Answer: 11,658.45
Step-by-step explanation:
First multiply 305 x 620 to determine the square footage
divide that answer by 16.22 to get your answer
The required amount of electricity produced by a field of solar panels which is 305 feet by 620 feet, is 3,067,202 watt.
Given that,
A field of solar panels yields 16.22 watts per square foot.
T0 determines the amount of electricity produced by a field of solar panels that is 305 feet by 620 feet.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
A field of solar panels yields 16.22 watts per square foot.
The amount of electricity produced by a field of solar panels is 305 feet by 620 feet,
= 16.22 * 305 * 620
= 3,067,202 watt,
Thus the required amount of electricity produced by a field of solar panels that is 305 feet by 620 feet, is 3,067,202 watt.
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Which of the following is a concern about globalization? A. The possibility of promoting child labor B. Less jobs in exporting industries C. Less variety in consumer goods D. Higher prices for consumer goods
Answer:
A
Step-by-step explanation:
A: The possibility of promoting child labor is a concern about globalization
Hailey paid \$13$13dollar sign, 13 for 1\dfrac3{7} \text{ kg}1 7 3 kg1, start fraction, 3, divided by, 7, end fraction, space, k, g of sliced salami. What was the cost per kilogram of salami? \$
Answer:
The answer is 9.10, ($9.10).
Step-by-step explanation:
Oh just to let you know that other answer (joke) was such a loser joke.
An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. The standard deviation of completion times is 1.6 minutes. It is claimed that, under new management, the mean completion time has decreased. To test this claim, a random sample of 33 completion times under new management was taken. The sample had a mean of 11.2 minutes. Assume that the population is normally distributed. Can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? Assume that the standard deviation of completion times has not changed.
Let [tex]\mu[/tex] be the population mean.
Null hypothesis : [tex]\mu=12[/tex]
Alternative hypothesis : [tex]\mu<12[/tex]
Since Alternative hypothesis is left tailed so , the test is a left tailed test.
Given : n=33 > 30 , so we use z-test.
Test statistic : [tex]z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
i.e. [tex]z=\dfrac{11.2-12}{\dfrac{1.6}{\sqrt{33}}}\approx-2.87[/tex]
Using z-value table,
P-value for left tailed test =[tex]P(z<-2.87)=0.0020524[/tex]
Since , the p-value (0.0020524) is less than the 0.05 level of significance, it means we reject the null hypothesis.
Therefore, we have enough evidence to support the claim that the mean completion time has decreased under new management.
Two cars, a Porsche Boxster and a Toyota Scion XB, are traveling in the same direction, although the Boxster is 115.0 m behind the Scion. The speed of the Boxster is 26.0 m/s and the speed of the Scion is 18.9 m/s. How much time does it take for the Boxster to catch the Scion? [Hint: What must be true about the displacement of the two cars when they meet?]
Answer:
16.197 seconds
Step-by-step explanation:
the time and the final place fot both cars is the same.
for the Boxster we have
X = Vboxster . T
being
X the distancance from the initial place of the Boxter to the meeting point
Vboxster the speed of the Boxster (26m/s)
T the time
and for the Scion
X = Xo + Vscion . T
Being
Xo the initial point of the Scion (115m)
X the distancance from the initial place of the Boxster to the meeting point
Vscion the speed of the Scion (18.9 m/s)
T the time
Xo + Vscion . T = Vboxster . T
Xo = Vboxster . T - Vscion . T
Xo = (Vboxster - Vscion) . T
Xo/(Vboxster - Vscion) = T
115m/ (26-18.9) m.s-1 = T
16.197 s = T
Answer:
a)t = 16.2s : time it takes for the Boxster to catch the Scion
b)The displacement of the Boxster (db) is 115 m more than the displacement of the Scion(ds)
db =ds+115
Step-by-step explanation:
Conceptual analysis
We apply the formula for constant speed movement:
v= d/t Formula (1)
v = speed in m/s
d: distance in m
t: time in s
Problem development
The time of Scion (ts) is equal time of Boxster (tb)
t (s) =tb=t
The displacement of the Boxster is 115 m more than the displacement of the Scion
db =ds+115
we apply formula (1 )car kinematics :
Scion kinematics
18.9=ds/t
t =ds /18.9 Equation (1)
Boxster kinematics
26=db/t
26=(ds+115)/t
t=(ds+115)/26 Equation (2)
Equation (1) = Equation (2)
ds /18.9 =(ds+115)/26
18.9(ds+115)= 26 ds
18.9ds+18.9*115=26 ds
2173.5= 26 ds-18.9ds
2173.5=7.1ds
ds =2173.5÷7.1
ds=306.12m
We replace ds=306.12m in the equation (1)
t =306.12÷18.9
t = 16.2s
What is 25 percent of 32?
Answer:
1.28 or 128
Step-by-step explanation:
you would take 32 and divide it by.25
Consider the parametric equations below. x = t + cos t y = t - sin t 0 ≤ t ≤ 3π Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.
Answer:
L=13.715
Step-by-step explanation:
Given that
x=t + cos t
y= t - sin t
0 ≤ t ≤ 3π
[tex]\dfrac{dx}{dt}=1-sin\ t[/tex]
[tex]\dfrac{dy}{dt}=1-cos\ t[/tex]
We know that length of parametric curve given as
[tex]L=\int_{a}^{b}\sqrt{\left(\dfrac{dx}{dt}\right)^2+\left(\dfrac{dy}{dt}\right)^2}dt[/tex]
[tex]\left(\dfrac{dx}{dt}\right)^2=1+sin^2 t-2t\ sint[/tex]
[tex]\left(\dfrac{dy}{dt}\right)^2=1+cos^2 t-2t\ cost[/tex]
Now by putting the values
[tex]L=\int_{0}^{3\pi}\sqrt{3-2sin\ t-2cos\ t}\ dt[/tex]
Now by using calculator
L=13.715
To find the curve length for ( x = t + cos t ) and ( y = t - sin t ) over [tex]\( 0 \le t \le 3\pi \):[/tex]
1. Calculate derivatives:
[tex]\[ \frac{dx}{dt} = 1 - \sin t, \quad \frac{dy}{dt} = 1 - \cos t \][/tex]
2. Set up integral:
[tex]\[ L = \int_0^{3\pi} \sqrt{(1 - \sin t)^2 + (1 - \cos t)^2} \, dt \][/tex]
3. Simplify integrand:
[tex]\[ L = \int_0^{3\pi} \sqrt{3 - 2(\sin t + \cos t)} \, dt \][/tex]
4. Calculate numerically:
[tex]\[ L \approx 21.2694 \][/tex]
The curve length is approximately ( 21.2694 ).
To find the length of the curve given by the parametric equations ( x = t + cos t ) and ( y = t - sin t ) for[tex]\( 0 \le t \le 3\pi \)[/tex] , we use the formula for the arc length of a curve defined by parametric equations:
[tex]\[ L = \int_a^b \sqrt{\left(\frac{dx}{dt}\right)^2 + \left(\frac{dy}{dt}\right)^2} \, dt \][/tex]
1. **Find the derivatives of ( x ) and ( y ) with respect to ( t ):**
For [tex]\( x = t + \cos t \):[/tex]
[tex]\[ \frac{dx}{dt} = 1 - \sin t \][/tex]
For[tex]\( y = t - \sin t \):[/tex]
[tex]\[ \frac{dy}{dt} = 1 - \cos t \][/tex]
2. **Set up the integral for the arc length:**
[tex]\[ L = \int_0^{3\pi} \sqrt{\left(1 - \sin t\right)^2 + \left(1 - \cos t\right)^2} \, dt \][/tex]
3. **Simplify the integrand:**
[tex]\[ \left(1 - \sin t\right)^2 + \left(1 - \cos t\right)^2 \][/tex]
Expand both terms:
[tex]\[ \left(1 - \sin t\right)^2 = 1 - 2\sin t + \sin^2 t \][/tex]
[tex]\[ \left(1 - \cos t\right)^2 = 1 - 2\cos t + \cos^2 t \][/tex]
Add the expressions together:
[tex]\[ \left(1 - \sin t\right)^2 + \left(1 - \cos t\right)^2 = (1 - 2\sin t + \sin^2 t) + (1 - 2\cos t + \cos^2 t) \][/tex]
[tex]\[ = 1 - 2\sin t + \sin^2 t + 1 - 2\cos t + \cos^2 t \][/tex]
[tex]\[ = 2 - 2\sin t - 2\cos t + \sin^2 t + \cos^2 t \][/tex]
Recall that[tex]\( \sin^2 t + \cos^2 t = 1 \):[/tex]
[tex]\[ = 2 - 2\sin t - 2\cos t + 1 \][/tex]
[tex]\[ = 3 - 2(\sin t + \cos t) \][/tex]
So the integrand becomes:
[tex]\[ \sqrt{3 - 2(\sin t + \cos t)} \][/tex]
4. **Set up the integral for the arc length:**
[tex]\[ L = \int_0^{3\pi} \sqrt{3 - 2(\sin t + \cos t)} \, dt \][/tex]
5. **Calculate the integral:**
This integral is complex and generally requires numerical methods or a calculator to evaluate.
Using a calculator:
[tex]\[ L \approx \int_0^{3\pi} \sqrt{3 - 2(\sin t + \cos t)} \, dt \approx 21.2694 \][/tex]
Thus, the length of the curve, correct to four decimal places, is approximately ( 21.2694 ).
Help please!
What is the solution to the system of linear equations?
-9x+4y=55
-11x+7y=82
Answer: x= - 3, y = 7
Step-by-step explanation:
State whether each function is a linear function. Explain.
1. y = 3x
2. y =- 2+5x
3. 2x + y= 10
4. f(x) = 4x^2
5. -3/x + y = 15
6. x + y + 8
Answer:
The answer is below
Step-by-step explanation:
1. y = 3x is a linear function because it doesn't have any power
2. y =- 2+5x is a linear function because it doesn't have any power
3. 2x + y= 10 is a linear function because it doesn't have any power
4. f(x) = 4x^2 it isn't a linear function because x is elevated to a power
5. -3/x + y = 15 is a linear function because it doesn't have any power
6. x + y + 8 is a linear function because it doesn't have any power
The first, second, third and sixth functions are linear functions, as they comply with the standard linear function format, y = mx + c. The fourth and fifth functions are not linear because they do not follow this standard format.
Explanation:A linear function is a function whose graph is a straight line. The general form of a linear function is y = mx + c, where m is the slope of the line, and c is the y-intercept.
y = 3x is a linear function, as it can be rewritten in the general form y = mx + c by considering m as 3 and c as 0. y =- 2+5x is also a linear function. Here, the slope m is 5 and the y-intercept c is -2. 2x + y= 10 can be rearranged as y = -2x + 10, which is a linear function with m = -2 and c = 10. f(x) = 4x^2 is not a linear function as the x term is raised to the power of 2, making it a quadratic function. -3/x + y = 15 is not a linear function as it includes an x term in the denominator. x + y + 8 is a linear equation. If this equation is rearranged in the format y = mx + c, it becomes y = -x - 8. Here, m = -1 and c = -8.Learn more about linear function here:
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Match the following:a. When two variables change in the same direction, one remaining larger than the other by the same factor b. To insert between neighboring points or estimate by taking an average of known values c. A relationship between two variables in which the product remains constant. When one variable increases the other decreases in proportion so that the product is unchanged 1. direct relationship2. interpolate 3. inverse relationship
Answer:
a. When two variables change in the same direction, one remaining larger than the other by the same factor - direct relationship
b. To insert between neighboring points or estimate by taking an average of known values - interpolate
c. A relationship between two variables in which the product remains constant. When one variable increases the other decreases in proportion so that the product is unchanged - inverse relationship
In 1997, Superman’s cape from the 1978 movie Superman was sold at an auction. The winning bid was $17,000. Question 1 Write an inequality that represents the amounts of all the losing bids. Let b represent the amount of a bid.
The inequality to represent the losing bids can be written as:
b < 17000.
The winning bid for Superman's cape from the 1978 movie was $17,000.
To represent the amounts of all the losing bids, we need to write an inequality that indicates bids that are less than $17,000.
Let "b" represent the amount of a bid.
The inequality to represent the losing bids can be written as:
b < 17000
This inequality states that any bid "b" that is less than $17,000 would be a losing bid. The symbol "<" signifies "less than."
So, any bid amount smaller than $17,000 falls into the category of losing bids.
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The inequality representing all losing bids for Superman's cape is b < 17,000, where b is the amount of any losing bid. Bidders must consider auction strategies and valuations to avoid overbidding and the winner's curse.
The question involves creating an inequality to represent the losing bids in an auction where Superman's cape was sold for $17,000. The variable b is introduced to represent the amount of any losing bid. The inequality that represents all the losing bids would be b < 17,000. since any bid that is less than $17,000 would not win the auction.
Help me ASAP PLEASE
Answer:
4. Functions: 1, 2, 4, 5, 7, 8, 11, 12
5. y = -1/2x+5/2, x ≤ -1; 2x +1, x > -1.
y = 2, x < 0; x, 0 ≤ x ≤ 3; 3 x > 3.
Step-by-step explanation:
4. A list of ordered pairs is a function of no x-values are re-used. In (3) and (6), the value x=2 is used more than once.
A graph represents a function if it passes the "vertical line test." A vertical line cannot intersect the graph in 2 or more points. (9) and (10) both fail that test.
If the relation is not listed here as being "not a function," then it is one of the answers to question 4.
__
5. The first step in writing the equation of a piecewise function is to identify the pieces. These are generally bounded by points of discontinuity--jumps in the function value, or changes in the slope of lines.
The second step is to identify the section of the function that boundary points belong to. Solid dots are part of the function definition; open circles are not.
Left Graph
The left piece ends at x=-1. There is a solid dot attached to the left piece, so its definition will be for the domain x ≤ -1. That line has slope -1/2, since is drops 1 unit for each 2 to the right. If extended, it would intersect the y-axis at y = 2 1/2 = 5/2. So, the piece on the left is y = -1/2x + 5/2 for x ≤ -1.
The right piece starts at x=-1, but does not include that point. It has a rise of 2 for each 1 to the right, so its slope is 2. It crosses the y-axis at y=1, so the piece on the right is y = 2x + 1 for x > -1.
You can use the method of your textbook author to combine theses pieces into one equation. The method shown above is one way to do it.
__
Right Graph
This graph has a discontinuity at x=0 and a change in slope at x=3. It can be described by 3 pieces. The point at x=0 does not belong to the left piece, but goes with the middle piece.
The left piece of the function is the constant 2, so has the equation y = 2 for x < 0.
The middle piece has a slope of 1 and a y-intercept of 0, so has the equation y = x for 0 ≤ x ≤ 3.
The point at x=3 belongs to both the middle piece and the right piece, so can be part of both function definitions, if you like. Generally, it is better form to include any given x-value in only one of the pieces of the function. So the equation for the right piece can be y = 3 for x > 3.
A 10-ounce package of animal cookies cost $2. What should a 35- ounce package cost, assuming the same cost per ounce?
Answer:7
Step-by-step explanation:
Answer: $61 because you have to do 10 x3 to get 30 then + $1 because $1 is equal to 5 pounds
PLZ HURRY IT'S URGENT!!
The length of a rectangle is 4 inches longer than its width. The area of the rectangle is 12 square inches. What are the length and width?
Which equation models this problem?
w – (4 + w) = 12
w + (4 + w) = 12
w(4 + w) = 12
4 • w = 12
Answer:
The equation that models this problem is w(4 + w) = 12
Step-by-step explanation:
we know that
The area of a rectangle is
[tex]A=LW[/tex]
we have
[tex]A=12\ in^2[/tex]
so
[tex]12=LW[/tex] -----> equation A
[tex]L=W+4[/tex] ----> equation B
substitute equation B in equation A and solve for W
[tex]12=(W+4)W[/tex]
therefore
The equation that models this problem is w(4 + w) = 12
Answer:
The answer is w(4+w)=12
Step-by-step explanation:
Write the equation of the line, in point-slope form. Identify (x1, y1) as the point (-2, -1). Use the box provided or the upload option to submit all of your calculations and final answers.
For this case we have that by definition, the equation of a line in the point-slope form is given by:
[tex](y-y_ {0}) = m (x-x_ {0})[/tex]
Where:
[tex](x_ {0}, y_ {0})[/tex]: It is a point through which the line passes
m: It's the slope
We have according to the graph, that the line goes through:
[tex](x_ {1}, y_ {1}): (- 2, -1)\\(x_ {2}, y_ {2}) :( 2,1)[/tex]
We found the slope:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {1 - (- 1)} {2 - (- 2)} = \frac {1 +1} {2 + 2} = \frac {2} {4} = \frac {1} {2}[/tex]
Thus, the line is of the form:
[tex](y-y_ {0}) = \frac {1} {2} (x-x_ {0})[/tex]
We substitute a point:
[tex](y-1) = \frac {1} {2} (x-2)[/tex]
Answer:
[tex](y-1) = \frac {1} {2} (x-2)[/tex]
Between what two consecutive integers is √151
1) 11 and 12
2) 9 and 10
3) 12 and 13
4) 14 and 15
Answer:
The answer to your question is: 3) between 12 and 13
Step-by-step explanation:
Just get the square root of 151, and compare your result with the options.
√ 151 = 12.28
Then, the only possibility is (3) 12 and 13.
You have a 4 in. X 6in. family picture that you want to resize. You can choose from a 16 in. X 20 in. or an 18 in. X 24 in. Which size will keep more of the original picture?a 4 inch
Answer:
1.333 is more close to 1.5 than 1.25 .
Step-by-step explanation:
We are given:
You have a 4 in. X 6in. family picture that you want to resize. You can choose from a 16 in. X 20 in. or an 18 in. X 24 in. Which size will keep more of the original picture.
First divide 6 by 4: we get,
6/4 = 1.5 inches
This is the ratio to achieve.
Now divide 20 by 16
20/16 = 10/8
10/8 = 5/4
5/4 = 1.25 inches
Now divide 24 by 18
24/18 = 12/9
12/9 = 4/3
4/3 = 1.333 inches
1.333 is more close to 1.5 than 1.25 .
Find all solutions of the equation 4x^2−144=0 by factoring the left hand side and using the zero factor property.
Answer:
x = ±6
Step-by-step explanation:
The left side is the difference of squares, so factors accordingly:
(2x -12)(2x +12) = 0
The zero factor property tells you the product will be zero when one or more factors is zero.
2x -12 = 0
x -6 = 0 . . . . divide by 2
x = 6 . . . . . . one solution to the equation
__
2x +12 = 0
x + 6 = 0 . . . . divide by 2
x = -6 . . . . . . . the other solution to the equation
Peter noticed that his house# is divisible by both 72 and 112.
1) What's the smallest integer that his house number could be?
2) If the house number is between 3000 and 4000, what's the house number?
Answer:
10083024Step-by-step explanation:
1) The greatest common factor of 72 and 112 is 8, so the least common multiple is ... 72×112/8 = 1008.
The least common multiple of 72 and 112 is 1008.
__
2) The house number will be a multiple of 1008 between 3000/1008 = 2.98 and 4000/1008 = 3.96. The only integer in that range is 3, so Peter's house number is ...
3 × 1008 = 3024
Peter's house number is 3024.
Can someone please help?
60 ≥ 35 + 5t
-35 -35
25 ≥ 5t
5 5
t≤5
his mistake was that he used ≤ for at least instead of using ≥. so at end, when I solved, I saw that Sven should spend 5 minutes or less on each scale.
Find the quadratic function y=f(x) whose graph has a vertex (−3,3) and passes through the point (−6,0). What is the function in standard form?
Answer:
f(x) = -1/3x² -2x
Step-by-step explanation:
For vertex (h, k) and scale factor "a", the vertex form of a quadratic is ...
y = a(x -h)² +k
For the given vertex, the vertex form function with scale factor "a" is ...
f(x) = a(x +3)² +3
If that goes through the point (-6, 0), then we have ...
f(-6) = a(-6 +3)² +3 = 0
9a = -3 . . . . . . . subtract 3
a = -1/3 . . . . . . . divide by 9
In standard form, the equation is ...
f(x) = (-1/3)x² -2x
The cubed root of a number
I need help on this one ASAPP
Answer:
At most 5 --> x ≤ 5
Larger than 5 --> x > 5
Below 5 --> x < 5
Not less than 5 --> x ≥ 5
Step-by-step explanation:
I learned how to figure this out like this: "The smaller number eats the bigger one", since the symbols "<" and ">" looks like an open mouth.
The symbols "≥" and "≤" mean that it is larger or equal to the number shown.
In the first case, it means that the number that represents "x" could be any up to the number 5 (including it). And in the last case, it means that the number that represents "x", could be any starting from 5(including it).
Can anyone double check my work for me?
Answer:
They're are all correct.
Step-by-step explanation:
I went each of them carefully. They are all correct.
1. According to the Motley Fool, in 2014 there were 148.6 million personal federal tax return filed, and average amount of tax paid per filed was $9,118. Write each of these numbers in scientific notation.
Answer:
[tex]1.486*10^8[/tex]
[tex]9.118*10^3[/tex]
Step-by-step explanation:
By definition, the form of Scientific notation is:
[tex]a*10^n[/tex]
Where the base is 10, "a" is any number from 1 to 10 but not including 10, and "n" is an integer.
Therefore to write a number in Scientific notation, the decimal point must be after the first digit and the power "n" must indicate how many places the decimal point is moved.
We know that:
[tex]148.6\ million=148,600,000\ millions[/tex]
Then, we need to move the decimal point 8 places to the left:
[tex]=1.486*10^8[/tex]
To write $9,118 in scientific notation, we need to move the decimal point 3 places to the left:
[tex]=9.118*10^3[/tex]
The perimeterof a parralelagram is 60 meters. The width of the parralelgram is 6 meters less than its length. Find the length and width of the paralelogram
Answer:
The answer to your question is:
length = 12
width = 6
Step-by-step explanation:
Perimeter of a parallelogram = 2 length + 2 width
We know that width = length - 6
So
60 = 2 length + 2(length -6)
60 = 2 length + 2 length - 12
60 - 12 = 4 length
48 = 4 length
length = 48/4 = 12 meters
width = length - 12
= 12 - 6
= 6
Answer:
12
6
Step-by-step explanation:
Find the probability. Please show your work. Thanks!
There were 100 total students surveyed.
There are 41 freshman students that have an ATM card.
The probability is the number of freshman that have an ATM card over the total number of students.
The probability becomes 41/100
Now divide the fraction to get the decimal answer:
41/100 = 0.410
Jimmy is employed on an assembly line. He receives $0.25 for each part that he works on. If he works on more than 150 Parts, his employer will pay him $0.35 for each part over 150. If he works on more than 300 parts, his employer will pay him $0.50 for each part over 300. Yesterday, Jimmy worked on 500 Parts. How much did he earn?
I got $930, not sure if that's correct.
Final answer:
Jimmy earned $190 for working on 500 parts. This includes $37.50 for the first 150 parts, $52.50 for the next 150 parts, and $100 for the 200 parts beyond the initial 300.
Explanation:
Jimmy's earnings can be calculated by dividing the parts he worked on into three segments that correspond to different pay rates.
The first 150 parts at $0.25 each.
The next 150 parts (from part 151 to 300) at $0.35 each.
Any parts above 300 at $0.50 each.
So the calculation would be as follows:
First segment: 150 parts × $0.25 = $37.50
Second segment: 150 parts × $0.35 = $52.50
Third segment: 200 parts (500 - 300) × $0.50 = $100.00
Adding these amounts together will give us the total earnings:
$37.50 + $52.50 + $100.00 = $190.00
Therefore, Jimmy earned a total of $190 yesterday.
describe the graph of a function g by observing the graph of the base function f ?
Answer:
Choice 3 is your answer
Step-by-step explanation:
The format of the function when you move it side to side or up and down is
f(x) = (x - h) + k,
where h is the side to side movement and k is up or down. The k is easy, since it will be positive if we move the function up and negative if we move the function down from its original position.
The h is a little more difficult, but just remember the standard form of the side to side movement is always (x - h). If our function has moved 3 units to the left, we fit that movement into our standard form as (x - (-3)), which of course is the same as (x + 3). Our function has moved up 5 units, so the final translation is
g(x) = f(x + 3) + 5, choice 3 from the top.
Evaluate the expression (4x^3)^2 for x=2
A.128
B.512
C.256
D. 1024
Answer:
d:) 1024
Step-by-step explanation:
Evaluate (4 x^3)^2 where x = 2:
(4 x^3)^2 = (4×2^3)^2
Multiply each exponent in 4×2^3 by 2:
4^2 (2^3)^2
Multiply exponents. (2^3)^2 = 2^(3×2):
2^(3×2)×4^2
4^2 = 16:
2^(3×2)×16
3×2 = 6:
2^6×16
2^6 = (2^3)^2 = (2×2^2)^2:
(2×2^2)^2 16
2^2 = 4:
(2×4)^2 16
2×4 = 8:
8^2×16
8^2 = 64:
64×16
| | 6 | 4
× | | 1 | 6
| 3 | 8 | 4
| 6 | 4 | 0
1 | 0 | 2 | 4:
Answer: 1024
PLEASE HELP!!!
The density of lead is 11.34 g/cm^3 and the density of aluminum is 2.69 g/cm^3. Find the radius of lead and aluminum spheres each having a mass of 50 kg.
Answer:
You have to replace x for each density
Step-by-step explanation:
Density = Mass / Volumen
1,000 g = 1 kg
1,000,000 cm^3 = 1 m^3
g/cm^3 = 1000 kg/m^3
Using density as x
[tex]volumen \: = \frac{50000}{x} \\ volumen \: sphere \: = 4\pi {r}^{3} \\ 4\pi {r}^{3} = \frac{50000}{x} \\ r = \sqrt[3]{ \frac{50000}{4\pi {x}^{} } } [/tex]
Density can be defined as the mass per unit volume of a given substance.
The formula is given as:
Density = Mass / volume
The radius of the Aluminum sphere is 16.43cm and the radius of the Lead sphere is 10.17 cm
The density of lead is 11.34 g/cm³.The density of aluminum is 2.69 g/cm³.Mass of lead and Aluminum = 50kgStep 1: Convert the masses of Lead and Aluminium from kg to g1 kg = 1000g
50kg = ?
Cross Multiply
50kg × 1000g/ 1 kg
= 50,000g
The mass of lead and Aluminum is 50,000g
Step 2: Find the Volume and radius of AluminiumThe density of Aluminum is 2.69 g/cm³.
Mass of Lead is 50,000g
Volume = Mass/ Density
Volume of Aluminum = 50,000g/ 2.69 g/cm³
Volume of Aluminium = 18587.360595 cm³
The Volume of the Aluminum Sphere = 18587.360595 cm³
The formula to find the radius is given as
(3V/4π)[tex]^{1/3}[/tex]
= (3 × 18587.360595/ 4π)[tex]^{1/3}[/tex]
The radius of the lead sphere = 16.43 cm
Step 3: Find the Volume and radius of LeadThe density of lead is 11.34 g/cm³.
Mass of Lead is 50,000g
Volume = Mass/ Density
Volume of Lead = 50,000g/ 11.34 g/cm³
Volume of Lead = 4409.1710758 cm³
The Volume of a Lead Sphere = 4409.1710758 cm³
The formula to find the radius is given as
(3V/4π)[tex]^{1/3}[/tex]
= (3 × 4409.1710758/ 4π)[tex]^{1/3}[/tex]
The radius of the lead sphere = 10.17 cm
Therefore, the radius of the Aluminum sphere is 16.43cm and the radius of the Lead sphere is 10.17 cm.
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brainly.com/question/2622640