Answers
Answer:
Part A)
Approximately 318.1318 meters.
Part B)
Approximately 137.7551 meters.
Step-by-step explanation:
The path of a projectile is given by the equation:
[tex]\displaystyle y = \sqrt{3} x -\frac{49x^2}{9000}[/tex]
Part A)
The range of the projectile will be given by the difference between its starting point and landing point. In other words, its two zeros.
Let y = 0 and solve for x:
[tex]\displaystyle 0 = \sqrt{3}x - \frac{49x^2}{9000}[/tex]
Factor:
[tex]\displaystyle 0 = x\left(\sqrt{3} - \frac{49x}{9000}\right)[/tex]
Zero Product Property:
[tex]\displaystyle x = 0 \text{ or } \sqrt{3} - \frac{49x}{9000} = 0[/tex]
Solve for each case:
[tex]\displaystyle x = 0 \text{ or } x = \frac{9000\sqrt{3}}{49}\approx 318.1318[/tex]
Hence, the range of the projectile is approximately (318.1318 - 0) or 318.1318 meters.
Part B)
Since the equation is a quadratic, the maximum height is given by its vertex. Recall that the vertex of a quadratic is given by:
[tex]\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
In this case, a = -49/9000 and b = √3.
Find the x-coordinate of the vertex:
[tex]\displaystyle x = - \frac{(\sqrt{3})}{2\left(\dfrac{-49}{9000}\right)} = \frac{4500\sqrt{3}}{49}[/tex]
Then the maximum height will be:
[tex]\displaystyle \displaystyle \begin{aligned} y\left(\frac{4500\sqrt{3}}{49}\right) &=\sqrt{3} \left(\frac{4500\sqrt{3}}{49}\right) -\frac{49\left(\dfrac{4500\sqrt{3}}{49}\right)^2}{9000} \\ \\ &= \frac{13500}{49} -\frac{6750}{49}\\ \\ &=\frac{6750}{49}\\ \\ &\approx 137.7551\text{ meters}\end{aligned}[/tex]
The maximum height reached by the projectile will be 137.7551 meters.
Related Questions
Someone help me with this please
Answers
MACARONI AND AN POT THATS AN WAAAAAPP
(7-4) + 17 / -14 + 2 x 5
Answers
Answer:
165/14
Step-by-step explanation:
(7-4) + 17 / -14 + 2 x 5
3 + 17/-14 + 2 x 5
3 - 17/14 + 2 x 5
3 - 17/14 + 10
165/14
Solve the fraction problems and reduce the answer to its lowest form:-
1)7/10×2/21
2)9/16×10/21
3)11/12×26/55
4)2/6×18/12×2/3
5)5/6×9/10
Answers
Answer:
1/1515/5613/301/33/4Step-by-step explanation:
1) 7/10 × 2/21
1/15
2) 9/16 × 10/21
90/336
15/56
3) 11/12 × 26/55
13/30
4) 2/6 × 18/12 × 2/3
72/216
1/3
5) ⅚ × 9/10
45/60
3/4
Cho 2 tập hợp A = {1;3;5;8}, B = {3;5;7;9}. Tìm A∩B và A∪B.
Answers
Answer:
gien
Step-by-step explanation:
Domain and range from graph
What is the domain of g?
Answers
Answer: A
Step-by-step explanation:
Answer:
-6 < x < 6
Step-by-step explanation:
Domain refers to the list of all x-values included in the function. In this instance, the list of x-values in this function is between -6 and 6.
What are the coordinates of A' after a 180 degree rotation about (-5, 3)?
Answers
Answer: (5,3)
Step-by-step explanation:
A 180 degree rotation will take you to sector b which is (+,+), so I knew it was going to be positive.
-5,3)
(+5,-3)
Half the difference of a number n and 20 is 30. What is the number?
Answers
Answer:
80Step-by-step explanation:
Half the difference of a number n and 20 ⇒ (n - 20)/2... is 30 ⇒ = 30Solve the equation for n:
(n - 20)/2 = 30n - 20 = 30*2n - 20 = 60n = 60 + 20n = 80The number is 80
Answer:
Number is 40
Step-by-step explanation:
Let the number be n
(n - 20)/2 = 30
(n - 20) = 2 × 30
n = (2 × 30) + 20
n = 60 + 20
n = 80
can you figure out what 2x° equals and (90-x)°
Answers
I HOPE IT WILL HELP YOU.
Have a great day ahead.
What is -(11+2b) in simplified form?
Answers
Answer and Step-by-step explanation:
To simplify, distribute the negative number.
-(11 + 2b)
-11 - 2b is the answer.
#teamtrees #PAW (Plant And Water)
I hope this helps!
Answer:
-11 -2b
Step-by-step explanation:
-(11+2b)
Distribute the minus sign
-11 -2b
How many solutions are there to the equation below?
11X-99 = 11(x-9)
A. infinitely many
B. 0
C.1
Answers
11x-99=11(x-9)
11x=11x-99+99
11x=11x
So now in this, x can be any number.
Eg- x=2 so 22=22
Same with each case
What is the transformation shown in the graph?
6
c
A
360° rotation
180° rotation
90° rotation
reflection
Answers
Answer:
Reflection is shown in the graph.
Which expression is equivalent to -9a – 10 – 6a + 7?
Answers
Answer: a = - 1/5 or a = -0.2
Step-by-step explanation:
-9a – 10 – 6a + 7 = 0
>> -9a-6a = 10-7
>> -15a = 3
>> -15a/ - 15 =3 / - 15 ( divide by -15 both side)
>> a = - 1/5 or -0.2
Does #6 look right? Im struggling on this
Answers
Answer and Step-by-step explanation:
-2 is the correct answer.
But, you should set up your number line like this:
-6 4
<-|-----------|----------|->
-2
4 - 6 = -2
#teamtrees #PAW (Plant And Water)
I hope this helps!
600 miles/day into miles per hour
Answers
The function f(x)=x^2+2 is not one to one. Determine a restricted domain that makes it one to one and find the inverse function
Answers
Answer:
Hope it helped
Step-by-step explanation:
The restricted domain that makes the given function one to one is (-∞,0] or [0.∞) and the inverse function would be f⁻¹ (x) = [tex]\sqrt{x-2}[/tex] if we restrict the domain of original function to [0.∞) and the inverse function would be f⁻¹ (x) = -[tex]\sqrt{x-1}[/tex] if we restrict the domain to (-∞,0] .
What is inverse of a function?An inverse function or an anti function is defined as a function, which can reverse into another function.
Now the given quadtratic function is,
f(x) = x² + 2
Now vertex of the given quadratic function is (0,2)
Thus the range of the function is [2,∞)
If we restrict the domain of this function to either (-∞,0} or [0.∞), it will become one to one function.
Now the inverse function is given as,
y = x² + 2
Upon interchanging x and y, we get:
x = y² + 2
⇒ y² = x - 2
or, y = ±[tex]\sqrt{x-2}[/tex]
Hence, the inverse function would be f⁻¹ (x) = [tex]\sqrt{x-2}[/tex] if we restrict the domain of original function to [0.∞) and the inverse function would be f⁻¹ (x) = -[tex]\sqrt{x-1}[/tex] if we restrict the domain to (-∞,0] .
Thus, the restricted domain that makes the given function one to one is (-∞,0] or [0.∞) and the inverse function would be f⁻¹ (x) = [tex]\sqrt{x-2}[/tex] if we restrict the domain of original function to [0.∞) and the inverse function would be f⁻¹ (x) = -[tex]\sqrt{x-1}[/tex] if we restrict the domain to (-∞,0] .
To learn more about function :
https://brainly.com/question/17210215
#SPJ2
ALGEBRA II! i need help with #2 with the same steps i took on #1
Answers
Solve for x: -2 - 4 > 8
(9th grade Algebra 1)
Answers
Answer:
A
Step-by-step explanation:
-2x-4>8
-2x>12
-x>6
x<-6
Answer:
[tex]x < - 6[/tex] (first option)
Step-by-step explanation:
[tex] - 2x - 4 > 8[/tex]
[tex] - 2x > 8 + 4[/tex]
[tex] - 2x > 12[/tex]
[tex] = x < - 6[/tex]
Write an algebraic expression for each verbal expression. 1. the sum of k and 8
2. 17 less than a number x times 9
6. four times the difference of a cubed and 8
PLZ HELP ASAP
Answers
Answer:
k + 8 = y
9x - 17
4(x²-8)
b) Convert 101, into denary number
Answers
If 101 is given in base b, then in base 10 you have
[tex]101_b = 1\times b^2 + 0\times b^1 + 1\times b^0 = b^2 + 1[/tex]
For instance, if b = 2, then
101₂ = 2² + 1 = 5₁₀
If b = 3, then
101₃ = 3² + 1 = 9₁₀
If b = 4, then
101₄ = 4² + 1 = 17₁₀
The answer depends entirely on the base of the given number.
measure at least pairs of corresponding angles in XJYN and ZSCH using a protractor. Record your measurements to the nearest 5. what do you notice?
Answers
Answer:
any file to have a reference?
any advice on geometry
Answers
Answer:
Just study and pay attention in class and take good notes. I would say that you should pay more attention when they teach you the trigonometry unit.
I’ve been stuck on this for days I just need a simple answer
Answers
Answer:
408
Step-by-step explanation:
Surface area formula is A=2(wl+hl+hw)
Substituting these values into the formula you would get
2·(3·8+4·8+4·3)=136
136 accounts for one rectangular prism.
Since you have 3 multiply 136 by 3 which would leave you with 408
Answer:
280 in²
Step-by-step explanation:
The opposite faces are congruent , then surface area (SA ) is
SA = top/ base + front/ back + 2 sides
note for the front/ back and 2 sides we have 3 + 3 + 3 = 9 in
SA = 2(8 × 4) + 2(8 × 9) + 2(4 × 9)
= 2 × 32 + 2 × 72 + 2 × 36
= 64 + 144 + 72
= 280 in²
A line is parallel to the x-axis and passes through the point (-5,4)
What is the equation of that line, the slope of that line, and what would be the slope of a line perpendicular to that given line?
Answers
9514 1404 393
Answer:
y = 4slope: 0slope of perpendicular: undefinedStep-by-step explanation:
The x-axis is a horizontal line. As such, it has a slope of zero. The equation of a horizontal line is ...
y = constant
__
For the line through (-5, 4), the constant must match the y-coordinate: 4. The equation is ...
y = 4
As we said above, the slope of that horizontal line is zero.
The perpendicular line will be a vertical line of the form x=constant. The slope of a vertical line is undefined.
help whhhahahahaha Helpppppppp
Answers
Answer:
320/420 = 4/3
Step-by-step explanation:
4/7= x /560
Cross multiply
7x = 2240
Divide by 7:
x=320
The school has 320 boys and 240 girls
I hope this helps u:)
Answer:
Problem(1): [tex]21[/tex]
Problem(2): Side length = [tex]\frac{1}{4}[/tex] Area = [tex]\frac{1}{16}[/tex]
Problem(3): Boys = [tex]320[/tex] Girls = [tex]240[/tex]
Step-by-step explanation:
(Notes steps are cut from this answer so that it isn't too long)
1. Problem (1)
One is given the following information:
[tex]x+\frac{1}{x}=5[/tex][tex](x-\frac{1}{x})^2[/tex]The most logical first step is to solve for the value of (x). One can solve for the numerical value of (x) with the first equation.
[tex]x+\frac{1}{x}=5[/tex]
Multiply the entire equation by (x),
[tex]x^2+1=5x[/tex]
Inverse operations put the equation in the general format of a quadratic equation. The general format of a quadratic equation is as follows,
[tex]ax^2+bx+c=0[/tex]
Put the given equation in this format,
[tex]x^2-5x+1=0[/tex]
Now use the quadratic formula to solve for the value of (x). The quadratic formula uses the coefficients of the terms in a quadratic equation to find the roots of the equation. The quadratic formula is as follows,
[tex]\frac{-b(+-)\sqrt{b^2-4ac}}{2a}[/tex]
Use the coefficients of the terms in the given quadratic equation in the formal, then simplify to solve for solutions of the given equation,
[tex]\frac{-(-5)(+-)\sqrt{(-5)^2-4(1)(1)}}{2(1)}[/tex]
Simplify,
[tex]\frac{-(-5)(+-)\sqrt{(-5)^2-4(1)(1)}}{2(1)}[/tex]
[tex]\frac{5(+-)\sqrt{21}}{2}[/tex]
Now substitute these values into the equation and simplify, even though there are two values of (x), there will only be one solution,
[tex]((\frac{5+\sqrt{21}}{2}-\frac{1}{\frac{5+\sqrt{21}}{2}})^2[/tex] [tex]((\frac{5-\sqrt{21}}{2}-\frac{1}{\frac{5-\sqrt{21}}{2}})^2[/tex]
[tex](\frac{5+\sqrt{21}}{2}-\frac{2}{5+\sqrt{21}})^2[/tex] [tex](\frac{5-\sqrt{21}}{2}-\frac{2}{5-\sqrt{21}})^2[/tex]
Convert to a common denominator,
[tex](\frac{5+\sqrt{21}}{2}*\frac{5+\sqrt{21}}{5+\sqrt{21}}-\frac{2}{5+\sqrt{21}}*\frac{2}{2})^2[/tex] [tex](\frac{5-\sqrt{21}}{2}*\frac{5-\sqrt{21}}{5-\sqrt{21}}-\frac{2}{5-\sqrt{21}}*\frac{2}{2})^2[/tex]
[tex](\frac{(5+\sqrt{21})^2-4}{2(5+\sqrt{21})})^2[/tex] [tex](\frac{(5-\sqrt{21})^2-4}{2(5-\sqrt{21})})^2[/tex]
Simplify,
[tex](\frac{25+10\sqrt{21}+21-4}{10+2\sqrt{21}})^2[/tex] [tex](\frac{25-10\sqrt{21}+21-4}{10-2\sqrt{21}})^2[/tex]
[tex](\frac{42+10\sqrt{21}}{10+2\sqrt{21}})^2[/tex] [tex](\frac{42-10\sqrt{21}}{10-2\sqrt{21}})^2[/tex]
[tex]\frac{1764+840\sqrt{21}+2100}{100+40\sqrt{21}+84}[/tex] [tex]\frac{1764-840\sqrt{21}+2100}{100-40\sqrt{21}+84}[/tex]
[tex]\frac{3864+840\sqrt{21}}{184+40\sqrt{21}}[/tex] [tex]\frac{3864-840\sqrt{21}}{184-40\sqrt{21}}[/tex]
[tex]21[/tex]
2. Problem (2)
All four sides of a square are congruent (have the same measure), thus dividing the perimeter of a square by (4) will yield the side length of the square,
[tex]Perimeter\ of\ the\ square: 4\\Side\ length: \frac{1}{4}[/tex]
The area is the two-dimensional space that a figure takes up, in the case of a square, the area is the side length times itself:
[tex]A=(\frac{1}{4})^2=\frac{1}{16}[/tex]
3. Problem (3)
Let (x) represent the amount by which the ratio of boys to girls was scaled down. Assuming that these are the only two genders in the school, one can state that the sum ratio coefficients times the scaling value for both boys and girls, will equal the total number of people in the school. Thus, one can form the following equation and solve it with inverse operations and simplification,
[tex]boys + girl = total\ students\\4x + 3x = 560\\7x = 560\\x = 80[/tex]
Now substitute this into the expression for the two genders in this scenario, respectively, to solve for the actual number of students of that gender,
Boys, Girls,
[tex]4(x)[/tex] [tex]3(x)[/tex]
[tex]4(80)[/tex] [tex]3(80)[/tex]
[tex]320[/tex] [tex]240[/tex]
(50 POINTS!!!!!) I NEED THE CORRECT ANSWER... FAST!
Answers
Answer:
don't know sorry forgive me
4. Find a pair of irrational numbers whose product is an integer.
Answers
Answer:
√2 and √3
Step-by-step explanation:
Answer:
Step-by-step explanation:
√2 and 5√2 are two irrational numbers
√2 * 5√2 = [tex]5*\sqrt{2*2} = 5 * 2 = 10[/tex]
and here 10 is an integer
what is the value of x when the distance between the points (-2,-3) (-3,x) is equal to 5
Answers
Answer:
(-3,-4)
Step-by-step explanation:
Seven less than four times a number is nine. FIND the number
Answers
Answer:
4
Step-by-step explanation:
4 times 4 is 16. 7 less than 16 is 9.
Answer:
4
Step-by-step explanation:
You can use a simple formula for finding the answer to problems like these. You read it out and put your information in order and use a variable (such as x) in place of the number.
4 * x - 7 = 9
Then solve by getting your variable alone on one side.
Add 7 to both sides: 4 * x = 16
Divide both sides by 4: x = 4
Bananas are $0.59/pound what is the constant of proportionality?
Answers
Answer:
Step-by-step explanation:
y = k x
Total cost = y
number of pounds = x
constant = 0.59
Equation
y = 0.59 x
8. 7.6 + (-7.1) = what does it equal plz help
Answers
Answer:
vsddddddddddddddddddddddddddddddddddddddddddddddddddddddbgtresxvzjdhdf;lsjb
Step-by-step explanation:
