Try this option:
x²+27=0;
[tex](x+\sqrt{-27})(x- \sqrt{-27})=0; \ => \ \left[\begin{array}{ccc}x=3 \sqrt{3}i\\x=-3 \sqrt{3}i \end{array}\right[/tex]
x = ± 3i√3
given x² + 27 = 0 (subtract 27 from both sides )
x² = - 27 ( take the square root of both sides )
x = ±[tex]\sqrt{-27}[/tex] = ± √(9 × 3 × -1 ) ← (i = √-1 )
= ± (√9 × √3 ×√-1 ) = ±3i√3
What is the value of x? Enter your answer in the box.
the value of x is 12
The amount of money Jesse spent, $75, is subtracted from the amount he had at the start, m. This expression is equal to the amount he has left, $55. Therefore, the equation is m−75=55. How much money, m, did Jesse have before buying the shoes?
Answer:
$130
Step-by-step explanation:
You are given the one-step linear equation ...
... m - 75 = 55
You solve it by adding 75 to both sides.
... m -75 +75 = 55 +75
... m = 130 . . . . . . . . . . . . . simplify
James works as a waiter. He served meals with bills of 23.59, 40.65, 30.50, and 15.68. If his total for tips was 17.67, what percent tip did he receive for serving these meals? Round the answer to the nearest percent
16%
the percent tips is calculated as
[tex]\frac{tips}{total bill}[/tex] × 100%
total bills = 23.59 + 40.65 + 30.50 + 15.68 = 110.42
percent tips = [tex]\frac{17.67}{110.42}[/tex] × 100% = 16%
HELP PLEASE!
Carmen is designing an intersection of the rail line and four streets. She wants to know which streets are parallel
Which streets are parallel? Check all that apply.
c || d
c || e
c || f
d || e
d || f
e || f
CHECK ALL THAT APPLY ITS NOT ONE ANSWER
Answer:
d║e, c║f
Step-by-step explanation:
The acute angle of intersection of e with t is ...
180° - 112° = 68°
This angle is the same as the acute angle at d, so d and e are parallel.
The acute angle of intersection of c with t is ...
180° -114° = 66°
This angle is the same as the acute angle at f, so c and f are parallel.
d║e, c║f
_____
Note that the acute angles at the intersections with t are all "corresponding". That is why their congruence means the associated lines are parallel.
Answer:
Option C. and D. are correct
Step-by-step explanation:
c//f
d//e
good luck:)
rounded 3,428,583 rounded to the nearest 10,000
3,400,000 because the 2 is the in the 10,000
Anyone have the answer to this? Need help ASAP?
For this case we have the following data:
Polynomial function of grade 5
Given roots: -2, 2,[tex]4 + i[/tex]
Having an imaginary root given by [tex]a + bi[/tex], the other root, in the same imaginary way, must be given by its complex conjugate, that is, [tex]a-bi[/tex].
In this way, the fourth root is given by:
[tex]4-i[/tex]
Since the polynomial function is grade 5, it must have 5 roots. Thus, the fifth root must be given by a real number.
Thus, the roots of the polynomial function are given by: three real roots and two imaginary roots.
Answer:
Option D
f(x) has 3 real roots x = -2, x = 2 and x = 4
complex roots occur in conjugate pairs
x = i is a root then x = - i is a root
there are therefore 2 imaginary roots
f(x) has 3 real roots and 2 imaginary roots
What is the value of sinC ?
Answer:
[tex]sin \:C =\frac{8}{17}[/tex]
Step-by-step explanation:
In a right triangle, the sine of an angle is the length of the opposite side divided by the length of the hypotenuse.
[tex]sin \:x =\frac{O}{H}[/tex]
From the formula above we know that the sine of an angle is the opposite side divided by the hypotenuse. The opposite side is AB and has a length of 8. The hypotenuse is AC with a length of 17. So we can write
[tex]sin \:C =\frac{8}{17}[/tex]
Consider the expression . It has been simplified below with some values unknown.
-33/-10- (-45.3+ 35.2)= -33/-10+?
What is the smallest and largest unknown value from the equation? Must say the smallest value and largest value.
Given expression is
-33/-10- (-45.3+ 35.2)
Problem says that it is simplified.
After simplification it gives:
-33/-10+?
Now we need to find the unknown value that goes in place of ?.
Notice that it is expression having only constants so we will get a unique answer not the smallest or largest value.
Now let's find the value of unknown that goes in place of ?
-33/-10- (-45.3+ 35.2)= -33/-10+?
we see that -33/-10 is on both sides so we can remove that
- (-45.3+ 35.2)= ?
Now let's simplify the left side by distributing the negative sign
+45.3 - 35.2= ?
10.1 = ?
Hence the unknown value is 10.1 that goes in place of ?.
Answer:
answer is 3 on edge
Step-by-step explanation:
wwww
To construct a square, Dominic uses his straightedge to draw AB⎯⎯⎯⎯⎯ . He opens the compass to the length of AB⎯⎯⎯⎯⎯ and draws a circle centered at point A, and then, without changing the compass opening, draws a circle centered at point B. He marks the intersections of the circles as points C and D. What should Dominic do next? Change the compass opening to the length of CA⎯⎯⎯⎯⎯ and draw a circle centered at point C and then at point D. Change the compass opening to the length of CD⎯⎯⎯⎯⎯⎯ and draw a circle centered at point C. Use a straightedge to join points C and A, C and B, D and A, and D and B. Use a straightedge to join points C and D with a line.
Points C and D are equidistant from points A and B, so Dominic's square could be ACBD. To draw that square, his next move should be ...
... Use a straightedge to join points C and A, C and B, D and A, and D and B
Scientific skills exercise: interpreting a scatter plot with two sets of data which variable is the independent variable--the variable that was controlled by the researchers? Is the independent variable on the x-axis or the y-axis?
In a scatter plot with two sets of data, the independent variable is the variable that was controlled by the researchers and is represented on the x-axis.
Explanation:In a scatter plot with two sets of data, the independent variable is the variable that was controlled by the researchers. The independent variable is typically represented on the x-axis of a scatter plot. It is the variable that is manipulated or changed to observe its effect on the dependent variable, which is plotted on the y-axis.
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Solve for x: 3x − 24 = 81
57/3
105/3
57
105
To solve for x, we need to get all our constants on one side of the equal sign and all our variables on the other side of the equal sign.
3x - 24 = 81
3x -24 + 24 = 81 +24
3x = 81 + 24
3x = 105
3x/3 = 105 / 3
x = 105 / 3
Answer:
[tex]x=\frac{105}{3}[/tex]
Step-by-step explanation:
To solve for x, we need to get all our constants on one side of the equal sign and all our variables on the other side of the equal sign.
[tex]3x-24=81[/tex]
[tex]3x-24+24=81+24[/tex]
[tex]3x=81+24[/tex]
[tex]3x=105[/tex]
[tex]\frac{3x}{3}=\frac{105}{3}[/tex]
Therefore, the answer is: [tex]x=\frac{105}{3}[/tex]
The number of caps a new online store sells increases by a factor of 4 each month. The function f(x) = 4x represents the number of caps sold in month x. When does the store sell 64 caps?
... f(x) = 4^x
Find... x for f(x) = 64
SolutionRewrite 64 as a power of 4, then equate exponents.
... 64 = 4^x
... 4^3 = 4^x
... 3 = x
The store sells 64 caps in month 3.
Which expression best estimates
How do I solve this?
x = 6
given
[tex]\frac{x+2}{x-2}[/tex] = [tex]\frac{4}{8}[/tex]
cross- multiply to obtain
8(x + 2) = 4(x - 2) ( distribute parenthesis on both sides )
8x + 16 = 4x - 8 ( subtract 4x from both sides )
4x + 16 = - 8 ( subtract 16 from both sides )
4x = - 24 ( divide both sides by 4 )
x = [tex]\frac{-24}{4}[/tex] = - 6
Hello there!
Answer: ⇒ x=-6
_________________________________________________________
Step-by-step explanation:
Apply fraction cross multiply.
[tex](x+2)*8=(x-2)*4[/tex]
Expand.
[tex]8x+16=4x-8[/tex]
Subtract by 16 from both sides of equation.
[tex]8x+16-16=4x-8-16[/tex]
Simplify.
[tex]8x=4x-24[/tex]
Subtract by 4x from both sides of equation.
[tex]8x-4x=4x-24-4x[/tex]
Simplify.
[tex]4x=-24[/tex]
Divide by 4 from both sides of equation.
[tex]\frac{4x}{4}=\frac{-24}{4}[/tex]
Simplify it should be correct answer.
[tex]x=-6[/tex]
__________________________________________________________________
Hope this helps!
Thank you for posting your question at here on brainly.
Have a great day!
-Charlie
_________________________________________________________________
According to the synthetic division below, which of the following statements are true?
Check all that apply.
A, D and E are correct
given ( x - 4 ) is a factor then x = 4 is a root
the remainder on division by (x - 4 ) = 0 as indicated by the 0 on the right side of the quotient
(x - 4 ) is a factor of 3x² - 13x + 4 → A
the number 4is a root of f(x) = 3x² - 13x + 4 → D ( explained above )
thus 3x² - 13x + 4 ÷ (x - 4 ) = 3x - 1 → E
the quotient line 3 - 1 0
3 and - 1 are the coefficients of the linear quotient and 0 is the remainder
The correct options are [tex]\boxed{{\mathbf{Option A, D and E}}}[/tex].
Further explanation:
In any synthetic division, the dividend polynomial [tex]F\left( x \right) = {a_n}{x^n} + {a_{n - 1}}{x^{n - 1}} + {a_{n - 2}}{x^{n - 2}} + \cdots {a_0}[/tex] and the divisor polynomial [tex]g\left( x \right) = x - b[/tex] can be written as,
[tex]\begin{aligned}b\left){\vphantom{1{\underline {\begin{array}{*{20}{c}}3&{ - 13}&4\\{ }&{12}&{ - 4}\end{array}} }}}\right.\!\!\!\!\overline{\,\,\,\vphantom 1{{\underline {\begin{array}{*{20}{c}}&{a}_n&{ a_{n-1}}&_\cdot_\cdot_\cdot{a_0}\\{ }&{}&{ }\end{array}} }}} \hfill \\\begin{array}{*{20}{c}}{{\text{ }}{c}_n}&_\cdot_\cdot_\cdot{ c_0}&{{\text{ }}0}\end{array} \hfill\\\end{aligned}[/tex]
Here, the monic polynomial is divided by the polynomial that provides the polynomial after division that is also a factor of the polynomial .
Given:
The synthetic division is given below.
[tex]\begin{aligned}4\left){\vphantom{1{\underline {\begin{array}{*{20}{c}}3&{ - 13}&4\\{ }&{12}&{ - 4}\end{array}} }}}\right.\!\!\!\!\overline{\,\,\,\vphantom 1{{\underline {\begin{array}{*{20}{c}}&3&{ - 13}&4\\{ }&{12}&{ - 4}\end{array}} }}} \hfill \\\begin{array}{*{20}{c}}{{\text{ }}3}&{ - 1}&{{\text{ }}0}\end{array} \hfill\\\end{aligned}[/tex]
Step by step explanation:
We have to determine the answer among all the options.
Option A: [tex]\left( {x - 4} \right)[/tex] is a factor of [tex]3{x^2} - 13x + 4[/tex].
It can be observed from the given synthetic division the polynomial is [tex]g\left( x \right) = \left( {x - 4} \right)[/tex] that is divisible by the polynomial [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].
Therefore, the polynomial [tex]g\left( x \right) = \left( {x - 4} \right)[/tex] is a factor of the polynomial [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].
Therefore, the option A is correct option.
Option B: [tex]\left( {x + 4} \right)[/tex] is a factor of [tex]3{x^2} - 13x + 4[/tex].
From the option A, it has been proved that [tex]g\left( x \right) = \left( {x - 4} \right)[/tex] is a factor of the polynomial
[tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex]
Therefore, [tex](x+4)[/tex] is a not factor of [tex]3{x^2} - 13x + 4[/tex].
Thus, the option B is not correct option.
Option C: The number [tex]-4[/tex] is a root of [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].
From the option A, it has been proved that [tex]g\left( x \right) = \left( {x - 4} \right)[/tex] is a factor of the polynomial
[tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex]
Now substitute 0 for [tex]g\left( x \right)[/tex] in the equation [tex]g\left( x \right) = \left( {x - 4} \right)[/tex] to find the root of the polynomial [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex] as,
[tex]\begin{aligned}0&= \left( {x - 4} \right) \hfill\\x&= 4 \hfill\\\end{aligned}[/tex]
It can be seen that the value of [tex]x[/tex] is 4 it means [tex]-4[/tex] is not a root of the polynomial [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].
Therefore, the option C is not correct option.
Option D: The number [tex]4[/tex] is a root of [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].
It can be seen that the value of [tex]x[/tex] is 4 in option C it means [tex]4[/tex] is a root of the polynomial [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].
Therefore, the option D is correct option.
Option E: [tex]\left( {3{x^2} - 13x + 4} \right) \div \left( {x - 4} \right) = \left( {3x - 1} \right)[/tex]
The option E is also correct as [tex](x-4)[/tex] is the factor of the polynomial [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].
Option F: [tex]\left( {3{x^2} - 13x + 4} \right) \div \left( {x + 4} \right) = \left( {3x - 1} \right)[/tex]
The option F is not correct as [tex]\left( {x + 4} \right)[/tex] is not the factor of the polynomial [tex]F\left( x \right) = 3{x^2} - 13x + 4[/tex].
Result:
Therefore, the correct options are [tex]\boxed{{\mathbf{Option A, D and E}}}[/tex].
Learn more:
Learn more about the function is graphed below https://brainly.com/question/9590016 Learn more about the symmetry for a function https://brainly.com/question/1286775 Learn more about midpoint of the segment https://brainly.com/question/3269852Answer details:
Grade: Medium school
Subject: Mathematics
Chapter: Synthetic division
Keywords: Synthetic division, polynomial, monic polynomial, function, factor, real number, root, divisible, addition, remainder, quotient, divisor, dividend.
Beth has 7/100 of a dollar. What is the amount of money Beth has?
Hey there!
Beth has seven cents or $0.07
Hope this helps!
Always remember you are a Work Of Art!
-Nicole :) <3
There are 100 penny's in a dollar. So 7/100 would mean the 7 is represented by penny's, therefor beth has 7 cents.
-Steel jelly
What is the remainder when the polynomial 8 x^2 +4x−3 is divided by 2x−1 ?
[tex]8x^2 +4x-3[/tex] is divided by 2x-1
We use long division
4x +4 ------------> Quotient
----------------------------
2x-1 8x^2 +4x−3
8x^2 - 4x (Subtract it from the top)
---------------------------
+ 8x -3
8x - 4 (Subtract it from the top)
----------------------------------
+1 ------------> Remainder
So , 1 is the remainder.
a number cube is labeled 1 to 6. the cube will be tossed once. what is the probability that the cube will show a number less than 3?
Answer:
1/3 of the time.
Step-by-step explanation:
This is because since the dice is being tossed 1 time, that would mean that there is only a 2 in 6 chance to roll a number under 3
The probability that the cube will show a number less than 3 is 1/3 and this can be determined by using the given data.
Given :
A number cube is labeled 1 to 6. the cube will be tossed once.
The following steps can be used in order to determine the probability that the cube will show a number less than 3:
Step 1 - According to the given data, a number cube is labeled 1 to 6. the cube will be tossed once.
Step 2 - So, the number under three is 1 or 2.
Step 3 - Therefore, the probability that the cube will show a number less than 3 is:
[tex]\rm P=\dfrac{2}{6}[/tex]
[tex]\rm P=\dfrac{1}{3}[/tex]
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Mo says that 0.23567 is not a rational number. Which of these explains why Mo is incorrect?
Mo Says that, 0.23567 is not a Rational Number.
Mo is Incorrect.
⇒She is Incorrect, because Decimal expansion of rational number is either terminating or Non terminating Repeating decimal.
As , 0.23567 is terminating decimal .So, it is a Rational Number.
A number, n, is multiplied by -3/8. The product is -0.5 What is the value of n?
Answer:
n=4/3
Step-by-step explanation:
n*(-3/8)=-0.5
n=0.5/3/8
n=1/2 / 3/8
n=4/3
Check:
4/3*-3/8=-0.5
4/3*-3/8=-1/2
-1/2=-0/5
CORRECT!
Order from least to greatest 0.044 0.445 0.004 0.040
A) 0.004 0.040 0.044 0.445
B) 0.040 0.004 0.044 0.445
C) 0.040 0.004 0.044 0.445
D) 0.445 0.044 0.040 0.004
A is th3e correct answer... ten hundreths thousandths
The U.S. Maritime Administration estimated that the cost per ton of building an oil tanker could be represented by the model y=104,000/x+235 where y is the cost in dollars per ton and x is the tons (in thousands). What size of oil tanker (in thousands of tons) can be built for $350 per ton? a. 62 thousand tons b. 6 thousand tons c. 532 thousand tons d. 178 thousand tons
(c)
substitute x = 350 into the equation for y
y = [tex]\frac{104000}{350}[/tex] + 235 ≈ 532 000
Final answer:
To find the size of the oil tanker that can be built for $350 per ton, solve the equation 350 = 104,000/x + 235 for x, yielding approximately 904 thousand tons. None of the multiple-choice options match this result.
Explanation:
The student is asked to calculate the size of an oil tanker that can be built for $350 per ton using the given model for cost per ton, which is y = 104,000/x + 235, where y is the cost in dollars per ton, and x is the tons in thousands. To find x, set the equation equal to 350 and solve for x.
350 = 104,000/x + 235
Subtract 235 from both sides to get:
350 - 235 = 104,000/x
115 = 104,000/x
To solve for x, multiply both sides by x and then divide both sides by 115:
x = 104,000 / 115
x ≈ 904.35
Since x is in thousands of tons, the size of the oil tanker that can be built for $350 per ton is approximately 904 thousand tons. However, this answer does not match any of the options provided in the multiple choice (a. 62 thousand tons, b. 6 thousand tons, c. 532 thousand tons, d. 178 thousand tons), suggesting there might be an error in the question or the offered choices.
What is the missing value in the data set that would make the mean equal 80? Show your work or explain how you got your answer.
{71, 91, 82, 90, 88, 61, 70, __ }
all the numbers have to equal 640
because mean is add the all up and devide by how many. Theres 8 numbers and times that by 80 to get 640
so add them all up
71
91
82
90
88
61
70
553
subtract 640 by 553
youre answer is 87
The missing value in the data set is 87.
Here,
The data set is,
{71, 91, 82, 90, 88, 61, 70, __ }
The mean of data set = 80
We have to find the missing value in data set.
What is Mean?
Mean is calculate as, Find the sum of the values by adding them all up. Divide the sum by the number of values in the data set.
Now,
The data set is,
{71, 91, 82, 90, 88, 61, 70, __ }
The mean of data set = 80
Hence,
Let the missing number in data set = x
Mean of data set = [tex]\frac{71+ 91+ 82+ 90+ 88+61+ 70+x}{8}[/tex]
[tex]80 = \frac{553+x}{8}\\\\640 = 553 + x\\\\x = 87[/tex]
Therefore, The missing value in the data set is 87.
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express the area of a rectangle with length 7ab and width 2a as a monomial area = _____
The area is the product of the length and width.
... Area = (7ab)×(2a) = (7×2)×(a×a)×(b)
... Area = 14a²b
What is the sum of all of the odd numbers from 1 to 59?
841
900
3,481
3,600
James has t toy cars and Paul has 13 more. How many cars will James have if Paul gives him half of his cars?
James will end up with his original t cars and half of (t+13) cars, so will have ...
... t + (t+13/2) = (3t +13)/2 . . . . cars James has after Paul's gift
To find out how many cars James will have after Paul gives him half of his cars, we need to determine the numbers of cars James and Paul have. We then calculate half of Paul's cars and add that to James' original number of cars.
Explanation:To find out how many cars James will have after Paul gives him half of his cars, we need to first determine how many cars Paul has in total.
We know that Paul has 13 more cars than James, so we can set up an equation:
Paul's cars = James' cars + 13. Next, we need to find out how many cars Paul will give to James, which is half of Paul's cars.
We can set up another equation: cars Paul gives to James = Paul's cars ÷ 2.
Finally, to find out how many cars James will have after Paul gives him half of his cars, we simply add the number of cars Paul gives to James to James' original number of cars.
Let's say James has 5 toy cars. Paul has 13 more, so Paul has 5 + 13 = 18 toy cars.
Half of Paul's cars is 18 ÷ 2 = 9 toy cars. James will have 5 + 9 = 14 toy cars after Paul gives him half of his cars.
Find the value of the expression 2x^4–5x^3+x^2+3x+2 for x=−5
A high ascent weather balloon is in the shape of cone pointing downwards. The cone has a height of h and a hemispherical top of a radius r. The surface area of the weather balloon is , and the volume is , where . For a weather balloon with a volume of 14000 , the surface area as a function of m is shown below.
Answer:
Matlab capacity to ascertain the surface territory of an inflatable
work surfaceArea = surfaceBalloon(Volume,M)
Step-by-step explanation:
% Matlab capacity to ascertain the surface territory of an inflatable
work surfaceArea = surfaceBalloon(Volume,M)
% compute R
cubeOfR = 3 * Volume * ones(1,length(M));
cubeOfR = cubeOfR ./(pi * (M+2));
R = power(cubeOfR,1/3);
% compute surface zone
power1 = power(M,2);
power1 = 1+ power1;
power1 = power(power1,1/2);
power1 = 2 + power1;
surfaceArea = pi .* power(R,2) .* power1;
end
% End of capacity
% Matlab content to utilize work surfaceBalloon to locate the surface zone of
% expand
clc;
V = 14000;
M = (0:10);
surfaceArea = surfaceBalloon(V,M);
plot(M,surfaceArea);
xlabel('M');
ylabel('Surface Area m^2');
ylim([2900 5000]);
title('M v/s Surface Area of an inflatable');
saveas(gcf,'surfaceAreaPlot','png'); % spare the chart
% end of primary content
Answer:
radius = ((3*Volume) ./ ((2+M).*pi)).^(1/3);
surfaceArea = pi .* radius.^2 .* (2+sqrt(1+M.^2));
Step-by-step explanation:
The OP didn't include this part, but the original problem has the equations written for you in the header. Here they are again:
A = [tex]\pi R^{2}[/tex](2 + [tex]\sqrt{1+M^{2} }[/tex])
V = [tex]\pi R^{3} (2+M)/3[/tex] where M = H/R
The problem is asking for the surface area of the balloon, but the only values that the user inputs are volume and M. We need to solve for the radius before we can complete the code. So, we can solve for R in one equation and plug it into the second equation.
Let's adapt the given equation V = [tex]\pi R^{3} (2+M)/3[/tex] and solve for R to get the equation for the radius.
V = [tex]\pi R^{3} (2+M)/3[/tex]
3*V = [tex]\pi R^{3} (2+M)[/tex]
[tex]\frac{3*V}{\pi (2+M)} = R^{3}[/tex]
R = [tex](\frac{3*V}{\pi (2+M)})^{1/3}[/tex]
Now, let's convert the equation for R to MATLAB code. Because we are using arrays, each operational symbol must be preceded by a "." unless it is a + or -.
R = [tex](\frac{3*V}{\pi (2+M)})^{1/3}[/tex]
radius = ((3*Volume) ./ ((2+M).*pi)).^(1/3);
Okay, so the hard part is done. The second line of code is easy: all you have to do is transform the given equation for surface area into MATLAB code while using the variable we named "radius" in the last step. Again, because we are performing operations with arrays, use "." in front of all operational symbols (except + and -).
A = [tex]\pi R^{2}[/tex](2 + [tex]\sqrt{1+M^{2} }[/tex])
surfaceArea = pi .* radius.^2 .* (2+sqrt(1+M.^2));
Putting it all together, your answer should be
radius = ((3*Volume) ./ ((2+M).*pi)).^(1/3);
surfaceArea = pi .* radius.^2 .* (2+sqrt(1+M.^2));
Please help! question attached
The expression predicts profit. When the expression is zero, the profit is zero.
The expression uses unit price as the indpendent variable. Then the zeros correspond to values of unit price that make profit = 0.
Your selection is correct.
A gold mine has two elevators, one for equipment and another for the miners. The equipment elevator descends 4 feet per second. The elevator for the miners descends 15 feet per second. One day, the equipment elevator begins to descend. After 30 seconds, the elevator for the miners begins to descend. What is the position of each elevator relative to the surface after another 14 seconds? At that time, which elevator is deeper?
The equipment elevator descends to 176 feet below the surface while the miners' elevator descends to 210 feet below the surface after 14 seconds. Therefore, the miners' elevator is deeper.
Explanation:To solve this, we first need to determine the position relative to the surface of both elevators in the gold mine. As the equipment elevator begins to descend first and moves at a speed of 4 feet per second, it had already traveled 30 (seconds) * 4 (feet per second) = 120 feet downward before the miners' elevator begins to descend.
Then, an additional 14 seconds pass. In these 14 seconds, the equipment elevator will descend a further 14 * 4 = 56 feet. Therefore, the equipment elevator is 120 + 56 = 176 feet below the surface.
The miners' elevator descends at 15 feet per second, and it has been moving for 14 seconds. Therefore, it is 15 * 14 = 210 feet below the surface. At this point in time, the miners' elevator is deeper than the equipment elevator by 210 - 176 = 34 feet.
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The equipment elevator will be at a depth of 176 feet, while the miners' elevator will be deeper at a depth of 210 feet from the surface after the given time. The miners' elevator is deeper.
Explanation:The position of each elevator relative to the surface after another 14 seconds can be found by first determining the distance each has traveled. The equipment elevator descends at 4 feet per second, and it had already been descending for 30 seconds before the miners' elevator started. Therefore, by the time the miners' elevator begins to descend, the equipment elevator will have descended 4 feet/second * 30 seconds = 120 feet.
From that point, after another 14 seconds, the equipment elevator descends an additional 4 feet/second * 14 seconds = 56 feet. Thus, its total descent is 120 feet + 56 feet = 176 feet from the surface.
On the other hand, once the miners' elevator starts, it descends at a rate of 15 feet per second. After 14 seconds, the miners' elevator will have descended 15 feet/second * 14 seconds = 210 feet.
Comparing both distances, the elevator for the miners is at 210 feet while the equipment elevator is at 176 feet from the surface. So, the miners' elevator is deeper.
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