The vehicle travels 110 feet distance in 1 second duration.
What is mean by mph?mph expresses the speed or velocity in miles per hour. Speed means rate of change of distance with respect to time.
speed = distance/time
hence, distance = speed x time
the above equation is the relationship between distance, speed and time
How can we calculate distance in feet?we will use the above equation and convert miles to feet and second to hour.
given, speed of vehicle = 75 mph
time = 1 second =1/3600 hour as 1 hour = 3600 second
distance travel by vehicle = speed x time
= 75 mph x 1/3600 hour
distance = 0.020833333 miles
we know, 1 mile =5280 feet
distance in feet = 110 feet
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The semicircular disk having a mass of 10 kg is rotating at ω = 4 r a d / s \omega = 4 rad/s ω=4rad/s at the instant θ = 60 ° \theta = 60° θ=60°.
The f< [tex]f_{max}[/tex] the semicircular disk does not slip at the given instant.
The semicircular disk having a mass of 10 kg.
ω = 4 rad/s, θ = 60 °
First we have to draw the free body diagram,
Calculate the distance AG.
[tex]$$\begin{aligned}A G & =\sqrt{O G^2+O A^2-2 \times O G \times O A \times \cos \theta} \\& =\sqrt{\left(\frac{4 \times 0.4}{3 \pi}\right)^2+0.4^2-2 \times \frac{4 \times 0.4}{3 \pi} \times 0.4 \times \cos 60^{\circ}} \\\end{aligned}$$[/tex]
=0.3477 m.
Calculate the angle ∝.
[tex]$$\begin{aligned}& \frac{\sin \alpha}{O G}=\frac{\sin 60^{\circ}}{0.3477} \\& \alpha=25.01^{\circ}\end{aligned}$$[/tex]
Calculate the normal acceleration at A.
[tex]$$\begin{aligned}a_{A, y} & =\omega^2\left(r_{A O}\right) \\& =4^2 \times 0.4 \\& =6.4 \mathrm{~m} / \mathrm{s}^2\end{aligned}$$[/tex]
Calculate the acceleration at G.
[tex]& \mathbf{a}_G=\mathbf{a}_A+\boldsymbol{\alpha} \times r_{G / A}-\omega^2\left(\mathbf{r}_{G / A}\right) \\[/tex]
[tex]& -a_{G, x} \mathbf{i}-a_{G, y} \mathbf{j}=\left\{\begin{array}{l}a_{A, x} \mathbf{i}+a_{A,} \mathbf{j}+\alpha \mathbf{k} \times A G(-\sin \alpha \mathbf{i}+\cos \alpha \mathbf{j}) \\-\omega^2[A G(-\sin \alpha \mathbf{i}+\cos \alpha \mathbf{j})]\end{array}\right\} \\[/tex]
[tex]& -a_{G, x} \mathbf{i}-a_{G, y} \mathbf{j}=\left\{\begin{array}{l}0+6.4 \mathbf{j}+\alpha \mathbf{k} \times 0.3477(-\sin 25.01 \mathbf{i}+\cos 25.01 \mathbf{j}) \\-4^2[0.3477(-\sin 25.01 \mathbf{i}+\cos 25.01 \mathbf{j})]\end{array}\right\} \\[/tex]
[tex]& -a_{G, x} \mathbf{i}-a_{G, y} \mathbf{j}=(0.3151 \alpha-2.352) \mathbf{i}+(0.147 \alpha-1.3584) \mathbf{j}\end{aligned}$$[/tex]
Equate i coefficient:
[tex]-a_{G, x}=0.3151 \alpha-2.352[/tex][tex]-a_{G, x}=0.3151 \alpha-2.352[/tex]
Equate j coefficient:
[tex]$$-a_{G, y}=0.147 \alpha-1.3584$$[/tex]
The free body diagram and the kinematic diagram of the semicircular disk is as follows:
Calculate the mass moment of inertia of the semicircular disk about point O.
[tex]$$\begin{aligned}I_0 & =\frac{1}{2}\left(\frac{1}{2} m r^2\right) \\& =\frac{1}{2}\left(\frac{1}{2} \times 10 \times 0.4^2\right) \\& =0.4 \mathrm{~kg} \cdot \mathrm{m}^2\end{aligned}$$[/tex]
Calculate the mass moment of inertia of the semicircular disk about point G.
[tex]$$\begin{aligned}I_G & =I_0-m(O G)^2 \\& =0.4-10\left(\frac{4 \times 0.4}{3 \pi}\right)^2 \\& =0.1118 \mathrm{~kg} \cdot \mathrm{m}^2\end{aligned}$$\\[/tex]
Consider moment equilibrium condition about point A.
[tex]$$\begin{aligned}& \sum M_A=I_G \alpha+\sum m a_G d \\& m g(A G \sin \beta)=I_G \alpha+m a_{G, x}(A G \cos \beta)+m a_{G, y}(A G \sin \beta) \\& 10 \times 9.81\left(0.3477 \times \sin 25.01^{\circ}\right)=\left\{\begin{array}{l}0.1118 \alpha+10 a_{G, x}\left(0.3477 \cos 25.01^{\circ}\right) \\+10 a_{G, y}\left(0.3477 \sin 25.01^{\circ}\right)\end{array}\right\} \\& 0.118 \alpha+3.151 a_{G, x}+1.47 a_{G, y}=14.42\end{aligned}$$[/tex]
Solve the equations (1), (2), and (3), the values obtained are as follows:
[tex]$$\begin{aligned}& \alpha=18.04 \mathrm{rad} / \mathrm{s}^2 \\& a_{G, x}=3.333 \mathrm{~m} / \mathrm{s}^2 \\& a_{G, y}=1.294 \mathrm{~m} / \mathrm{s}^2\end{aligned}$$[/tex]
Consider the force equilibrium along the horizontal direction:
[tex]$$\begin{aligned}& \sum F_x=m a_{G, x} \\& f=m a_{G, x} \\& f=10 \times 3.33\end{aligned}$$[/tex]
f=33.33 N.
Consider the force equilibrium along the vertical direction:
[tex]$$\begin{aligned}& \sum F_y=m a_{G, y} \\& m g-N=m a_{G, y} \\& (10 \times 9.81)-N=10 \times 1.294 \\& N=85.16 \mathrm{~N}\end{aligned}$$[/tex]
Calculate the maximum frictional force at point A.
[tex]$$\begin{aligned}f_{\max } & =\mu_s N \\& =0.5 \times 85.16 \\f_{\max } & =42.58 \mathrm{~N}\end{aligned}$$[/tex]
Since, f< [tex]f_{max}[/tex]the semicircular disk does not slip at the given instant.
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The temperature at 4pm is 43 degrees. Throughout the night it steadily falls 6 degrees.
What is the rate of change in this situation?
Answer:
The rate of change in this situation is 6 degrees per hour.
Step-by-step explanation:
The rate of change in this situation is -6 degrees per hour. To find this, we need to divide the change in temperature by the amount of time over which the change occurs. In this case, the temperature falls from 43 degrees to 43-6=<<43-6=37>>37 degrees, so the change in temperature is 43-37=<<43-37=6>>6 degrees. Since the temperature falls over the course of one night, the rate of change is 6 degrees / 1 night = -6 degrees per hour.
A football field is 150 meters long. Karl takes 30 seconds to run the entire length. How fast was Karl running?
Answer:
5 m/s
Step-by-step explanation:
Divide the distance by Karl's time to find the rate at which Karl was running:
150/30 = 5 meters per second
A, B and C are interior angles of a triangle ABC. Show that
(i) sin (B+C/2) = cos (A/2)
(ii) if angle A= 90°, then find the value of tan (B+C/2)
Answer:
ok i can do it if u want then see my m.s.g
The required solutions to the given triangle ABC below as:
(i) sin (B+C/2) = cos (A/2)
(ii) if angle A= 90°, then the value of tan (B+C/2) is is undefined.
What are Interior Angles?Interior angles are defined as the pair of angles created on the inner side of the parallel lines and on the opposite sides of the transversal when two parallel lines are intersected by a transversal are referred to as alternate internal angles.
Given that A, B, and C are interior angles of a triangle ABC.
To solve the question, we would consider trigonometric ratios of complementary angles.
sin (90° - θ) = cosθ
We know that for ΔABC,
∠A + ∠B + ∠C = 180° (Angle sum property of triangle)
∠B + ∠C = 180° - ∠A
On dividing both sides by 2, we get,
(∠B + ∠C)/2 = (180° - ∠A)/2
(∠B + ∠C)/2 = 90° - ∠A/2
Applying sine angles on both sides:
sin {(∠B + ∠C)/2} = sin (90° - ∠A/2)
Since, sin (90° - θ) = cos θ, we get
sin (∠B + ∠C)/2 = cos A/2
(ii) if angle A= 90°, then find the value of tan (B+C/2)
If cos A/2 = 0 so ∠A = 90°
sin (∠B + ∠C)/2 = cos A/2 = 0
tan (B+C/2) = ∞
Thus, the value of tan (B+C/2) is undefined.
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Several friends bought flowers to make table centerpieces. Write the ratios of purple flowers to white flowers for each friend.
The ratio of purple flower to white flowers is 1:1 for each friend.
What do we mean by centerpiece?A system of arrangement where objects are set at the center position.
In another words the piece that kept in the center position.
As example, for the purpose of decorating a table with flowers, we need to keep the flowers in such a way that all the flowers occupy the center position.
Which ratio that we need to maintain while decorating a table as a centerpiece?If we want to display a table as centerpieces with white and purple flowers, we must keep the two flowers in the same ratio to look the display more attractive.
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suppose the probability of finding a prize in your cereal box is 0.990.99. what are the odds of finding a prize? express your answer in the form a:ba:b.
If you assume that there is a 0.990.99 percent chance that you will find a prize in the cereal box, the odds are 99:1.
In mathematics, what does fundamental probability mean?A probability is a measure of how likely or likely it is that a certain event will occur. Probabilities can be represented as percentages between 0% and 100% as well as proportions between 0 and 1.
Probability's significanceHow likely an event is to occur is determined by the concept of probability. For instance, meteorologists can predict the possibility of rain by looking at weather patterns. In epidemiology, probability theory is used to understand the relationship between exposures as well as the risk of health effects.
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Which of the following statement(s) is/are correct for congruent triangles?
A
Congruent triangles have same shape but different size.
B
Congruent triangles have both same shape and same size.
C
Corresponding angles and corresponding sides of congruent triangles are equal.
D
Congruent triangles have same size but different shape.
Answer:
B. Congruent triangles have both same shape and same size.
C. Corresponding angles and corresponding sides of congruent triangles are equal.
Angles 4 and 8 are what type of angles?
A. Alternate exterior angles
B. Same side interior angles
C. Alternate interior angles
D. Corresponding angles
Answer:
D. Corresponding angles
Step-by-step explanation:
Corresponding angles are angles located on the same side, the intersection of transversal and two or more straight lines. So, answer is D
A company began construction of a new manufacturing plant. The plant was completed on october 31, 2024. Expenditures on the project were as follows ($ in millions): on july 1, 2023, the company obtained a $76 million construction loan with a 9% interest rate. The loan was outstanding through the end of october, 2024. The company's only other interest-bearing debt was a long-term note for $100 million with an interest rate of 11%. This note was outstanding during all of 2023 and 2024. The company's fiscal year-end is december 31
The interest amount that will be capitalized is $4.04 million.
What is the interest amount that will be capitalized?The entire cost to purchase a good or service is referred to as an expense. A $30 million piece of equipment with a six-year useful life, for instance, is considered a capital expenditure. An expense is something that calls for the transfer of funds, or fortune in general, from one person or group to another as payment for a good, service, or other type of cost. Rent is a cost to a tenant. Tuition is a cost to parents or students.
The following can be deduced from the information:
Average Expenditure for 2023
= 78 million* 6/6 month + 46 million ** 3/6 month
= 101 million
Amount of interest that should capitalized in 2023 using a specific interest method
= Average expenditure for 2023 * interest rate *6/12 month
= $101 million * 8% * 6/12
= $4.04 million
The interest amount is $4.04 million.
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ASAP ANSWER PLEASE
ABC was rotated 90° clockwise around the origin to form A'B'C'. A'B'C' was dilated using a scale factor of 1/2 with a center of dilation at the origin. The result is A''B''C'', shown in the coordinate plane. What are the coordinates of ABC? Show your work.
The coordinates of ABC are A = (-2, -1) B = (-2, -10) C" = (-14, -1)
How to determine the coordinates of ABC?The coordinates of the triangle A"B"C" are given as
A" = (0.5, -1) B" = (5, -1) C" = (0.5, -7)
The transformation is given as
Rotation of 90° clockwise around the originDilation by 1/2 with a center of dilation at the originWhen these transformations are combined, we have
(x, y) ⇒ (-y/2, x/2)
So, we have
A" = (0.5, -1) B" = (5, -1) C" = (0.5, -7)
This gives
A = (-2, -1) B = (-2, -10) C" = (-14, -1)
Hence, the coordinates are A = (-2, -1) B = (-2, -10) C" = (-14, -1)
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Describe the transformation of f(x)=x^5 represented by g(x) = (x − 2)³—1
The graph of g is a translation 2 (blank) units and 1 unit (blank)
of the graph of f
Identify the graph of g.
The transformation from the parent function is a translation by 2 units right and 1 unit up
How to describe the transformation from the parent function?From the question, we have the following function that can be used in our computation:
f(x) = x³
g(x) = (x − 2)³ - 1
First, we have the transformation to be:
From f(x) = x³ to f'(x) = (x − 2)³
This means the function is translated right by 2 units
Next, we have:
From f'(x) = (x − 2)³ to g(x) = (x − 2)³- 1
This means the function is translated up by 1 unit
Hence, the transformation is 2 units right and 1 unit up
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44 out of 60 as a persentage
Answer: 73.3%
Step-by-step explanation:
take 44 and divide it by 60
44/60 = 0.0733 repeating
move the decimal place to the right twice
0.0733 --> 73.3%
Takeo ha two different boxe left to pack before hi move. Box 1 ha a volume of 2,166 cubic centimeter. Box 2 ha a volume of 1,260 cubic centimeter. What i the total volume of pace, in cubic centimeter, that Takeo ha available to pack?
Box 1 has a volume of 2,166 cubic centimeters and Box 2 has a volume of 1,260 cubic centimeters.The total volume of space available to Takeo is 3,426 cubic centimeters.
To find the total volume of space available to Takeo, first we take the volume of Box 1, which is 2,166 cubic centimeters. Then we take the volume of Box 2, which is 1,260 cubic centimeters. Finally, we add these two volumes together to get the total volume of 3,426 cubic centimeters.Takeo is in the process of packing before his move. He has two boxes to pack and each box has a different volume. Box 1 has a volume of 2,166 cubic centimeters and Box 2 has a volume of 1,260 cubic centimeters. By adding these two volumes together, Takeo has a total volume of 3,426 cubic centimeters of space available to pack before his move.
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0.442÷26.7812 pleaseeeeeeeeeeeeeeeee
Answer: The correct answer is 0.0165041148268188
Step-by-step explanation:
Complete division (no rounding precision):
0.442 ÷ 26.7812 = 0.0165041148268188
the null hypothesis claims that the proportion of community college students who work full-time is 0.45. the alternative hypothesis is that this proportion is greater than 0.45. which sample proportion will have the smallest p-value?
The sample proportion will have the smallest p-value is for Z=3 that can be calculated by taking comparisons between Z=1,2 and 3.
Null hypothesis H0= P=0.45
Alternative hypothesis H1= P>0.45
The null hypothesis assumes that any form of distinction among the selected traits which you see in a fixed of records is because of chance. For example, if the predicted income for the playing recreation are truely same to 0, then any distinction among the common income withinside the records and 0 is because of chance.
H=1000, x1=500, x2=600 and x3=700
P1= x1/h=500/1000=0.5
P2=x2/h=600/1000=0.6
P3=x3/h=700/1000=0.7
Z1=P1-P/(P(1-P)/h)61/2 = 0.5-0.45/(0.45*0.55/1000)^1/2 = 0.32
P-value for Z1=P(Z1>0.32)=0.37748
Z2=P2-P/(P(1-P)/h)61/2 = 0.6-0.45/(0.45*0.55/1000)^1/2 = 0.95
P-value for Z2=P(Z2>0.95)=0.17106
Z3=P3-P/(P(1-P)/h)61/2 = 0.7-0.45/(0.45*0.55/1000)^1/2 = 1.59
P-value for Z3=P(Z3>0.95)=0.055917
Thus, the smallest P-value will be for Z3.
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What value of x is in the solution set of the inequality 9(2x 1) < 9x – 18? –4 –3 –2 –1
The value of x in the solution set of the inequality is -4.
What are inequalities?Inequalities are of two types, > and <. The > sign means that left hand side is greater than the right hand side, while the < sign means that the left hand side is less than than the right hand side.
How to solve inequalities?We can solve the inequality by assuming the inequality sign as the = sign, except that when we divide or multiply one side by (-1), the inequality sign will reverse (for eg it will change from > to <).
9(2x+1) < 9x - 18
2x+1 < x - 2
2x < x - 3
x < -3
This means that x can be any value less than -3 (but not equal to -3 since the sign is < and not ≤) . Hence, the answer is -4.
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Answer:
-4
Step-by-step explanation:
taking test
simplfy y2 when y = -9
The solution to the expression y² is 81 when y = -9
How to simplify the expression at the given valueFrom the question, we have the following parameters that can be used in our computation:
y = -9
Also, from the question, we have
y2
Express the exponents in the above expression properly
So, we have the following representation
y²
Substitute the known values in the above equation, so, we have the following representation
y² = (-9)²
Remove the bracket in the expression
'This gives
y² = 9²
Evaluate the exponent
So, we have the following representation
y² = 81
Hence, the solution is 81
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1 2/5m-3/5(2/3m+1) please help me
Answer:
m - 3/5 or m - 0.6-----------------------------------------
Simplify the expression:
1 2/5m - 3/5(2/3m + 1) = Convert mixed number to fraction 7/5m - 3/5(2/3)m - 3/5 = Distribute 7/5m - 2/5m - 3/5 = Simplify(7 - 2)/5m - 3/5 = Collect terms with m5/5m - 3/5 = Simplifym - 3/5 AnswerAs Venus revolves around the sun, it travels at a speed of approximately 22 miles per second. Convert this speed to miles per minute. At this speed, how many miles will Venus travel in 6 minutes?
Answer: In 6 minutes, Venus will travel 1320 * 6 = 7920 miles.
Step-by-step explanation: To convert the speed from miles per second to miles per minute, we multiply the speed by the number of seconds per minute. There are 60 seconds per minute, so Venus travels 22 * 60 = 1320 miles per minute.
In 6 minutes, Venus will travel 1320 * 6 = 7920 miles.
Find the tables with unit rates greater than the unit rate in the graph. Then arrange these tables in order from least to greatest unit rate. x y 7 13 14 26 x y 5 9 10 18 x y 9 17 18 34 x y 11 21 22 42 x y 10 19 20 38 x y 13 25 26 50 x y 12 23 24 4
Except table 2, all tables have greater unit rate than the graph.
The required arrangements of tables is Table 2 < Table 1 < Table 3 < Table 5 < Table 4 < table 7 < Table 6
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
From the given graph it is clear that the line passes through the points (0,0) and (11,20). So, unit rate of graph is
m=20-0/11=20/11=1.818
Similarly, we need to calculate the unit rate for each table.
m1=26-13/14-7=1.81
m2=18-9/10-5=9/5=1.81
m3=34-7/18-9=1.88
m4=42-21/22-11=21/11=1.90
m5=38-19/20-10=1.9
m6=50-25/26-13=25/13=1.923
m7=46-23/24-12=23/12=1.9166
Hence, Except table 2, all tables have greater unit rate than the graph.
The required arrangement of tables is Table 2 < Table 1 < Table 3 < Table 5 < Table 4 < Table 7 < Table 6
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What’s the solution to 2x-2y=6 and 4x+4y=28
Answer
x=5 y=2
Step-by-step explanation:
Help me out please !!!!!!!!
Answer: 3 boxes
Step-by-step explanation:
she has 3 stuffed animals left and its not manditory to fill a box so you would put the threee remaining into one box
Please helppp I’m giving brainlyest
Answer:
B
Step-by-step explanation:
the shape will reflect b
Would you rather receive a 3% raise followed by a 9% raise or a 9% followed by a 3%
It is better to receive a 9% raise followed by a 3% raise, rather than a 3% raise followed by a 9% raise.
What is the percentage increase?
The concept of percent increase is basically the amount of increase from the original number to the final number in terms of 100 parts of the original.
It is generally better to receive a 9% raise followed by a 3% raise, rather than a 3% raise followed by a 9% raise.
This is because the percentage raise you receive is applied to your current salary. If you receive a 3% raise first, your salary will be higher when you receive the 9% raise, so the 9% raise will be applied to a higher base salary. This means that you will receive a larger increase in salary overall if you receive the 9% raise first.
For example, let's say you are currently making $50,000 per year. If you receive a 3% raise followed by a 9% raise, your salary would increase to $51,500 after the first raise and then to $56,365 after the second raise, for a total increase of $6,365.
On the other hand, if you receive a 9% raise followed by a 3% raise, your salary would increase to $54,500 after the first raise and then to $56,365 after the second raise, for a total increase of $5,865.
In this example, you would receive a larger increase in salary overall if you received the 9% raise first. This is because the 9% raise is applied to a lower base salary, resulting in a larger increase in salary overall.
Of course, the actual amount of the raise will depend on your current salary and the percentage of the raise. In general, though, it is usually better to receive a larger percentage raise first, followed by a smaller percentage raise.
Hence, It is better to receive a 9% raise followed by a 3% raise, rather than a 3% raise followed by a 9% raise.
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HELP WILL MARK BRAINLIEST
The measures of dilated triangle A'B'C' are A'B'= 4.1 units, A'C'= 2.2 units and B'C'= 4.2 units.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
Given that, center of dilation is P and scale factor is 1/3.
In the given triangle ABC, AB=12.4 units, AC=6.7 units and BC=12.7 units
Now, A'B'=12.4/3
A'B'= 4.1 units
A'C'=6.7/3
A'C'= 2.2 units
B'C'=12.7/3
B'C'= 4.2 units
Therefore, the measures of dilated triangle A'B'C' are A'B'= 4.1 units, A'C'= 2.2 units and B'C'= 4.2 units.
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A preschool has 100 feet of fencing to enclose 3 sides of a rectangular playground. The fourth side is formed by a wall of the school. The function A(x) = 100x − 2x2 represents the possible area of the playground with side length x feet. Which range is appropriate for this situation?
Answer:
This answer assumes that the function is A(x) = 100x − 2x^2. The function as written is A(x) = 100x - (4 or 4x)
The domain is 0 - 50 feet.
Step-by-step explanation:
The area function is a polynomial with a vertex (hghest area possible) at (25,1250). This is telling us that for a side length of 25 feet, the area is at a maximum of 1250 ft^2. This is actually not totally correct. We only need 3 sides of fencing since the school wall will make up the fourth. The given equation does not seem to allow for this caveat, since it uses 100 feet for all four sides.
Given the equation, the domain for the function A(x) is positive for all values between 0 and 50 feet. The domain is 0 - 50 feet.
Determine the intercepts of the line. Do not round your answers.4x−1=3y+5. x intercept: (?,?), y intercept: (?,?)
Answer:
x intercept= (1.5,0)
y intercept= (0,-2)d
Step-by-step explanation:
Rearrange the equation to be in the form y=mx+c:
4x-1=3y+5
y=(4x-6)/3
y=4/3(x)-2
y intercept= c from equation above =-2
y intercept=-2
x intercept => when y=0
sub 0=y
0=4/3(x)-2
2=4/3(x)
x=1.5
Select all the expression that are equivalent to 8^-6 x 8^-5
Answer:
f(x)=3x+4 and g(x)=2x3
find.
a:fg(x)
b:gf(x)
Please help me with this
a) The equation is y = 4/x².
b) The value of x is 2/9 when y = 25.
What is relationship?
The relation in mathematics is the connection between two or more sets of values. Assume that there are two sets of ordered pairs, x and y. If set x and set y are related, then the values of set x are referred to as the domain while the values of set y are referred to as the range.
Given table is
x 1 2 3 4
y 4 1 4/9 1/4.
Given that y is inversely proportional to the square of x.
y∝ 1/x²
y = k/x² where k is proportional constant.
Putting x = 1 and y = 4 in equation y = k/x²:
4 = k/1²
k = 4
Putting x = 2 and y = 1 in equation y = k/x²:
1 = k/2²
k = 4
Putting k = 4 in y = k/x²:
y = 4/x²
Putting y = 25 in y = 4/x²
25 = 4/x²
25x² = 4
Divide both sides by 25:
x² = 4/25
Take square root on both sides:
x = 2/5
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please help meee!!!!
5. The constant of proportionality is $0.4 per pound
4. The constant of proportionality is is 3 ounces of almond per ounces of dark chocolate
Determining Constant of proportionalityFrom the question, we are to determine the constant of proportionality from the given table
From the given information, we have that
There is a proportional relationship between x and y
That is,
y ∝ x
Then,
y = kx
Where k is the constant of proportionality
From the table,
When x = 5 pounds, y = $2
Then,
2 = k × 5
k = $2/5pounds
k = $0.4/pound
k = $0.4 per pound
4.
x is proportional to y
Then,
y = cx
Where c is the constant of proportionality
From the table,
When x = 3 ounces of dark chocolate, y = 9 ounces of almond
Then,
9 = c × 3
c = 9/3
c = 3 ounces of almond / ounces of dark chocolate
c = 3 ounces of almond per ounces of dark chocolate
Hence, the proportionality constant is 3 ounces of almond per ounces of dark chocolate
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