Part 1 - ApplicationPhysics shows that when an object is thrown upward with an initial velocity of v then its approximate height is given by this quadratic function.s = − 4. 9t^2+ vot + hA ball is thrown upward from the top of a building 15 meters high, at a velocity of 2.8m/sec. Answer thefollowing questions. Be sure to show and explain all work.a) Find the maximum height and the time in which it was attained (round to 3 decimal places)b) When does it reach the ground? (round to 3 decimal places)c) Sketch a graph to illustrate your answers.
Answers
Since the ball is thrown upward from a building 15 meters high with a speed of 2.8m/s, replace h=15 and v=2.8 into the equation:
\(s=-4.9t^2+2.8t+15\)a)
The vertex of the parabola has the coordinates of the maximum height and the time it takes for the object to reach the maximum height. Since the graph of a parabola is symmetrical about the vertical line that passes through the vertex, we can simply find the time that it takes for the object to go back to the height of 15 meters, which is twice the time that it takes for it to reach its maximum height.
Then, replace s=15 and solve for t:
\(\begin{gathered} 15=-4.9t^2+2.8t+15 \\ \Rightarrow0=-4.9t^2+2.8t \\ \Rightarrow0=t(-4.9t+2.8) \end{gathered}\)Then, the times at which the object is at a height of 15 meters are given by:
\(\begin{gathered} t_1=0 \\ \\ -4.9t_2+2.8=0 \\ \Rightarrow t_2=\frac{2.8}{4.9} \\ \Rightarrow t_2=0.57143\ldots \end{gathered}\)The time at which the object reaches the maximum height is:
\(t=\frac{t_1+t_2}{2}=\frac{0+0.57143\ldots}{2}=0.2857\ldots\)Replace t=0.2857... into the equation to find the maximum height:
\(\begin{gathered} s=-4.9(0.2857)^2+2.8(0.2857\ldots)+15 \\ =15.4 \end{gathered}\)Then, the maximum height is 15.4 meters and it takes 0.286 seconds to reach it.
b)
To find the time that it takes for the object to reach the ground, replace s=0 and solve for t:
\(\begin{gathered} 0=-4.9t^2+2.8t+15 \\ \Rightarrow t=\frac{-2.8\pm\sqrt[]{2.8^2-4(-4.9)(15)}}{2(-4.9)} \\ \\ \therefore t_1=\frac{2+\sqrt[]{154}}{7}\approx2.059 \\ \therefore t_2=\frac{2-\sqrt[]{154}}{7}\approx-1.487\ldots \end{gathered}\)Since the negative time can be intepreted as an instant before the ball is thrown, the only meaningful result is t=2.06. Then, the ball reaches the ground after 2.06 seconds.
c)
Use the fact that the graph passes through the points (0,15), (0.286,15.4) and (2.06,0) to sketch it:
Related Questions
Determine the equation of the line below using the given slope and point.
Slope = m = 4 , Point (-3,-11)
Answers
\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{-11})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-11)}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-3)}) \implies y +11 = 4 ( x +3) \\\\\\ y+11=4x+12\implies {\Large \begin{array}{llll} y=4x+1 \end{array}}\)
The equation is:
⇨ y + 11 = 4(x + 3)Work/explanation:
Recall that the point slope formula is \(\rm{y-y_1=m(x-x_1)}\),
where m is the slope and (x₁, y₁) is a point on the line.
Plug in the data:
\(\rm{y-(-11)=4(x-(-3)}\)
Simplify.
\(\rm{y+11=4(x+3)}\)
Hence, the point slope equation is y + 11 = 4(x + 3).Simplified to slope intercept:
\(\rm{y+11=4x+12}\)
\(\rm{y=4x+1}\) <- this is the simplified slope intercept equation
The Venn diagram below shows the events A and B, and the probabilities p, q and r.
It is known that P(A)=0.43 , P(B)=0.62 and P(A∩B)=0.27 .
Calculate the value of p
Calculate the value of q
Calculate the value of r
Find the value of P (A given NOT B)
Answers
The value of q is 0.35.
The value of p is 0.16.
The value of r is 0.27.
The value of P(A given NOT B) is approximately 0.4211.
To calculate the values of p, q, and r, we can use the information provided in the Venn diagram and the probabilities of events A and B.
Given:
P(A) = 0.43
P(B) = 0.62
P(A∩B) = 0.27
Calculating the value of p:
The value of p represents the probability of event A occurring without event B. In the Venn diagram, p corresponds to the region inside A but outside B.
We can calculate p by subtracting the probability of the intersection of A and B from the probability of A:
p = P(A) - P(A∩B)
= 0.43 - 0.27
= 0.16
Therefore, the value of p is 0.16.
Calculating the value of q:
The value of q represents the probability of event B occurring without event A. In the Venn diagram, q corresponds to the region inside B but outside A.
We can calculate q by subtracting the probability of the intersection of A and B from the probability of B:
q = P(B) - P(A∩B)
= 0.62 - 0.27
= 0.35
Therefore, the value of q is 0.35.
Calculating the value of r:
The value of r represents the probability of both event A and event B occurring. In the Venn diagram, r corresponds to the intersection of A and B.
We are given that P(A∩B) = 0.27, so the value of r is 0.27.
Therefore, the value of r is 0.27.
Finding the value of P(A given NOT B):
P(A given NOT B) represents the probability of event A occurring given that event B does not occur. In other words, it represents the probability of A happening when B is not happening.
To calculate this, we need to find the probability of A without B and divide it by the probability of NOT B.
P(A given NOT B) = P(A∩(NOT B)) / P(NOT B)
We can calculate the value of P(A given NOT B) using the provided probabilities:
P(A given NOT B) = P(A) - P(A∩B) / (1 - P(B))
= 0.43 - 0.27 / (1 - 0.62)
= 0.16 / 0.38
≈ 0.4211
Therefore, the value of P(A given NOT B) is approximately 0.4211.
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A college student takes the same number of credits each semester. They had 8 credits when they started, and after 5 semesters, they had 58 credits.
Which of these expresses the rate at which they is earning credits?
Answers
Answer:
There are 10 credits per semester.
Step-by-step explanation:
Given that: A college student takes the same number of credits each semester.
They had 8 credits when they started, and after 5 semesters, they had total 58 credits.
Now, In which rate they are earning credits per semester,
for that use the formula:
\(rate=\frac{change of credits}{total no of semeters}\)
rate=50/5
The change in credits is 58-8 = 50, since the
student earned 50 credits in 5 semesters.
So the rate at which they are earning credits per semester is:
Rate = 10 credits per semester.
Hence, there are 10 credits per semester.
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Cuanto mide el largo de un rectángulo cuyo perímetro es 16cm y su área 12 cm al cuadrado ?
Answers
Hay dos rectángulos posibles que satisfacen las condiciones dadas: uno de 2 cm de largo y 6 cm de ancho, y otro de 6 cm de largo y 2 cm de ancho.
The counting number just before C5F sixteen is
Answers
the counting number just before C5F16 is 3,072.
30 points !! :) Thank you in advance
Answers
The solutions of the quadratic equation are: x = 1
The x-intercept is x = 1
What is the Solution to the quadratic equations?The formula for the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
The y-intercept is the point at which the graph crosses the y-axis and in this case it is: y = 1
The x-intercepts are where the graph touches the x-axis and in this case, it is x = 1
The zeros of the quadratic equation are the x-intercepts and since the curve does not cross, then we can say that the zeros are x = 1 and x = 1 which signifies double root and as such the solution is x = 1
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The length of GF is 4 m. What is the radius of the circle? Round to the nearest tenth.
Answers
Therefore, the radius of the circle is π/45 meters.
What is circle?A circle is a two-dimensional geometric shape consisting of all the points in a plane that are at a given distance, called the radius, from a given point, called the center. It can also be defined as the set of all points that are equidistant from a given point in a plane. The distance around a circle is called the circumference, while the distance across the circle through the center is called the diameter. The ratio of the circumference to the diameter is a constant value known as pi (π), which is approximately 3.14.
Here,
We can use the formula for arc length and sector angle of a circle:
Arc length = (angle/360) x 2πr
where r is the radius of the circle.
We are given that the length of arc GF is 4 m and the sector GF makes an angle of 32 degrees. Substituting these values into the formula, we get:
4 = (32/360) x 2πr
Simplifying:
4 = (4/45)πr
r = (4/45)π x (1/4)
r = π/45
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Without graphing, compare the slopes and the intercepts of the
graphs of the functions f(x) = x + 1 and g(x) = f(2x).
Answers
Answer:
graph f(x) passes through the y-axis at 1:00 whereas g(x) passes through the origin.
expand the number 0.398
Answers
Answer:
00.398
Step-by-step explanation:
Answer:
Do you mean in expanded form? If so it's 0.3+0.09+0.008 I believe.
Two boys earn money mowing lawns. Jacob mowed 12 lawns this week. He mowed
3 times as many lawns as Kevin mowed.
In which equation does the box represent the number of lawns Kevin mowed?
A. 3 + □ = 12
B. 3 × □ = 12
C. 12 + 3 = □
D. 12 × 3 = □
Answers
12/3=4
-> 3 x 4 = 12
Answer:
3 × □(4) = 12
Step-by-step explanation:
because Jacob mowed 12 lawns this week and He mowed
3 times as many lawns as Kevin mowed.
18 more than the product of 16 and 2
Answers
Answer:
50
Step-by-step explanation:
18+(16×2)
18+32
=50
Please Help Me ( Its not that Hard Im just really tired)
I did abut 5 hours of khans im losing my mind i I fail another khan
I will consider marking brainliest
Answers
q = 1 r - 2
--- ---
3. 9
r = 3q + 2
----
3
Answer:
\(q=\frac{3r-2}{9}\)
Step-by-step explanation:
9q = 3r - 6 + 2
9q = 3r - 4
\(q=\frac{3r-2}{9}\)
John states that the product of two real numbers is a real number. Extending this to imaginary numbers John states that the product of two imaginary numbers must be imaginary. Is his statement correct?
Answers
Answer:
no because these "imaginary numbers" can have the same value as 2 real numbers that add up to a real number. Example:7 3+4=7 x+y (Algebra so not real numbers)= infinite possibilities
Step-by-step explanation:
Given \($\triangle RST \cong \triangle XYZ$\). Points \($P$\) and \($W$\) lie on \($ST$\) and \($YZ$\), respectively. Which of the following statements are true?
A) If \($P$\) is the midpoint of \($\overline {ST}$\) and \($W$\) is the midpoint of \($\overline {YZ},$\) then \($\triangle RSP\cong \triangle XYW$\).
B) If \($\overline {RP}$\) bisects \($\angle SRT$ and \($\overline {XW}$\) bisects \($\angle YXZ$\), then \($\triangle RSP\cong \triangle XYW$\).
C) If \($RP=XW$\), then \($\triangle RSP\cong \triangle XYW$\).
D) If \($\overline {RP}\perp\overline {ST}$\) and \($\overline {XW}\perp\overline{YZ}$\), then \($\triangle RSP\cong \triangle XYW$\).
Answers
The triangles ΔRST and ΔXYZ are congruent, then all the same construction make triangles congruent. All the options are correct.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
If two triangles are congruent, then the ratio of the corresponding sides will be one.
The triangles ΔRST ≅ ΔXYZ. Points P and W lie on ST and YZ, respectively.
The diagram is given below.
A) If P is the midpoint of ST and W is the midpoint of YZ then ΔRSP ≅ ΔXYW is true.
B) If RP bisects ∠SRT and XW bisects ∠YXZ, then ΔRSP ≅ ΔXYW is true.
C) If RP = XW, then ΔRSP ≅ ΔXYW is true.
D) If RP ⊥ ST and XW ⊥ YZ, then ΔRSP ≅ ΔXYW is true.
All the options are correct.
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![Given [tex]$\triangle RST \cong \triangle XYZ$[/tex]. Points [tex]$P$[/tex] and [tex]$W$[/tex] lie on](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/g8x7FwPB2O18HNRDmWbSF6wS2lk6Vfaz.png)
Use a linear approximation to estimate 3√28 write your exact answer with fractions
Answers
The estimated value of 3√28 using linear approximation is 82/27 which is answered in form of fraction.
What is linear approximation?A general function can be approximated using a linear function in mathematics using the term "linear approximation" (more precisely, an affine function). They are frequently utilised in the finite difference method to create first order approaches for resolving or approximating solutions to equations.
We need to find the approximate value of ∛28 using linear approximation
Let f(a) = ∛a
then F(27) = ∛27 = 3
We compute the derivative of f(a) as being
\(f(a)=a^{\frac{1}{3}}\) ⇒ \(f'(a)=\frac{1}{3}a^{-\frac{2}{3}}\)
Hence,
\(f'(a)=\frac{1}{3}a^{-\frac{2}{3}}\) = \(\frac{1}{3}(3)^{-2}=\frac{1}{3}(\frac{1}{9})=\frac{1}{27}\)
Recall the equation of a line is given by
⇒ y - b = m(x - a)
⇒ \(y-3=\frac{1}{27}(x-27)\)
⇒ \(y=\frac{1}{27}x-1+3\)
⇒ \(y=\frac{1}{27}x+2\)
So the approximation at x= 27.5 would be
⇒ \(y=\frac{1}{27}(28)+2\)
⇒ y = 82/27
⇒ y = 3.037
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After 4 minutes of reading, Aaron was on page 14 of his book. After 8 minutes he was on page 20. Which equation models the page number, y, in terms of minutes x?
Group of answer choices
y = −1.5x + 8
y = 8x + 1.5
y = –8x + 1.5
y = 1.5x + 8
Answers
Kim had 2 1/3 pounds of candy. Eric eats 2/5 of Kims candy. How much candy did Eric eat?
Answers
The quantity of candy that Eric ate would be = 14/15
How to calculate the quantity of candy eaten by Eric?The quantity of Candy Kim had = 2⅓ pounds.
The quantity of Kims candy that Eric ate = 2/5
That is 2/5 of 2⅓.
The actual quantity of candy that Eric ate = 2/5× 7/3 = 14/15
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If a black card is drawn from an ordinary deck of cards, what is the probability that the card is a club?
Answers
Solution
Since there are 13 clubs and there are 52 cards in a deck
\(\begin{gathered} \text{ The probability that the card is a club is:} \\ \\ \frac{13}{52}=\frac{1}{4} \end{gathered}\)The probability is 1/4
If l || m, classify the marked angle pair and give their relationship, then solve for X.
Answers
Given their relationship the angles are congruent.
8x-71=5x+7
3x-71=7
3x=78
X=26
Find m∟1 and m∟2. Tell which theorem can be use
Answers
Answer: Angle 1 = 150 - corresponding angles
Angle 2 = 150 - alternate exterior angles
Step-by-step explanation:
To find the measure of angles ∠1 and ∠2, we are using vertical angle theorem and corresponding angles concept.
From the given figure measure of one of the angle is 150°.
What are angles of parallel lines?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.
Corresponding angles are angles that occur on the same side of the transversal line and are equal in size. They are either both obtuse or both acute.
Here, ∠1 = 150° (Corresponding angles)
∠1 =∠2 = 150° (Vertically opposite angles are congruent)
To find the measure of angles ∠1 and ∠2, we are using vertical angle theorem and corresponding angles concept.
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Write an equivalent expression. 4x - x
Answers
Answer:
5x-2x
Step-by-step explanation:
4x-x = 3x
so,
5x-2x = 3x
The equivalent expression would be; 5x-2x
What are equivalent expressions?Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.
To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.
We are given that the expression as; 4x - x
We need to find an equivalent expression.
Therefore, solving further;
4x-x = 3x
Thus, we can also create one expression as;
5x-2x = 3x
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A pair of dice are tossed twice. Find the probability that the first roll is a total of at least 5 and the second roll is a total of at least 4.
Answers
The probability that the first roll is a total of at least 5 and the second roll is a total of at least 4 is 0.764 or 76.4%.
What is the probability?The probability is the chance that an expected event occurs out of many possible events.
For two independent events happening, we use the rule of multiplication of independent events based on dice probabilities.
The event that the first roll is a total of at least 5 = A
In the event that the second roll is a total of at least 4 = B
The number of faces on each die, n = 6
The probability of event A = ³⁰/₆ = ⁵/₆
The probability of event B = ³³/₃₆ = ¹¹/₁₂
Multiplying the two probabilities, P(A) and P(B) = ⁵/₆ × ¹¹/₁₂
= ⁵⁵/₇₂ = 0.764
Thus, there is a ⁵⁵/₇₂ or 0.764 chance that the first roll is at least 5 and the second roll is at least 4.
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What combination of transformations is shown below?
Answers
Answer:
Rotated then translated
Step-by-step explanation:
michael sang 5 songs. Every song was 7/8 minutes long. For how much time did he sing in total?
Answers
Answer:
262.5 seconds 4.375 minutes
Step-by-step explanation:
7/8 of a minute is 52.5 seconds
52.5x5=262.5 seconds
262.5/60= 4.375 minutes
Answer:
4 3/8 minutes.
Step-by-step explanation:
5 * 7/8 = 35/8
35/8 = 32/8 + 3/8
= 4 + 3/8
= 4 3/8
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The table shows a proportional relationship.
Workout (hours) 1 2 3
Calories Burned 320 640 960
Create a description in words for the table.
The number of hours working out is dependent on the number of calories burned. For a one-hour workout, there are 320 calories burned, and for a two-hour workout, there are 640 calories burned.
The number of hours working out is dependent on the number of calories burned. For every 320-hour workout, there is 1 calorie burned, and for every 640-hour workout, there are 2 calories burned.
The number of calories burned is dependent on the number of hours working out. For a one-hour workout, there are 320 calories burned, and for a two-hour workout, there are 640 calories burned.
The number of calories burned is dependent on the number of hours working out. For every 320-hour workout, there is 1 calorie burned, and for every 640-hour workout, there are 2 calories burned.
Answers
The description for the table in word will be A. The number of hours working out is dependent on the number of calories burned. For a one-hour workout, there are 320 calories burned, and for a two-hour workout, there are 640 calories burned.
What is a proportional relationship?Proportional connections are those in which the ratios of two variables are equal. Another way to think about them is that one variable in a proportional relationship is always a constant value multiplied by the other. This is known as the "constant of proportionality."
In this case, the table shows a proportional relationship between workout and calories burned. In 1 hour, 320 calories are burned.
In conclusion, the correct option is A.
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Find the values of x and y.
PLEASE HELP ME I DONT GET THIS
Answers
Three quarters of a number is 27. What is two ninths of the number?
Answers
Answer:
8
Step-by-step explanation:
let x be the number , then
\(\frac{3}{4}\) x = 27 ( multiply both sides by 4 to clear the fraction )
3x = 108 ( divide both sides by 3 )
x = 36
the number is 36, so
\(\frac{2}{9}\) × 36 = 2 × 4 = 8
The two ninths of the number is 8
We know that Three quarters of a number is \(\frac{3}{4}\) times of a number
Hence we will assume the number x ,
\(\frac{3}{4} of x = 27\)
\(x = 27 X \frac{4}{3}\)
\(x = 36\)
Now as we know the number is 36
Therefore , the two ninths of the number assumed as y
We will multiply the number 36 by 2 and then divide by 9
Hence,
\(y = 36 X \frac{2}{9}\)
\(y = 8\)
Thus, the two ninths of the number 36 is 8
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If y = x² + 2x,
find the value of y when x = 5
Answers
_____________________________
Hey!!
Solution,
X=5
Now,
y=x^2+2x
=(5)^2+2*5
=25+10
= 35
So the value of y is 35
hope it helps
Good luck on your assignment
___________________________
For the given equation y = x² + 2x, the value of y when x = 5 is, 35
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
An equation, y = x² + 2x
The value of y when x is equal to 5 = ?
after putting value of x in a equation
⇒ y = 5² + 2 × 5
⇒ y = 25 + 10
⇒ y = 35
Hence, the value of y is 35
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Which shapes are similar but not congruent to shape 1
Answers
There are countless possibilities for shapes that are similar but not congruent to shape 1, as long as they maintain the same proportions and shape.
There are many shapes that are similar but not congruent to shape 1. Similar shapes have the same shape, but their sizes may be different. In contrast, congruent shapes have the same shape and size.
One example of a similar shape to shape 1 is a rectangle that is twice as long and half as wide. Another example could be a square that is three times larger in area than shape 1.
A parallelogram that has the same base as shape 1 but is three times as tall is also similar but not congruent.
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The Unit Circle
For the given central angle, determine the distance traveled along the unit from the point (1. 0)
210°
a. 3.67 units
b. 1.17 units clockwise
c. 1.83 units
d. 7.33 units
Please select the best answer from the choices provided
Answers
Answer:
A. 3.67 units
Step-by-step explanation:
I calculated it logically