Answer:
Parallel lines are lines that never intersect because they have the same slope (m). So, this means that they only possible difference in there equations is the y-intercept (b). ... The slope in each equation is one-half, but each equation has a different y-intercept.
Seven and one-half foot-pounds of work is required to compress a spring 2 inches from its natural length. Find the work required to compress the spring an additional 3 inch.
Answer:
Apply Hooke's Law to the integral application for work: W = int_a^b F dx , we get:
W = int_a^b kx dx
W = k * int_a^b x dx
Apply Power rule for integration: int x^n(dx) = x^(n+1)/(n+1)
W = k * x^(1+1)/(1+1)|_a^b
W = k * x^2/2|_a^b
From the given work: seven and one-half foot-pounds (7.5 ft-lbs) , note that the units has "ft" instead of inches. To be consistent, apply the conversion factor: 12 inches = 1 foot then:
2 inches = 1/6 ft
1/2 or 0.5 inches =1/24 ft
To solve for k, we consider the initial condition of applying 7.5 ft-lbs to compress a spring 2 inches or 1/6 ft from its natural length. Compressing 1/6 ft of it natural length implies the boundary values: a=0 to b=1/6 ft.
Applying W = k * x^2/2|_a^b , we get:
7.5= k * x^2/2|_0^(1/6)
Apply definite integral formula: F(x)|_a^b = F(b)-F(a) .
7.5 =k [(1/6)^2/2-(0)^2/2]
7.5 = k * [(1/36)/2 -0]
7.5= k *[1/72]
k =7.5*72
k =540
To solve for the work needed to compress the spring with additional 1/24 ft, we plug-in: k =540 , a=1/6 , and b = 5/24 on W = k * x^2/2|_a^b .
Note that compressing "additional one-half inches" from its 2 inches compression is the same as to compress a spring 2.5 inches or 5/24 ft from its natural length.
W= 540 * x^2/2|_((1/6))^((5/24))
W = 540 [ (5/24)^2/2-(1/6)^2/2 ]
W =540 [25/1152- 1/72 ]
W =540[1/128]
W=135/32 or 4.21875 ft-lbs
Step-by-step explanation:
1. A helicopter is at a position from two VORS (VHF Omnidirectional
Radio Range, an aircraft navigation system operating in the VHF band -
not covered in chapter) as in the diagram shown below. Given the angles
shown, find the third angle.
Helicopter
74.0°
66.0°
VOR
VOR
The position of the helicopter and the two VORs forms a triangle and the third angle formed by these three entities is 40 degrees
The diagram is not shown; however, the question can still be answered.
The given angles are:
[tex]\theta_1 = 74.0^o[/tex]
[tex]\theta_2 = 66.0^o[/tex]
Represent the third angle as [tex]\theta_3[/tex]
The helicopter and the 2 VORs form a triangle.
So, we make use of the following theorem to calculate the third angle
[tex]\theta_1 + \theta_2 + \theta_3= 180^o[/tex] ---- sum of angles in a triangle
Substitute known values
[tex]74.0^o + 66.0^o + \theta_3= 180^o[/tex]
[tex]140.0^o + \theta_3= 180^o[/tex]
Collect like terms
[tex]\theta_3= 180 -140.0^o[/tex]
[tex]\theta_3= 40^o[/tex]
Hence, the third angle is 40 degrees.
Learn more about angles in a triangle at:
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How do you Find the acute Angle A when sinA=0.616?
Answer:
arcsin0.616
Step-by-step explanation:
arcsino.616
f(x) = 2x3 + 7x2 – 4x – 5
g(x) = 3x – 2
Find (f - g)(x).
A. (f - g)(x) = 2x3 + 7x2 – 2 – 3
O B. (f – g)(x) = 2x3 + 7x2 – 2 – 7
O C. (f - g)(x) = 2x3 + 7m2 – 72 – 3
O D. (f - g)(x) = 2x3 + 7x2 – 73 – 7
Answer:
A. 6
B. 2
C. 8
D. 3
all the answers to the previous questions
D.) = 3
The value of the function (f -g)(x) will be 2x^3 + 7x^2 - 7x - 3
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable, Linear function is a function whose graph is a straight line
We are given that the function as;
[tex]f(x) = 2x^3 + 7x^2 - 4x - 5[/tex]
[tex]g(x) = 3x - 2[/tex]
We need to find the function as (f - g)(x)
(f -g)(x) = f(x) -g(x)
(f -g)(x) = 2x^3 + 7x^2 - 4x - 5 - 3x + 2
(f -g)(x) = 2x^3 + 7x^2 - 7x - 3
Therefore, the correct option is C 2x^3 + 7x^2 - 7x - 3
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Six sophomores and 14 freshmen compete
Answer:
(6C1)(5C1)/20C2
Step-by-step explanation:
Was right on egde
2( 1/5 m− 2/5 )+ 3/5
Answer:
2m/5-1/5
Step-by-step explanation:
2*m-2/5+3/5
2(m-2)/5+3/5
2(m-2)/5+3/5
2m-4/5+3/5
2m/5-1/5
Find the ÷98 and place a point on the # line
Answer:
Draw a number line starting with -100, -95, -90, -85, -80, -75, -70, -65, -60, -55, -50, all the way to 0. Then put a point mark at where the -98 would be.
Find an upper bound for E(h) the error of the machine approximation of the two-point forward difference formula for the first derivative and then find the h corresponding to the minimum of E(h).
The two-point forward difference formula for f'(x) is:_________
Answer:
I doubt it is not going to be a great
Write the additive inverse of each of the following rational numbers:
Answer:
(1)-3/4, (2) 5/21, (3)4/43
A broken pipe is leaking at a rate of 200 fluid ounces per
minute. How many gallons per hour will leak from the
pipe?
Answer:
93.75 gal/hr
Step-by-step explanation:
200 oz · 60 mins = 12000 oz/hr
1 gal ⇔ 128 oz
12000 oz/128 oz = 93.75 gal
how to solve 8(y-7) in digits
Answer:
y = 7
Step-by-step explanation:
Equate the equation to equal 0.
8(y-7) = 0
Open up the bracket:
8y - 56 = 0
Add 56 to both sides:
8y = 56
Divide both sides by 8:
y = 7
A line contains the piont (4,5) and is perpendicular to a line with a slope of -2/3. Write an equarion of the line satisfying the given conditions. Write the answer in slope-intercept form
Answer:
[tex]y=\frac{3}{2}x-3.5[/tex] or, preferably, [tex]y=\frac{3}{2}x-\frac{7}{2}[/tex]
Step-by-step explanation:
First is to find the perpendicular slope. In this case, you swap the numerator and denominator and then multiply that fraction by -1.
In this case, -2/3's inverse slope is 3/2.
Now, the initial y=3/2 passes through 7.5,5
So, you must subtract 3.5 from that to make it pass through 4,5.
In this way, you get the answer in slope-intercept form.
Answer:
y = [tex]\frac{3}{2}[/tex] x - 1
Step-by-step explanation:
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{2}{3} }[/tex] = [tex]\frac{3}{2}[/tex] , then
y = [tex]\frac{3}{2}[/tex] + c ← partial equation in slope- intercept form
To find c substitute (4, 5) into the partial equation
5 = 6 + c ⇒ c = 5 - 6 = - 1
y = [tex]\frac{3}{2}[/tex] x - 1 ← equation of line
Solve the following systems of equations using the substitution method. 6x + 2y = 82 and x − y = 3 y = 4x − 1 and x + y = 9 4x + 3y =17 and y = 5 − x
Step-by-step explanation:
puhhh ! that way of typing can be misleading.
let me sum up what equations I think the problem definition specified :
1)
6x + 2y = 82
x - y = 3
2)
y = 4x - 1
x + y = 9
3)
4x + 3y = 17
y = 5 - x
solving 1)
x - y = 3 => x = y + 3
putting this into the first equation
6×(y+3) + 2y = 82
6y + 18 + 2y = 82
8y +18 = 82
8y = 64
y = 8
x = y + 3 = 8 + 3 = 11
solving 2)
using the first equation in the second equation
x + (4x - 1) = 9
5x - 1 = 9
5x = 10
x = 2
y = 4x - 1 = 4×2 - 1 = 8 - 1 = 7
solving 3)
using the second equation in the first equation
4x + 3×(5 - x) = 17
4x + 15 - 3x = 17
x + 15 = 17
x = 2
y = 5 - x = 5 - 2 = 3
look at the image for the question
The double number line shows that Toni can type 180 words in
2 minutes.
Based on the ratio shown in the double number line, how many words can Toni type in 3 minutes?
Answer:
120 words
Step-by-step explanation:
as a ratio it's
2:180
In real life the longer you do something the more words you type
so since you can't get to 3 from 2 easily you go to 1 instead.
2:180
1:360
3:120
30 is what percent of 44?
Answer:
68.18
Step-by-step explanation:
→ Set up an equation
[tex]\frac{44x}{100} =30[/tex]
→ Times both sides by 100
44x = 3000
→ Divide both sides by 44
68.18
Molly and Lynn both set aside money weekly for their savings. Molly already has $650 set aside and adds $35 each week. Lynn already has $825 set aside but adds only $15 each week. Which inequality could they use to determine how many weeks, w, it will take for Molly’s savings to exceed Lynn’s savings?
FINAL ANSWER: D
Given : Molly and Lynn both set aside money weekly for their savings.
Molly already has $650 set aside and adds $35 each week.
Lynn already has $825 set aside but adds only $15 each week.
To Find : inequality to determine how many weeks, w, it will take for Molly’s savings to exceed Lynn’s savings
Solution:
Molly already has $650
adds $35 each week.
=> added in w weeks = 35w
After w weeks = 650 + 35w
Lynn already has $825
adds $15 each week.
added in w weeks = 15w
After w weeks = 825 + 15w
Molly’s savings to exceed Lynn’s savings
⇒ 650 + 35w > 825 + 15w
⇒ 20w > 175
⇒ 4w > 35
⇒ w > 35 /4
At least 9 weeks
Answer:
D
Step-by-step explanation:
First, to eliminate some answers you can figure out which way the sign should go. The question wants to know when Molly's savings will be larger so the sign should open towards her side of the equation. Since her savings are represented on the left the sign should be a greater than, >.
Then, figure out where the variables belong. The variable represents the number of weeks that have passed, so they should be multiplied by the number that is affected by the passing of weeks. This is the amount each person saves, aka the independent variable. So the "w" variable should be next to the 35 and 15.
Find the distance between the origin and the points (-8, 4)
Answer:
poop everyday and night
Step-by-step explanation:
cool kid
John runs a computer software store. Yesterday he counted 140 people who walked by the store, 63 of whom came into the store. Of the 63, only 25 bought something in the store.
(a) Estimate the probability that a person who walks by the store will enter the store. (Round your answer to two decimal places.)
(b) Estimate the probability that a person who walks into the store will buy something. (Round your answer to two decimal places.)
(c) Estimate the probability that a person who walks by the store will come in and buy something. (Round your answer to two decimal places.)
(d) Estimate the probability that a person who comes into the store will buy nothing. (Round your answer to two decimal places.)
Answer:
.................
Step-by-step explanation:
............
7
Abdul's gas tank is
1
3
full. After he buys 12 gallons of gas, it is
full. How many gallons can Abdul's tank hold?
9
Answer:
27
Step-by-step explanation:
Let T be the capacity of the tank.
Since the tank was 1/3 full and ends up 7/9 full.
[tex]\frac{7}{9}[/tex]T - [tex]\frac{1}{3}[/tex]T = 12
Simplifying the left side of the equation, tells us how much 12 gallons fills.
[tex]\frac{4}{9}[/tex]T = 12
Now we solve for T:
T = 12*9/4
T = 27
Solve for y in terms of x.
2/3y-4=x
A y= 3/2x+6
B y=-2/3x+4
C y=-3/2x+6
D 2/3x+4
HELPPPPP ASP PLZZZZZ
Answer:
[tex](f-g)(x)[/tex]
[tex]f(x)-g(x)[/tex]
[tex]x^{2} -6x-27-x+9[/tex]
[tex]x^{2} -7x-18[/tex]
----------------------
[tex](f*g)(x)[/tex]
[tex]=f(x)g(x)[/tex]
[tex](x^{2} -6x-27)(x-9)[/tex]
[tex]=x^{3} -15x^{2}+27x+243[/tex]
----------------------
[tex]\frac{f}{g} (x)[/tex]
[tex]\frac{x^{2} -6x-27}{x-9}[/tex]
[tex]\frac{(x-9)(x+3)}{x-9}[/tex]
[tex]x+3[/tex]
-----------------------
[tex](f+g)(x)[/tex]
[tex]f(x)+g(x)[/tex]
[tex]=x^{2} -6x-27+x-9[/tex]
[tex]=x^{2} -5x-36[/tex]
------------------------
OAmalOHopeO
------------------------
Factorise: x^3 + x^2 + x^2y + xy + y
Plz also show me the process.
Complete the table for the given rule.
Rule: y is 0.75 greater than x
x y
0
3
9
The complete table is
x y
0 0.75
3 3.75
9 9.75
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
What is substitution?Substitution means putting numbers in place of letters to calculate the value of an expression or equation.
According to the given question.
We have values of x.
Also, one rule that y is 0.75 greater than x.
So, we have a equation for finding the value of y i.e.
[tex]y = x + 0.75..(i)[/tex]
For finding the value of y
At x = 0, substitute x = 0 in equation (i)
[tex]y = 0 + 0.75\\\implies y = 0.75[/tex]
At x = 3, substitute x = 3 in equation (i)
[tex]y = 3+0.75\\\implies y = 3.75[/tex]
At x = 9, substitute x = 9 in equation (i)
[tex]y = 9+0.75\\\implies y = 9.75[/tex]
Hence, the complete table is
x y
0 0.75
3 3.75
9 9.75
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Find the equation of the linear function represented by the table below in slope-intercept form.
Answer:
y=-4x-5
Step-by-step explanation:
The slope of the line is - 4, the equation of line is y=-4x-5
Find the area of the figure. (Sides meet at right angles.)
Answer:
56
Step-by-step explanation:
A=(3*4)+(4*(4+3+4))=56
Worth a lot of points.
Answer:
It's the last one.
Step-by-step explanation:
For example, if you have 0, the absolute valeu of 0 is 0. A postive number like 2, has an absolute value of 2. 0 is not greater than 0 and 2 is not greater than 2. Hope this helps!
Answer: Kayla is incorrect. The absolute value of 0 or a positive number is equal to the number.
Absolute numbers cannot be negative numbers. Therefore, an absolute number of a positive number will always be the positive number.Lauren bought 15 rainbow and balloon stickers for her little sister. The rainbow stickers cost 3 cents apiece and the balloon stickers cost 6 cents apiece. If Lauren spent exactly 81 cents, how many of each type of sticker did she buy?
Answer:
3 rainbow stickers and 12 balloon stickers
Step-by-step explanation:
Let x = rainbow count
Let y = balloon count
x + y = 15
x = 15 - y
3x + 6y = 81
3(15 - y) + 6y = 81
45 - 3y + 6y = 81
3y = 36
y = 12
x = 15 - 12
x = 3
Im new to this app!
And im looking for help!!
Please help ASAP!!!
Please!!!!
y=x²-10x-7
a>0 so we will be looking for minimum
x=-b/2a=10/2=5
y=25-50-7=-32
Answer: (5;32)
Please Help!! Whoever helps and gets it correct gets Brainliest and 5 star rating!!
Answer:
the reasoning states that "all the numbers begin with a 7 or an 8"
however this is not accurate as they can be in different placements
which can make a big difference in the total estimate.
for example:
the number could've been an 8, or an 80
they both begin with an 8
however have totally different values and could have messed up the total estimated number.
hope this helps :D
