Answer:
100,000,001
I hope this helps, have a great day/night!
9s-5t=-4u solve for s
Answer: s= -4u/9 + 5t/9
Step-by-step explanation: Hope it helps
Step-by-step explanation:
First of all, we have to take -5t to the other side and after taking it to the other side it will be +5t, then we have to take (only) 9 to the other as it is 9s (multiplication) it will be division if u take it to the other side.
Done
Apple Picking
Name
josiph
Linda and Robin went apple picking. After picking all day, Linda had 15 more
apples than Robin. Together, they gathered 105 apples. Figure out how many
apples Linda got and how many Robin got. Linda got 1/3 of all her apples from
the first tree and % of all her apples from the second tree. She got the rest of her
apples from the third tree. Robin got 1/3 of all her apples from the first tree and
5/9 of all her apples from the second tree. She got the rest of her apples from
the third tree. Who got more apples from the third tree? How many more?
We can write the system of equations:
x = y + 15
x + y = 105
Solving the system, we will see that Robin has 45 apples and Linda 60 apples.
How many apples do Robin and Linda got?Here we can only solve the first part, as the second is incomplete.
Let's define the variables:
x = apples that Linda has.
y = apples that Robin has.
We know that Linda has 15 more apples than Robin, and that between the two there are 105 apples, so we can write the system of equations:
x = y + 15
x + y = 105
To solve this, we can replace the first equation into the second one, so we get:
(y + 15) + y = 105
2y + 15 = 105
2y = 105 - 15 = 90
y = 90/2 = 45
So Robin has 45 apples, and Linda has 15 more, so she has:
x = 45 + 15 = 60
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[02.06]
Solve and graph the absolute value inequality: 12x + 4 > 8. (1 point)
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
-9-8-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4
5 6 7 8 9
-9-8-7-6-5-4-3 -2 -1 0 1 2 3 4 5 7 8 g
-9-8-7 -6 -5 -4 -3 -2 -1 0 1
2
3
4
5 6
7
8 9
given that
[tex]|2x+4|>8[/tex]consider the chances,
[tex]2x+4>8[/tex][tex]2x<4[/tex][tex]x<2[/tex][tex]-2x-4<8[/tex][tex]-2x<12[/tex][tex]x>-6[/tex]therefore x lies between -6 and 2
[tex]-6the answer is option 1.On a coordinate plane, a graph decreases between (2.5, 2) and (4.5, 0.25).
How does this graph change between (2.5, 2) and (4.5, 0.25)?
The graph of the coordinate plane is attached below.
Any point on a plane can be uniquely identified by a pair of numerical coordinates using a cartesian coordinate system, which employs signed distances between two fixed perpendicular oriented lines and the point measured in the same unit of length.
The intersection of the ordered pairs serves as the origin of each reference coordinate line, sometimes referred to as an axis of the system or simply an axis (plural axes) (0, 0).The locations of the perpendicular projections of the point onto the two axes, which are displayed as signed distances from the origin, can also be used to derive the coordinates.The graph of the line decreases between (2.5, 2) and (4.5, 0.25) and the graph increases between (2.5, 2) and (4.5, 0.25)
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How can I do point-slope form?through (-5, 3), slope= -8/5
ANSWER
y - 3 = -8/5 (x + 5)
EXPLANATION
The point-slope form of the equation of a line, that has a slope m and passes through point (x1, y1) is:
[tex]y-y_1=m(x-x_1)[/tex]In this problem m = -8/5 and the given point is (-5, 3). The equation is:
[tex]y-3=-\frac{8}{5}(x+5)[/tex]i have no clue how to do this someone pls help me
Using proportions, it is found that:
a) The graph for the distance-time journey is given at the end of the answer.
b) The average speed for the whole journey was of 25 miles per hour.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations such as multiplication or division from the rates of the variables.
Proportions are applied to find the relation between velocity, distance and time, as velocity is distance divided by time, that is:
v = d/t.
Then, applying cross multiplication, the distance is given by:
d = vt.
On the first interval of his trip, for the first 15 minutes = 1/4 of an hour, he traveled at a velocity of 40 mph, hence the distance is:
d = 40 x 1/4 = 10 miles.
During the second interval, of 25 minutes, from 15 minutes to 40 minutes, he stopped, hence his distance remained constant at 10 miles.
During the third interval, of 20 minutes = 1/3 of an hour, Tim completed the journey at a velocity of 45 mph, hence the complete distance is given by:
d = 10 + 45 x 1/3 = 10 + 15 = 25 miles.
The graph with these three intervals is given at the end of the answer.
He drove a distance of 25 miles in one hour, hence his average speed is given as follows:
v = d/t = 25/1 = 25 miles per hour.
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Write down the sequence then solve
the problem.
On Monday I had 1 cup of tea, Tuesday I had 3
cups, on Wednesday I have 6 cups and on
Thursday I have 11 cups.
How many cups of tea did I have on Sunday?
1,3
38
Answer:
48.
Step-by-step explanation:
The sequence is
1, 3, 6, 11,
The differences are 2, 3, 5, 8, 12, 17
2nd difference 1 2 3 4 5
So, the next difference is 5+3 = 8 (Friday) so on that day you had 11+8 = 19 cups.
The next 2 differences are 8+4 = 12 and 12 + 5 = 17.
Saturday you had 19+12 = 31.
Sunday you had 31 + 17 = 48.
many subjects don’t give honest answers to questions about activities that are illegal or sensitive in some other way. one study divided a large group of white adults into thirds at random. all were asked if they had ever used cocaine. the first group was interviewed by telephone: 21% said "yes." in the group visited at home by an interviewer, 25% said "yes." the final group was interviewed at home but answered the question on an anonymous form that they sealed in an envelope. of this group, 28% said they had used cocaine.
28% is the correct answer because it is the closest to true value sine people are sensitive about information like this.
Solve the question on the image attached.
Possible answers:
A) 1
B) 3
C) 5
Should be B.
There is a nested function structure. Let's first look at the limit of the interior (f(0)). The point we need to pay attention here is to look at the limits from the right and left. If both values are equal, we can say that it has a limit at that point.
If we express it algebraically;
[tex]lim_{x\to{0^-}}f(x)=lim_{x\to{0^+}}f(x)[/tex] then,[tex]lim_{x\to{0}}f(x)=exist[/tex]The left limit and the right limit of [tex]f(0)[/tex] are equal and equal to [tex]2.[/tex]
[tex]lim_{x\to{0^-}}f(x)=2[/tex][tex]lim_{x\to{0^+}}f(x)=2[/tex]The left limit and the right limit of f(2) are equal and equal to 3.
[tex]lim_{x\to{2^-}}f(x)=3[/tex][tex]lim_{x\to{2^+}}f(x)=3[/tex]As I have drawn with colored arrows in the graph below, we approach from the left and from the right, and if they both point to the same point, we can talk about the existence of the limit at that point. Otherwise, this function does not have a limit at that point.
Please help
:(
It’s due
Answer: 28
Step-by-step explanation: 28
A person randomly selects one of six envelopes Each envelope contains a check that the person gets to keep. Determine the person's expectation if three envelopes contain a 491 check and three envelopes contain a 51003 checkThe expected value is $(Simplify your anwwer Type an integer or a decimal)
The probability formula is given by:
[tex]\text{ P(E) =}\frac{\text{ N(Required outcome)}}{\text{ N(Total outcome)}}[/tex]The person selects one of six envelopes.
There is a probability that the person selects an envelope that contains a $491 of 3 envelopes OR an envelope that contains a $1003 check of 3 envelopes
[tex]\begin{gathered} \text{ P(select one containing \$491 check) =}\frac{3}{6}=\frac{1}{2} \\ \text{ P(select one containing \$1003 check) =}\frac{3}{6}=\frac{1}{2} \end{gathered}[/tex]Then, the expected value is given by
[tex]\begin{gathered} \text{ P(Expected Value) =(}\frac{1}{2}\times491)\text{ +(}\frac{1}{2}\times1003) \\ =245.5+501.5 \\ =747.0 \end{gathered}[/tex]
The point (-2, K) lies on the circle x^2 +y^2. Find the values of k. Show all the steps
Answer:
Should be 0
Step-by-step explanation:
Question
What is the value of m?
0.61m−1.51m=9
The value of m = -10, which we get by solving the given equation
The given equation is
0.61m - 1.51m = 9
⇒-0.9m = 9 (we get the minus sign because 0.61 is smaller than 1.51)
⇒-0.9m/(-0.9) = 9/(-0.9) (dividing both sides of the equation by -0.9)
⇒m = -90/9
⇒m = -10
Thus on solving the given equation we get the value of m as -10
That is m=-10
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(24÷ 3) x 4-(30 ÷ 3)
Answer:
22
Step-by-step explanation:
2 Simplity
A) x² - 2x /x² - 4
Answer:
x/x+2
Step-by-step explanation:
from numerator factor out an x to get x(x-2), in the denominator you can factor it because its a perfect square to get (x+2)(x-2)
cause there are no more add or subtract, you can cancel out x-2 to get x/x+2
Answer:
X³ -4x-2
--------------
x
write 70 1/3% as a fraction in simplest form.
How to get the answer is the main question for me. I got it wrong on the assignment.
The fraction 70 1/3% in simplest form is 24.67%.
Firstly converting mixed fraction to fraction. For conversion to fraction rewriting the fraction -
Fraction = (3×70 + 1)/3%
Then performing the multiplication in numerator of the fraction to find the fraction in simplest form
Fraction = (73 + 1)/3%
Performing addition in numerator of the fraction to find the fraction in simplest form
Fraction = 74/3 %
We have got the improper fraction as numerator is greater than denominator. Now performing division to find the fraction in simplest form
Fraction = 24.67%
Thus, the fraction in simplest form is 24.67%
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A bag contains 8 red marbles, 3 blue marbles, and 1 green marble. Find P(not blue).
a. 9
C.
1
4
b.
413
d.
314
Answer:
3/4
Step-by-step explanation:
Probability
8 red marbles, 3 blue marbles, and 1 green marble = 12 total marbles
8 red marbles+ 1 green marble = 9 not blue marbles
P ( not blue ) = not blue marbles / total marbles
= 9/12 = 3/4
Answer:
9
Step-by-step explanation:
8+3+1=12
12-3=9
umm ok i think i got it wrong or overcomplicated it lol
hope this helped
Find the value of x.
Round to the nearest tenth.
28 22 11
Please help!!
Step-by-step explanation:
your teacher gave you the law of sines already.
this was the only "trick" needed to solve this.
now, we just need to use it.
to be considered : a, b, c are always the sides opposite to the angles A, B, C.
so,
sin(28)/11 = sin(x)/22
sin(x) = 22×sin(28)/11 = 2×sin(28) = 0.938943126...
x = 69.87481894...° ≈ 69.9°
give me a multi step equation with an answer of -8
A multi step equation with an answer of -8 can be expressed as: 2x + 20 = 4.
x = -8 when solved.
What is a Multi Step Equation?A multi step equation can be an equation that has variables or/and terms on both sides, of which we can solve for the variable in the equation by isolating the variable to one side of the equation using inverse operations.
For example, a multi step equation can be expressed as 2x + 20 = 4.
Solve for x in the equation:
2x + 20 - 20 = 4 - 20 [subtraction property of equality]
2x = -16
2x/2 = -16/2 [division property of equality]
x = -8
Thus, 2x + 20 = 4 is a multi step equation that has a solution of -8.
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Please Help, Urgent and in detail
z = [tex]\frac{13}{20}+\frac{19}{20}i[/tex] is in the form z = a+ ib, where a = 13/20 and b = 19/20
Exact value of |z| = 1.151
Argument of z = 55.6197
Consider the complex number z = (2+7i)/(6+2i)
6a. Here z is in a rational form and we need to simplify it to represent it in the form a+ ib.
Multiplying and dividing the conjugate of the denominator to z, we get,
z = [tex]\frac{2+7i}{6+2i} \times \frac{6-2i}{6-2i}[/tex]
⇒ z = [tex]\frac{12 +38i +14}{6^2+2^2}[/tex]
⇒ z = [tex]\frac{26+38i}{40}[/tex]
⇒ z = [tex]\frac{13}{20}+\frac{19}{20}i[/tex]
is in the form z = a+ ib, where a = 13/20 and b = 19/20
6b.modulus of z = |z| = √(a²+b²)
= [tex]\sqrt{\frac{13^2}{20^2} +\frac{19^2}{20^2} }[/tex]
= [tex]\sqrt{\frac{530}{400}}[/tex]
= √(53/40)
= 1.151
6c. Argument of z = tan⁻¹(b/a)
= tan⁻¹((19/20)/(13/20))
= tan⁻¹(19/13)
= 55.6197
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Georgina has a total of $5000 invested in a savings account that receives 0.6% APY and a CD that receives 0.9% APY. How much does she have invested in each account if her total annual interest earned is $37.50?
The amount that Georgina has invested in savings account and CD are $ 2500 each.
Given that:-
Total amount invested in savings account and CD = $ 5000.
APY in savings account = 0.6 %
APY in CD = 0.9 %
Total interest earned = $ 37.5
Let the amount invested in savings account be x.
Hence, according to the data given in the question, we can write,
Amount invested in CD = 5000 - x
Interest in savings account in a year = x*(0.6)*1/100 = 0.006x
Interest in CD in a year = (5000-x)*(0.9)*1/100 = (0.009)(5000-x) = 45 - 0.009x
Hence,
0.006x + 45 - 0.009x = 37.5
45 - 37.5 = 0.009x-0.006x
7.5 = 0.003x
x = 7.5/(0.003)
x = 7500/3 = 2500
Hence, Georgina has invested $2500 in each savings account and CD.
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Betsie tried to solve an equation step by step. \qquad\begin{aligned} 3(a+7)&=-33\\\\ \\ a+7&=-11&\green{\text{Step } 1}\\\\ \\ a&=-4&\blue{\text{Step } 2}\\\\ \end{aligned} 3(a+7) a+7 a =−33 =−11 =−4 Step 1 Step 2 Find Betsie's mistake.
The mistake is at a + 7 = -11 ⇒ a = -18 and not -4.
Betsie made a mistake while solving the equation 3(a+7) = -33
We try to solve this equation step-by-step and will identify her mistake on the way.
3(a+7) = -33
Dividing by 3 on both sides,
⇒ (a+7) = -11
Subtracting 7 from both sides,
⇒ a = -11 -7
⇒ a = -18 is the solution.
Betsie made the mistake at the step where we have to subtract 7 from both sides. Instead of subtracting 7 from the right side, she added 7 on the next step.
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what is the simplified form for 3x -(2x-5)
Answer:
1x-5
Step-by-step explanation:
3x-(2x-5) Write equation
3x-2x-5 Open Parentheses
1x-5 Answer; This is how much it can be simplified.
A) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over times, x measured in seconds. During what interval(s) of the domain is the water balloon's height staying the same?
A.0 ≤ x ≤ 2
B.2 ≤ x ≤ 5
C.5 ≤ x ≤ 6
D.6 ≤ x ≤ 8
B) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. During what interval(s) of the domain is the water balloon's height increasing?
A.0 ≤ x ≤ 2
B.40 ≤ y ≤ 70
C.5 ≤ x ≤ 8
D.40 ≤ y ≤ 10
C) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. During what interval(s) of the domain is the water balloon's height decreasing the fastest?
A.5 ≤ x ≤ 9.5
B.8 ≤ x ≤ 9.5
C.6 ≤ x ≤ 8
D.5 ≤ x ≤ 6
D) The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds. Justify your answer from Part C.
A.5 ≤ x ≤ 9.5 is the interval where the balloon's height is decreasing.
B.8 ≤ x ≤ 9.5 is the interval where the slope is the steepest.
C.6 ≤ x ≤ 8 is the interval where the balloon's height decreases the most.
D.5 ≤ x ≤ 6 is the interval where the slope is the steepest.
Please help as fast as possible <3
As shown in the reference graph attached hereby with the question statement, if the linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time "x" measured in seconds, then,
(A) During (2 ≤ x ≤ 5) seconds in the time domain, the water balloon's height remains the same.
(B) During (0 ≤ x ≤ 2) seconds, the height of the water balloon is increasing.
(C) During (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.
(D) From Part (C), it can be justified that 5 ≤ x ≤ 9.5 is the interval where the balloon's height is decreasing, and, (5 ≤ x ≤ 6) is the interval where the slope is the steepest.
As per the question statement and the reference graph attached alongside, the linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time "x" measured in seconds.
We are required to determine the correct time domains for four different situations, by observing the plotted graph.
Part (A) is to determine the correct time domain where the water balloon's height remains the same.
From the graph, it is clear that, the height remains constant at (y = 70), parallel to the x-axis from the 2nd second to the 5th second. Hence, During (2 ≤ x ≤ 5) seconds in the time domain, the water balloon's height remains the same.
Part (B) is to determine the correct time domain where the height of the water balloon is increasing.
From the graph, it is clear that, the slope of the concerned graph rises only from [(y = 40) to (y = 70)], starring from the 0th second until the 2nd second. Hence, During (0 ≤ x ≤ 2) seconds in the time domain, , the height of the water balloon is increasing.
Part (C) is to determine the correct time domain where the height of the water balloon decreases the fastest.
From the graph, it is clear that, the graph decreases thrice, first from [(y = 70) to (y = 40)], starting at the 5th second uptil the 6th second, then from [(y = 40) to (y = 10)], starting at the 6th second uptil the 9th second and lastly, from [(y = 10) to (y = 0)], starting at the 9th second till the 9.5th second. Here, we can easily calculate that, the balloon dropped 30ft in 1 sec at the first instance, 30ft in 3 seconds at the second instance and, 10ft in 0.5 seconds.
Since, [(30/1) > (10/0.5) > (30/3)],
Or, [30 > 20 > 10],
Thus, During (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.
Part (D) is to determine the correct statement mentioned under it's options, with judgement based on Part (C).
Option (i) states that [(5 ≤ x ≤ 9.5) is the interval where the balloon's height is decreasing] which is true, as we can observe from the graph that the slope is decreasing during the time interval of 5 to 9.5th seconds, although at different rates at different intervals.
Option (ii) states that [(8 ≤ x ≤ 9.5) is the interval where the slope is the steepest] which means that, during this above said interval, the height of the balloon drops the fastest which is false, as we have already proved in part (C) that during (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the fastest.
Option (iii) states that, [(6 ≤ x ≤ 8) is the interval where the balloon's height decreases the most] which is false, as balloons height falls the farthest by 30fts in two separate intervals, between (5 ≤ x ≤ 6) seconds and (6 ≤ x ≤ 9) seconds.
Finally, Option (iv) states that [(5 ≤ x ≤ 6) is the interval where the slope is the steepest] which means that, during this above said interval, the height of the balloon drops the fastest which is true, as we have already proved in part (C) that during (5 ≤ x ≤ 6) seconds, the height of the water balloon decreases the maximum in the shortest time period.
Time Domain: Time domain refers to the analysis of mathematical functions, physical signals or time series of economic or environmental data, with respect to the time interval over which, the function occurs.To learn more about Time Domain, click on the link below.
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10. Find the zero of the function
Hint: put the equation into
standard form and then solve for x.
below(x-intercept).
f(x) = x - 8
A zero function is a constant function for which, regardless of the inputs, the output value is always zero.A zero function's input can be any real number, but its output is always zero, hence it can take any value from the real numbers
Solve the problem ?
A function that is almost entirely 0 is referred to as a zero function.The constant function with constant coefficients is also referred to as "the zero function." In general, finding the zeros of the function f(x) involves setting the function to zero.The zeroes of the function are the values of x that correspond to the set equation.Find the values of x where f(x) = 0 to determine a function's zeros. Any substitution for the variable in a function that results in a zero answer is known as the zero.The x-intercept(s) of the function's graph, or the actual zero of a function, is the location on a graph where the function's graph crosses the x-axis.The function f (x) = x - 8 has zeros.
To make f (x) = x - 8 = 0, find x.
Start by factoring f (x),
then f(x) =(x-8)=0
f (8 ) = 0
x = 8
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The formula for the area of the shaded region on the diagram is: Area of the circle - Area of the square The area of the circle is 78.1 cm² rounded to 1 decimal place. The area of the square is 21.4 cm² truncated to 1 decimal place. Write the error interval for the area, a, of the shaded region in the form m < a < n
The error interval for the area will be expressed as 64.2< a < 63.93
Error intervals may be defined as the limits of accuracy when a number has been rounded or truncated. They are the range of possible values that a number could have been before it was rounded or truncated. According to the question, Area of circle = 78.1 cm² and Area of square = 21.4 cm². If we round the area to one decimal point, we get the Area of circle = 78.1 + 0.05 and = 78.1 - 0.05 that is 78.15 and 78.05. Also, the Area of square = 21.4 - 0.05 and = 21.4 + 0.05 we get 21.35 and 21.45. Now, Area of shaded region in the form m < a < n. So, n = 78.15 - 21.35
=> n= 56.8 and
m = 78.05 - 21.45
=> m = 56.6
Area of shaded region is 56.6< a < 56.8.
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Swimming pool on a certain hot summer day, 606 people used the public swimming pool the daily prices are $1.75 for children and $2.50 for adults the receipts for admission totaled $1357.50. How many children and how many adults swam at the public pool that day
On a hot summer day, 606 people used the public swimming pool; daily admission prices are $1.75 for children and $2.50 for adults; admission receipts totaled $1357.50; 396 adults and 210 children swam at the public pool that day.
What is permutations and combination?A set's subsets can be created in two ways: combination and permutation. When the subset's components are combined, they can be listed in any order.The subset's components are listed in a permutation in a specific order. Permutations include the arrangement of people, digits, numbers, alphabets, letters, and colors. Choosing the menu, cuisine, clothes, subjects, and team are all examples of combinations.When creating permutations, we use the notation nPr, where n represents the number of available options, P represents the permutation, and r represents the number of options you are selecting.To calculate the permutation, use the formula nPr = n! / (n - r)!Therefore,
1.75C + 2.50A = 1357.50
C + A = 606
C = 606-A
1.75(606 - A) + 2.50A = 1357.5
1060.5 - 1.75A + 2.50A = 1357.5
1060.5 + 0.75 A = 1357.5
0.75 A = 297
A = 297/0.75
A = 396
No of adults = 396
Therefore children = 606-396
No of children = 210
396 adults and 210 children swam at the public pool that day
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A material’s density is a measure of its mass per unit volume. In other words, D = M
V
. Use
this relationship to calculate the density of a shiny metal object whose mass was 200 g,
and whose volume was measured to equal 10.4 mL. Round answer to 1 d.p.
The density of the material of mass 200 g and volume 10.4 ml is 19.2 g/ml.
According to the question,
We have the following information:
Density is defined as the mass per unit volume.
So, we have the formula of density:
Density = Mass/volume
Mass of the metal object = 200 g
Volume of the metal object = 10.4 ml
Density = 200/10.4 g/ml
Density = 19.231 g/ml
Now, we will round it off to nearest 1 decimal point.
We know that when the digit is greater than 5 then the number is increased by 1 and when the digit is less than 5 then the number remains same.
So, we have:
Density = 19.2 g/ml
Hence, the density of the metal object is 19.2 g/ml.
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What is the slope of the line that passes through the points (-8, -6)(−8,−6) and (-8, 4)(−8,4)? Write your answer in simplest form.
er 10 ft long rests against a vertical wall. if the bottom of the ladder slides away from the wall at a rate of 0.5 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall?
The angle between the ladder and the ground changes when the bottom of the ladder is 8 ft from the wall is -1/12 radians per second.
Denoting the distance in feet between the wall and the base of the ladder by x and the angle in radians between the ladder and the ground by y, it is noted;
cos(y) = x/10
which implies;
y = arccos(x/10)
Denoting time in seconds by t, it is further noted that;
[tex]\frac{dx}{dy} = \frac{dy}{dx} \frac{dx}{dt}[/tex] (chain rule)
Noting (using a standard table of derivatives for convenience)
[tex]\frac{dy}{dx}= -\frac{1}{\sqrt{1-(0.1x)^2} }(0.1)[/tex] (also by chain rule)
The above equation changes as;
[tex]\frac{dy}{dx}= -\frac{0.1}{\sqrt{1-0.1x^2} }[/tex]
It is noted from the question that in this particular system;
[tex]\frac{dx}{dt} = 0.5[/tex] feet per second
So (denoting the derivative as a function of x)
[tex]\frac{dy}{dt}(x)=\frac{dy}{dx} \frac{dx}{dt} = - \frac{0.05}{\sqrt{1-0.01x^2} }[/tex]
At last;
[tex]\frac{dy}{dt}(8)=\frac{dy}{dx} \frac{dx}{dt} = - \frac{0.05}{\sqrt{1-0.01(64)} }[/tex]
= [tex]\frac{0.05}{\sqrt{1-0.64} }[/tex]
= [tex]\frac{-0.05}{\sqrt{0.36} }[/tex]
= -5/60
= -1/12 radians per second
The angle between the ladder and the ground changes when the bottom of the ladder is 8 ft from the wall is -1/12 radians per second.
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