The cube root of our varies inversely with the square of S which to equations model this relationship?
Answers
The question states as follows;
"The cube root of r varies inversely with the square of s."
The general form of an inverse relationship is shown below;
[tex]y=\frac{k}{x}[/tex]Substituting the variables, we would now have;
[tex]\sqrt[3]{r}=\frac{k}{s^2}[/tex]Therefore, the third option is correct.
Also;
[tex]\begin{gathered} \sqrt[3]{r}=\frac{k}{s^2} \\ \text{Observe that}_{} \\ \sqrt[3]{r}=r^{\frac{1}{3}} \end{gathered}[/tex]Therefore, we can alo have the expression;
[tex]\begin{gathered} r^{\frac{1}{3}}=\frac{k}{s^2} \\ \text{Cross multiply, and we'll have;} \\ s^2r^{\frac{1}{3}}=k \end{gathered}[/tex]The fifth option is also correct.
ANSWER:
The third and fifth options are both correct models of the inverse relationship given.
Related Questions
Give the equation of the transformed quadratic toolkit function shown below.()=−(+1)2+2()=−(−1)2+2()=−(+1)2+2()=(−1)2−2
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The Solution:
Given:
Required:
Determine the function of the given graph.
The required equation is:
[tex]y=-\left(x-1\right)^{2}+2[/tex]Answer:
[option 2]
Question 5 of 10 Which function is increasing? O A 19-(0) OB. Rx) = 5* O C. f( 10w -() OD. (X) = (0.5)
Answers
Increasin function:
f(x) = a^x
Where a must be greater than 1:
A. 1/15 = 0.06 NO
B. 5 YES
C. 1/5 NO
D. 0.5 NO
Correct option B.5
5>1
write each fraction in simplest form 3/12
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3/12 is 1/4 in its simplest form
in a cave a stalactites gets 4 millimeters longer each year.this year it is 72 centimeters longhow many years until it is 1 meter long
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in a cave a stalactites gets 4 millimeters longer each year.this year it is 72 centimeters long
how many years until it is 1 meter long
we have that
the linear equation that represent this situation is equal to
y=4x+720
where
y ------> length in mm
x ----> number of years
Remember that
72 cm=720 mm
so
For y=1 m ------> y=1,000 mm
substitute in the equation
1,000=4x+720
4x=1,000-720
4x=280
x=70 years
therefore
answer is 70 yearsAttached is my question, thank you. And x^2=squared i just can’t find the button to do it.
Answers
From the question we are given
[tex]\text{Profit }=Total\text{ Revenue }-total\text{ cost}[/tex]Annual total cost in $ is given by
[tex]C(x)=3600+100x+2x^2_{}[/tex]And an Annual total revenue in $ is given as
[tex]R(x)=500x-2x^2[/tex]Where x is the number of pairs of boots sold
We are to find the profit function
Using the detains given we have
Profit function P(x) is
[tex]P(x)=R(x)-C(x)[/tex]Therefore,
[tex]\begin{gathered} P(x)=500x-2x^2-\lbrack3600+100x+2x^2\rbrack \\ P(x)=500x-2x^2-3600-100x-2x^2 \\ P(x)=-4x^2+400x-3600 \end{gathered}[/tex]Therefore, the profit function is
[tex]P(x)=-4x^2+400x-3600[/tex]Next we are to find determine the number of pair of boots that will maximize annual profit
Plotting the graph of the Profit function we have
Hence, at maximum we have the points (50, 6400)
Therefore, x = 50
This implies that the number of boots that will maximize the annual profit is 500
A spring is attached to the ceiling and pulled 17 cm down from equilibrium and released. After 3 seconds the amplitude has decreased to 13 cm. The spring oscillates 14 times each second. Find a function that models the distance, D the end of the spring is below equilibrium in terms of seconds, t, since the spring was released.
Answers
The end of the spring is below equilibrium in terms of seconds, t, since the spring was released is D(t) = 17([tex]0.957^{t}[/tex])cos(28πt)
What is equilibrium?A state of balance between opposing forces or actions that is either static (as in a body acted on by forces whose resultant is zero) or dynamic (as in a reversible chemical reaction when the rates of reaction in both directions are equal).
Given that, a spring is attached to the ceiling and pulled 17 cm down from equilibrium and released. After 3 seconds, the amplitude has decreased to 13 cm. The spring oscillates 14 times each second.
Amplitude begins at 17 cm, [tex]A_{0}[/tex] = 17 cm
The amplitude decreases by 13/3 = 4.33 per second = 0.043%
The amplitude function can be then modelled as =
A(t) = [tex]A_{0}[/tex][tex](1-0.043)^{t}[/tex]
A(t) = [tex]A_{0}[/tex][tex]0.957^{t}[/tex]
The spring oscillates 14 times each second, therefore,
T = 1/14
2π/B = 1/14
B = 28π
The graphical equation is;
D(t) = [tex]A_{cos}[/tex](Bt-C)+D
Horizontal shift = 0
Vertical shift = 0
Hence, The end of the spring is below equilibrium in terms of seconds, t, since the spring was released is D(t) = 17([tex]0.957^{t}[/tex])cos(28πt)
For references on equilibrium, click;
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How does graphing the line help us represent the value of k (constant of proportionality)?
Answers
Answer:
The graph of the line shows that the value of k is the y-coordinate of the point where the x-coordinate is equal to 1.
k = 2.5
1 seagull eats 2.5 pounds of garbage.
Explanation:
First, we need to draw the point (4, 10) on the graph because 4 seagulls eat 10 pounds of garbage. Then, we need to draw a line that passes through this point, and through (0, 0). Finally, we need to identify the number of pounds of garbage when the number of seagulls is 1 or identify the point (1, k). So, we get:
Therefore, the value of k = 2.5 is the constant of proportionality and tell us the number of pounds of garbage that each seagull eat.
So, the graph of the line shows that the value of k is the y-coordinate of the point where the x-coordinate is equal to 1. Also, k represents the slope of the line.
can you find the domain of a piecewise functuon
Answers
a piecewise function
x+ 4 , if -4 ≤x <3
. 3 ≤ x < 6
Then ,answer is [ -4,6)
Which of the follwoing shows the area of circle with a diameter of 8 km? a. 16 km2 50.27km2 X b. 4tkm? ~ 12.57km? c.21km? ~ 6.28km? d. Akm? ~ 3.14km2
Answers
The formula of the area of a circle is
[tex]A=\pi r^2[/tex]where r is the radius
in this case, we have the length of the diameter, the diameter is twice the radius
d= diameter
d=2r
therefore
r=d/2
r=8/2
r=4
we substitute the value of the radius in the formula
[tex]A=\pi r^2=\pi(4)^2=16\pi=50.27\operatorname{km}^2[/tex]the area of a circle with a diameter of 8km is 16pi km^2 or 50.27km^2
A department store sells a pair of shoes with an 87% markup if the store sells the shoes for 193.21 then what is their non-markup price
Answers
Answer:
103.32
Step-by-step explanation:
p = non-markup price of shoes
0.87p = amount of markup
selling price = p + 0.87p = 193.21
1.87p = 193.21
p = 103.32
check: p + 0.87p = 193.21?
103.32 + 89.89 = 193.21? YES
Help please this is a practice question for points-The other options are $18 and $27
Answers
Let the y value for brand A = Y₁
when x = 2 y = 24
[tex]\begin{gathered} Y_1\text{ =}\frac{24}{2}=12 \\ Y_1\text{ = 12x} \end{gathered}[/tex]Write the following equation x2 +9y2 + 10x – 18y + 25 = 0 in vertex form.Identify the type of conic section and its direction.
Answers
The equation of the conic section is:
[tex]x^2+9y^2+10x-18y+25=0[/tex]Square terms are positive and have different coefficients. Then, we can say it is an ellipse.
To find the vertex form, we need to group x and y:
[tex](x^2+10x)+(9y^2-18y)+25=0[/tex]The grouped terms of y can be factored:
[tex](x^2+10x)+9(y^2-2y)+25=0[/tex]It will be convenient to group the 25 with the group of x, since we can have a perfect square trinomial (since the square root of 25 is 5, which is half ten):
[tex](x^2+10x+25)+9(y^2-2y)=0[/tex]We can factor the first goup:
[tex](x+5)^2+9(y^2-2y)=0^{}[/tex]Now, we can try to make another perfect square trinomila from the second term. We need a number whose square root multiplied by 2 gives us 2 (the coefficient of y) This number will be one. Then, we can sum 1 inside the parenthesis, but we need to substract 9 outside it in order not to alter the equation. (it is 9 because we added 1 inside a parenthesis that is multiplied by 9).
[tex](x+5)^2+9(y^2-2y+1)-9=0^{}[/tex]Now, we can factor the second group of terms and reorganize:
[tex](x+5)^2+9(y-1)^2=9^{}[/tex]Now, to get the equation in the vertex form, we need a 1 in the right side of the equation. Then, we can divide everything (both sides) by 9:
[tex]\frac{(x+5)^2}{9}+(y-1)^2=1[/tex]The equation of the ellipse is now on its vertex form. Since the number dividing the x term (9) is higher than the number dividing the y term (1) we can say that the direction of the ellipse is horizontal. It´s longer axis is parallel to the x axis of the plane.
27, 9, 3, 1, 1/3,1/9....What is the value of the 10th term in the sequence?
Answers
1. Identify if the sequence has a common difference or a common ratio.
Common difference: subtract each term from the next term:
[tex]\begin{gathered} 9-27=-18 \\ 3-9=-6 \\ 1-3=-2 \end{gathered}[/tex]There is not a common difference.
Common ratio: Divide each term into the previous term:
[tex]\begin{gathered} \frac{9}{27}=\frac{1}{3} \\ \\ \frac{3}{9}=\frac{1}{3} \\ \\ \frac{1}{3}=\frac{1}{3} \\ \\ \frac{\frac{1}{3}}{1}=\frac{1}{3} \\ \\ \frac{\frac{1}{9}}{\frac{1}{3}}=\frac{3}{9}=\frac{1}{3} \end{gathered}[/tex]The common ratio is 1/3; it is a geometric sequence.
2. Use the next fromula to write the formula to find the nth term in the sequence:
[tex]\begin{gathered} a_n=a_1*r^{n-1} \\ \\ r:common\text{ }ratio \end{gathered}[/tex][tex]a_n=27*(\frac{1}{3})^{n-1}[/tex]Evaluare the formula above for n=10 to find the 10th term:
[tex]\begin{gathered} a_{10}=27*(\frac{1}{3})^{10-1} \\ \\ a_{10}=27*(\frac{1}{3})^9 \\ \\ a_{10}=27*\frac{1}{3^9} \\ \\ a_{10}=27*\frac{1}{19683} \\ \\ a_{10}=\frac{27}{19683} \\ \\ a_{10}=\frac{1}{729} \end{gathered}[/tex]Then, the 10th term is 1/729William bought 3 pizzas for himself and 6 friends. Each pizza has m slices. Select all of the following expressions that represent the number of slices of pizza per person. Al (m + m + m) 7 m7 3m 7
Answers
12
From the information given,
Wiliam bought 3 pizzas and each had m slices. This means that the total number of slices in the 3 pizzas is 3 * m = 3m
He bought the the pizzas for himslef and 6 friends. This means that the total number of people that shared 3m slices of pizzas is 1 + 6 = 7
Thus, the expression that represent the number of slices of pizza per person are
c) 3m/7
The table below shows the probability distribution of a random variable Z. Z P(Z) -11 0.06 -10 0.36 -9 0.43 -8 0.03 -7 0.02 -6 0.1 What is the mean of the probability distribution? Write your answer as a decimal. Submit
Answers
The mean (μ) of a discrete random variable (z) is calculated as follows:
[tex]\mu=\Sigma z\cdot P(z)[/tex]Substituting with data:
[tex]\begin{gathered} \mu=-11\cdot0.06-10\cdot0.36-9\cdot0.43-8\cdot0.03-7\cdot0.02-6\cdot0.1 \\ \mu=-0.66-3.6-3.87-0.24-0.14-0.6 \\ \mu=-9.11 \end{gathered}[/tex]A population of bacteria is growing according to the equation P(t) = 1850e ^ (0.09t). Estimate when the population will exceed 2402t=Give your answer accurate to one decimal place.
Answers
We will have the following;
[tex]\begin{gathered} 2402=1850e^{0.09t}\Rightarrow\frac{2402}{1850}=e^{0.09t}\Rightarrow\frac{1201}{925}=e^{0.09t} \\ \\ \Rightarrow ln(\frac{1201}{925})=0.09t\Rightarrow t=\frac{ln(1201/925)}{0.09} \\ \\ \Rightarrow t=2.901289829...\Rightarrow t\approx2.9 \end{gathered}[/tex]So, the population will exceed 2402 bacteria after 2.9 units of time.
Ming prepared three chemical solutions with temperatures -5, -4, and -3. what is the correct compares of the three temputures?
Answers
So we will like to compare the three numbers -5, -4 and -3. We will like to compare the three temperatures. To know wich numbers is less than the other we can draw the real line
The more to the left the number are the lesser it is therefore
[tex]-5<-4<-3[/tex]6) Identifyas amonomial, binomial, or trinomial.4x2 – y + 0z4 binomial monomial Trinomial
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For this problem we have the following expression given:
[tex]4x^2-y+0z^4[/tex]Since any number multiplied by 0 is 0 then our expression becomes:
[tex]4x^2-y[/tex]And since we have two terms we can categorize the expression as a binomial.
how do u know if an equation has rational, irrational or complex solution
Answers
We have the equation:
[tex]49a^2-16=0[/tex]We can factorize this equation as:
[tex]\begin{gathered} 49a^2-16=0 \\ (7a)^2-4^2=0 \\ (7a-4)(7a+4)=0 \end{gathered}[/tex][tex]\begin{gathered} 7a-4=0\longrightarrow a_1=\frac{4}{7} \\ 7a+4=0\longrightarrow a_2=-\frac{4}{7} \end{gathered}[/tex]In this case, we have 2 rational solutions.
If the solution implies the square root of -1, then we would have 2 complex solutions.
If the solution implies a square root that does not have a rational solution, then we have 2 irrational solutions.
We can see it when we apply the quadratic formula:
[tex]x=-\frac{b}{2a}\pm\frac{\sqrt[]{b^2-4ac}}{2a}[/tex]The term with the square root defines what type of solution we have:
If b^2-4ac<0, then we have complex solutions.
If the square root of b^2-4ac does not have a rational solution (b^2-4ac is not a perfect square), then we have irrational solutions.
If b^2-4ac is a perfect square (its square root have a rational solution), we will have rational solutions.
Evaluate log3/8 91 using the change of base formula. Round your answer to one decimal place.
Answers
We have to apply the change of base formula:
[tex]\log _b(a)=\frac{\log _x(a)}{\log _x(b)}[/tex]We can apply this to our expression as:
[tex]\log _{\frac{3}{8}}(91)=\frac{\ln(91)}{\ln(\frac{3}{8})}=\frac{\ln (91)}{\ln (3)-\ln (8)}\approx\frac{4.511}{1.099-2.079}=\frac{4.511}{-0.980}\approx-4.6[/tex]Answer: -4.6
Example 1: Choose a point in Quadrant 2, 3, or 4 to be on the terminal arm of an angle in standard position. Determine the principal angle in radians. Include a sketch.Example 2: Using a different quadrant than in Example 1 (but still not Quadrant 1), choose a reciprocal trig ratio. Determine all of the primary and reciprocal ratios for that angle, as well as the principal angle in radians.
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Example 1:
The quadrants with their numbering (I, III,III, and IV) are shown below.
Now let us draw an angle in quadrant II.
We have drawn the angle above such that its measure from the positive x-axis is 135° . The angle 135° in radians is 3π/4.
Example 2:
Let us now choose an angle in the 3rd quadrant.
What volume of ice cream is contained in a 10 cm-high ice cream cone with a base radius of 4 cm?
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We would find the volume of the ice cream contained in the cone by applying the formula for determining the voume of a cone which is expressed as
Volume = 1/3 x pi x radius^2 x height
From the information given,
height = 10
radius = 4
pi is a constant whose value is 3.142
Thus,
Volume = 1/3 x 3.142 x 4^2 x 10
Volume = 167.57
rounding to the nearest whole number,
Volume = 168 cubic cm
Solving a proof I know how to start it just confused how to put it all together
Answers
Given that ABCD is a parallelogram, prove that
[tex]\begin{gathered} \bar{AB}\cong\bar{CD} \\ \bar{BC}=\bar{DA} \end{gathered}[/tex]step 1: Sketch the parallelogram
step 2: The diagonal AC, divides the parallelogram into two triangles
[tex]\begin{gathered} \Delta ADC\text{ and }\Delta ABC \\ Note\text{ that,} \\ \angle DAC=\angle ACB\text{ ( the angles are alternate)} \\ \angle DCA=\angle BAC\text{ (the angles are alternate)} \\ side\text{ AC = AC (common sides for both triangles)} \end{gathered}[/tex]step 3: By the ASA (Angle-Side-Angle) congruency theorem,
[tex]\begin{gathered} \Delta ADC\cong\Delta ABC \\ (The\text{ two triangles are congruent)} \end{gathered}[/tex]Hence, by CPCT (corresponding parts of congruent triangles)
[tex]\begin{gathered} \bar{AB}\cong\bar{CD}\text{ } \\ \bar{BC}\cong\bar{DA} \end{gathered}[/tex]Using the explicit formula, find the 3rd term f(n)=5+4(n-1)
Answers
Answer:
13
Explanation:
The explicit formula of a sequence is given below:
[tex]f\mleft(n\mright)=5+4\mleft(n-1\mright)[/tex]When n=3
[tex]\begin{gathered} f\mleft(3\mright)=5+4\mleft(3-1\mright) \\ =5+4(2) \\ =5+8 \\ =13 \end{gathered}[/tex]The 3rd term of the sequence is 13.
Can you please help me with this question from math? A) He will receive a refund of $435.B) He will receive a refund of $442.C) He will pay $435.D) He will pay $442.
Answers
ANSWER:
A) He will receive a refund of $435.
STEP-BY-STEP EXPLANATION:
According to the table for your income and marital status you must pay a total of $4091
If you already paid a total of $4,526, then:
[tex]\begin{gathered} t=4526-4091 \\ \\ t=435 \end{gathered}[/tex]Which means, they owe you a total of $435 back.
Therefore, the correct answer is A) He will receive a refund of $435.
7. Marco was asked to rotate thecoordinate P(3,-4) 180 degrees about theorigin. Then, he decided to perform atranslation of (x, y+2) followed by adilation of 2. Marco was convinced thatP and P'" had the same coordinates. IsMarco correct? Explain your reasoning.
Answers
Let's take this, step by step.
First step:
Rotate the coordinate 180 degrees about the origin.
When a 180 degrees rotation about the origin is performed the coordinates (x, y) changes to (-x, -y)
Thus, P(3, -4) changes to P'(-3, 4)
Second Step:
Perform a translation of (x, y+2)
P'(-3,4) = P''(-3, 4+2) = P''(-3, 6)
Third step:
Perform a dilation of 2.
P''(-3, 6) = P'''(-3*2, 6*2) = P'''(-6, 12)
We can see that,
P(3, -4) while P'''(-6, 12)
Therefore, P and P''' do not have the same coordinates
What angle will make a rotational symmetry?A. 8B. 50C. 45D. 60
Answers
To find the angle, we will simply divide 360 by the number of sides
Number of sides = 8
That is;
Angle = 360 / 8 = 45 degree
Hello everybody! Can anyone help me with this? I just need to know if it's a Direct variation, a inverse variation, or neither? (Look at the photo) Thanks!
Answers
Remember that
A relationship between two variables, x, and y, represent a proportional variation (direct variation) if it can be expressed in the form y=Kx
An equation of the line that passes through the origin
A relationship between two variables, x, and y, represents an inverse variation if it can be expressed in the form y=1/x
There is a vertical asymptote at x=0
therefore
Looking at the graph
we have an inverse variationanswer is IAbc is isosceles triangle and right angled at C then TanA
Answers
When we have a right angled triangle, it means the triangle has a right angle and two acute angles all equally summing up to 180 degrees.
When we have an isosceles triangle, it means there are two equal acute angles.
Therefore, by combining these two statements, we can get the value of the acute angles. A plot is given below.
[tex]\begin{gathered} 90+x+x=180 \\ 90+2x=180 \\ \text{Subtract 90 from both sides to get:} \\ 2x=90 \\ \text{Divide both sides by 2 to get:} \\ x=45^o \end{gathered}[/tex]Next step is to get Tan A.
We can use trigonometric ratios and Pythagoras theorem to get:
[tex]\begin{gathered} AB^{}=\sqrt[]{AC^2+BC^2} \\ AB=\sqrt[]{1^2+1^2} \\ AB=\sqrt[]{2} \end{gathered}[/tex]For Tan A, we employ the Soh Cah Toa to get:
[tex]\begin{gathered} \tan A=\frac{\text{opposite}}{\text{adjacent}} \\ \tan A=\frac{1}{1}=1 \end{gathered}[/tex]Therefore, Tan A = 1
"You are solving a system of equations of two linear equations in two variables, and you discover that there are no solutions to the system"
Answers
"You are solving a system of equations of two linear equations in two variables, and you discover that there are no solutions to the system"
So, it will mean the lines are parallel
so, the graph which describe the system is pink
The answer is option D