If varies inversely as . It is known that = 10 when = 3, find the value of when = 5.
Answers
Answer:
y = 6
Step-by-step explanation:
If x varies inversely proportional as y.
\(x=\dfrac{k}{y}\), k is constant of proportionality
or
k = xy
When x = 3 and y = 10
k = 3×10
k = 30
Put x = 5,
\(y=\dfrac{k}{x}\\\\y=\dfrac{30}{5}\\\\y=6\)
So, the value of y is 6 when x is 5.
Related Questions
The length of 7 (the minor arc) is 15 cm. What is the circumference of Z?
Answers
Answer:450 cm
Step-by-step explanation:
What do you put on the X axis of an ogive?
Answers
The X-axis (horizontal axis) often represents a "class boundaries" of such an ogive, whereas the Y-axis (vertical axis) typically shows the frequency count.
Explain about the ogive graph?A sort of frequency polygon that displays cumulative frequencies is an ogive, often known as a cumulative frequency polygon.
In other words, the graph adds the cumulative percents from left to right.On an ogive graph, "class boundaries" are shown along the x-axis while cumulative frequency is shown on the y-axis. Comparable to a histogram, an ogive features a single point that indicates in which the top right corner of the rectangular would be located in place of rectangles. This type of graph is typically simpler to make from such a frequency table.Thus, The X-axis (horizontal axis) often represents a class boundaries being measured of such an ogive.
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Find the angles a,b,c and d
Answers
a=180-79=101
c=180-83=97
a+c+d+b=360
101+97+2x=360
198+2x=360
2x=360-198=162
X=162/2=81
a=101
b=97
b and d=81
find the area of shaded regions below. give your answer as a completely simplified exact values in terms of pi
Answers
The area of the shaded region in the figure in terms of pi is
81 - 20.25π m²How to find the area of the shaded portionThe shaded portion is a portion of a squared which has two semi circles of diameter equal to the side of the square.
The area of the two semi circle will be subtracted from the area of the square to give the area of the shaded region
Area of a square is solved by the formula
= length * width
= 9 * 9 = 81 m²
Area of the two semi circle
= 0.5πr² * 2
= πr²
and r = 9/2 = 4.5
= 20.25π m²
area of shaded portion
= 81 - 20.25π m²
The area of the shaded region in terms of pi is (81 - 20.25π) m²
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V=IR
In an experiment I and R are both measured correct to 1 decimal place.
When I= 4.0 and R=2.7, find the lower bound for V.
Answers
Answer:
10.75
Step-by-step explanation:
4.0×2.7=10.8
lower bound of 10.8 is 10.75
Question 37 1 pts Which of the following is a solution to the differential equation: t². d^2y/dt^2 - 6t dy,dt + 12 = 0
a.y=t² + 1 b.y=t³+2t^4
c.no solution d.y = t-1 Question 38 1 pts Newton's law of cooliing states that the rate of change of the temperature T of an object is proportional to the temperature difference between the temperature S of the surroundings and the temperature T. Write down the differential equation. A cup of tea is prepared from boiling water at 100 degrees and cools to 50 degrees in 3 minutes. The temperature in the room is 20 degrees. What will the tea temperature be after a very long time? a.dT/dt=k(S-T); T≈ 20 degrees after a very long time b.dt/dT =k(ST); T≈ 30 degrees after a very long time c.dt/dT =K(S-T); T≈ 0 degrees after a very long time d.dt/dT = K (S+T); T≈ 30 degrees after a very long time
Answers
Question 37: The following is a solution to the differential equation y = t - 1. d.
Question 38: The tea temperature be after a very long time is dT/dt = k(S - T); T ≈ 20 degrees after a very long time. a.
To determine the solution to the given differential equation: t²(d²y/dt²) - 6t(dy/dt) + 12 = 0, we can solve the equation by assuming a solution in the form of y = tⁿ, where n is a constant.
By differentiating y with respect to t, we can substitute the derivatives into the differential equation to determine the value of n.
Let's differentiate y = tⁿ with respect to t:
dy/dt = n × tⁿ⁻¹
d²y/dt² = n(n-1) × tⁿ⁻²
Substituting these derivatives into the differential equation:
t²(n(n-1)tⁿ⁻²) - 6t(ntⁿ⁻¹) + 12 = 0
Simplifying the equation:
n(n-1)tⁿ - 6ntⁿ + 12 = 0
n(n-1)tⁿ - 6ntⁿ = -12
Since this equation must hold for all values of t, the coefficients of the tⁿ terms on both sides of the equation must be equal.
We can equate the coefficients:
n(n-1) = 0
n = 0 or n = 1
The general solution to the differential equation is y = c₁ + c₂ × t, where c₁ and c₂ are constants.
According to Newton's law of cooling, the rate of change of the temperature T of an object is proportional to the temperature difference between the object's temperature T and the surroundings' temperature S.
We can write the differential equation as follows:
dT/dt = k(S - T)
dT/dt represents the rate of change of temperature, k is the proportionality constant, and (S - T) represents the temperature difference between the object and the surroundings.
The cup of tea starts at 100 degrees and cools to 50 degrees in 3 minutes, with the room temperature at 20 degrees.
We can assume that the temperature of the tea will tend toward the room temperature as time goes to infinity.
This option correctly represents that as time goes to infinity, the temperature T of the tea will approach the temperature S of the surroundings, which is approximately 20 degrees.
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Solve forx.
(-2+4)
11
1
18
-18
2
9
3
-9
Answers
Answer:
2
Step-by-step explanation:
come on man if you are in -2 dollar debt and someone gives you 4 more dollars you now have 2 dollars
Find the angle between the following two vectors.
< 8, 3 > and < 4, −3 >
Answers
The angle between the two vectors < 8, 3 > and < 4, −3 > is 57.43°
How to determine the angle between the following two vectors?Given: vectors < 8, 3 > and < 4, −3 >
To find the angle between two vectors, we can use the dot product method:
First, you will compute the dot product and magnitudes of both vectors. Thus,
Let a = < 8, 3 > and b = < 4, −3 >
a · b = <8, 3> ·<4, -3> = 8(4) + (3)(-3) = 32-9 = 23
|a| = √(8² + 3²) = √(64+9) = √73
|b| = √(4² + (-3)²) = √(16 + 9) = √25 = 5
By using the angle between two vectors formula using dot product,
θ = cos⁻¹ [ (a · b) / (|a| |b|) ]
θ = cos⁻¹ (23 / √73 · 5)
θ = cos⁻¹ (23/42.72) = 57.43°
Therefore, the angle between the following two vectors is 57.43°
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the box in the center of a boxplot marks: group of answer choices the range covered by the middle half of the data. the full range covered by the data. the range covered by the middle three-quarters of the data. the span of one standard deviation on each side of the mean.
Answers
The box in the center of a boxplot marks the range covered by the middle half of the data.
Specifically, it represents the interquartile range (IQR), which is the range between the first quartile (Q1) and the third quartile (Q3) of the data. The box covers the middle 50% of the data, with the median (or second quartile, Q2) represented by a horizontal line within the box.
The whiskers of the boxplot extend to the minimum and maximum values within 1.5 times the IQR from the nearest quartile. Any values outside of this range are plotted as individual points, or outliers.
What is data?
Data refers to any collection of facts, figures, or information that can be processed or analyzed to gain insights or knowledge. Data can take many forms, including numerical, categorical, textual, or multimedia.
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What initial investment must be made to accumulate $120000 in 12 years if the money is invested in a mutual fund that pays 14%annual interest, compounded monthly? Use the analytical solution to find the answer.
Answers
What initial investment must be made to accumulate $120000 in 12 years if the money is invested in a mutual fund that pays 14%
annual interest, compounded monthly?
Remember that
The compound interest formula is equal to
\(A=P(1+\frac{r}{n})^{nt}\)where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
A=$120,000
t=12 years
r=14%=14/100=0.14
n=12
substitute in the given formula
\(120,000=P(1+\frac{0.14}{12})^{12\cdot12}\)Solve for P
P=$22,583.42The height after t seconds of an object projected upward with an initial velocity of 48 feet per second from a 210-foot tower can be modeled by h=−16t^2 + 48t +210. The height of a neighboring 50-foot tall building is modeled by the equation h=50. The time (t) when the object will be at the same height as the building is found to be t = –2 and t = 5. Which statement BEST describes the validity of these solutions? A. Neither solution is valid since time values cannot be squared. B. The solution t = – 2 is the only solution since 5 seconds is an unreasonable amount of time for the object to reach a height of 50 feet. C. The solution t = 5 is the only valid solution to this system since time cannot be negative. D. Both are valid solutions to this system since both values make the equation h=−16t^2+ 48t + 210 true.
Answers
Given:
The height h of an object after t seconds is
\(h=-16t^2+48t+210\)
The height of a neighboring 50-foot tall building is modeled by the equation h=50.
The time (t) when the object will be at the same height as the building is found to be t = –2 and t = 5.
To find:
The statement which describes the validity of these solutions.
Solution:
We have,
\(h=-16t^2+48t+210\)
Here, t is the time in seconds.
For t=-2,
\(h=-16(2)^2+48(-2)+210\)
\(h=-64-96+210\)
\(h=50\)
For t=5,
\(h=-16(5)^2+48(5)+210\)
\(h=-400+240+210\)
\(h=50\)
So, the value of h is 50 at t=-2 and t=5.
We know that time is always positive so it cannot be negative value. It means t=-2 is not possible.
The solution t = 5 is the only valid solution to this system since time cannot be negative.
Therefore, the correct option is C.
Write the equation of the line that has a slope of 1/3 and passes through the point (6,8).
Answers
We are asked to determine the equation of a line with a slope 1/3. The general form of a line equation is:
\(y=mx+b\)Where "m" is the slope and "b" the y-intercept.
Now, we substitute the value of the slope:
\(y=\frac{1}{3}x+b\)Now, to determine the value of "b" we will use the fact that the line passes through the point (x, y) = (
6, 8). Now, we plug in these values in the equation:
\(8=\frac{1}{3}(6)+b\)Solving the product on the right side we get:
\(8=2+b\)Now, we subtract 2 from both sides:
\(\begin{gathered} 8-2=2-2+b \\ 6=b \end{gathered}\)Now, we substitute the value in the equation of the line:
\(y=\frac{1}{3}x+6\)And thus we get the equation of the line.
Plane H is shown. Plane H contains four points. Points A, C, and D form a diagonal line on the left. Point B is to the right of point C. Which points are coplanar and noncollinear? points A and D points C and D points A, C, and D points A, B, and D
Answers
Answer:
d
Step-by-step explanation:
edg 2021
Answer:
d
Step-by-step explanation:
the total weight of 3 puppies is 2 pounds 4 ounces. how much does puppy weight in ounces. convert to ounces
Answers
Answer:
60 ounces
Step-by-step explanation:
there are 16 ounces in a pound plus the extra 4 ounces times 3 is 60 ounces in total
ANSWER QUICKlY ASAP!!!!
Answers
Answer:
\( \sqrt{9 } = 3 \)
is the line through points P(-3,-2) and Q(2,3) perpendicular to the line through points R(10,-1) and S(15,-6)
Answers
Answer:
hope this helps you
We want to see if the two given lines are perpendicular or not.
We will see that yes, the lines are perpendicular.
First, let's define a general linear equation, it is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
Two lines are perpendicular if the slope of one is equal to the inverse of the opposite of the slope of the other.
Also, if a line passes through two points (x₁, y₁) and (x₂, y₂) then the slope of the line is given as:
\(a = \frac{y_2 - y_1}{x_2 - x_1}\)
So we can get the slopes of the two given lines, for line PQ we have:
\(a = \frac{3 - (-2)}{2 - (-3)} = 1\)
For line RS we have:
\(a = \frac{-6 - (-1)}{15 - 10} = -1 = -(1/1)\)
So you can see that the slope of line RS is equal to the inverse of the opposite of line PQ.
Then yes, the lines are perpendicular.
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When solving two-step equations, you are using the reverse order of operations to solve the two-step equations.
Select one:
True
False
Answers
Therefore , the solution of the given problem of equation comes out to be False.
What is an equation?In order to demonstrate consistency between two opposing statements, variable words are frequently used in sophisticated algorithms. Equations are academic phrases that are used to demonstrate the equality of different academic figures. Consider expression the details as y + 7 offers. In this case, elevating produces b + 7 when partnered with building y + 7.
Here,
False.
The order of operations we use to solve two-step equations is the same order we use to solve every other mathematical statement,
which is commonly recalled by the acronym PEMDAS. (parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right).
The fundamental distinction is that we are carrying out the operations against the equation's representation. For instance, consider the following equation:
=> 2x + 5 = 11
To get the following result, we would first subtract 5 from both sides, then divide by 2.
=> x = 3
In order to "undo" the operations that were carried out on the variable in the original equation, we are utilising the same series of operations as usual, but in reverse order.
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Please answer ASAP! A function graphed f(x) is graphed on the coordinate plane. What is the function rule in slope-intercept form? Enter your answer in the box.
Answers
Write each fraction as a mixed number.
3 4/9
43/9
32/5
Answers
The value of the fractions in the mixed fraction form is 3(⁷/₉), 4(⁷/₉), and 6(²/₅) respectively.
What is a mixed fraction?A mixed fraction is a fraction that is created by fusing a fraction with a whole number. The fraction is defined as the division of the whole part into an equal number of parts.
The given fractions 34/9, 43/9, and 32/5 can be written in the form of the mixed fraction as below:-
To write the fractions in the form of the mixed fraction first divide the fraction by the complete number and put the remainder on the numerator.
34/9 = 3(⁷/₉)
43/9 = 4(⁷/₉)
32/5 = 6(²/₅)
Therefore, the value of the fractions in the mixed fraction form is 3(⁷/₉), 4(⁷/₉), and 6(²/₅) respectively.
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All Things Algebra), 2013
After falling 17°, the
temperature of the lake
is now 24. What was the
starting temperature?(Write an equation to represent the problem)
Answers
Answer:
43°
x-17=24
Step-by-step explanation:
the tempertaure fell 17° and now its 24° so to get there you would have to subtract
x-17°=24°
43°
y = 7-x when x = -1
Thank you so much !!
Answers
Answer:
Y = 8
Step-by-step explanation:
7- -1 is 8. If you're subtracting a negative, you're basically adding.
So 7+1 is 8.
The yearbook staff receive 75 submissions for yearbook articles. Paul will accept 2/5
of all submissions. Currently, Paul plans for the yearbook to have 156 pages.
How many more pages will Paul need to add to the yearbook to have 2 articles on every 13 pages? Show your work and explain your thinking.
Answers
Answer:
2/5 of 75 is 30 thats all i have for because i am haveing trouble with the same question
Step-by-step explanation:
3. Judy took a taxi. The meter said $45. She tips the driver 15%. How much money does the the driver get in tips?
Answers
Answer:
6.75$
Step-by-step explanation:
because 15% of 45$ is 6.75$
Leon has a piece of cheese shaped like a triangular prism that he needs to wrap in plastic wrap. a triangular prism. the triangular base has a base of 4 inches and height of 3 inches. the height of the prism is 7 inches. what is the minimum amount of plastic wrap that he needs to cover the entire piece of cheese? 42 inches squared 84 inches squared 96 inches squared 108 inches squared
Answers
The minimum amount of plastic wrap needed to cover the entire piece of cheese is : 84 squared inches.
What is a triangular prism?A triangular prism is a solid geometrical shape made of three rectangles and two triangles.
Analysis:
base of triangle = 4 inches, height of triangle = 3 inches, length of rectangles = 7 inches
Total surface area of the triangular prism = area of two triangles + plus area of two slant rectangles + area of 1 straight face rectangle.
for the slant rectangle, the width of the rectangle, half the base of the triangle and the height of triangle form right- angled triangle using Pythagoras to solve for the width of the rectangle we have
\(l^{2}\) = \(2^{2}\) + \(3^{2}\)
l = \(\sqrt{13}\) = 3.6
Total surface area = 2(1/2bh) + 2(l x b) + L x B
= 2 ( 1/2 x 2 x 3) + 2( 7 x 3.6) + 7 x 4 = 84.4 = 84 squared inches.
in conclusion, the amount of plastic needed is 84 inches squared.
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What is 859 divided by 3 with remainder
Answers
Answer:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
So all you have to do is use long division because a calculator won't help you with this if you are looking for a remainder so basically you just divide then you will get...
\(\frac{859}{3}=?\\?=286 R: 1\)
So the answer is 286 and a remainder of 1.
The result of the division problem ; with the quotient and remainder respectively are 286 and 1
Numerator = 859Denominator = 3__ 286 ______quotient
______
3 | 859
__6
-
__259
__24
-___19
-___18
____1 ________ remainder
Therefore, the quotient and remainder of the divison expression are 286 and 1
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In the diagram below, determine the value of x:
Answers
9514 1404 393
Answer:
55°
Step-by-step explanation:
130° is an external angle to the small triangle at lower left, so is the sum of the remote interior angles. The unmarked interior angle at the bottom of that triangle is then 130° -30 = 100°.
That is an exterior angle of the large triangle that has remote interior angles of 45° and x°. So, ...
x° + 45° = 100°
x° = 100° -45°
x° = 55°
_____
Alternate solution
The sum of the interior angles of a quadrilateral is 360°. Three of the angles in the bounding quadrilateral are x°, 45°, 30°. The fourth is the reflex angle that is (360° -130°) = 230°. So, we have ...
x° +45° +230° +30° = 360° . . . . . angles CCW from lower right
x° = 360° -305°
x° = 55°
Can you please help me
Answers
Answer:
complementary angle: 63
supplementary angle: 153
Step-by-step explanation:
Complementary angles mean angles that add up to 90. Therefore 90-27=63
Supplementary angles are angles that add up to 180. Therefore 180-27=153
Tim celebrated his dental school acceptance by completing the seven days trek to Machu Pichu (Day 7: Aguas Calientes elevation 2,430 m). Tim is in good physical condition. He runs 3-5 miles per day, weight trains, and plays midfield in the local soccer club. (Review pages 527-the top of 531 in Guyton and Hall).
Answers
Tim, who is in good physical condition and engages in regular exercise, celebrated his dental school acceptance by completing a seven-day trek to Machu Picchu, reaching an elevation of 2,430 meters in Aguas Calientes.
According to the information provided, Tim maintains a good level of physical fitness through various activities such as running 3-5 miles per day, weight training, and participating in soccer as a midfielder. These activities contribute to his cardiovascular endurance, muscular strength, and overall physical well-being.
To celebrate his dental school acceptance, Tim embarked on a challenging adventure: a seven-day trek to Machu Picchu. Machu Picchu is located in Peru and is known for its breathtaking landscapes and high elevation. Tim successfully completed the trek, reaching an elevation of 2,430 meters in Aguas Calientes.
Tim's dedication to regular exercise, including running, weight training, and playing soccer, likely played a significant role in his ability to complete the physically demanding trek. His cardiovascular fitness from running, muscular strength from weight training, and agility and endurance from playing soccer all contribute to his overall physical condition. These factors, combined with his determination and good health, allowed him to accomplish the challenging feat of completing the seven-day trek to Machu Picchu.
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Please help. I will give brainliest. thank you. math isn't my strong suit lol.
Answers
Answer:
b) 1
Step-by-step explanation:
First, bring the -3 to the right side.
x²+4x + 4
now use b²-4ac.
4²-4(1)(4)
16-16
0
If discriminant < 0 there are 2 imaginary solutions
if discriminant > 0 there are 2 real solutions
if discriminant = 0 there is 1 real solution
The discriminant here is 0 so it has one real solution
A tank of water in the shape of a cone is being filled with water at a rate of 12 m/sec. The base radius of the tank is 26 meters, and the height of the tank is 18 meters. At what rate is the depth of
Answers
The depth of the water in the cone-shaped tank is increasing at a rate of approximately 1.385 meters per second.
To determine the rate at which the depth of the water is changing, we can use related rates. Let's denote the depth of the water as h(t), where t represents time. We are given that dh/dt (the rate of change of h with respect to time) is 12 m/sec, and we want to find dh/dt when h = 18 meters.
To solve this problem, we can use the volume formula for a cone, which is V = (1/3)πr^2h, where r is the base radius and h is the depth of the water. We can differentiate this equation with respect to time t, keeping in mind that r is a constant (since the base radius does not change).
By differentiating the volume formula with respect to t, we get dV/dt = (1/3)πr^2(dh/dt). Now we can substitute the given values: dV/dt = 12 m/sec, r = 26 meters, and h = 18 meters.
Solving for dh/dt, we have (1/3)π(26^2) (dh/dt) = 12 m/sec. Rearranging this equation and solving for dh/dt, we find that dh/dt is approximately 1.385 meters per second. Therefore, the depth of the water in the tank is increasing at a rate of about 1.385 meters per second.
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