Answer:
The quotient decreases
Step-by-step explanation:
Give the expression :
10 / d
What happens to the expression as d increases. from small positive to large positive ;
d in the expression is the denominator ;the value obtained by dividing the numerator by the denominator is the quotient.
Since the value of the numerator is constant ;
As the value of d increases, the quotient obtained becomes smaller `
For instance,
Let
d = 2;
10 /2 = 5
d = 3
10 / 3 = 3.333
d = 4
10 / 4 = 2.5
And the trend continues
Answer:
2.5 on khan
Step-by-step explanation:
A train is spotted 10 miles south and 8 miles west of an observer at 2:00 pm. At 3:00 pm the train is spotted 5 miles north and 16 miles east of the observer. a. How far did the train travel in the first hour? b. If the train continues at this pace where will it be in relation to the observer at 5:00 pm? Write a function that will give the train's position at any given time c. d. At 2:00 pm a cyclist is traveling due east and is next to the observer. If the cyclist is traveling at 10 mph, do they collide with the train when the bike goes over the train tracks?
Answer:
a. The distance the train travelled in the first hour is approximately 28.3 miles
b. The location of the train at 5:00 p.m. is 53 miles east, and 46 miles west
c. The location of the train at any given time by the function, f(t) = (-8 + 24·t, -10 + 15·t)
d. The train does not collide with the cyclist when the bike goes over the train tracks
Step-by-step explanation:
a. The given information on the train's motion are;
The location south the train is spotted = 10 miles south and 8 miles west
The time the observer spotted the train = 2:00 pm
The location the train is spotted at 3:00 p.m. = 5 miles north and 16 miles east
Therefore, the difference between the two times the train was spotted, t = 3:00 p.m. - 2:00 p.m. = 1 hour
Making use of the coordinate plane for the two locations the train was spotted, we have;
The initial location of the train = (-10, -8)
The final location of the train = (5, 16)
Therefore the distance the train travelled in the first hour is given by the formula for finding the distance, 'd', between two points, (x₁, y₁) and (x₂, y₂) as follows;
[tex]d = \sqrt{\left (x_{2}-x_{1} \right )^{2}+\left (y_{2}-y_{1} \right )^{2}}[/tex]
Therefore;
[tex]d = \sqrt{\left (5-(-10) \right )^{2}+\left (16-(-8) \right )^{2}} = 3 \cdot\sqrt{89}[/tex]
The distance the train travelled in the first hour, d = 3·√89 ≈ 28.3 miles
b. The speed of the train, v = (Distance travelled by the train)/Time
∴ v ≈ 28.3 miles/(1 hour) = 28.3 miles per hour
The speed of the train in the first hour, v ≈ 28.3 mph
The direction of the train, θ, is given by the arctangent of the slope, 'm', of the path of the train;
[tex]\therefore The \ slope \ of \ the \ path \ of \ the \ train, \, m =tan(\theta) = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
∴ m = tan(θ) = (5 - (-10))/(16 - (-8)) = 0.625
c. Distance = Velocity × Time
At 5:00 p.m., we have;
The time difference, Δt = 5:00 p.m. - 3:00 p.m. = 2 hours
The distance, d₁ = (28.3 mph × 2 hours = 56.6 miles
Using trigonometry, we have the horizonal distance travelled, 'Δx', in the 2 hours is given as follows;
Δx = d₁ × cos(θ)
∴ Δx = 56.6 × cos(arctan(0.625)) ≈ 48
The increase in the horizontal position of the train, relative to the point (5, 16), Δx ≈ 48 miles
The vertical distance increase in the two hours, Δy is given as follows;
Δy = 56.6 × sin(arctan(0.625)) ≈ 30
The increase in the vertical position of the train, relative to the point (5, 16), Δy ≈ 30 miles miles
Therefore; the location of the train at 5:00 p.m. = ((5 + 48), (16 + 30)) = (53, 46)
The location of the train at 5:00 p.m. = 53 miles east, and 46 miles west
c. The function, 'f', that would give the train's position at time-t is given as follows;
The P = f(28.3·t, θ)
Where;
28.3·t = √(x² + y²)
θ = arctan(y/x)
Parametric equations
y - 5 = 0.625·(x - 16)
∴ y = 0.625·x - 10 + 5
The equation of the train's track is therefore, presented as follows;
y = 0.625·x - 5
d = 28.3·t
The y-component of the velocity, [tex]v_y[/tex] = 3*√89 mph × sin(arctan(0.625)) = 15 mph
Therefore, we have;
y = -10 + 15·t
The x-component of the velocity, vₓ = 3*√89 mph × cos(arctan(0.625)) = 24 mph
Therefore, we have;
x = -8 + 24·t
The location of the train at any given time, 't', f(t) = (-8 + 24·t, -10 + 15·t)
d. The speed of the cyclist next to the observer at 2:00 p.m., v = 10 mph
The distance of the cyclist from the track = The x-intercept = 5/0.625 = 8
The distance of the cyclist from the track = 8 miles
The time it would take the cyclist to react the track, t = 8 miles/10 mph = 0.8 hours
The location of the train in 0.8 hours, is f(0.8) = (-8 + 24×0.8, -10 + 15×0.8)
∴ f(0.8) = (11.2, 2)
At the time the cyclist is at the track along the east-west axis, at the point (8, 0), the train is at the point (11.2, 2) therefore, the train does not collide with the cyclist when the bike goes over the train tracks.
If the cyclist is travelling at 10 mph the train does not collide with the cyclist when the bike goes over the train tracks.
The location south the train is spotted = 10 miles south and 8 miles west
The time the observer spotted the train = 2:00 pm
The location of the train is spotted at 3:00 p.m. = 5 miles north and 16 miles east
Thus, the difference between the two times the train was spotted,
t = 3:00 p.m. - 2:00 p.m. = 1 hour
What is the distance?The distance is the product of velocity and time.
Distance = Velocity × Time
The initial location of the train = (-10, -8)
The final location of the train = (5, 16)
Therefore the distance the train travelled in the first hour
[tex]d = \sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} } \\d = \sqrt{(5 -(-10) )^{2} +(16-(-8) )^{2} }[/tex]
d = 3√89
The distance the train travelled in the first hour, d = 28.3 miles
b. The speed of the train, v = (Distance travelled by train)/Time
∴ v ≈ 28.3 miles/(1 hour) = 28.3 miles per hour
The speed of the train in the first hour, v ≈ 28.3 mph
The direction of the train, θ, is given by the arc tangent of the slope, 'm', of the path of the train;
∴ m = tan(θ) = (5 - (-10))/(16 - (-8))
m = 0.625
c. Distance = Velocity × Time
At 5:00 p.m., we have;
The time difference, Δt = 5:00 p.m. - 3:00 p.m. = 2 hours
The distance, d₁ = (28.3 mph × 2 hours = 56.6 miles
Using trigonometry, we have the horizontal distance travelled, 'Δx', in the 2 hours is given as follows;
Δx = d₁ × cos(θ)
∴ Δx = 56.6 × cos(arctan(0.625)) ≈ 48
The increase in the horizontal position of the train, relative to the point (5, 16), Δx ≈ 48 miles
The vertical distance increase in the two hours, Δy is given as follows;
Δy = 56.6 × sin(arctan(0.625)) ≈ 30
The increase in the vertical position of the train, relative to the point (5, 16), Δy ≈ 30 miles miles
Therefore; the location of the train at 5:00 p.m. = ((5 + 48), (16 + 30)) = (53, 46)
The location of the train at 5:00 p.m. = 53 miles east, and 46 miles west
c. The function, 'f', that would give the train's position at time-t is given as follows;
The P = f(28.3·t, θ)
28.3·t = √(x² + y²)
θ = arctan(y/x)
Parametric equations
y - 5 = 0.625·(x - 16)
∴ y = 0.625·x - 10 + 5
The equation of the train's track is, therefore, presented as follows;
y = 0.625·x - 5
d = 28.3·t
The y-component of the velocity,
= 3 × √89 mph × sin(arctan(0.625)) = 15 mph
Therefore, we have
y = -10 + 15·t
The x-component of the velocity,
vₓ = 3 × √89 mph × cos(arctan(0.625))
= 24 mph
Therefore, we have;
x = -8 + 24·t
The location of the train at any given time, 't',
f(t) = (-8 + 24·t, -10 + 15·t)
d. The speed of the cyclist next to the observer at 2:00 p.m., v = 10 mph
The distance of the cyclist from the track = The x-intercept
= 5/0.625 = 8
The distance of the cyclist from the track = 8 miles
The time it would take the cyclist to reach the track, t = 8 miles/10 mph = 0.8 hours
The location of the train in 0.8 hours, is f(0.8)
= (-8 + 24×0.8, -10 + 15×0.8)
∴ f(0.8) = (11.2, 2)
therefore, If the cyclist is travelling at 10 mph the train does not collide with the cyclist when the bike goes over the train tracks.
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If one half life is the amount of time it takes for a radio active isotope to decay by a factor of 2, approximately which percent describes how much of the initial quantity of a substance would remain after 2-3 half lives?
A.0.25
B.0.20
C.0.75
D.0.50
Answer:
the answer for this question is option c
A cube has a surface area of 24. What's the volume?
a 48
b 12
c 16
d 8
Answer:
Step-by-step explanation:
The voloum is 8 cubic cm.
if the surface area is 24 the volume is 8.
Kevin knit scarves for his friends. Altogether, the scarves had a total length of
442.8 in. If he knit 9 scarves, and each scarf was the same length, how long
was each scarf? Write your answer in feet.
Kevin knit 9 scarves, and each scarf was 49.2 inches long.
Converting this length to feet, we find that each scarf is 4.1 feet long.
Let's use the variable "L" to represent the length of each scarf in inches. Since Kevin knit 9 scarves, we can write the equation for the total length of all scarves as:
[tex]\(L_{\text{total}} = L \times 9\)[/tex]
We are given that the total length of all scarves is 442.8 inches. So, we can write:
[tex]\(442.8 \text{ inches} = L \times 9\)[/tex]
To find the length of each scarf, we need to isolate "L" on one side of the equation. To do that, we can perform the following steps:
Divide both sides of the equation by 9 to get:
[tex]\(\frac{{442.8 \text{ inches}}}{{9}} = \frac{{L \times 9}}{{9}}\)[/tex]
Simplifying, we get:
[tex]\(49.2 \text{ inches} = L\)[/tex]
Now, we have found the length of each scarf in inches (49.2 inches). To convert this length to feet, we know that 1 foot is equal to 12 inches. So, to find the length in feet, we divide the length in inches by 12:
[tex]\(L_{\text{feet}} = \frac{{L_{\text{inches}}}}{{12}}\)[/tex]
Substituting the value of [tex]\(L_{\text{inches}}\)[/tex] with 49.2 inches:
[tex]\(L_{\text{feet}} = \frac{{49.2 \text{ inches}}}{{12}}\)[/tex]
Now, let's perform the division:
[tex]\(L_{\text{feet}} = 4.1 \text{ feet}\)[/tex]
So, each scarf is 4.1 feet long.
Kevin knit 9 scarves, and each scarf was 49.2 inches long.
Converting this length to feet, we find that each scarf is 4.1 feet long.
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PLEASE HELP I NEED IT NOW
Liam puts $60 in savings in March and 150% of this amount in savings in April. How much does Liam put in savings in April? Round to the nearest whole dollar. *
Answer:
Savings in March: $60
Savings in April: $60 + 150% of $60=$60 +$90=$150
Step-by-step explanation:
Liam adds another 150% of the original amount to his savings. So, his total amount does not change but the amount increases by $90 (150% of $60).
URGENT!!!!!!!! PLEASE HELP ASAP TIMED!!!!!!!!!!!!!!! HELP!!!!!!!!!!!!!!!!!
Answer:
Height of building = 86.9 ft
Step-by-step explanation:
I've drawn a triangle image to depict this question and I have attached it.
From the attached image, we can see that ABC is the height of the building.
We can see the distance from your eye to the ground indicated and also the distance from the horizontal distance from the building to you indicated.
We can use pythagoras theorem to find AB.
AB/57 = tan 55°
AB = 57 × 1.4281
AB = 81.4 ft
Now, total height of the building is AB + BC.
BC = 5.5 ft since B is parallel to your eye and height from there to the ground is 5.5 ft.
Thus;. Height of building = 81.4 + 5.5 = 86.9 ft
Lee is selling spirit wear for a
fundraiser. Hats cost $8 and shirts cost $12. Lee sold $272 worth of spirit wear in the first month. If Lee sold a total of
28 items, how many hats did Lee sell?
Please write an equation as well.
Answer:
16 hats
Step-by-step explanation:
8h+12s=272
h+s=28
isolate s to get s=28-h
substitute that in for s and solve for h
you will get h=16 meaning 16 hats were sold
I WAS IN THE HOSPITAL AND MISSED A MATH LESSON HELP PLZZZ
Answer:
30 ft
Step-by-step explanation:
[tex]C=\frac{n^2}{5} +175\\\\355=\frac{n^2}{5} +175\\\\180=\frac{n^2}{5}\\\\n^2=900\\\sqrt{n^2} =\sqrt{900} \\n=30[/tex]
Solve. 382.04 – 6,3 *
I need help
3x^2=20-7x
factor step by step please?
Answer:
x=5/3 or x=-4
Step-by-step explanation:
Please answer this!! sorry if you keep seeing my questions I suck at math !!
Answer:
AB = 12
BC = 9
Step-by-step explanation:
x= -4
AB -4+16 = 12
BC -4+13 = 9
12+9 = 21
-9+3y=24 write an equivalent equation in slope intercept form
ig hanganaahajssislaalalla
i don't understand this can someone help me please
Answer:
Total interest to be paid: $210
Total amount to be repaid: $3,710
Step-by-step explanation:
You can ignore the monthly payment for this problem.
For simple interest, the formula is I = PRT where I = interest earned, P = principal amount borrowed/deposited, R = rate as a decimal, and T = time in years.
I = (3,500)(0.06)(1)
I = 210
Then add that to the amount borrowed ($3,500) and you're done.
3,500 + 210 = $3,710
Please let me know if you have questions.
HELP I NEED HELP ASAPD DHEWUHFWUFHWKEJFB;KWFBEUFB;KWEGFWKFJBWKBFKWEFBIWEUFBWIEFBWEIBFWEFBIWUEFIWEU HEP !!! ANSWER PLEASE!!
Answer:
I think it's 25
Step-by-step explanation:
I used a protractor
Mr. Thomsen is buying two types of gift
cards to give as prizes to employees at a
company meeting. He will buy restaurant
gift cards that each cost $50. He will also
buy movie theater gift cards that each
cost $20. He has $450 to buy a total of
15 gift cards. How many of each type of gift cards can he buy?
Answer:
he can buy 6 gift cards, 7 theatre cards with a remainder of $10.
Step-by-step explanation:
Watch ne
The diameter of a circle is 4 m. Find its area to the nearest tenth.
m
Answer A=
Answer:
area = 12.6 m²
Step-by-step explanation:
r = 4/2 = 2
area = πr² = (3.14)(2²) = 12.56 m²
I need this question really badly
Answer:
yeah same for me but with ice cream
If I donate 250 milliliters in 12 minutes and need to reach 825 milliliters, how long will it take to complete the donation?
Answer:
17,160
Step-by-step explanation:
250. Milliliters = 12 minutes
1 liter= 250/12
= 20.83
Therefore the time required to reach 825 ministers
= 825×20.8
= 17,160
Hence the time needed is 17, 160
HELP ... answer correctly pls
Use the expression below to answer the question.
-3/4 x 2/5
Which situation can be modeled by the expression?
A. Zach owes 3/4 of the original price of his car. Each month he pays 2/5 of the original price. How many months will it take Zach to pay off his car?
B. Zach owes 3/4 of the original price of his car. Each month he pays 2/5 of how much he still owes on the car. What fraction of the original price does Zach owe after this month’s payment?
C. Abdi owes Kim 3/4 of a dollar. He needs to borrow more money from Kim. Abdi then borrows 2/5 of how much he owes. By what fraction of a dollar does the amount Abdi owes Kim change?
D. Abdi owes Kim 3/4 of a dollar. He pays her 2/5 of how much he owes. What fraction of a dollar does Kim receive from Abdi?
Answer:
D.
Step-by-step explanation:
The situation that can be modeled by the expression -3/4 x 2/5 is:
Abdi owes Kim 3/4 of a dollar. He pays her 2/5 of how much he owes.
The expression -3/4 x 2/5 gives us the fraction of a dollar that Kim receives from Abdi, which is -3/10 of a dollar.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
The expression -3/4 x 2/5 means that we multiply -3/4 by 2/5.
Multiplying two fractions involves multiplying their numerators together and their denominators together. So,
-3/4 x 2/5 = (-3 x 2) / (4 x 5) = -6/20 = -3/10
Therefore,
The situation that can be modeled by the expression -3/4 x 2/5 is:
Abdi owes Kim 3/4 of a dollar. He pays her 2/5 of how much he owes.
The expression -3/4 x 2/5 gives us the fraction of a dollar that Kim receives from Abdi, which is -3/10 of a dollar.
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How many more miles per gallon does Mrs. Sanchez get than Mr. White?
Mrs. Sanchez
y = 36x
Let x represent number of gallons and y represent numbers of miles.
Mr. White
# of gallons miles
2.5
76
5
152
15
456
18
547.2
miles per gallon
Answer:
5.6 miles per gallon
Step-by-step explanation:
Equation for Mrs Sanchez: y = 36x
The rate of change = miles/gallon for Mrs Sanchez = 36 miles/gallon
Let's find the rate of change for Mr White:
Rate of change = change in y/change in x
Using two pairs of values form the table given, (2.5, 76) and (5, 152),
Rate of change = (152 - 76)/(5 - 2.5) = 76/2.5
Rate of change = miles/gallon = 30.4 miles/gallon
The difference between the miles per gallon of Mrs Sanchez and Mr White = 36 - 30.4 = 5.6 miles per gallon.
Therefore, Mrs Sanchez gets 5.6 miles per gallon than Me White
One third of a number, decreased by 3/4 gives 1/3. What is the number?
Answer:
hmmmm
Step-by-step explanation:
pls help need it ASAP will give brainlist
Answer:
BE = 3.5 m
Step-by-step explanation:
Δ ACB and Δ EDB are similar, so the ratios of corresponding sides are equal, that is
[tex]\frac{BE}{BA}[/tex] = [tex]\frac{BD}{BC}[/tex] , substitute values
[tex]\frac{BE}{21}[/tex] = [tex]\frac{3}{18}[/tex] ( cross- multiply )
18 BE = 63 ( divide both sides by 18 )
BE = 3.5
simplify the expression PLEASE PLEASE HELP
Answer:
y ^8
Step-by-step explanation:
Answer:
y^8
------------
When there is a parenthesis around a variable with an exponent, and there is another exponent outside of this parenthesis, we multiply the two numbers together. This means: 4 * 2, or 8. Moreover, the answer to this question is y^8
help with this nth term homework please answer true of false
The radius of a circle is 44 centimeters. What is the circle's circumference?
Answer:
276
Step-by-step explanation:
Circumference = 2πr
= 276
Tickets for a school play cost $6 each. Brandy sold 8 tickets to her father, then sold another x tickets to her aunt. Brandy ended up collecting $66.
Write an equation that can be used to find x, number of tickets sold to her aunt.
PLS HELP I DONT UNDERSTAND
Can somebody please help me????
Answer:
It's the third option
Step-by-step explanation:
One sides needs to have Lunches and the other needs to have how many is sold
It also needs to be clear and option 2 Is not as clear as 1 and 3
the only options that leaves us is 1 and 3
option 1 has the wrong labels
so.it is OPTION 3
A model of a volcano has a height of 12 in., and a diameter of 12 in.
What is the approximate volume of the model?
Use 3.14 to approximate pi, and express your final answer as a decimal.
Enter your answer as a decimal in the box.
Answer:
452.16 cm³
Step-by-step explanation:
I assume the shape of the volcano is a cone.
V = (1/3)πr²h
r = d/2 = 12 in./2 = 6 in.
V = (1/3)(3.14)(6 in.)²(12 in.)
V = 452.16 in.²
Answer:
Step-by-step explanation:
Radius r = 6 inches
Height h = 12 inches
volume of cone = πr²h/3 ≈ 3.14∙6²∙12 = 1,356.48 in³
3 Given: AC= AD, CB = DB Prove: AABON AABD po Statements Reasons 1
pls help 100 points
Answer:
. Statement. 1. AD ≅ CE & DB ≅ EB Side. 2. ∠B ≅ ∠B Angle. 3. AD + DB ≅ CE + EB or AB ≅ BC Side. 4. ΔABE ≅ ΔBCD. 5. ∠1 ≅ ∠2. 6. ∠1 & ∠3
Step-by-step explanation:
Which statement is true of the right triangles ABC and DEF?
Area of ABC is greater than area of DEF.
Area of ABC is less than area of DEF.
Area of ABC is equal to the area of DEF.
There is not enough information to compare the areas of triangles ABC and DEF
Answer:
The answer is A
Step-by-step explanation:
edge21
The statement which is true of the right triangles ABC and DEF is Area of ABC is greater than area of DEF.
What is Right Angled Triangle?Right angled triangle are those triangle for which one of the angle is 90 degrees.
Given two right angled triangles, ABC and DEF.
Area of a triangle = 1/2 × base × height
Area of ΔABC = 1/2 × 14 × 6
= 42 square units
Base of ΔDEF = √(7² + 4²) = √65
Height of ΔDEF = √(5² + 8²) = √89
Area of ΔDEF = 1/2 × √65 × √89
= 38.03 square units
Hence the correct option is Area of ABC is greater than area of DEF.
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