \end{gathered}[/tex]From the exercise we know that:
[tex]\begin{gathered} \frac{dV}{dt}=300\frac{\operatorname{mm}^3}{s}\to(5) \\ 3l^2\frac{dl}{dt}=300\frac{\operatorname{mm}^3}{s}\to(2)=(5) \\ \frac{dl}{dt}=\frac{300}{3l^2}\frac{\operatorname{mm}^3}{s}\to(6) \end{gathered}[/tex]The exercise asks us to calculate the rate of change of the surface (4) so we substitute the differential of length (6) in (4)
[tex]\begin{gathered} \frac{dS}{dt}=12\cdot l\cdot(\frac{300}{3l^2}\frac{\operatorname{mm}^3}{s}) \\ \frac{dS}{dt}=\frac{1200}{l}\frac{\operatorname{mm}}{s} \end{gathered}[/tex]what is the rate of change of the cube’s surface area when its edges are 50 mm long?
[tex]\begin{gathered} l=50\operatorname{mm} \\ \frac{dS}{dt}=\frac{1200}{50\operatorname{mm}}\frac{\operatorname{mm}^3}{s} \\ \frac{dS}{dt}=24\frac{\operatorname{mm}^2}{s} \end{gathered}[/tex]The answer is 44mm²/sRelated Questions
vertex, domain and range, and zeros in this parabola, could you tell me them?
Answers
The vertex, domain, range and zeros of the parabola are -2, (-∞, +∞), (-2,+∞) and -0.5 and 2.5 respectively.
What is parabola ?Parabola is a curve like shape, in which any point is equal distance from a fix point.
The vertex of the parabola in the given graph is -2.
The domain of parabola is all the possible values of x,
in the given graph, the value of x is from -∞ to +∞
So the domain of parabola is (-∞, +∞)
The range of parabolas is all the values of y corresponding to values of x,
in the graph, the value of y≥-2
The range of parabola is (-2,+∞)
Zeros are values on the x-axis, which are 0.
So there are two zeros, -0.5 and 2.5.
To know more about Parabola on:
https://brainly.com/question/4074088
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Convert the following mixed number to improper fraction10 /2/57 3/20
Answers
The question asks us to convert mixed fractions to improper fraction.
The first Mixed fraction is:
[tex]\begin{gathered} 10\frac{2}{5} \\ \text{whole number = 10} \\ \text{ numerator = 2} \\ \text{ denominator = 5} \end{gathered}[/tex]In order to convert this into an improper fraction, we need to follow some steps:
1. Multiply the denominator by the whole number.
2. Add the result of the multiplication in step 1 to the numerator.
3. The result from step 2 is the new numerator and use the current denominator as the new denominator.
Let us now apply these steps to answer the question
1. Multiply the denominator by the whole number.
[tex]5\times10=50[/tex]2. Add the result of the multiplication in step 1 to the numerator.
[tex]50+2=52[/tex]3. The result from step 2 is the new numerator and use the current denominator as the new denominator.
[tex]\begin{gathered} \text{new numerator = 52} \\ \text{new denominator = 5} \\ \therefore\frac{52}{5} \end{gathered}[/tex]Therefore, the answer is:
[tex]10\frac{2}{5}=\frac{52}{5}[/tex]Now, let us use the same rules for the next question.
[tex]7\frac{3}{20}[/tex]1. Multiply the denominator by the whole number.
[tex]7\times20=140[/tex]2. Add the result of the multiplication in step 1 to the numerator.
[tex]140+3=143[/tex]3. The result from step 2 is the new numerator and use the current denominator as the new denominator.
[tex]\begin{gathered} \text{new numerator= 143} \\ \text{new denominator = 20} \\ \therefore\frac{143}{20} \end{gathered}[/tex]Therefore, the final answer is:
[tex]7\frac{3}{20}=\frac{143}{20}[/tex]Suppose tortilla chips cost 32.5 cents per ounce what would a bag of chips cost if it contained 20oz round the answer to the nearest cent
Answers
The Solution:
Given:
cost per ounce = 32.5 cents
Required:
To find the cost of a bag of chips that contains 20 oz.
Recall:
ounce = oz
[tex]\begin{gathered} 1\text{ oz}=32.5\text{ cents} \\ \\ 20\text{ oz }=20\text{ ounces} \\ \\ Cost\text{ of 20 oz is :} \\ \\ 20\times32.5\text{ cents=650 cents }=\text{\$}6.50 \end{gathered}[/tex]Therefore, the correct answer is $6.50
I need the answer to number 2 please answer it like the paper so that I can understand it better. Please
Answers
Elijah made an error of subtracting the numbers and not including the imaginary sign (letter i)
The correct midpoint is (6, 3i)
Explanation:The two points are 8 + 4i and 4 + 2i
Elijah got the midpoint as (2, 1).
To determine Elijah's error, let's calculate the midpoint of a complex number:
[tex]\text{Midpoint = (}\frac{a\text{ + b}}{2}),\text{ (}\frac{c\text{ + d}}{2})i[/tex]let 8 + 4i = a + ci
let 4 + 2i = b + di
The real numbers will be added together. The imaginary numbers will also be added together.
substituting the values in the formula:
[tex]\begin{gathered} \text{Midpoint = (}\frac{8\text{ + 4}}{2}),\text{ (}\frac{4\text{ + 2}}{2})i \\ \text{Midpoint = }\frac{12}{2},\text{ }\frac{6}{2}i \\ \\ \text{Midpoint = (6, 3i)} \end{gathered}[/tex]Elijah made an error of subtracting the numbers. Also Elijah didn't include the letter representing the imaginary numbers (i).
The correct midpoint is (6, 3i)
A triangle has angles that are 38º and 47º. Find the measure of the third angle. 177 ° 95° 133 °85 °
Answers
hello,
As we know, a triangule has 3 angles and the sum of them must be equal to 180º. So, let's calculate the question:
38 + 47 + x = 180
85 + x = 180
x = 180 - 85
x = 95º
What is the definition of function?Hos inputs andoutputsInputs haveEvery input hosonly ONE outputxrches andy-wolvesdifferent outputsevery time
Answers
The definition of function is
9. You want to be able to withdraw the specified amount periodically from a payout annuity with the given terms. Find how much the account needs to hold to make this possible. Round your answer to the nearest dollar. Regular withdrawal: $4500 Interest rate: 4.5% Frequency quarterly Time: 24 years Account balance: $
Answers
This is a question on Future Value of Annuity. There is a present sum from which withdrawals will be made. We therefore employ the formulae thus:
[tex]PVA=\text{PMT(}\frac{1-(1+\frac{i}{m})^{-mn}}{\frac{i}{m}}\text{)}[/tex]Where:
PVA = Present Value of Annuity
PMT = Periodic sum
i = Interest Rate
n = Number of interest periods
m = Compunding frequency
Substituting, we have:
[tex]\begin{gathered} P\text{VA}=4500(\frac{1-(1+\frac{0.045}{4})^{-(4\times24)}}{\frac{0.045}{4}}) \\ P\text{VA}=263,340 \end{gathered}[/tex]PVA = $263,340
May 10, 12:38:01 AMA survey was given to a random sample of 195 residents of a town todetermine whether they support a new plan to raise taxes in order toincrease education spending. Of those surveyed, 39 respondents saidthey were in favor of the plan. At the 95% confidence level, what is themargin of error for this survey expressed as a proportion to thenearest thousandth? (Do not write +).Submit AnswerAnswer:
Answers
It is given as,
x= 39.
n= 195.
Estimate for sample proportion= 0.75
Z critical value(using Z table)=1.96
Confidence interval formula is ,
[tex]p\pm Z\times\frac{\sqrt[]{p\times(1-p)}}{\sqrt[]{n}}[/tex][tex]0.75\pm1.96\times\frac{\sqrt[]{0.75\times(1-0.75)}}{\sqrt[]{195}}[/tex][tex]0.75\pm1.96\times\frac{0.433}{1.396}[/tex][tex]1.358\text{ , 0.14206}[/tex]
Lower limit for confidence interval=0.14206
Upper limit for confidence interval= 1.38.
The margin error is determined as,
[tex]1.38-0.14206=\text{ 1.237.}[/tex]What is the length of side s of the square shown below?45°6S90°A. 2.B. 6C. 3D. 5.2E. 3.2F. .6
Answers
The diagram shows a square with one side marked as s, while the diagonal that cuts across measures 6 units.
The diagonal results in a right angled triangle with two sides measuring 45 degrees and one side measuring 90 degrees. Now that we have a right angled with one angle, and two sides (one is given as 6, and one is unknown), we now calculate side s as follows;
[tex]\begin{gathered} \cos 45=\frac{\text{adj}}{\text{hyp}} \\ We\text{ use the ratio for cosine because the sides shown are the} \\ \text{adjacent (between the right angle and the reference angle) and} \\ \text{hypotenuse (facing the right angle)} \\ \cos 45=\frac{s}{6} \\ \cos 45=\frac{1}{\sqrt[]{2}} \\ \text{Therefore,} \\ \frac{1}{\sqrt[]{2}}=\frac{s}{6} \\ \text{Cross multiply and you have} \\ \frac{6}{\sqrt[]{2}}=s \\ \text{Rationalize the expression and you have} \\ 3\sqrt[]{2}=s \\ \text{Therefore} \\ s=3\sqrt[]{2} \end{gathered}[/tex]The correct answer is option E
According to the diagram, an 8-foot-tall statue casts a shadow on the ground that is 15 feet in length. Based on this information, which trigonometric ratio has the value 8/15 ?A. cos CB. tan BC. cos BD. tan C
Answers
the right optio is tan C because...
[tex]undefined[/tex]Write the following Equation as a EXPONENTIAL equation do not simplify your answer
Answers
Answer:
[tex]V=14^5[/tex]Explanation:
Given the logarithmic equation:
[tex]\log_{14}(V)=5[/tex]The relationship between the logarithm and exponential forms is given below:
[tex]\log_ba=c\implies b^c=a[/tex]That is:
• The base (b) in the logarithmic form becomes the base of the exponent.
,• The answer (c) in the logarithmic form becomes the exponential form.
Thus, the given equation in exponential equation is:
[tex]V=14^5[/tex]Hi I just wanted you to check over my work to let me know if I did it correct
Answers
Answer:
Hello, Which part would you like to have checked?
I can't seem to make out your work from that of the assignment.
Step-by-step explanation:
Just let me know, here to help!
Can you please help me out with a question
Answers
the figure is composed by a 4 triangles and a cube
to find the area of a triangle we need the base and height. the base is 15ft
to find the height we mut use the pithagorean theorem
h= height of the traingle
[tex]h^2=(15ft)^2+(7.5ft)^2[/tex]resolving we have
[tex]h=\sqrt[\square]{281.25}\text{ = 16.78 aprox}[/tex]and now he have all the measures
each triangle at the top has an area equal to
[tex]A=\frac{16.78ft\cdot15ft}{2}=127.78sq\text{ ft}[/tex]now we multiply that by 4: 127.78sq ft*4=503.1 sq ft
for the bottom part, there are 5 squares of side 15ft
each square has an area = 15ft*15ft = 225 sq ft
multipliying that by 5: 225sqft*5=1125 sq ft
the total area is 1125 sq ft+503.1sqft=1628.1 sq ft rounded is 1628 sq ft
For the volume of the piramid, we use
[tex]V=\frac{1}{3}A\cdot h[/tex]where A is the area of the base and h is the height
so volume of piramid:
[tex]V=\frac{1}{3}\cdot225\text{sqft}\cdot15ft=1125ft^3[/tex]for the volume of the cube we multiply the side length 3 times:
[tex]V\mleft(cube\mright)=(15ft)^3=3375ft^3[/tex]Adding the two volumes:
1125ft^3+3375ft^3=4500 cubic feet
Hello, May I please get some assistance with this homework question? I posted an image below Q2
Answers
Solving (a)
The two functions we have are:
[tex]\begin{gathered} f(x)=3x+3 \\ g(x)=x^2 \end{gathered}[/tex]We are asked to find the composite function:
[tex](f\circ g)(x)[/tex]Step 1. The definition of a composite function is:
[tex](h\circ k)(x)=h(k(x))[/tex]In this case:
[tex](f\circ g)(x)=f(g(x))[/tex]This means to plug the g(x) expression into the value of x of the f(x) function.
Step 2. Substituitng g(x) as the value for x in f(x):
[tex](f\circ g)(x)=f(g(x))=4(x^2)+3[/tex]Simplifying:
[tex](f\circ g)(x)=\boxed{4x^2+3}[/tex]Step 3. We also need to find the domain of this composite function.
The domain of a function is the possible values that the x-variable can take. In this case, there would be no issues with any x value that we plug as the x-value. Therefore, the domain is all real numbers.
The domain of fog is all real numbers.
Answer:
[tex](f\circ g)(x)=\boxed{4x^2+3}[/tex]The domain of fog is all real numbers.
A Ferris wheel with a 200-foot diameter is spinning at a rate of 10 miles per hour. Find the angular speed of the wheel in radians per minute.
Answers
1) Gathering the data from the question:
Diameter = 200'
Spinning at 10mph
2) Let's convert the units to start working through that:
[tex]\begin{gathered} m------ft \\ 1------5280 \\ -- \\ 1h=60\min \end{gathered}[/tex]So, 1 mile=5280 ft and 1 hour = 60minutes. Then we can convert:
[tex]\frac{10m}{60}=\frac{10\times5280}{60}=\frac{880ft}{\min }[/tex]2.2) Since we have the diameter, then we can state the radius of this Ferris Wheel is 100 ft. Let's plug into the Circumference formula to get the circumference of the Ferris Wheel:
[tex]\begin{gathered} C=2\pi r \\ C=2\pi\cdot100 \\ C=200\pi \end{gathered}[/tex]2.3) We can find the angular velocity since we have the speed and the Circumference. Note that the angular velocity is given as quotient between the speed and the circumference:
[tex]\frac{880}{200\pi}=\frac{22}{5\pi}[/tex]Note that this is given in revolutions per minute. And 1 revolution corresponds to one lap (2π radians). So we need another final conversion for the unit wanted for the question is radians per minute.
[tex]\frac{22}{5\pi}\times2\pi=\frac{44}{5}=8.8[/tex]3) Thus the answer is:
[tex]8.8\: radians\: per\: minute[/tex]Evaluate: 4+8/2 x (6 - 3)163325
Answers
We have to evaluate the expression:
[tex]\begin{gathered} 4+\frac{8\cdot(6-3)}{2}_{} \\ 4+\frac{8\cdot3}{2} \\ 4+\frac{24}{2} \\ 4+12 \\ 16 \end{gathered}[/tex]To solve this, we have to solve the operations in this order:
- First, the operations within the parenthesis.
- Second, the multiplications and quotients.
- Lastly, the additions and substractions.
Answer: 16
hi! I have the answers to A. AND B. which are k=1.243% for a and k= 0.20% for bWhere y is the population after t time, A is the initial population and k is the growth constant.Therefore, for each case, we calculate the value of k:(a)t = 4y = 1375000A = 1309000Solving for k:1375000=1309000⋅ek⋅4e4k=137500013090004k=ln(13750001309000)k=ln(13750001309000)4k=0.01229≅0.0123→1.23%(b)t = 4y = 1386000A = 1375000Solving for k:1386000=1375000⋅ek⋅4e4k=138600013750004k=ln(13860001375000)k=ln(13860001375000)4k=0.00199≅0.002→0.20%(c)To compare we calculate the quotient between both periods:
Answers
Solution
The population growth rate formula is given as
[tex]P=P_0e^{rt}[/tex]Where P is the final population
Po= is the initial population
P is the final population
r is the rate
t is the time taken
If it has been calculated that the growth rate from 2012 to 2016 is 1.23% and from 2016 to 2020 is 0.20%
(c) From these two growth rates, it can be seen that 1.23% is greater than 0.20%, we can conclude that the growth rate from 2012 to 2016 is greater than the growth rate from 2016 to 2020
(d) If the current growth rate continues,, the time it will take for the population to reach 1.5million is as shown below:
[tex]\begin{gathered} P=1500000 \\ P_0=1386000 \\ r=0.20 \\ t=\text{?} \\ P=P_0e^{rt} \\ P=P_0e^{0.2t} \end{gathered}[/tex]This becomes
[tex]\begin{gathered} 1500000=1386000e^{0.2\times t} \\ \frac{1500000}{1386000}=e^{0.2t} \\ 1.08225=e^{0.2t} \\ \ln e^{0.2t}=\ln 1.08225 \\ 0.2t=\ln 1.08225 \end{gathered}[/tex][tex]\begin{gathered} t=\frac{\ln 1.08225}{0.2} \\ t=\frac{0.0790432}{0.2}=0.395 \end{gathered}[/tex]Answer Summary
(a) The growth rate from 2012 to 2016 is 1.23%
(b) The growth rate from 2016 to 2020 is 0.20%
(c) In comparison, the growth rate from 2012 to 2016 is greater than the growth rate from 2016 to 2020
(d) The time it will reach the 1.5 million if the current growth rate continues is 0.395years
-Solve the system of equations – X – 8y = 49 and —x – 2y = 7 by combining theequations.
Answers
ANSWER
x = 7
y = -7
EXPLANATION
Given:
- x - 8y = 49 ..........(equ 1)
- x - 2y = 7 ............(equ 2)
Desired Outcome
The values of x and y.
Multiply Equation 2 by -1
[tex]equ\text{ 2}\times-1\Rightarrow x+2y\text{ = -7 ............}(equ\text{ 3})[/tex]Add Equation 1 with Equation 3
[tex]\begin{gathered} -\text{ x - 8y = 49} \\ x\text{ + 2y = -7} \\ ------ \\ -6y\text{ = 42} \\ y\text{ = }\frac{42}{-6} \\ y\text{ = -7} \end{gathered}[/tex]Solve for x from equation 3
[tex]\begin{gathered} x\text{ + 2y = -7} \\ x\text{ + 2}(-7)\text{ = -7} \\ x\text{ - 14 = -7} \\ x\text{ = -7 + 14} \\ \text{x = 7} \end{gathered}[/tex]Hence, the values of x and y are 7 and -7 respectively.
As smart phones have grown in popularity, regular cell phones have fallen out of favor. As aresult, one electronics retailer estimates that 20% fewer regular cell phones will be sold everyyear. If the retailer sells 605,390 regular cell phones this year, how many will be sold 3 yearsfrom now?If necessary, round your answer to the nearest whole number.
Answers
309960
Explanation
exponential decay function is a function that shrinks at a constant percent decay rate. The equation can be written in the form
[tex]\begin{gathered} y=a(1-b)^x \\ \text{where a is the initial cost} \\ b\text{ is the decrease percnetage ( in decimal)} \\ x\text{ is the time} \end{gathered}[/tex]so
Step 1
Let
[tex]\begin{gathered} a=605390 \\ b=20\text{ = 0.2} \\ x=\text{ 3 ( years)} \end{gathered}[/tex]replace
[tex]\begin{gathered} y=a(1-b)^x \\ y=605390(1-0.2)^3 \\ y=605390(0.8)^3 \\ y=605390(0.512) \\ y=309959.68 \\ \text{rounded to the whole number} \\ y=309960 \end{gathered}[/tex]therefore, the answer is
309960
I hope this helps you
The beam of light house makes one complete revolution every 20 seconds how many degrees is it rotate in five seconds
Answers
Answer:
Every 5 seconds the beam rotates 90 degrees;
[tex]90^{\circ}[/tex]Explanation:
Given that the beam of a lighthouse makes one complete revolution every 20 seconds.
one complete revolution is;
[tex]360^{\circ^{}}[/tex]The rate of rotation is;
[tex]r=\frac{360^{\circ}}{20}=18^{\circ}\text{ per second}[/tex]The number of degrees it will rotate in 5 seconds is;
[tex]\begin{gathered} x=5\times r=5\times18^{\circ}per\text{ second} \\ x=90^{\circ} \end{gathered}[/tex]Therefore, every 5 seconds the beam rotates 90 degrees;
[tex]90^{\circ}[/tex]ASGC is also considering adding tennis racquets to the product lines it produces. This would require a $500,000 modification to its factory as well as the purchase of new equipment that costs $1,600,000. The variable cost to produce a tennis racquet would be $55, but John thinks that ASGC could sell the racquet at a wholesale price of $75. John thinks that if ASGC sells the racquet at a lower price, many other retailers might decide to carry it. However, the vice president of ASGC thinks that the tennis racquet is a superior product and that ASGC should sell it for $99.99 to upscale country clubs only. The higher price would give a prestige image. Questions based on the above (10 pts)7. If ASGC produces tennis racquets, how many racquets must it sell at $75.00 and $99.99 to break even? •Breakeven units at 75.00 _______________________________. •Breakeven units at 99.99 _______________________________. •Which price do you recommend and why? __________________________
Answers
Solution
[tex]undefined[/tex]Geometry Question: Given segment EA is parallel segment DB, segment EA is congruent to segment DB, and B is the mid of segment AC; Prove: segment EB is parallel to segment DC (reference diagram in picture)
Answers
Construction: Join ED.
The corresponding diagram is given below,
According to the given problem,
[tex]\begin{gathered} AE=BD \\ AE\parallel BD \end{gathered}[/tex]Since a pair of opposite sides are parallel and equal, it can be claimed that quadrilateral ABDE is a parallelogram.
Then, as a property of any parallelogram, it can be argued that,
[tex]\begin{gathered} AB=DE \\ AB\parallel DE \end{gathered}[/tex]Given that B is the mid-point of AC,
[tex]\begin{gathered} AB=BC \\ AB\parallel BC \end{gathered}[/tex]Combining the above two results,
[tex]\begin{gathered} BC=DE \\ BC\parallel DE \end{gathered}[/tex]It follows that ABCD also forms a parallelogram.
Again using the property that opposite sides of a parallelogram are equal and parallel. It can be claimed that,
[tex]\begin{gathered} EB=DC \\ EB\parallel DC \end{gathered}[/tex]Hence proved that segment EB is parallel to segment DC,
[tex]\vec{EB}=\vec{DC}[/tex]What is the radius of Earth, in meters, written as a single-digit number multiplied by a power of 10?
Answers
Given:
The Radius of earth = 6,378,100 meters
To find:
The radius of earth in single-digit number multiplied by power of 10.
Step by step solution:
R = 6,378,100 meters
R = 6.3781 × 10^6
From here we have calculated the value of the radius in terms of single digit number.
Ivanna bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $450 less than the desktop. She paid for the computers using two different financing plans. For the desktop the interest rate was 6.5% per year, and for the laptop it was 9% per year. The total finance charges for one year were $409. How much did each computer cost before finance charges?
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Solution:
According to the problem, the laptop costs $450 less than the desktop. Let x the cost of the laptop, then we get the following equation:
[tex]x\text{ + 450 = cost of the desktop}[/tex]now, the total finance charge of $409 is from 9% of the cost of the laptop and 6.5% of the cost of the desktop. According to this, we get the following equation:
[tex]0.09(x)+0.065(x+450)=409[/tex]Applying the distributive property, we get:
[tex]0.09x+0.065x+29.25=409[/tex]now, placing like terms on each side of the equation, we get:
[tex]0.09x+0.065x=409-29.25[/tex]this is equivalent to:
[tex]0.155x\text{ = 379.75}[/tex]solving for x, we get:
[tex]x\text{ = }\frac{379.75}{0.155}=2450[/tex]this means that:
The cost of the laptop is x = 2450
and
The cost of the desktop is x+450 = 2450 +450 = 2900.
So that, we can conclude that the correct answer is:
Cost of the laptop = 2450
Cost of the desktop =2900.
desktop price be x
laptop price (x+450)
For the desktop the interest rate was 9% per year,
Interest = 9%x
and for the laptop it was 6% per year.
Interest = 6%(x+450)
The total finance charges for one year were $300
9%x + 6%(x+450) = 300
9x+6(x+450) = 300*100
9x+6x +2700=30000
15x= 30000-2700
15x=27300
x= 1820
What is the logarithmic form of 9^2=81
Answers
Given the equation:
[tex]9^2=81[/tex]Let's write the equation in logarithmic form.
To write in logarithmic form, take the logarithm of base 9 of the right side of the equation equal to the exponent (2).
Thus, we have:
[tex]log_981=2[/tex]Therefore, the logarithmic form of the given equation is:
[tex]log_981=2[/tex]• ANSWER:
[tex]log_981=2[/tex]which table represents points on the graph of h (x) = 3 root -x+2
Answers
Given the function :
[tex]h(x)=\sqrt[3]{-x+2}[/tex]To find which table represents the given function, let x with the numbers given in the table and find the corresponding value of h(x)
So, when x = 0
[tex]h(0)=\sqrt[3]{0+2}=\sqrt[3]{2}[/tex]Now look to the tables which table has y = 3root of 2
We can deduce that the first two tables are wrong
Now, substitute with x = 2
[tex]h(2)=\sqrt[3]{-2+2}=\sqrt[3]{0}=0[/tex]So, this result will be agreed with the third table
so, the answer is: Table 3
Six office desks that are 7 1/12 feet long are to be placed together on a wall that is 42 7/12 feet long. Will they fit on the wall? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. Yes, if no more than a total of foot is needed for spacing between desks. (Type an integer or a simplified fraction.) B. No, they do not all fit along the wall.
Answers
Answer:
[tex]\text{Yes, If no more than a total of }\frac{1}{12}foot\text{ is needed for spacing between desks}[/tex]Explanation:
Given that six office desks that are 7 1/12 feet long are to be placed together.
The length of the six desks is;
[tex]\begin{gathered} 6\times7\frac{1}{12} \\ =6\times7+6\times\frac{1}{12} \\ =42\frac{6}{12} \end{gathered}[/tex]Given that the wall is 42 7/12 feet long.
Then the length of the six desks is shorter than the length of the wall.
[tex]42\frac{7}{12}-42\frac{6}{12}=\frac{1}{12}[/tex]Therefore, it will fit on the wall if no more than a total of 1/12 foot is needed for spacing between desks.
[tex]\text{Yes, If no more than a total of }\frac{1}{12}foot\text{ is needed for spacing between desks}[/tex]the volume of prism A is 144^3 if the base is 24^2 what is the height of prism A?
Answers
Answer
Height of prism A = 6 units
Explanation
The volume of a prism is given as the product of the area of a face that occurs on two sides of the prism and the distance between the two faces.
In the case of this face being a base, the volume of the prism is given as
Volume = (Area of Base) × (Perpendicular height)
Volume = 144 m³
Area of base = 24 m²
Perpendicular height = h = ?
Volume = (Area of Base) × (Perpendicular height)
144 = (24) × (h)
144 = 24h
We can rewrite this as
24h = 144
Divide both sides by 24
(24h/24) = (144/24)
h = 6 units
Hope this Helps!!!
Calculate the value of the expression 3x-7 when x = 2
Answers
Given:
The expression is,
[tex]3x-7[/tex]To find:
The value when x = 2.
Explanation:
Substitute x = 2 in the given expression, we get
[tex]\begin{gathered} 3(2)-7=6-7 \\ =-1 \end{gathered}[/tex]Thus, the value of the expression when x = 2 is -1.
Final answer:
The value of the expression when x = 2 is,
[tex]-1[/tex]12 ft-What is the volume of atriangular pyramid that is12 ft tall and has a basearea of 5 square ft?cubic feet
Answers
EXPLANATION:
Given;
We are given a triangular pyramid with the following dimensions;
[tex]\begin{gathered} Base\text{ }area=5ft^2 \\ Height=12ft \end{gathered}[/tex]Required;
We are required to calculate the volume of this pyramid from the dimensions given.
Step-by-step solution;
The volume of a triangular pyramid is given by the formula;
[tex]Volume=\frac{1}{3}Bh[/tex]Where the variables are;
[tex]\begin{gathered} B=base\text{ }area \\ h=height \end{gathered}[/tex]The volume now will be calculated as follows;
[tex]\begin{gathered} Volume=\frac{1}{3}\times5\times12 \\ \\ Volume=20 \end{gathered}[/tex]Therefore,
ANSWER:
[tex]V=20ft^3[/tex]Volume = 20 cubic feet