23.-28. In a manner similar to Example 1, (a) identify input and
output consistent with the general proportional model; (b) write
an equation for the model; (c) determine a numerical value for the
constant k; and (d) solve the problem.
24. The speed of a skidding car is directly proportional to the
square root of the length of the skid. On a snowy road, a car
with good brakes traveling at 40 mph would skid approxi-
mately 178 ft. If the skid marks of a similar car on a similar
road were 400 ft, how fast would this car be traveling?
24. If the skid marks of a similar car on a similar road were 400 ft, how fast would this car be
traveling?
Answers
The direct variation that of the speed to the skid length implies that the speed increases as the length increases
The car would be traveling at 59.96 mph
How to determine the speed of the skidding car?A direct variation that illustrates the speed of the skidding car is:
s = k√l
Where:
s represents the speed of the carl represents the length of the skidk represents the proportionality constantMake k the subject in s = k√l
k = s /√l
Rewrite as:
s₁ /√l₁ = s₂ /√l₂
Substitute known values
40 /√178 = s₂ /√400
Evaluate the square root of 40
40 /√178 = s₂ /20
Multiply both sides by 20
800 /√178 = s₂
Evaluate the quotient
s₂ = 59.96
Hence, the car would be traveling at 59.96 mph
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Related Questions
PLEASE HELP ME IN THIS QUESTION!!!
Answers
Answer:
CD = 16
Step-by-step explanation:
Segments EF and EC are tangent and secant respectively to the circle drawn from external point E.
Thus, by tangent-secant theorem:
[tex]ED\times EC= EF^2[/tex]
[tex]\implies x(x+x+7)= (15)^2[/tex]
[tex]\implies 2x^2+7x= 225[/tex]
[tex]\implies 2x^2+7x-225=0[/tex]
Comparing above quadratic equation with [tex]ax^2+bx+c=0[/tex], we find:
a = 2, b = 7, c = -225
Now, we find the value of the discriminant
[tex]\implies b^2-4ac= (7)^2-4(2)(-225)= 1849[/tex]
Now, by quadratic formula:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]\implies x=\frac{-7\pm\sqrt{1849}}{2(2)}[/tex]
[tex]\implies x=\frac{-7\pm (43)}{4}[/tex]
[tex]\implies x=\frac{-7+ 43}{4}\: or\:x=\frac{-7- 43}{4} [/tex]
[tex]\implies x=\frac{36}{4}\: or\:x=\frac{- 50}{4} [/tex]
[tex]\implies x=9\: or\:x=-12.5 [/tex]
x represents length, so it can't be negative.
[tex]\implies x\neq -12.5[/tex]
[tex]\implies x=9[/tex]
CD = x + 7
-> CD = 9 + 7
-> CD = 16
Amelia is using substitution to determine if 8 is a solution to the equation. Complete the statements. 6a = 42 for a = 8 First, Amelia must substitute 8 for the using. To simplify, Amelia must. 8 a solution of the equation.
Answers
Amelia must substitute 8 for the variable using parentheses. To simplify, Amelia must multiply 8 by 6. 8 is not a solution of the equation.
What is algebraic expression?
Algebraic expression are the expression which consist the variables, coefficients of variables and constants.
The algebraic expression are used represent the general problem in the mathematical way to solve them.
Amelia is using substitution to determine if 8 is a solution to the equation. The equation which is Amelia is solving for a = 8 is,
[tex]6a = 42[/tex]
First, Amelia must substitute 8 for the variable using parentheses as,
[tex]6(8) = 42[/tex]
To simplify, Amelia must. multiply 8 by 6.
[tex]48 \neq 42[/tex]
The left hand side of the eqqation is not equal to the right hand side. Thus, 8 is not a solution of the equation.
Thus, Amelia must substitute 8 for the variable using parentheses. To simplify, Amelia must multiply 8 by 6. 8 is not a solution of the equation.
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Answer:
it is a
Step-by-step explanation:
The box plots show the number of days spent at a national park by two different groups of visitors.
Two box plots are shown together. The title is Time Spent at Park. The number line goes from zero to five by a scale of one half. For Group A, the whiskers range from one half day to five days, and the box ranges from two days to three and one half days. A line divides the box at three days. For Group B, the whiskers range from one day to four and one half days, and the box ranges from two days to four days. A line divides the box at three and one half days.
Select all the statements that are supported by the random samples.
About 75% of visitors in Group A spent 3.5 days or more at a national park.
About , 75 %, of visitors in Group A spent , 3.5, days or more at a national park.
About 50% of visitors in Group B spent 3.5 days or less at a national park.
About , 50 %, of visitors in Group B spent , 3.5, days or less at a national park.
About 25% of both Groups A and B spent 2 days or less at a national park.
About , 25 %, of both Groups A and B spent , 2, days or less at a national park.
Group A had greater variability in the number of days spent at a national park.
Group A had greater variability in the number of days spent at a national park.
Group B had a greater median and a greater spread in the number of days spent at a national park.
Answers
The answer is B i took the quiz
Sylvie needs $110 for a concert ticket. She already has $16 and she can earn the rest by working 10 hours at her job. If h represents her hourly earnings, which of the following equations can be solved to find Sylvie’s hourly earnings? Select all that apply.
A. 110 – 16 = 10h
B. 110 = 16h + 10
C. 16 = 110 – h
D. 110 = 16 + 10h
E. 110 + 16 = 10h
Answers
Answer:
The correct answers are:
A.) 110 - 16 = 10h
B.) 110 = 16h + 10
Step-by-step explanation:
Sylvie needs $110 for a concert ticket and already has $16 in her pocket. She can make up the difference by working an additional 10 hours at her job.
To earn the $110 required for the concert ticket, she'll need to work 10 hours in addition to the $16 she already has.
As a result, the following calculation can be used to calculate her hourly rate:
110 = 16 + 10h
110 - 16 = 10h
I hope this helps! ^-^
Phoebe spent $12.87 at the bookstore. She paid with a $20 bill. How much is her change?
Answers
Answer:
$7.13
Step-by-step explanation:
Very simple, we subtract 12.87 from 20 and the answer is 7.13.
So should get back $7.13 as her change
Figure #2 Volume =____ in^3
Answers
Answer:
480 in^3
Step-by-step explanation:
Multiplying the length of each of the sides together gives the volume, so [tex]12*4*10=480[/tex]
you must multiply each side together in order to find the volume
.
apair of gloves
that were originally $18 but are
marked 75% off. How much
money did Marissa save?
met
t
h
Answers
Answer:
13.5
Step-by-step explanation:
because 18 times 75 equals 1350 then you divide 1350 by 100 and you get 13.5
Vic has 14 coins in nickels and quarters the value of this coins is 1.70 how many quarters does he have
Answers
Answer:
4 quarters
Step-by-step explanation:
4 quarters = $1
14 nickels = $0.70
can you please help me?
Answers
Answer:
$91.30
Step-by-step explanation:
Hours worked on Monday: 8.30 hours (4.15 in the morning and 4.15 in the afternoon)
8.30 hours x $11 per hour: $91.30
indicate the formula for the following conditions.
P(n,r) = ?
Answers
Answer:
P (n,r)= [tex]\frac{n!}{(n-r)!}[/tex]
Step-by-step explanation:
P (n,r)= ?
complete formula for permutation of objects in a set:
P (n,r) = [tex]\frac{n!}{(n-r)!}[/tex]
help! will give brandie’s t to correct answer
Answers
Answer:
0.25+0.6= 0.9166666667 or 11/12
Step-by-step explanation:
hope this helps
PLEASE HELP MEEEEE PLEASE ASAP
Answers
Let f(x)=3x-4 and g(x)=x^2-5. Find f(g(3))
Answers
Answer:
hello
g (x)= x² - 5
g (3) = 3² - 5 = 9 - 5 = 4
Step-by-step explanation:
A vertical mast is held in place by wires from the top of it to the ground the mast is 60m tall and the wires from the top of it to the ground is 25m from the foot of the mats.How long is each wire
Answers
Answer:
65 m
Step-by-step explanation:
The length of the mast, 60 m, is a leg of a right triangle.
The distance the wire is from the foot of the mast is the other leg.
The length of the wire is the hypotenuse of the right triangle.
We can use the Pythagorean theorem to find the length of the wire.
a² + b² = c²
60² + 25² = c²
3600 + 625 = c²
c² = 4225
c = 65
Answer: 65 m
what is the median of the data set below? 45 57 41 67 33 43 A.41 B.44 C.54 D.67
Answers
Answer:
41
Step-by-step explanation:
The middle number is the median
The graph of the function f(x) = −3x2 − 3x + 6 is shown. Which statements describe the graph? Select three options.
On a coordinate plane, a parabola opens down. It goes through (negative 2, 0), has a vertex at (negative 0.5, 6.75), and goes through (1, 0).
The vertex is the maximum value.
The axis of symmetry is x = negative one-half.
The domain is all real numbers.
The range is all real numbers.
The function is decreasing from (−∞, 6.75).
Answers
i need help on this question
Answers
Answer:
1st question
Sry if its wrong xx
Which scatterplot represents the data that would be best modeled by a quadratic function?
Answers
A scatter plot uses dots to represent values for two different numeric variables and determine whether or not two variables have a relationship or correlation.
What is a scatterplot?
Your information is incomplete. Therefore, an overview of the scatterplot will be given. A scatterplot simply means is a type of plot using Cartesian coordinates to display values for two variables for a set of data.
In this case, a scatter plot uses dots to represent values for two different numeric variables and determine whether or not two variables have a relationship or correlation.
The position of each dot on the horizontal and vertical axis shows the values for an individual data point.
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A.
when are non-forfeiture provisions used?
when the insured names a beneficiary
b. when the insured stops making premium payments on a cash value policy
c. when the insured converts a term policy
d. when the insured dies and there is a settlement
Answers
Answer: should be B
Step-by-step explanation:
Which polynomial is a quartic trinomial?
A. -x^4-5x^2 + 1
B. x^2 + 4
C. x^3 + 2x^2 - 8x + 16
D. 3x^5 + 7x^2 - 9x^4
Answers
Answer:
A
Step-by-step explanation:
a quartic trinomial is a polynomial of degree 4 , with 3 terms
The only polynomial to fit this description is A
Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis, each salesman earns his paycheck differently.
Salesman A works strictly on commission. He earns $65 per sale, with a maximum weekly commission of $1,300.
Salesman B earns a weekly base salary of $300, plus a commission of $40 per sale. There are no limits on the amount of commission he can earn.
Salesman C does not earn any commission. His weekly salary is $900.
The weekly paycheck amount for each salesman, p, is a function of the number of sales, s, they had in that week.
Salesman A Salesman B Salesman C
s = 0 (0, ) (0, ) (0, )
s = 1 (1, ) (1, ) (1, )
s 10 (10, ) (10, ) (10, )
Answers
Answer 84.500
Step-by-step explanation: you have to multiply 1,300x65 then 300x 40
and then 12,000
A rectangular box with a square base and no top is to have a volume of 108
Answers
The value in cubic yards is 3.996yd³.
What is the volume of the rectangular box?The volume of a rectangular box can be calculated if you know its three dimensions: width, length, and height.
A rectangular box with a square base and no top is to have a volume of 108ft³.
We are to convert the dimension to cubic yards. Using the conversion factor
1 ft³ = 0.0370yd³
108ft³ = x
Cross multiply
1 × x = 108 × 0.0370
x = 3.996
Hence, the value in cubic yards is 3.996yd³.
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The following two-way table shows the data for the students of two different grades in a school:
Member of Public Library Not Member of Public Library Total
25
3
28
Grade 6
Grade 7
Total
23
7
30
48
10
58
Based on the relative row frequency, the students of which grade are more likely to be members of the public library?
The students of both grades are equally likely to be members of the public library
No conclusion can be drawn about the chances of a student being a member of the public library
Answers
.) What is the sum? -3/4+(-3/4)
Answers
Answer:
The answer is -1.5
Step-by-step explanation:
Hope that helps.
Answer:
Step-by-step explanation:
-3/4 + (-3/4) remove parentheses
-3/4- 3/4 calculate the difference
-3/2 or - 1 1/2 or -1.5
A circular clock has a circumference of 27 inches. Find the approximate diameter of the clock. Use 3.14 for π . Round to the nearest hundredth if necessary.
Answers
Answer:
8.60 inches
Step-by-step explanation:
The equation for circumference is 2πr. So we can solve for r (radius).
27inches=2πr
divide both sides by 2π :
r=4.299
The equation for diameter is 2*r so we just multiply
4.299 *2 = 8.598
since we have to round to the hundredth place the answer would be
8.60
The approximate diameter of the circular clock is 8.60 inches.
What is Circumference of a Circle?Circumference of a circle is defined as the total length of the boundary of the circle.
The concept is same as the perimeter for straight sided figures.
Given that,
Circumference of the clock = 27 inches
The formula to find the circumference is,
C = 2πr
where r is the radius.
2r is the diameter.
2πr = 27
2r = 27 / 3.14
2r = 8.5987 ≈ 8.60
Hence the diameter of the clock is 8.60 inches.
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1. (03.04)
What are the zeros of f(x) = (x - 5)(x – 4)(x - 2)? (2 points)
Answers
Answer:
for x=5, x=4 , x=2
Step-by-step explanation:
zero points, the x values that make this formula to be zero.
5-5=0
4-4=0
2-2=0
these values satisfied
The function g is defined by the following rule.
g(x) = 5x-1
Answers
Answer:
Below
Step-by-step explanation:
. SCULPTURE An artist creates two metal sculptures in the shape of regular octagons. A side of the larger sculpture is 3.5 times longer than a side of the smaller octagon. The area of the smaller octagon is 19.28 square inches.
a. What is the area of the larger octagon?
b. The artist is going to pack the sculptures in a cylindrical box to take them to an art show. To the nearest inch, what is the diameter of the smallest box he can use? Explain your reasoning. (Hint: Find the radius of the larger octagon.)
Answers
By using what we know about octagons, we will see that:
a) The area is 244.89 in^2b) The diameter is 18.58 inWhat is the area of the larger octagon?
For an octagon of side length S, the area is:
A = 2*(1 + √2)*S^2
In this case, the area of the smaller octagon is:
19.28 in^2 = 2*(1 + √2)*S^2
Solving for S we get:
S = √( 19.28 in^2/(2*(1 + √2))) = 2.03 in
If we apply an enlargement of a factor 3.5, the new side length is:
S' = 3.5*2.03 in = 7.11 in
Then the area of the larger octagon is:
A' = 2*(1 + √2)*(7.11 in)^2 = 244.89 in^2
b) For an octagon of side length S, the radius is:
R = S*√(1 + 1/√2)
Then the radius of the larger octagon is:
R' = (7.11 in)*√(1 + 1/√2) = 9.29 in
Then the diameter of the box must be:
D = 2*R' = 2*9.29 in = 18.58 in
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What is the area of the shaded sector of the circle? 20pi units squared 40pi units squared 180pi units squared 400
Answers
The area of the sector with a radius of 20 units and a central angle of 162° is 180π unit².
What is the sector of a circle?
A sector is the portion of a circle enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger is the major sector.
The radius of the sector =20 units
Central angle subtended by sector = 162° = 162π/180 radians
As we know the area of a sector= 0.5r²α
where r is the radius and α is the central angle.
So, the area of the given sector = 0.5*20²* 162π/180
The area of the given sector = 180π unit²
Therefore, The area of the sector with a radius of 20 units and a central angle of 162° is 180π unit².
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Answer:
its c
Step-by-step explanation:
Simplify 15(10-4-2)
14
015/2
52-4110
O 105-4110
Answers
[tex]\qquad\qquad\huge\underline{\boxed{\sf Answer☂}}[/tex]
let's simplify ~
[tex]\qquad \sf \dashrightarrow \: \sqrt{5} (10 - 4 \sqrt{2} )[/tex]
[tex]\qquad \sf \dashrightarrow \: ( \sqrt{5} \times 10) - ( \sqrt{5} \times 4\sqrt{2)} [/tex]
[tex]\qquad \sf \dashrightarrow \: 10 \sqrt{5} - 4\sqrt{10} [/tex]