Answer:
Step-by-step explanation:
h(x)=ax^2
Given h=30 when x=150 we get
a(150)^2=30
a=30/22500=1/750 so
h(x)=x^2/750
The equation [tex]\rm h(x)= \frac{1}{750} x^2[/tex] represents the height of the cable at a distance x feet from the center.
It is given that the cable for a certain suspension bridge is modeled by a parabola with vertex (0,0).
It is required to derive the equation that represents the height of cable at a distance x feet from the center.
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
We have the bridge is modeled by a parabola with vertex (0,0)
We know the general equation of parabola:
[tex]\rm y= a(x-h)^2+k[/tex] with vertex (h,k)
Here the value of h = 0 and k = 0
[tex]\rm h(x)= ax^2[/tex] ( ∵ y = h(x) represented the function in terms of height)
We have h = 30 at x = 150 (From the question)
Putting the value of h and x in the parabola equation, we get:
[tex]\rm 30 = a(150)^2[/tex]
[tex]\rm a = \frac{1}{750}[/tex]
Putting the value of 'a' in the parabola equation, we get:
[tex]\rm h(x)= \frac{1}{750} x^2[/tex]
Thus, the equation [tex]\rm h(x)= \frac{1}{750} x^2[/tex] represents the height of the cable at a distance x feet from the center.
Know more about the parabola here:
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What is the correct standard form of the equation of the parabola?
Enter your answer below. Be sure to show each step of your work.
Answer:
Step-by-step explanation:
the standard form for an equation of a parabola is y = a[tex]x^{2}[/tex] + bx + c
also standard form is (x-h)^2 = 4p(y-k)
-(x+3)^2 =4(y-3) for the shown parabola
What is the correct form of the partial fraction decomposition for StartFraction 6 x + 7 Over (x + 2) squared EndFraction?
StartFraction A Over x + 2 EndFraction + StartFraction B Over (x + 2) squared EndFraction
StartFraction A Over x + 2 EndFraction + StartFraction B x + C Over (x + 2) squared EndFraction
StartFraction A Over x EndFraction + StartFraction B Over x + 2 EndFraction + StartFraction C Over (x + 2) squared EndFraction
StartFraction A Over x EndFraction + StartFraction B Over x + 2 EndFraction + StartFraction C x + D Over (x + 2) squared EndFraction
Answer:
its B
Step-by-step explanation:
edge 2020-2021
Answer:
The answer's B!
Step-by-step explanation:
I got it right on Edge 2021! :)
What is the area of the triangle?
Answer:
5 units²
Step-by-step explanation:
Area of the triangle = ½ × base × height
base = 2
height = 5
Plug in the values into the formula
Area = ½ × 2 × 5
Area = ½ × 10
Area = 5 units²
a snowboarder travels 135 meters in 9 seconds how far will the snowboarder travel in 18 seconds
Answer:
The snowboarder travels 270 m in 18 seconds.
Step-by-step explanation:
Given that,
A snowboarder travels 135 meters in 9 seconds.
We need to find how far will the snowboarder travel in 18 seconds.
9 seconds = 135 m
1 second = (135/9) m
In 18 seconds,
[tex]t=\dfrac{135}{9}\times 18\\\\=270\ m[/tex]
So, the snowboarder travels 270 m in 18 seconds.
QUESTION 1
1.1 Given the arithmetic series: - 7 - 3+1 ........... + 173
1.1.2 Calculate the sum of the series.
Step-by-step explanation:
answer is 3,818
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How do I expand the brackets for the equation 5x(6x+1)?
Step-by-step explanation:
30x+5×=35×
35x is your answer
solve for x 7x - 6 = 9x + 6
x = -6
Step-by-step explanation:
7x - 6 = 9x + 6
Add 6, both sides;
7x-6+6 = 9x+6+6
7x=9x+12
Subtract 9x, both sides;
7x-9x = 9x+12-9x
-2x = 12
Divide by same term (-2 in this case);
-2x/-2 = 12/-2
x = -6
Therefore, the value of x is -6
PLEEEEASEEEE I NEED HELP WITH THE ANSWER NOWWWWW!!
i BEG YOUUU GUUUYYYYSSS PLEASEEEE
Answer:
2.4 x 10^4 is the answer in Scientific notation.
Step-by-step explanation:
Divide the 22 million by the 900 texts a month to get 24,444 then round to 24,000
the question is in the picture
In 1906, San Francisco felt the impact of an earthquake with a magnitude of 7.8.
Many pundits claim that the worst is yet to come, with an earthquake 200,010 times
as intense as the 1906 earthquake ready to hit San Francisco. If the pundits ability
to predict such earthquakes were correct, what would be the magnitude of their
claimed earthquake? Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
the population of a town in 1995 was 60,000. the population increased by 25% in 2007.find the population in 2007.
Answer:
75,000
Reason: 25 percent of 60,000 is 15,000. Since the population increased 25 percent more of 60,000, we add 15,000 to 60,000. Thus, the answer is 75,000
Suppose that in a random sample of size 200, standard deviation of the sampling distribution of the sample mean 0.08. researcher wanted to reduce the standard deviation to 0.04. what sample size would be required?
Answer:
400
Step-by-step explanation:
The computation of the sample size needed is shown below:
Since at the sample size of 200 there is a standard deviation of 0.08
But when the standard deviation is 0.04 so the sample size is 400
As sample standard deviation would be inversely proportional to the square root of the sample size
Help please is for now
A ball is thrown straight up from the top of a building 144 ft tall with an initial velocity of 48 ft per second. The height
s(t) (in feet)
of the ball from the ground, at time t (in seconds), is given by
s(t) = 144 + 48t − 16t^2.
Find the maximum height attained by the ball.
Answer:
180feet
Step-by-step explanation:
Given the function that models the height of a ball
s(t) = 144 + 48t − 16t^2.
At maximum height, the velocity is zero ie. ds/dt = 0
ds/dt = 48 - 32t
0 = 48 - 32t
48 = 32t
t = 48/32
t = 1.5secs
Get the maximum height
s(t) = 144 + 48t − 16t^2.
s(1.5) = 144 + 48(1.5)-16(1.5)^2
s()1.5) = 144 + 72 - 16(2.25)
s(1.5) = 144 + 72-36
s(1.5) = 180 feet
Hence the maximum height attained by the ball is 180feet
A local television station sends out questionnaires to determine if viewers would rather see a documentary, an interview show, or reruns of a game show. There were 300 responses with the following results:
90 were interested in a interview and documentary, but not reruns
12 were interested in an interview show and reruns, but not a documentary
42 were interested in reruns but not an interview show
72 were interested in an interview show but not a documentary
30 were interested in a documentary and reruns
18 were interested in an interview show and reruns
24 were interested in none of the three
Required:
How many are interested in exactly one kind of show?
Answer:
144
Step-by-step explanation:
The best way to attempt this question is to solve it using a Venn diagram
From the given information, Let;
D = documentaries
I = interview shows
G = game show reruns
From the images attached below, we will see how the Venn diagrams are being drawn step by step and calculated.
i.e
= 300 - (90 + 60 + 24 + 6 + 12 + 18 + 24)
= 300 - 234
= 66
∴
No of those interested in exactly one kind of show = 66 + 60 + 18
= 144
∴[tex]\text{144 are interested in exactly one kind of show.}[/tex]
Dave's bank account balance reads -$345. What does this mean?
Answer:
hes in debt 345 dollars
Step-by-step explanation:
What value of "p" will the pair of equations
3x + 4y = 12 and px + 12y = 30 NOT have a
unique solution? (Hint: find the slopes
and equate]
Answer:
9
Step-by-step explanation:
Slope is the same as coefficient of x
From the equation
3x+4y=12
Y=(-3/4)x+3
The slope for this eqn is -3/4
For this equation
Px+12y=30
12y=-p+30
Y= (-p/12)x +30/12
The slope is -p/12
To get p
-p/12=-3/4
P=9
The value of "p" is 9 for the pair equations [tex]3x + 4y = 12[/tex], [tex]px + 12y = 30[/tex] which do not have a unique solution. The condition for the pair of equations that do not have a unique solution is that their slopes are equal i.e., [tex]m_1=m_2[/tex].
Solutions to a system of linear equationsA system of linear equations can have,
no solutionexactly one solution or unique solutioninfinitely many solutionsConditions:A system of linear equations is said to have no solution if and only if their slopes are equal and y-intercepts are not equal i.e., [tex]m_1=m_2[/tex] and [tex]c_1\neq c_2[/tex]A system of linear equations is said to have a unique solution or exactly one solution if and only if their slopes must not be equal i.e., [tex]m_1\neq m_2[/tex]A system of linear equations is said to have infinitely many solutions if and only if their slopes, as well as y-intercepts, are equal i.e., [tex]m_1=m_2[/tex] and [tex]c_1=c_2[/tex]Calculating the "p" value for the given pair of equations:Given pair of equations
[tex]3x + 4y = 12\\px + 12y = 30[/tex]
Representing them in the slope-intercept form:
[tex]y=-\frac{3}{4} x+3\\y=-\frac{p}{12}x+\frac{5}{2}[/tex]
As we know that the slope of an equation in the form [tex]y=mx+c[/tex] is m
So, for the two equations slopes are,
[tex]m_1=-\frac{3}{4}[/tex] and
[tex]m_2=-\frac{p}{12}[/tex]
Since it is given that there is no unique solution for the given pair of equations we can write,
[tex]m_1=m_2[/tex]
⇒[tex]-\frac{3}{4} =-\frac{p}{12}[/tex]
⇒[tex]p=9[/tex]
Therefore, the value of "p" when the pair of equations [tex]3x + 4y = 12[/tex] and [tex]px + 12y = 30[/tex] do not have a unique solution is 9.
Learn more about linear equations here:
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What is the common difference between successive terms in the sequence? 0.36, 0.26, 0.16, 0.06, -0.04, -0.14,
Answer:
The common difference between successive terms in the sequence is -0.1
Step-by-step explanation:
Common difference in an arithmetic sequence:
In an arithmetic sequence, the difference between consecutive terms is always the same, and this difference is called common difference.
0.36, 0.26, 0.16, 0.06, -0.04, -0.14
Subtraction of each term by its predecessor. So
0.26 - 0.36 = 0.16 - 0.26 = -0.1
The common difference between successive terms in the sequence is -0.1
What is a square root inequality?
Answer:
(Figure 1) Hence squaring both sides of an inequality will be valid as long as both sides are non-negative. Since square roots are non-negative, inequality (2) is only meaningful if both sides are non-negative. ... Hence, squaring inequalities involving negative numbers will reverse the inequality.
Step-by-step explanation:
Hope this helps have a ncie day :)
What is the slope-intercept form of the equation -3x + y=12
Write the following numbers in decreasing order: −4; 1 2/3 ; 0.5; −1 3/4 ; 0.03; −1; 1; 0; -103; 54
100 points (plz answer asap)
Answer:
-103; -4; -1 3/4; -1; 0; 0.03; 0.5; 2/3; 1; 54
Decreasing order means from largest to smallest
The ordered list is:
54, 1 2/3, 1, 0.5, 0.03, 0, -1, -1 3/4, -4, -103
giving brainliest !! *easy*
um here’s the graph
How do you identify horizontal asymptotes? How do you know the equation of the asymptote?
Step-by-step explanation:
If the polynomial in the numerator is a lower degree than the denominator, the x-axis (y = 0) is the horizontal asymptote. If the polynomial in the numerator is a higher degree than the denominator, there is no horizontal asymptote.
please help! 50 points
Use the drawing tool(s) to form the correct answers on the provided graph.
Consider the function given below.
Answer:
See attached
x- intercepts
(-2, 0), (-1, 0), (1, 0)y- intercept
(0, -2)Find the slope of the line that passes through (6, 8) and (10, 9).
Simplify your answer and write it as a proper fraction, improper fraction, or integer
Step-by-step explanation:
Slope is equal to the change in y over the change in x, or rise over run.
[tex]m = \frac{change \: in \: y}{change \: in \: x} [/tex]
The change in x is equal to the difference in x-coordinates, and the change in y is equal to the difference in y-coordinates.
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
Substitute in the values of x and y into the equation to find the slope.
[tex]m = \frac{9 - (8)}{10 - (6)} [/tex]
Simplify.
[tex]m = \frac{1}{4} [/tex]
Therefor, the slope is 1/4.
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A person who is 6 feet tall stands by a flagpole and casts a shadow that is 3 feet long. At
the same time, the flagpole casts a shadow that is 20 feet long. How tall is the flagpole?
Please explain how you would set this question up then provide the answer.
Which story can be represented by Ask Your Teacher
Rob bought 3 pounds of roast beef. He made sandwiches for a picnic and used 1/4 pound of roast beef in each sandwich. How many sandwiches did Rob make?
Rob made 3 sandwiches. He put 1/4 pound of roast beef in each sandwich. How many pounds of roast beef did Rob use?
Rob bought 1/4 pound of roast beef. He made 3 sandwiches for a picnic. How many pounds of roast beef did Rob put in each sandwich?
Rob bought 3 pounds of roast beef. He used 1/4 pound to make a sandwich for a picnic. How many pounds of roast beef does Rob have left?
HELP I AM ON A TEST
Divide 3 pounds by 1/4 pound per sandwich.
3 / 1/4
When dividing by a fraction flip the fraction over and change divide to multiply:
1. 3 x 4/1 = 12/1 = 12 total sandwiches.
2. Multiply amount per sandwich by number of sandwiches:
3 x 1/4 = 3/4 total
3. Divide total bought by number of sandwiches:
1/4 /3 = 1/4 x 1/3 = 1/12 pound per sandwich
4. Subtract the amount used from total:
3 - 1.4 = 2 3/4 pounds left.
Answer:
3 ./. 1/4
Step-by-step explanation:
What is a prime polynomial?
Answer:A polynomial with integer coefficients that cannot be factored into polynomials of lower degree , also with integer coefficients, is called an irreducible or prime polynomial . Example 1: x2+x+1.
Step-by-step explanation:
Answer:
A polynomial with integer coefficients that cannot be factored into polynomials of lower degree , also with integer coefficients, is called an irreducible or prime polynomial . Example 1: x2+x+1.
Give the sum of -2 3/8 + 1 1/4 in simplest form