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
The value of 5x2 - 11x + 18 is
when x = 2.4 and
whenx = -3.
Answers
f(x)=5x^2-11x+18
[tex]\\ \sf\longmapsto f(2.4)[/tex]
[tex]\\ \sf\longmapsto 5(2.4)^2-11(2.4)+18[/tex]
[tex]\\ \sf\longmapsto 5(5.76)-26.4+18[/tex]
[tex]\\ \sf\longmapsto 28.8-26.4+18[/tex]
[tex]\\ \sf\longmapsto 2.4+18[/tex]
[tex]\\ \sf\longmapsto 20.4[/tex]
And
[tex]\\ \sf\longmapsto f(-3)[/tex]
[tex]\\ \sf\longmapsto 5(-3)^2-11(-3)+18[/tex]
[tex]\\ \sf\longmapsto 5(9)+33+18[/tex]
[tex]\\ \sf\longmapsto 45+51[/tex]
[tex]\\ \sf\longmapsto 96[/tex]
The value of 5x² - 11x + 18 is when x = 2.4 and when x = -3 will be 20.4 and 96.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
The quadratic expression is given below.
⇒ 5x² - 11x + 18
The value of the expression at x = 2.4, then the value of the expression will be
⇒ 5(2.4)² - 11(2.4) + 18
⇒ 28.8 - 26.4 + 18
⇒ 20.4
The value of the expression at x = -3, then the value of the expression will be
⇒ 5(-3)² - 11(-3) + 18
⇒ 45 + 33 + 18
⇒ 96
The value of 5x² - 11x + 18 is when x = 2.4 and when x = -3 will be 20.4 and 96.
More about the value of expression link is given below.
https://brainly.com/question/23671908
#SPJ2
Given f(x)=(2x+1)^3. Find f^−1(x). (inverse)
Answers
Answer:
Step-by-step explanation:
[tex]f(x)=y=(2x+1)^3\\Exchanging\ x\ and\ y\\\\x=(2y+1)^3\\\\\\Finding\ y\\\sqrt[3]{x} =2y+1\\\\2y=\sqrt[3]{x}-1\\\\\boxed{y=\dfrac{\sqrt[3]{x}-1}{2} =f^{-1}(x)}[/tex]
Interval notation of x<2
Answers
interval notation of x<2
x=1
Last year, the girl's basketball team had 20 ninth-grade students and 10 sixth-grade students. what was the ratio of sixth-grade students to total students on the team
Answers
a fifth of the sum of number a and 34
Write as an algebraic expression
Answers
The answer you are looking for is 1/5(a+34).
Solution/Explanation:
"Of"="multiplication (x)."
So, therefore, write it like this, to get the better picture and visualization,
1/5 times the sum of a number "a" and "34."
"Sum" obviously is related to "addition."
So, therefore, we can simplify the algebraic expression a little bit more,
1/5 times (a+34).
Now, we can finally write it like this.
1/5x(a+34).
The more proper way to write it, however is like this:
1/5(a+34).
So, therefore, the final answer is 1/5(a+34).
I hope that this has helped you. Enjoy your day, and take care!
The given statement is required in the form of an algebraic expression.
The statement is a fifth of the sum of number a and 34.
The sum means addition
So, the sum is [tex]a+34[/tex]
The statement states a fifth of which, means multiplied by [tex]\dfrac{1}{5}[/tex]
The algebraic expression will be the product of [tex]\dfrac{1}{5}[/tex] and [tex](a+34)[/tex]
The algebraic expression is [tex]\dfrac{1}{5}(a+34)[/tex]
Learn more:
https://brainly.com/question/19245500
https://brainly.com/question/23270878
18. Mabel gave Margo a bag containing red, white, and
blue marbles. The bag contained half as many red
marbles as blue ones, and 1/4 of the marbles in the
bag were white. If 8 of the marbles were red, how
many marbles were in the bag?
Answers
So the answer comes out to be 30 marbles in the bag
Answer:
32.
Step-by-step explanation:
Let the number of red marbles be x then the number of blue = 2x
So we have 8 red and 16 blue marbles.
If the total number of marbles are y marbles the number of white one = y/4.
So y = y/4 + 8 + 16
3/4y = 24
y = 24 * 4/3
= 96/3
= 32 marbles.
=
I own the collector’s edition of my favorite Pokemon card. It used to be worth $120 USD. Now it is worth $150 USD.
What is the percent change?
Answers
Answer:
25% increase
Step-by-step explanation:
= [tex]\frac{150-120}{120}[/tex] x 100
= [tex]\frac{30}{120}[/tex] x 100
= 0.25 x 100
= 25% increase
geometry 1.4 - Segment Addition Postulate & Midpoint
i don’t know how to do this so if anyone could also give a in depth explanation i’ll give branliest
Answers
Answer:
28
Step-by-step explanation:
AB + BC = AC
14 + 3x-4 = 4x+4
Combine like terms
10 +3x = 4x+4
Subtract 3x from each side
10+3x-3x = 4x+4-3x
10 = x+4
Subtract 4 from each side
10-4 =x-4+4
6 =x
We want AC
AC = 4x+4 = 4*6+4 = 24+4 = 28
Let's see
AB+BC=AC14+3x-4=4x+43x+10=4x+410-4=4x-3xx=6AC
4(6)+4=24+4=28
what is the relationship between the location of plate boundaries and the formation of mountainsa
Answers
Answer:
Movements of tectonic plates create volcanoes along the plate boundaries, which erupt and form mountains. A volcanic arc system is a series of volcanoes that form near a subduction zone where the crust of a sinking oceanic plate melts and drags water down with the subducting crust.
Name the algebraic property demonstrated in the example below:
3 ⋅ (x ⋅ y) = (3 ⋅ x) ⋅ y
Answers
Answer:
It's Associative Property of Multiplication.
Thank You
If g(x) = x^2 + 3, find g(4).
11 19 16 8
Answers
Answer:
19
Step-by-step explanation:
g(x) = x^2 +3
substituing x for 4,
g(4) = 4^2 + 3
g(4) = 16 + 3
g(4) = 19
How do you factorise with letters and numbers please explain clearly example
7ab+14b how do I put that in brackets and what are the rules when factoring
Answers
Answer:
7b(a+2)
Step-by-step explanation:
First. look at the coefficient. See if they are common multiple of some number. If so find the GCF between them.
Then find the variable both terms share.
Put the GCF coeffiecnt and the variable both terms share outside the parentheses.
Inside the parenthesis will be a term that multiplied by the term outside of the parenthesis will equal the original equation.
For example, 7ab+14b.
Set up equation.
[tex]7ab + 14b[/tex]
Both terms share a b variable and 7 and 14 GCF is 7 so
let factor out 7b.
[tex]7b(a + 2)[/tex]
Why is inside the parenthesis is the term (a+2). If we divide 7ab+14b by 7b separately we get
[tex]a + 2[/tex]
what is 5/12 + 1/4. Im in 7th grade btw
Answers
Answer:
2/3
I hope this helps!! :)
A trader sold 250 articles for $525,000.00 at a profit of 25%.
a.Calculate the cost of each article.
b.If the trader had wanted 45% profit on the cost price then how much would he sell the articles?
Answers
Answer:
a. $2100 b. $945000
Step-by-step explanation:
You have to divide 525000 and 250 to solve for "a". To solve for "b" you need to find %100 of the profit and do %100 of the profit times 0.45 to see how much is %45 of profit.
Prove the following
Answers
Answer:
Step-by-step explanation:
Sin² x - Cos² x = (1 - Cos² x ) - Cos² x {Sin² x + Cos² x = 1}
= 1 - 2Cos² x
= - (2Cos x -1)
[tex]= -(\dfrac{2}{Sec^{2} x} - 1)\\\\=-(\dfrac{ 2}{Sec^{2} \ x}-\dfrac{Sec^{2} \ x}{Sec^{2} \ x})\\\\=-(\dfrac{2-Sec^{2} \ x}{Sec^{2} \ x})\\\\=\dfrac{2-Sec^{2} \ x }{-Sec^{2} \ x}[/tex]
Hence proved
(a+b+c)^2 - a^2+b^2..................
Answers
Answer:
[tex]2b^2 + c^2 + 2ab + 2ac + 2bc[/tex]
Step-by-step explanation:
Whenever you have a parentheses to a power of a number you have to make it the parentheses times itself, so (a+b+c)^2 becomes (a+b+c)(a+b+c), where you then multiply a by a, a by b, a by c, b by a, b by b, b by c, and so on and then add all those numbers up. If you do that you would get a^2 + ab + ac + ab + b^2 + bc + ac + bc + c^2, where you then add them up to get a^2 + b^2 + c^2 + 2ab + 2ac + 2bc. Since you have - a^2 after this, you cancel out the a^2, and finally, you have + b^2 so you add b^2 to it and you get a final answer of 2b^2 + c^2 + 2ab + 2ac + 2bc.
help plss
----------------------------
Answers
Answer:
it ebtween 10 and negetive 4.5
Step-by-step explanation:
Please help will mark branliest
Answers
Answer:
RS = 17
Step-by-step explanation:
QS = 62
RS = ?
QR = 45
QS - QR = RS
62 - 45 = 17
Thus RS = 17
please answer this question I have for you now
Answers
Answer:
A. 10
Brainliest, please!
Step-by-step explanation:
(1, 2)(x, 5) = 1/3
5 - 2 / x - 1 = 1/3
3 / x - 1 = 1/3
x - 1 = 3 / 1/3
x - 1 = 9
x = 9 + 1
x = 10
(5 - 2)/(x - 1) = -3
3 / (x - 1) = -3
So (x - 1) = -1
x = 0
4. Determine both the HCF and LCM of 25 and 200
Answers
Answer:
The LCM of 25 and 200 is 200.
Explanation:
Find the prime factorisation of 25
25 = 5 × 5
Find the prime factorisation of 200
200 = 2 × 2 × 2 × 5 × 5
Multiply each factor the greater number of times it occurs in steps 1 or 2 above to find the LCM:
LCM = 2 × 2 × 2 × 5 × 5
LCM = 200
Answer:
the HCF of 25 and 200 is 25 because it divides both of them and is maximum factor of them.
LCM of 25 and 200 is 200 because it can be divided by both 200 and 25
You are offered two jobs. One with a yearly salary of $53,749, and the other an hourly
job with a rate of $26 per hour. Both require you to work for 45 hours a week. How
much more will you make by taking the hourly job?
Answers
Answer:
$1170
Step-by-step explanation:
you will have to multiply the the rate you earn hourly by 45hours then it will state the more you'll be making hourly $26×45=$1170
Evaluate each expression if a=12, b=9, and c=4
b^2+2^a-c^2=?
Answers
Answer:
you have to substitute the value of the variables then solve
If HJ=7x-27, find the value of x
Answers
Answer:
x= HJ+27/7
Step-by-step explanation:
HJ + 27 = 7x
HJ+27/7 = x
is this a function? help lol
Answers
Answer:
what is this lol can u tell u
Answer: no
Step-by-step explanation: Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.
On a winter day, the temperature changes by -3 1/2 degrees Fahrenheit in 1 3/4 hour. What is the average change in the temperature in 1 hour? Please answer fast and explain how you got that answer. Don't put a link i will report you. Please explain!
Answers
Answer:
-2 degrees per hour
Step-by-step explanation:
Rate of change = -3 1/2 / 1 3/4
= -7/2 / 7/4
= -7/2 * 4/7
= -28/14
= - 2
lines of latitude also called parallels do what
Answers
Answer:
Hi, there!
Lines of latitude are also called parallels because they never touch one another.
Step-by-step explanation
Circles of latitude are often called parallels because they are parallel to each other; that is, planes that contain any of these circles never intersect each other:
If DE = 4x+10 and EF= 2x-1 and DF = 9x-15 find DF
Answers
Answer:
89
Step-by-step explanation:
show your work
Fill in the missing work and justification for step 3 when solving 2(x + 1) = 10
Answers
Answer:
subtraction property of equality
2x +2 - 2 = 10 - 2
Find the value of the expression when x = 4 and y = 6.
8x + 2y + 3
Answers
Answer:
47
Step-by-step explanation:
8(4) + 2(6) + 3 = 47
32 + 12 + 3 = 47
Question
What is the measure of JKL?
A. 186°
B. 174
C. 87
D. 267
Answers
Answer: 174
Step-by-step explanation: