Part A. To solve for the distance travelled during the interval, all we have to do is to plug in values of t = 3 and t = 3.5 in the equation and the difference would be the answer:
when t = 3: s = 16 (3)^2 = 144 m
when t = 3.5: s = 16 (3.5)^2 = 196 m
Therefore the distance travelled within the interval is:
196 m – 144 m = 52 m
Part B. The velocity is calculated by taking the 1st derivative of the equation. v = ds / dt
s = 16 t^2
ds / dt = 32 t = v
when t = 3: v = 32 (3) = 96 m / s
when t = 3.5: v = 32 (3.5) = 112 m / s
Therefore the average velocity is:
(96 + 112) /2 = 104 m / s
Part C. We can still use the formula v = 32 t and plug in the value of t = 3
v = 32 t = 32 (3)
v = 96 m / s
To calculate the distance and velocities for the ball in question, we use the formula s(t)=16t^2, calculate differences, and use limits as the intervals approach an instant.
Explanation:The formula s(t)=16t2 gives the distance s(t) in feet that a ball has traveled after t seconds when dropped from a state of rest. To find the distance during the time interval [3,3.5], we calculate s(3.5) and s(3), and then find the difference: s(3.5) = 16 × (3.5)2 and s(3) = 16 × (3)2.
The average velocity over the interval [3,3.5] is the change in distance divided by the change in time, which is computed as ∆ s/ ∆ t.
For the instantaneous velocity at t=3, we compute the average velocities over smaller and smaller intervals approaching the instant t=3. As these intervals become smaller, the average velocity approaches the instantaneous velocity.
given g(x)=Squareroot x-4 and h(x)=2x-8, what are the restriction on the domain of gofh?
x>?
The domain of the (goh)(x) will be [6, ∞).
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The functions are given below.
g(x) = √(x - 4) and h(x) = 2x - 8
Then the function f of g (x) will be
(goh)(x) = g(h(x))
(goh)(x) = √((2x - 8) - 4)
(goh)(x) = √(2x - 12)
Then the domain of the (goh)(x) will be
We know that the value under the square root should be greater than zero.
2x - 12 ≥ 0
2x ≥ 12
x ≥ 6
The domain of the (goh)(x) will be [6, ∞).
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Factor completely 16a^3b^7 + 2a^6 b4 − 22a ^4 b^5.
2(8a3b7 + a6b4 − 11a4b5)
2a3b4(8b3 + a3 − 11ab)
a3b4(16b3 + 2a3 − 22ab)
8b3 + a3 − 11ab
Answer:
2a3b4(8b3 + a3 − 11ab)
Find the standard form of the equation of the parabola with a focus at (-8, 0) and a directrix at x = 8
Answer:
x = -1/32 * y^2
Step-by-step explanation:
If you take a certain number and add a zero to the right of it and subtract the result from 143, you'll get the tripled imagined number. What is the imagined number?
Final answer:
To find the imagined number, we need to follow the given steps: add a zero to the original number, subtract it from 143, and set the result equal to the tripled imagined number.
Explanation:
To find the imagined number in this question, we need to follow the given steps. Let's assume the original number is x. Adding a zero to the right of it gives us 10x. Subtracting this result from 143 gives us 143 - 10x. According to the question, this result is equal to the tripled imagined number, so we have 143 - 10x = 3x. To solve for x, we can rearrange the equation as 143 = 13x, and then divide both sides by 13. Therefore, the imagined number, x, is 11.
A certain kind of bacteria growing on your kitchen counter doubles every 30 mins.. Assuming that you start with only one bacterium, how many bacteria could be present at the end of 180 mins.
The number of bacteria in a petri dishes 524 and growing at a rate of 7% every month how many bacteria will be there in seven months
7% = 0.07
since it is growing add that to 1 = 1.07
now that is to the power of length of time 1.07^7
now multiply
524 x 1.07^7 = 841.429 ( round answer as needed)
Larry mixed 15 grams of salt with 210 grams of a 5% salt solution in water. What is the percent of salt in his new solution?
Based on its degree, what kind of polynomial is this? h(x)=-x^2+2x-5
Given triangle JKL.
Write the coordinates of vertex J and its reflection J' across the y-axis.
Answer:
(5, -2) = J'(-5, -2) = JStep-by-step explanation:
an air traffic controller spots two planes at the same altitude flying toward each other. Their flight paths form a right angle at point p. One plane is 150 miles from point P and is moving at 450 miles per hour. The other plane is 200 miles from point P and is moving at 450 miles per hour. What is the distance s between the planes as a function of time t?
The problem states that the paths of the two planes form a right triangle, therefore this means that the distance between the two is the hypotenuse. Given that information, we can use the hypotenuse formula for finding the distance formula:
c^2 = a^2 + b^2 ---> 1
Where c is the hypotenuse, in this case the distance between the two planes.
First let us find the value of a. We know that one plane is 150 miles from point P and this distance is decreasing by a rate of 450 miles per hour, therefore a is:
a = 150 – 450 t ---> 2
We also know that the other plane is 200 miles away and this distance decreases by a rate of 450 miles per hour also, therefore b is:
b = 200 – 450 t ---> 3
Substituting equations 2 and 3 to 1:
c^2 = (150 - 450 t)^2 + (200 – 450 t)^2
c^2 = 22500 – 135000t + 202500t^2 + 40000 – 180000t + + 202500t^2
c^2 = 405,000 t^2 – 315,000 t + 62,500 (ANSWER)
One more than 16 times the population density of New Mexico equals the population density of Texas to the nearest whole number , what is New Mexico's populations density ?
To solve for New Mexico's population density, we represent the given condition in a mathematical equation: '1 + 16x = y', where 'x' is the population density of New Mexico and 'y' is the Texas population density. We solve for 'x' by rearranging the equation to: 'x = (y - 1) / 16'. The specific population density of New Mexico can be calculated when the density of Texas is known.
Explanation:The seemingly complicated question is basically one about algebra. It can be expressed as: '1 + 16x = y', where 'x' is the population density of New Mexico and 'y' is the population density of Texas. To find 'x' (New Mexico's population density) given the value for 'y', we need to rearrange the equation by subtracting 1 from both sides to get '16x = y - 1', and then divide both sides by 16 to solve for 'x': 'x = (y - 1) / 16'.
Without specific population density values for Texas ('y'), we cannot compute an actual numeric value for New Mexico's population density. However, we can use this equation to perform the necessary calculations once we know the population density (per square mile, for instance) of Texas.
This focuses on math skills including algebra and application of formulas, important aspects of high school math curriculum.
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A certain forest covers an area of
4000
km2
. Suppose that each year this area decreases by
5.25%
. What will the area be after
14
years?
A = P(1-r)^t
A = 4000(1-0.0525)^14
A = 4000(0.9475)^14
A = 4000(0.9475)^14
A = 4000(0.470012124)
A = 1880.048
the answer is roughly 1880 square km
Answer:
Step-by-step explanation:
Thast 6% I don’t know why it’s tuping my answers different ?? I need help for this one
The graphs of f(x) = 10x and its translation, g(x), are shown.
What is the equation of g(x)?
g(x) = 10x – 3
g(x) = 10x + 3
g(x) = 10x – 3
g(x) = 10x + 3
Answer:
The equation for the function g(x) is:
[tex]g(x)=(10)^{x-3}[/tex]
Step-by-step explanation:
We are given graphs of two functions f(x) and g(x).
The function f(x) is an exponential function and is given by:
[tex]f(x)=(10)^x[/tex]
Now, we are asked to find the equation for the transformed function g(x).
We could see that the graph of the function g(x) passes through (3,1),(4,10) , (5,100) and so on.
This means that the equation or the expression for the function g(x) is given by:
[tex]g(x)=(10)^{x-3}[/tex]
( Since, when x=3 we have:
[tex]g(x)=(10)^{3-3}=10^0=1[/tex]
when x=4 we have:
[tex]g(x)=(10)^{4-3}\\\\g(x)=(10)^{1}\\\\g(x)=10[/tex]
and so on)
Answer:
(x)=(10)^(x-3)
Step-by-step explanation:
Just did it on edge 2020 :) Hope i helped!!
how much money will you have if you started with $1000 and put it in an account that earned 5% every year for 15 years
Which number is the largest? 1.2 × 104, 4.5 × 10−3, 3.8 × 103, 7.5 × 103
1.2 × 104
4.5 × 10−3
3.8 × 103
7.5 × 103
Answer: 1.2 x 10^4
Step-by-step explanation:
pls hit thanks and rate!
The results of a study indicate that the mean weight of adult skunks in an area is between 4.3 kg and 4.9 kg. What is the study’s margin of error?
Since we are given the range of the area, the margin of error can be calculated by firstly calculating the difference of the range and dividing by 2. This is expressed in this formula:
Margin of error = ± (Upper range – Lower range) / 2
Margin of error = ± (4.9 kg – 4.3 kg) /2
Margin of error = ± 0.3 kg
Write the following fractions as decimals 2/10,3/100
Answers:
A. .2
B. .03
C. .093
D. .1456
Have a blessed day ☺️
PLZ HELP ME! NEED THE ANSWER AS SOON AS POSSIBLE! WILL REWARD THE BRAINLIEST: The table below shows the distance y, in miles, traveled by a truck in x hours: Time (x) (hours) 1 2 3 4 Distance (y) (miles) 50 100 150 200 Part A: What is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and distance traveled by the truck. [Choose the value of the correlation coefficient from 1, 0.8, 0.5, 0.02.] (4 points) Part B: What is the value of the slope of the graph of distance versus time between 3 and 4 hours, and what does the slope represent? (3 points) Part C: Does the data in the table represent correlation or causation? Explain your answer. (3 points)
John must have at least 289 test points to pass his math class. He already has test scores of 72, 78, and 70. Which inequality will tell him at least how many more points he needs to pass the class
A. 72 + 78 + 70 + x < 289
B. 72 + 78 + 70 + x ≤ 289
C. 72 + 78 + 70 + x ≥ 289
D. 72 + 78 + 70 + x > 289
Answer:
C. [tex]72+78+70+x\geq 289[/tex]
Step-by-step explanation:
Let x represent the number of points John needs to pass the class.
We have been that John must have at least 289 test points to pass his math class. He already has test scores of 72, 78, and 70.
After scoring x points on John's total score would be [tex]72+78+70+x[/tex].
Since John needs at least 289 test points to pass his math class, so the total number of points should be greater than or equal to 289.
We can represent this information in an inequality as:
[tex]72+78+70+x\geq 289[/tex]
Therefore, the inequality [tex]72+78+70+x\geq 289[/tex] represents the number of more points John needs to pass the class.
The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius. The temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during a 6-hour period. What is a cosine function that models this reaction?
f(t) = −30 cos (pi/3) t + 20
f(t) = −60 cos (pi/3) t + 30
f(t) = 30 cos (6t) + 20
f(t) = 60 cos (6t) + 30
Answer:
Option 1 - [tex]f(t)=-30 sin(\frac{\pi}{3}t)+20[/tex]
Step-by-step explanation:
Given : The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius. The temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during a 6-hour period.
To find : What is a cosine function that models this reaction?
Solution :
General form of cosine function is [tex]f(x)=A cos(Bx)+C[/tex]
Where A is the amplitude
[tex]B=\frac{2\pi}{\text{Period}}[/tex]
C is the midline
Now, We have given
The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius.
A is the average of temperature,
i.e, [tex]A=\frac{-10-50}{2}=-30[/tex]
Period of 1 cycle is 6 hour
So, [tex]B=\frac{2\pi}{6}=\frac{\pi}{3}[/tex]
The temperature is at its lowest point when t = 0 and we know lowest point is -10
So, [tex]f(t)=A\cos t+C[/tex]
[tex]-10=-30\cos 0+C[/tex]
[tex]C=20[/tex]
Substituting the values we get,
The cosine function is [tex]f(t)=-30 sin(\frac{\pi}{3}t)+20[/tex]
Therefore, Option 1 is correct.
The function $f$ satisfies \[f(x) + f(2x + y) + 5 x y = f(3x - y) + 2x^2 + 1\]for all real numbers $x$, $y$. determine the value of $f(10)$.
A hospital gives a survey to all surgical patients asking them to rate the quality of their hospital experience. One month after surgery, the hospital contacts the patients again to ask if there were any complications from the surgery. Last year, the results of the surveys showed that of the patients who had a poor hospital experience, 23% had post-surgical complications. What conclusion can be drawn from this study?
Solutions:
As given in the question , patients who had a poor hospital experience, 23% had post-surgical complications.
Option (C) appears the right choice from my point of view which is c) Most patients who have a poor hospital experience also have post-surgical complications.
The reason being , that the patients who suffer from these complications have experienced badly in the last hospital where they were diagnosed or cured.
Answer:
a) Some patients who have a poor hospital experience also have post-surgical complications.
Step-by-step explanation:
Given is :
Last year, the results of the surveys showed that of the patients who had a poor hospital experience, 23% had post-surgical complications.
The conclusion that can be drawn from this study is - Some patients who have a poor hospital experience also have post-surgical complications.
If we turn the percentage in figures, we can see that almost 2.3 person or 2 patients out of 10 patients have a poor hospital experience and also have post-surgical complications.
So, this is a low value that is why the correct answer is Some patients who have a poor hospital experience also have post-surgical complications.
The cartesian coordinate system can be used to describe three dimensional space using three axes insyead of two. what are the labels
what is the resulting number when you add 4 tens and 3826
Indicate the equation of the line that is the perpendicular bisector of the segment with endpoints (4, 1) and (2, -5).
Answer:
The correct answer is x+3y=-3
Step-by-step explanation:
My fist step to solving this question would be to find the mid-point of the given line. The mid point of (4,1) and (2,-5) is (3,-2). The mid point is where the perpendicular bisector connects or bisects the given segment. My second step would be to graph the two given points and to connect them, forming a line. This way, I would know the slope of the line and then I would be able to find the slope of the perpendicular bisector, since the slope for perpendicular lines is the opposite reciprocal of the given line. In doing this, I discovered that the slope of the segment with the given endpoints is 3 which means that the slope of the perpendicular bisector will be x. So, so far we've got a point of intersection and a slope which is all we need to formulate the equation of the line that we are looking for.
In the end, our answer will be x+3y=-3.
What is the sign of the product (−4)(6)(9)(3)?
A) Positive, because the products (−4)(6) and (9)(3) are negative and the product of two negative numbers is positive
B) Positive, because the products (−4)(6) and (9)(3) are positive and the product of two positive numbers is positive
C) Negative, because the product (−4)(6) is negative and the product (9)(3) is positive, and the product of a negative number and a positive number is negative
D) Negative, because the product (−4)(6) is negative and the product (9)(3) is negative, and the product of two negative numbers is a negative number
Hello,
The correct answer is C) Negative, because the product (-4)(6) is negative and the product (9)(3) is positive, and the product of a negative number and a positive number is negative.
Hope this helps!!!!
How to draw exactly two planes intersect the third plane does not intersect the other two?
What is the value of x?
A. 68°
B. 62°
C. 112°
D. 124°
please show your work
Given: QR = 59; RT = 59 Prove: QR = RT StatementsReason 1. QR = 59; RT = 591. Given 2. 59 = RT2. Symmetric Property of Equality 3. QR = RT3. Which property listed below is the final reason in the proof.
Answer:
By using transitive property
QR=RT
Step-by-step explanation:
Given
QR=59
RT=59
To prove that QR=RT
1. Statement QR=59; RT=59
Reason : Given in the question.
2. Statement: 59=RT
Reason: By using symmetric property of equality .
Symmteric property is that property of equality
if
ab=bc
Then ,
bc=ac
3. Statement: QR=RT
Reason: By using transitive property of equality.Transitive property : If ac=bc
and bc=ca
Then , ab=ca
Hence proved.
Let h = (v0^2)/4.9 sin(theta)cos(theta) model the horizontal distance in meters traveled by a projectile? If the initial velocity is 52 meters/second, which equation would you use to find the angle needed to travel 200 meters?
A) 275.92sin(2Theta)=200
B) 551.84sin(2Theta)=200
C) 200sin(2 Theta)=200
D)10.61sin(2THeta)=100
Answer:
A) 275.92sin(2Theta)=200
a p e x