Answers
1. 3(2) + 5=6+5 = 11
2. 4(3) - 7 =12-7= 5
3. 2(3) - 4 =6-4 = 2
4. 6(4) - 2(3) =24-6 = 18
5. 2+3-4+5 = 5-4+5= 1+5 = 6
6. 7(4) - 2(2) = 28-4= 24
7. 2(3)(4) + 1 = 24+1 = 25
8. 2(3)(4) - 4 = 24-4 = 20
9. 8(2) /4 = 16/4 = 4
10. 6(3)/2 =18/2 = 9
11. 4(2) + 7 = 8+7 = 15
12. 2(4) - 7 = 8-7 = 1
13. 2(3) + 3(2) = 6+6 = 12
14. 6(2) - 1 = 12-1 = 11
15. 3(4) - 2 = 12-2 = 10
Related Questions
An ice company charged $3.10 for 5 bags of ice. If a convenience store bought 2 bags of ice, how much would it have cost them?
Answers
Answer:
$1.24
Step-by-step explanation:
use a proportion.
$3.10/5 = x/2
5x = 2 × $3.10
x = $1.24
Answer:
$1.24
Step-by-step explanation:
$3.10 for 5 bags
I bag = 310/5= 62
Move the decimal point back two times which is 0.62
2 bags cost 0.62*2= 1.24
= $1.24
Consider the line y = 3x - 1.
Find the equation of the line that is perpendicular to this line and passes through the point (-8, 3)
Find the equation of the line that is parallel to this line and passes through the point (-8, 3).
Answers
Answer:
y = -1/3x + 1/3
Step-by-step explanation:
The slopes of perpendicular lines are negative reciprocals.
The given line is
y = 3x - 1
This equation is written in the slope-intercept form, y = mx + b, where m is the slope.
slope of given line = m = 3
slope of perpendicular line = -1/3
Now we need the equation of the line with slope -1/3 that passes through the point (-8, 3)
y = mx + b
y = -1/3x + b
3 = (-1/3)(-8) + b
3 = 8/3 + b
9/3 = 8/3 + b
b = 1/3
y = -1/3x + b
y = -1/3x + 1/3
40% of Damien‘s marbles are blue. Damien has three marbles how many of the marbles are not blue
Answers
40% of Damien’s marbles are 6/5 or 1.2.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Damien has three marbles.
40% of Damien’s marbles are blue.
That means,
40% of 3 blue marbles.
So, using the percentage formula,
40% of 3,
= 40 x 3/100
= 120/100
= 12/10
= 6/5
= 1.2
Therefore, 1.2 marbles are blue.
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A spinner is divided into six equal parts numbered 1, 2, 3, 4, 5, and 6. In a repeated experiment, Ryan spun the spinner twice. The theoretical probability of both spins being odd numbers is 9 over 36.
If the experiment is repeated 140 times, predict the number of times both spins will be odd numbers.
140
70
36
35
Answers
So, based on the theoretical likelihood, we anticipate that 35 times out of 140 repeats, both spins will be odd numbers.
What is probability?Probability is a branch of mathematics that deals with the study of random events and the likelihood of their occurrence. Probability is expressed as a number between 0 and 1, with 0 indicating that an event is impossible to occur and 1 indicating that an event is certain to occur. The probability of an event A, denoted by P(A), is calculated as the number of favorable outcomes for the event divided by the total number of possible outcomes. For example, if a fair six-sided die is rolled, the probability of rolling a 3 is 1/6 because there is only one favorable outcome (rolling a 3) out of the total 6 possible outcomes. Probabilities can be used to make predictions about the likelihood of future events and to make decisions under uncertainty. Probabilities can also be used to describe the distribution of random variables and to quantify the relationship between different events. Probability theory is widely used in many fields, such as statistics, engineering, finance, physics, and biology, among others.
Here,
The theoretical probability of both spins being odd numbers is 9 over 36, which means that for every 36 times the experiment is repeated, we expect 9 of those times to result in both spins being odd numbers.
If the experiment is repeated 140 times, we can use the theoretical probability to estimate the number of times both spins will be odd numbers as follows:
140 * (9/36) = 35
So, based on the theoretical probability, we predict that both spins will be odd numbers 35 times out of 140 repetitions.
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factor the common factor out of each expression 9+8b^2
Answers
Answer:
9+8b^(2)
Step-by-step explanation:
common factors are -1, 1
Helppppppppp ASAP plzzzzzzzz
Answers
Answer:
from the origin of the graph(which is the center) go right 3 then mark a point( should be a little before the number 4, then from the origin again go up to the number 4 and mark another point. then run a line connecting the two dots you made
Step-by-step explanation:
Find the volume of the smaller region cut from the solid sphere rho≤4 by the plane z=2. The volume is (Type an exact answer, using π as needed.)
Answers
To find the volume of the smaller region cut from the solid sphere by the plane z = 2, we can use the method of slicing. We need to determine the limits of integration and set up the integral to calculate the volume. The volume is an exact value expressed using π.
To find the volume of the smaller region cut from the solid sphere by the plane z = 2, we can imagine slicing the sphere into thin disks parallel to the xy-plane. Each disk has a radius determined by the distance from the z-axis to the sphere's surface at that particular z-coordinate. In this case, the solid sphere has a radius of 4. The plane z = 2 intersects the sphere at the height z = 2. The smaller region is formed by the portion of the sphere below this plane.
To calculate the volume, we integrate the area of each slice over the range of z-values that make up the smaller region. Since the sphere is symmetric, we can consider only the upper half and double the volume at the end. The limits of integration for z are from -4 to 2, as the sphere extends from -4 to 4. The radius of each disk at a particular z-coordinate can be determined using the equation of the sphere, which is ρ = 4.
Therefore, the volume can be calculated as follows:
\[ V = 2 \cdot \int_{-4}^{2} \pi \cdot (4^2 - z^2) \, dz \]
Simplifying the integral and solving, we have:
\[ V = 2 \cdot \pi \int_{-4}^{2} (16 - z^2) \, dz \]
\[ V = 2 \cdot \pi \left[ 16z - \frac{z^3}{3} \right]_{-4}^{2} \]
\[ V = 2 \cdot \pi \left[ (16 \cdot 2 - \frac{2^3}{3}) - (16 \cdot -4 - \frac{(-4)^3}{3}) \right] \]
\[ V = 2 \cdot \pi \left[ 32 - \frac{8}{3} - (-64 + \frac{64}{3}) \right] \]
Simplifying further, we get:
\[ V = 2 \cdot \pi \left[ 32 - \frac{8}{3} + \frac{192}{3} \right] \]
\[ V = 2 \cdot \pi \left[ \frac{352}{3} \right] \]
Therefore, the volume of the smaller region cut from the solid sphere by the plane z = 2 is \(\frac{704}{3}\pi\) cubic units.
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50 minus 17 4/6 plzzzzzzzzzz answer rn
Answers
Answer:
32 1/3 or 2/6
Step-by-step explanation:
but 1/3 is better
Answer:
decimal form= 32.3
Step-by-step explanation:
fraction form 32 1/3
The graph of $y = f(x)$ is shown below, in red. Find the equation that corresponds to the blue graph.
Enter your answer in the form "$y = \dotsb$".
Answers
The blue graph which is the red graph is shifted to the left by 2 units. The second one which is the red graph is shifted up by 3 units.
What is graph representation?
Graphical Representation is a method using which we can analyze numerical data. It helps us finding a relation between data, ideas, information and concept in a diagram. It is one of the very important learning strategies and is easy to understand as well. It is dependent on the type of information in any particular domain. There are various types of graphical representation. It helps and allows to study the relationship between two variables where the change in the variable amount with respect to another variable within the given interval of time can be measured. The series distribution and frequency distribution for any given problem can be studied using it.
Here,
The blue graph is the red graph shifted to the left by two units
And therefore it's equation is :
\(y=f(x+2)\)
The second one is the red graph which is shifted up by three units.
And thus the equation for this will be:
\(y=f(x)+3\)
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You start at (2, 2). You move up 8 units. Where do you end?
Answers
Answer: (2, 10) hope this helps have a good day
Step-by-step explanation:
Bounce world offers birthday parties for $140 plus $6 per person. If you can spend no more than $240, how many people can you invite to the party?
Answers
Answer
The most people you can invite with no more than $240, is 16 people.
Step-by-step explanation:
6x+140=240
6x = 100
x = 16.6666667
Therefore
x = 16.
What is the percentage increase of R20 to R22.
Answers
Answer: 10%
Step-by-step explanation: R20 = 100
Therefore R1 = 100%÷ R20 = 5%. The difference between R22 and R20 is R2, therefore the increase in % is R2×5%=10%.
Answer:
+10%
Step-by-step explanation:
i got it right on edge
When analyzing two quantitative variables, what is the first thing that should be done?.
Answers
When analyzing two quantitative variables the first thing that should be done make a scatterplot.
When comparing two quantitative variables, a scatterplot is the most useful display technique. We plot the variable we consider the response variable on the y-axis and the explanatory or predictor variable on the x-axis.
How do we know which variable is which? The explanatory variable, in general, attempts to explain or predict the observed outcome. A study's outcome is measured by the response variable. One may even consider investigating whether one variable causes variation in another variable; for example, a popular research study found that taller people are more likely to earn higher wages. In this case, the explanatory variable Height would be used to explain the variation in the response variable Salaries.
When summarizing the relationship between two quantitative variables, we must consider the following:
1.Association/Direction (i.e. positive or negative)
2.Form (i.e. linear or non-linear)
3.Strength (weak, moderate, strong)
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What is the angle between the vectors − 2i 3j k and i 2j − 4k?
Answers
The angle between the vectors can be found using the dot product. The formula is θ= |A| =√(x12 + y12 + z12) The angle between the vectors -2i + 3j + k and i + 2j - 4k is approximately 137.8 degrees.
v1 • v2 = (-2i + 3j + k) • (i + 2j - 4k)
= -2 - 6 + 1 = -7
|v1| = \(\sqrt{((-2)^2 + 3^2 + 1^2)}\)
=\(\sqrt{(4 + 9 + 1)}\)
=\(\sqrt{14}\)
|v2| = \(\sqrt{((1)^2 + 2^2 + (-4)^2)}\)
= \(\sqrt{(1 + 4 + 16) }\)
= (\(\sqrt{21}\)
θ= |A| (-7/\(\sqrt{14}\)\(\sqrt{21}\))
= |A| (-7/21*14)
= |A|(-7/294)
= 137.8 degrees
The angle between two vectors can be found using the dot product formula. This formula isθ= |A| =√(x12 + y12 + z12). In the case of the vectors -2i + 3j + k and i + 2j - 4k, this formula can be used to find the angle between them. The dot product of the two vectors is -2 - 6 + 1 = -7. The magnitude of the first vector, |v1|, can be found using the Pythagorean theorem, which is
\(\sqrt{((-2)^2 + 3^2 + 1^2)}\)
= \(\sqrt{(4 + 9 + 1)}\)
= \(\sqrt{14}\).
The magnitude of the second vector, |v2|, can be found using the Pythagorean theorem, which is
\(\sqrt{((1)^2 + 2^2 + (-4)^2)}\)
= \(\sqrt{(1 + 4 + 16)}\)
= \(\sqrt{21}\)
Once the dot product and magnitudes are known, the angle between the two vectors can be found using the formula .Therefore, the angle between the two vectors is approximately 137.8 degrees.
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triangles abc and xyz are similar. the length of the sides of abc are 121 cm, 105 cm, and 98 cm. the length of the smallest side of xyz is 52 cm, what is the length of the longest side of xyz? round your answer to one decimal place.
Answers
Since triangles abc and xyz are similar, their corresponding sides are proportional.
Let's label the sides of triangle xyz as a, b, and c. We know that the smallest side of xyz (side a) is 52 cm. We need to find the length of the longest side of xyz (which we can label as side c).
We can set up a proportion to solve for c: 121/52 = 105/b = 98/c
Solving for b, we get: 121/52 = 105/b
b = (105*52)/121
b ≈ 45.6
Now we can set up a new proportion to solve for c: 121/52 = 98/c
Multiplying both sides by c, we get: 121c/52 = 98
Solving for c, we get:
c = (98*52)/121
c ≈ 42.3
Therefore, the length of the longest side of xyz is approximately 42.3 cm.
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A student who is at the 40th percentile of first-year gpas is also likely to be at the 40th percentile of second-year gpas. true false
Answers
False. We would anticipate the second-year GPA to be slightly higher than the 40th percentile based on the regression impact.
How does your GPA translate?
Your grade point average (GPA) is calculated by dividing the total number of credits you have earned in high school by the sum of all of your course grades. The majority of colleges and secondary schools use a 4.0 scale to report grades.Given this,
A student who has a first-year GPA in the 40th percentile
is likely to have a second-year GPA in the same range.
The scatter plot is shaped like a football. ————— (False)
If the scatter diagram is shaped like a football, then all of the data points are drawn in a circle. As a result, the data does not fit well.
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Solve for x. Round to the nearest tenth, if necessary.
Answers
Sin(38) = 1.3/x
Cross multiply
xsin38 = 1.3
Divide through by sin38
x = 1.3/sin38
x = 1.3/0.6157
x = 2.111
x ≈ 2.11 units
Answer:
x = 2.1
Step-by-step explanation:
We have:
=
=> sin38 × x = sin90 × 1.3
=> x = 1.3 ÷ sin38
=> x = 2.11155001... = 2.1
<3 Have a nice day!!
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The function f(t)=16t2 represents the distance (in feet) a dropped object falls in t seconds. The function g(t)=s0 represents the initial height (in feet) of the object. A necklace is dropped from a height of 64 feet. After how many seconds does the necklace hit the ground?
Answers
By solving a quadratic equation, we will see that the necklace hits the ground 2 seconds after it is dropped.
After how many seconds the necklace hits the ground?We know that the function:
f(t) = 16*t^2
Represents the distance that an object falls down in t seconds.
If the necklace is dropped from a height of 64 feet, the necklace will hit the ground when the distance that an object falls down in t seconds is equal to 64 feet, so we just need to solve the quadratic equation:
f(t) = 64
16*t^2 = 64
t^2 = 64/16 = 4
t = √4 = 2
The necklace will hit the ground after 2 seconds.
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find the Surface Area of this shape
Answers
Answer:
V≈94423.71
Step-by-step explanation:
V=πr2h=π·342·26≈94423.7088
If a =
-5x and b = 3x – 4i, then find the value of the a^3b in fully simplified form. (Please help)
Answers
The expression -5x is a monomial, while 3x - 4i is a complex number
The simplified form of the expression a^3b is -375x^4 - 500x^3i
How to determine the productThe given parameters are:
a = -5x
b = 3x - 4i
The value of the expression a^3b is calculated as follows:
\(a^3b = (-5x)^3 * (3x - 4i)\)
Evaluate the exponent
\(a^3b = -125x^3 * (3x - 4i)\)
Open the bracket
\(a^3b = -375x^4 - 500x^3i\)
Hence, the simplified form of the expression a^3b is -375x^4 - 500x^3i
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The set of all solution points of an equation is the ___ of the equation.
Answers
The graph of an equation is the collection of all of its solution points.
Consider the function y=f(x). All the ordered pair ( a, b) such that b=f(a) is called the graph of the equation.
A linear equation is a two-variable equation with a line as the graph. A collection of points in the coordinate plane that are all solutions to the equation make up the graph of the linear equation.The solution set consists of all points whose y-coordinate is greater than or equal to 1.
These points are contained in the shaded region in the graph below. This kind of region is called a half-plane because it is one of two parts of the plane into which a boundary line divides it.
To find the equation of a graphed line, find the y-intercept and the slope in order to write the equation in y-intercept (y = m(x) + b) form. The slope is the ratio of the y-to-x change.Therefore, the set of all solution points of an equation is the graph of the equation.
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4. What are the Z-scores for the following Confidence Interval levels? Remember, you MUST account for both tails of the curve, positive and negative, when identifying each. That means you will need to do a little math to obtain the correct z-value. 3 Points 68%= 85% = 99% =
Answers
In order to calculate the z-scores for the given Confidence Interval (CI) levels, we need to use the Z-table. It is also known as the standard normal distribution table. Here are the z-scores for the given Confidence Interval levels:1. 68% CI: The confidence interval corresponds to 1 standard deviation on each side of the mean.
Thus, the z-score for the 68% \(CI is ±1.00.2. 85% CI\): The confidence interval corresponds to 1.44 standard deviations on each side of the mean.
We can calculate the z-score using the following formula:\(z = invNorm((1 + 0.85)/2)z = invNorm(0.925)z ≈ ±1.44\)Note that invNorm is the inverse normal cumulative distribution function (CDF) which tells us the z-score given a certain area under the curve.3. 99% CI: The confidence interval corresponds to 2.58 standard deviations on each side of the mean. We can calculate the z-score using the following formula:\(z = invNorm((1 + 0.99)/2)z = invNorm(0.995)z ≈ ±2.58\)
Note that in general, to calculate the z-score for a CI level of (100 - α)% where α is the level of significance, we can use the following formula:\(z = invNorm((1 + α/100)/2)\) Hope this helps!
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Natural gas is to be produced from a geologic formation confined on the top and bottom by impervious shale layers. Let φ=0.3, b=100 m,αp=4×10−9 Pa−1 and; rho=0.1hp Where rho gas density (kg/m3),hp pressure head expressed as meters of water (m). Calculate the gas mass produced if the pressure head is reduced from 100 m to 30 m over an area of 10,000 m2.
Answers
Answer:
Step-by-step explanation:
To calculate the gas mass produced, we can use Darcy's Law, which relates the flow of gas through a porous medium to the pressure gradient. The formula for Darcy's Law is:
Q = -k * A * (dP/dx)
Where:
Q is the flow rate (m^3/s)
k is the permeability of the medium (m^2)
A is the cross-sectional area (m^2)
dP/dx is the pressure gradient (Pa/m)
Given:
φ = 0.3
b = 100 m
αp = 4 × 10^(-9) Pa^(-1)
ρ = 0.1 hp (gas density)
Pressure head (initial) = 100 m
Pressure head (final) = 30 m
Area (A) = 10,000 m^2
First, we need to calculate the permeability (k) using the porosity (φ) and the compressibility (αp) as follows:
k = φ² * αp
k = 0.3² * (4 × 10^(-9) Pa^(-1))
k = 9 × 10^(-11) m^2
Next, we can calculate the pressure gradient (dP/dx) by subtracting the final pressure head from the initial pressure head and dividing it by the distance (b):
dP/dx = (Pressure head (final) - Pressure head (initial)) / b
dP/dx = (30 m - 100 m) / 100 m
dP/dx = -0.7 Pa/m
Now, we can calculate the flow rate (Q) using Darcy's Law:
Q = -k * A * (dP/dx)
Q = -9 × 10^(-11) m^2 * 10,000 m^2 * (-0.7 Pa/m)
Q = 6.3 × 10^(-4) m^3/s
Finally, we can calculate the gas mass (m) using the flow rate (Q) and the gas density (ρ):
m = Q * ρ
m = 6.3 × 10^(-4) m^3/s * 0.1 kg/m^3
m = 6.3 × 10^(-5) kg/s
Therefore, the gas mass produced when the pressure head is reduced from 100 m to 30 m over an area of 10,000 m^2 is approximately 6.3 × 10^(-5) kg/s.
To calculate the gas mass produced, Using Darcy's Law and the given values, we can determine the gas mass produced when the pressure head is reduced from 100 m to 30 m over an area of 10,000 m2.
The gas mass produced can be calculated by first determining the permeability (k) using the given values of porosity (φ), compressibility (αp), gas density (ρ), and thickness (b). With the obtained value of k, we can then use Darcy's Law to calculate the gas flow rate. However, since the time period is not specified, we cannot directly calculate the gas mass produced. The gas flow rate obtained from Darcy's Law represents the volume of gas flowing per unit time. To calculate the gas mass produced, we need to integrate the flow rate over time. Without the time component, we cannot determine the exact gas mass produced. Therefore, the calculation of the gas mass produced requires information about the time period or additional data.
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Which equations support the fact that rational numbers are closed under addition?
Select each correct answer.
03√5 + √5 = 4√5
√10 + (-√10) = 0
¯ ½ + 0.5 = 1
3√16 + 3√16 = 6√/16
Answers
All of the equations provided support the fact that rational numbers are closed under addition. In mathematics, closure refers to the property of a set that states that when you perform an operation on any two elements in that set, the result is always another element in that same set.
In the case of rational numbers and addition, we want to show that when we add any two rational numbers together, the result is always another rational number. To do this, we can use the fact that a rational number is any number that can be written as a fraction of two integers. So, let's take the equation ¯ ½ + 0.5 = 1 as an example. We can see that both 1/2 and -1/2 are rational numbers (since they are both fractions of integers), and when we add them together, we get 0, which is also a rational number. Therefore, we can conclude that the set of rational numbers is closed under addition. Similarly, we can look at the other equations provided. The equation √10 + (-√10) = 0 involves irrational numbers (since the square root of 10 is not a fraction of integers), but it is still an example of closure, since the result of the addition is still a rational number (in this case, 0).
The equation 3√16 + 3√16 = 6√/16 involves radicals, but we can simplify it to 6(4)/4, which simplifies further to 6. Since 6 is a rational number (it can be written as the fraction 6/1), we can see that this equation also supports the fact that rational numbers are closed under addition.
Finally, the equation 03√5 + √5 = 4√5 involves both a rational and an irrational number. However, we can simplify it to (3+1)√5, which equals 4√5. Since 4√5 is also a rational number (it can be written as the fraction 4√5/1), we can conclude that this equation also supports the fact that rational numbers are closed under addition.
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Sum of two numbers 25 and their quotient 4
Answers
Answer:
x = 20
y = 5
Step-by-step explanation:
x + y = 25
x/y = 4
Your Answer is in the above attachment
Hope it Helps :)
Graph y = 2x and find the x intercept
some help I don't get it
Answers
if a pool is 20,000 gallons and when the hose is placed in the pool to start filling up there are already 5000 gallons in there. The pool is filling up at a 1250 gallons per hour rating. how long would it take to fill up?
Answers
Answer:
12 hours
Step-by-step explanation:
Consider the two triangles.
В.
To prove that the triangles are similar by the SAS
similarity theorem, it needs to be shown that
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Answers
Answer:
By Both
Step-by-step explanation:
You have all 3 corresponding sides are proportional so you have SSS. That is
24/8=15/5=18/6
You also have SAS because 15/5=18/6 and you have the angle between the sides that I'm referring to in that proportion.
To prove that the triangles are similar by the SAS similarity theorem the two sides and angles are proportional.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
From definition of similar triangles the 3 corresponding sides are proportional so you have SSS.
Such that 24/8=15/5=18/6
We also have SAS because 15/5=18/6 and you have the angle between the sides.
Hence, to prove that the triangles are similar by the SAS similarity theorem the two sides and angles are proportional.
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You make 10$ an hour babysitting and 20$ an hour lifeguard you need to make at least 120$ next week to buy a concert ticket you can work at most 10 hours a week use y for number of hours babysitting and x for hours lifeguard
Answers
Answer:
Which of these sentences from the excerpt most strongly supports the correct answer to Question 5?
Answer choices for the above question
Quesiton 5 says
Which of these inferences about the author’s point of view is best supported by the entire excerpt?
From: The Immortal Life of Henrietta Lacks" lesson
A. “She’s simply called HeLa, the code name given to the world’s first immortal human cells—her cells, cut from her cervix just months before she died.”
B. “I’ve spent years staring at that photo, wondering what kind of life she led, what happened to her children, and what she’d think about cells from her cervix living on forever—bought, sold, packaged, and shipped by the trillions to laboratories around the world.”
C. “One scientist estimates that if you could pile all HeLa cells ever grown onto a scale, they’d weigh more than 50 million metric tons—an inconceivable number, given that an individual cell weighs almost nothing.”
D. “All of the stories mentioned that scientists had begun doing research on Henrietta’s children, but the Lackses didn’t seem to know what that research was
Step-by-step explanation:
Which of these sentences from the excerpt most strongly supports the correct answer to Question 5?
Answer choices for the above question
Quesiton 5 says
Which of these inferences about the author’s point of view is best supported by the entire excerpt?
From: The Immortal Life of Henrietta Lacks" lesson
A. “She’s simply called HeLa, the code name given to the world’s first immortal human cells—her cells, cut from her cervix just months before she died.”
B. “I’ve spent years staring at that photo, wondering what kind of life she led, what happened to her children, and what she’d think about cells from her cervix living on forever—bought, sold, packaged, and shipped by the trillions to laboratories around the world.”
C. “One scientist estimates that if you could pile all HeLa cells ever grown onto a scale, they’d weigh more than 50 million metric tons—an inconceivable number, given that an individual cell weighs almost nothing.”
D. “All of the stories mentioned that scientists had begun doing research on Henrietta’s children, but the Lackses didn’t seem to know what that research was
100 POINTS
final part/questions so i can complete my written math assignments
Task 2: Height of a Projectile
The height of a projectile that has been launched upward can be determined by finding the sum of the product of one-half of the object’s acceleration and t2, the product of the object’s initial velocity and t, and the object’s initial height, where t represents the number of seconds after the object has been launched. An object’s acceleration can be assumed to be -32 ft/s2, which is the acceleration due to gravity.
A. Why do you think the acceleration due to gravity is represented by a negative number?
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B.Write a formula to represent the height of a projectile for any given time t.
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C.If a projectile is launched into the air from the ground with an initial velocity of 192 feet per second, how long after launch will the projectile be at a height of 320 feet? Show your work.
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D. Can you use your previous answer to determine how long it will take for the object to reach its maximum height? If so, determine how long it will take and find the maximum height.
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E.How long after launch will the projectile land on the ground? Show your work.
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F. If the initial velocity stays the same, but the height the projectile is launched from changes, how would the amount of time it takes for the projectile to reach its maximum height change? How would its maximum height change?
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G. Assuming the velocity stays the same, at what height above the ground does the projectile need to be launched to increase the amount of time it will take for the projectile to return to the ground by one second?
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Answers
A. The acceleration due to gravity is represented by a negative number because it acts in the opposite direction of the upward motion of the projectile. It pulls the object downward, causing it to decelerate and eventually fall back to the ground.
B. The formula to represent the height of a projectile at any given time t is: h = (0.5 * a * t^2) + (v * t) + h0, where h is the height, a is the acceleration (-32 ft/s^2), t is the time, v is the initial velocity, and h0 is the initial height.
C. To find the time when the projectile is at a height of 320 feet, we can set h = 320 in the formula and solve for t. 320 = (0.5 * -32 * t^2) + (192 * t) + 0. Solve the quadratic equation to find the value of t.
D. To find the time it takes for the object to reach its maximum height, we need to find the time when the velocity becomes zero. Set v = 0 in the formula and solve for t. Then substitute the value of t into the formula to find the maximum height.
E. To find the time when the projectile lands on the ground, we need to find the time when the height becomes zero. Set h = 0 in the formula and solve for t.
F. If the initial velocity stays the same but the height the projectile is launched from changes, the amount of time it takes for the projectile to reach its maximum height will remain the same. However, the maximum height will change based on the initial height.
G. To increase the amount of time it takes for the projectile to return to the ground by one second, we need to find the height that corresponds to that additional time. Set the time to (t + 1) in the formula and solve for h. Subtract the initial height from the result to find the height above the ground from which the projectile needs to be launched.
Comment if you need more help!
~~~Harsha~~~