Answer:
x² + y² = 6
Circle Center at the origin; r = square root 6
(x - 0)² + (y - 0)² = (✓6)²
x² + y² = 6
50 de 100 ün en sade halı acil
Answer:
srry buddy I don't understand your language
I am from India
can ask it in English
then I could help you
A race-car is driving counter-clockwise on a circular track with a radius of 1.9 miles. The car starts at the 3 o'clock position and travels at a constant speed of 85.5 miles per hour.
What distance (in miles) has the race-car traveled if the car has swept out an angle of 212 degrees?
_____miles
What is the measure of the angle swept out by the car (in radians) if the car has traveled 4.9 miles?
_____radians
Define a function, h, that gives the race-car's distance above the horizontal diameter of the track (in miles) in terms of the number of hours since the race-car started driving, t.
Answer:
The answer is below
Step-by-step explanation:
The car is moving in a circular track with a radius of 1.9 miles. The distance covered by the car if the track is revolved once = 2π * radius of the track.
a) Since the car has swept out an angle of 212 degrees, the distance covered by the race car = [tex]\frac{212}{360}*2\pi(1.9)=7.03 \ miles[/tex]
b) If the car traveled 4.9 miles, the angle swept out (θ) is:
[tex]4.9= \frac{\theta}{360} * 2\pi r\\\\\theta=\frac{4.9}{2\pi (1.9)}*360 \\\\\theta=147.76^o=147.76^o*\frac{\pi}{180} \\\\\theta=2.58\ rad[/tex]
c) h = distance covered, t = time in hourss.
Hence:
h = 85.5t
The race-car's motion round the track is a repeating motion that can be
described by a sinusoidal function.
The correct responses are;
Distance travelled when the car swept an angle of 212° ≈ 7.03 milesIf the car has travelled 4.9 miles, the angle swept out, θ ≈ 2.58 radiansThe function is; [tex]\underline{h(t) = 1.9\cdot sin(45\cdot t)}[/tex].Reasons:
Known parameters are;
Radius of the track, r = 1.9 miles
Point the car starts = 3 O'clock
Speed of the car = 85.5 mph
Required:
Distance swept out when the car traveled an angle of 212°.
Solution;
Distance of one complete turn = 2·π·r
Angle of one complete turn = 360°
Therefore, at 212°, we have;
[tex]\dfrac{212^{\circ}}{360^{\circ}} \times 2 \times 1.9 \times \pi \approx 7.03[/tex]
Distance travelled when the car swept an angle of 212° ≈ 7.03 milesRequired:
The measure of the angle swept out by the car if the car has travelled 4.9 miles.
Solution;
Let, θ represent the angle, we have;
[tex]\dfrac{\theta}{2 \cdot \pi} \times 2 \times 1.9 \times \pi \approx 4.9 \ miles[/tex]
We get;
[tex]{\theta} = \dfrac{4.9 \ miles}{2 \times 1.9 \ miles \times \pi } \times 2\cdot \pi \approx 2.58 \ radians[/tex]
If the car has travelled 4.9 miles, the angle swept out, θ ≈ 2.58 radiansRequired:
The function, h, that gives the distance of the above the horizontal
diameter of the track (in miles) in terms of the number of hours since the
race-car started driving, t.
Solution;
The function that gives the car height can be presented as follows;
The angular velocity, ω = [tex]\dfrac{v}{r}[/tex]
Therefore;
[tex]\omega = \dfrac{85.5 \ mph}{1.9 \ miles} = 45 \ rad/hour[/tex]
The general form of the sinusoidal function is h = A·sin[k·(θ - b)] + c
Therefore, we get;
h = 1.9·sin[k·(θ - b)] + c
The period, T = 2·π/ω = 2·π/k
Therefore, given that ω·t = θ, we get;
h = 1.9·sin[ω·t - b] + c = 1.9·sin[45·t - b] + c
The vertical sift, c, and the horizontal shift, b, can both be taken as zero,
given that the sin(0) = 0, therefore;
h = 1.9·sin[0] + c = c = 0, such that the at the start, t = 0, the car is at a
distance of h = 0 above the horizontal line.
The function, h, that gives the distance of the car above the
horizontal track, in terms of the number of hours since the car started
driving, t, is therefore;
[tex]\underline{h(t) = 1.9\cdot sin(45\cdot t)}[/tex].Learn more here:
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A pool is filled with 2,980 quarts of water. How many gallons of water are in the pool?
A. 4 gallons
B. 745 gallons
C. 2,980 gallons
D. 11,920 gallons
Answer:
b.
Step-by-step explanation:
Lily took a loan of $1200 with simple interest for as many years as the rate of
interest. If she paid $432 as interest at the end of the loan period, what was the
rate of interest? *
Answer:
sax
SI = $432
P = $1200
rate = x
time = x
= 432 = t×p×r / 100
= 432 = x × 1200 × x / 100
= 432 = x × 12 × x
= 432 = 2x × 12
= 432/12 = 2x
= 6 = 2x
= 6 ÷ 2 = x
= 3 = x
The rate of interst is 3%
Step-by-step explanation:
HOLA! PLEASE HELP ME ASAP!!! I will give brianlest answer!
Answer:
The value for x should be 35
Step-by-step explanation:
Answer:
32 degrees
Step-by-step explanation:
35 + x + 29 + 84 = 180
148 + x = 180
x = 32
Cargo shipping, an automobile manufacturer is preparin shipment of a cars andvtrucks on a cargo ship that can carry 21,600 tons
The cars weigh 3.6 tons each and the trucks weihgt 7.5 tons each. 1. Wtite thevequation thatvrepresents the weight constraint of a shipment let be the number of cars and be the numbers of trucks.
Answer:
3.6c + 7.5t <= 21,600
Step-by-step explanation:
Let c = number of cars, and let t = number of trucks.
c cars weigh 3.6c tons, and t trucks weigh 7.5t tons.
3.6c + 7.5t <= 21,600
for every 0.5 miles emily makes 0.80 in charity how much does he make for 16 miles
Answer:
25.6
Step-by-step explanation:
16*2=32
32*0.8=25.6
Answer:
25.6
Step-by-step explanation:
16x.8=12.8
because he makes it every half mile we have to multiply by 2\
12.8*2=25.6
if he walks 16 miles he makes 25.6
Factor completely::::
I’m taking test rn lol
Answer:
A. 2
Step-by-step explanation:
∛8 = 2
There is only one correct value to it so it can't be negative and positive 2, the answer is positive 2 so,
= 2
Justin says that if the diameter of any circle is 15 feet then its radius must 10
be 7.5 feet. Is Justin correct?
A person who is standing on a ledge throws a rock into the air. The rock reaches a maximum height of 676 feet
above the ground after 1.5 seconds.
If the rock hits the ground below the ledge 8 seconds after it is thrown, which quadratic function can be used to find
the height of the rock above the ground t seconds after it is thrown?
Answer:
The quadratic equation is [tex]h(t) = -318.22t^2 + 954.67t + 12728.89[/tex]
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta= b^{2} - 4ac[/tex]
Quadratic equation:
[tex]ax^2 + bx + c = 0[/tex]
The rock reaches a maximum height of 676 feet above the ground after 1.5 seconds.
This means that:
[tex]-\frac{b}{2a} = 1.5[/tex]
[tex]y_{v} = -\frac{b^2-4ac}{4a} = 676[/tex]
If the rock hits the ground below the ledge 8 seconds after it is thrown
This means that:
[tex]64a + 8b + c = 0[/tex]
Relation of b and a:
[tex]-\frac{b}{2a} = 1.5[/tex]
This means that:
[tex]b = -3a[/tex]
Relationship of c and a:
[tex]64a + 8b + c = 0[/tex]
[tex]64a - 24a + c = 0[/tex]
[tex]c = -40a[/tex]
Finding a:
[tex]y_{v} = -\frac{(-3a)^2-4a(-40a)}{4a} = 676[/tex]
[tex]9a^2+160a = -2704a[/tex]
[tex]9a^2 + 2864a = 0[/tex]
[tex]a(9a + 2864) = 0[/tex]
Since it is a quadratic equation, a cannot be 0.
[tex]9a + 2864 = 0[/tex]
[tex]9a = -2864[/tex]
[tex]a = -\frac{2864}{9}[/tex]
[tex]a = -318.22[/tex]
Finding b and c:
[tex]b = -3a = -3(-318.22) = 954.67[/tex]
[tex]c = -40a = -40(-318.22) = 12728.89[/tex]
The quadratic equation is given by:
[tex]h(t) = -318.22t^2 + 954.67t + 12728.89[/tex]
The quadratic equation is [tex]h(t) = -318.22t^2 + 954.67t + 12728.89[/tex]
I have a quick question please someone answer Is 5/8 irrational?
Answer:
no
Step-by-step explanation:
5/8=0.6250 so its rational
Answer: no
Step-by-step explanation: 5/8 is rational because it is another way of writing the ratio 5:8. So no, 5/8 is not an irrational number.
A battery company produces 20,000 batteries per day. Each day they randomly select 200 to test. If they find that 4 are dead, how many dead batteries would they expect to find among the entire 20,000?
Answer: 400 because when they test 200 they get that 4 are dead wich is 1/50 of 200 so 1/50 times 20,000 is 400
Step-by-step explanation:
z + 4 = 75 I need help
Answer:
z = 71
Step-by-step explanation:
this is the answer for this equation
Answer:
z=71
Step-by-step explanation:
if a bag of rice cost #120,how many kilograms of rice can one buy for #40
Complete Question:
If a 100kg bag of rice cost #120, how many kilogram of rice can one buy for #40
Answer:
33 kilograms.
Step-by-step explanation:
Given the following data;
100 kg of rice = #120
1 kg of rice = #x
Cross-multiplying, we have;
100x = 120
x = 120/100
x = 1.2
Now, to find how much #40 can buy;
[tex] Quantity = \frac {Cost}{Cost \; of \; a \; bag} [/tex]
Substituting into the equation, we have;
[tex] Quantity = \frac {40}{1.2} [/tex]
Quantity of rice = 33.33 ≈ 33 kilograms.
Method II
100 kg of rice = #120
x kg of rice = #40
Cross-multiplying, we have;
120x = 40 * 100
x = 4000/120
x = 33.33 ≈ 33 kilograms.
Can someone please help me on this?
what does 6 and 18 have in common
A discount of 10 percent was given. If a further discount of 10percent was given in the reduced price, calculate the total single discount given in the marked price .
Answer:
let marked price = x
on 10% discount, price= x-10%of x
=x-(10x/100)
=x-(x/10)
=9x/10
on further 10% discount, total discount = 10% of 9x/10
=10/100 * 9x/10
= 9x/100
= 9%of x
hence, the single discount given on marked price is 9%
Step-by-step explanation:
If 3.78 liters of cranberry juice costs $6.95, then how much will Niki pay for 7.56 L?
Answer:
She will pay $13.9 for 7.56 liters
Step-by-step explanation:7.56 minus 3.78 equals to 3.78. This means we can just simply add another $6.95, so $6.95 plus $6.95 equals to $13.9
Which of the following functions is graphed below?
A. y = |x + 5|+ 4
B. y = |x -5| + 4
C. y = |x + 5| - 4
D. y = |x- 5| - 4
Answer:it’s c y=|x-5|-4
Step-by-step explanation:
The correct function which is graphed is,
D. [tex]y = |x- 5| - 4[/tex]
We have to give that,
A graph of a function is shown in the image.
Now, From the graph;
Two points on the function are (0, 1) and (5, 4).
Since both points are lies on the graph of a function, hence it satisfies the equation of the function.
From the given function,
A. [tex]y = |x + 5|+ 4[/tex]
Substitute x = 0, y = 1;
1 = |0 + 5| + 4
1 = 5 + 4
1 = 9
Which is not true.
B. [tex]y = |x -5| + 4[/tex]
Substitute x = 0, y = 1;
1 = |0 - 5| + 4
1 = 5 + 4
1 = 9
Which is not true.
C. [tex]y = |x + 5| - 4[/tex]
Substitute x = 0, y = 1;
1 = |0 + 5| - 4
1 = 5 - 4
1 = 1
Which is true.
And, Substitute x = 5, y = 4;
4 = |5 + 5| + 4
4 = 10 + 4
4 = 14
Which is not true.
D. [tex]y = |x- 5| - 4[/tex]
Substitute x = 0, y = 1;
1 = |0 - 5| - 4
1 = 5 - 4
1 = 1
Which is true.
And, Substitute x = 5, y = 4;
4 = |5 - 5| + 4
4 = 0 + 4
4 = 4
Which is true.
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Rahul is an engineer and designed an electric car which is moving at an average speed of 56 km per hour. One day, he is travelling and testing his car. If he travelled 7 hours on that day, how much distance does he travelled?
Answer: He travelled 392 km that day.
Step-by-step explanation:
We are given that,
Speed of electric car = 56 km per hour.
Time = 7 hours
We know that,
Distance = Speed x Time
If he travelled 7 hours on that day, then Distance traveled in 7 hours on that day= (56 km per hour) x (7 hours)
i.e. Distance traveled in 7 hours on that day== 392 km
Hence, he travelled 392 km that day.
What is the answer of 1/3 x 1/4
Answer:
1/12
Step-by-step explanation:
Multiply across
Hope this helps
PLESE SOMEONE HELP ME WILL GIVE BRAINLIEST
Answer:
a. area of triangle: A=1/2(b)(h)
A= 1/2 (3)(2.4)
A= 3.6cm^2
All the triangles have the same area, so Total area of the triangles is
A= 4(3.60)
A= 14.4 cm^2
Area of the square: A= s^2 (3)^2= 9cm^2
Total surface area o the Pyramid: 14.4+ 9=23.4cm^2
b. Lateral surface area of the Pyramid: A= 1/2 P(l)
A= 1/2 (12)(4)
A= 24cm^2
P is perimeter of the base= (3)(4)=12cm
l s the slant height= 4cm
Step-by-step explanation:
Bob and Larry went on a tricycle ride. They rode for the same amount of time, but Bob cycled 10 miles per hour slower than Larry. If Bob cycled 14 miles and Larry cycled 21 miles, find the speed that both Larry and Bod rode their tricycles.
Step-by-step explanation:
so basically they are asking you to subtract, hope this helps, use a calculator if needed
DONT ANSWER IF YOU DONT KNOW THE ANSWER
Simplify each expression
mc0011
mc0012
mc0013
mc0014
mc0015
Answer:
A
Step-by-step explanation:
A is the answer for the first question I did the math on edge
The second one after is B
We are Simplifying Rational Expressions with Negative Exponents
Answer:
A.) Afriv
Step-by-step explanation:
Heat oven to 350°F. Generously grease 12-cup fluted tube pan with shortening or cooking spray. In large 1-gallon plastic food storage bag, mix granulated sugar and cinnamon.
2
Separate dough into 16 biscuits; cut each into quarters. Shake in bag to coat. Arrange in pan, adding walnuts and raisins among the biscuit pieces. Sprinkle any remaining sugar over biscuits.
3
In small bowl, mix brown sugar and butter; pour over biscuit pieces.
4
Bake 30 to 40 minutes or until golden brown and no longer doughy in center. Loosen edges of pan with metal spatula. Cool in pan 5 minutes. Turn upside down onto serving plate; replacing any biscuit pieces and caramel from pan. Pull apart to serve. Serve warm.
Решите уравнение: а) 6x = 18;
б) –3x = 15; в) 7x = -63;
г) 5x - 3 = 12; д) — 4х + 1 = 13; е) -x+ 9 = 16.
Answer:
6x=18
x=18/6
x=3.
-3x=15
x=15/-3
x=-5
7x=-63
x=-63/7
x=-9
5x-3=12
5x=12+3
5x=15
x=15/5
x=3
-4x+1=13
-4x=13-1
-4x=12
x=12/-4
x=-3
-x+9=16
-x=16-9
-x=7
x=7/-1
x=-7
Rachel has $9 in a savings account. The interest rate is 5%, compounded annually.
To the nearest cent, how much interest will she earn in 3 years?
Find the interquartile range (IQR) of the data in the box plot below.
eggs
Number of eggs laid
Answer:
5
Step-by-step explanation:
The interquartile range is the 3rd quartile minus the 1st quartile. The 3rd quartile is 8 and the 1st quartile is 3.
8 - 3 = 5
The interquartile range (IQR) of the data is 5.
From the box plot we can write,
Minimum = 2
First Quartile, Q1 = 3
Median = 6
Third Quartile, Q3 = 8
Maximum = 10
So, Interquartile range (IQR)
= Q3 - Q1
= 8 - 3
= 5
Thus, the interquartile range (IQR) of the data is 5.
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A number b is at least - 3.
Answer:
-3 ≥ b is your inequality
Step-by-step explanation:
If f(1) = 1 and f(n) = f(n-1)2 – 4 then find the value of f(4).