Answers
Answer:
B) -6.61, 0.61
Step-by-step explanation:
Answer obtained by graphing the formula.
Related Questions
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?
Answers
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]
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.
Answers
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:
https://brainly.com/question/16014064
Can someone please help me on this?
Answers
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.
Answers
Step-by-step explanation:
so basically they are asking you to subtract, hope this helps, use a calculator if needed
z + 4 = 75 I need help
Answers
Answer:
z = 71
Step-by-step explanation:
this is the answer for this equation
Answer:
z=71
Step-by-step explanation:
Cory has received the following grades this term: 75, 87, 90, 88, 79. Find the mean
Answers
Answer:
83.8
Step-by-step explanation:
first you add the grades together: 75 + 87 + 90 + 88 + 79 = 419
then you divide by the amount of grades: 419 / 5 = 83.8
If f(1) = 1 and f(n) = f(n-1)2 – 4 then find the value of f(4).
Answers
f(2) = -5f(2-1) = -5f(1) = -5(2) = -10
f(3) = -5f(3-1) = -5f(2) = -5(-10) = 50
So, f(4) = ?
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
Answers
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.
To learn more about the function visit:
https://brainly.com/question/11624077
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Radius = 5 CD = 8 Find AE
Answers
Answer:
123
Step-by-step explanation:
213
2.
Find the products using
a. (5x - 2)(5x + 2)
Answers
HOLA! PLEASE HELP ME ASAP!!! I will give brianlest answer!
Answers
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
50 de 100 ün en sade halı acil
Answers
Answer:
srry buddy I don't understand your language
I am from India
can ask it in English
then I could help you
DONT ANSWER IF YOU DONT KNOW THE ANSWER
Simplify each expression
mc0011
mc0012
mc0013
mc0014
mc0015
Answers
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.
I have a quick question please someone answer Is 5/8 irrational?
Answers
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.
I’m taking test rn lol
Answers
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
Aiden is eating from the box of cereal shown. Find the total surface area of the box. cereal 13.5 in. 2.5 in. 8 in. Total surface area?
Answers
Answer:
Step-by-step explanation:
Two of the sides are 13.5 inches by 2.5 inches, two sides are 13.5 inches by 8 inches, and two sides are 2.5 inches by 8 inches.
Surface area = 2*13.5*2.5 + 2*13.5*8 + 2*2.5*8
giving brainliest and 20 points! please solve this. :D
Answers
Answer:
1.) 7x+5y
2.)-19m+14r
3.)22b+40c
4.)10x+25
5.)7m+7
Step-by-step explanation:
ez
what does 6 and 18 have in common
Answers
if a bag of rice cost #120,how many kilograms of rice can one buy for #40
Answers
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.
1/3 plus 1/4 so what is the answer
Answers
Answer:
The answer is 7/12
Answer:
7/12
Step-by-step explanation:
What is (8 + (−2) − 4) and (3 − 5)
Answers
Step-by-step explanation:
(8+(-2)-4)
=8-2-4
=2
(3-5)
=-2
What is the surface area of this wedge.?
Answers
Answer:
the surface area of the wedge is 360ft²
Step-by-step explanation:
6x5x3x4 = 360ft²
PLESE SOMEONE HELP ME WILL GIVE BRAINLIEST
Answers
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:
Find a difference equivalent to the product shown.
5(x-y)
answers (one is right.)
5x-5y
5x-y
x-5y
-5x-5y
Answers
Answer:
5x-5y
Step-by-step explanation:
You are using the distributive property
You can also think of it as multiplying 5 by x and 5 by y and then subtracting it just as it is subtracting in the original equation
Answer:
5x-y.
Step-by-step explanation:
so its 5 times x, minus 7. easy. 5x,-y. rephrase it. hhen a variable is next to a number, it means multiply.
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?
Answers
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:
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.
Answers
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
A number b is at least - 3.
Answers
Answer:
-3 ≥ b is your inequality
Step-by-step explanation:
If you are graphing it on a number line, the circle over -3 is filled in, and the arrow goes to the right
Find the interquartile range (IQR) of the data in the box plot below.
eggs
Number of eggs laid
Answers
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.
Learn more about Interquartile range (IQR) here:
https://brainly.com/question/31758606
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(giving brainiest)
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
Answers
Answer:
b.
Step-by-step explanation:
Решите уравнение: а) 6x = 18;
б) –3x = 15; в) 7x = -63;
г) 5x - 3 = 12; д) — 4х + 1 = 13; е) -x+ 9 = 16.
Answers
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
