The distance traveled by the ball as a function of time, s(t) = 16•t² ft., and the rate of change, based on calculus, gives;
(a) During the time interval [6, 6.5], the distance traveled is 100 feet
(b) In the interval, [6, 6.5], the average velocity is 200 ft/s
(c) The calculated average velocities in ft/s, for the respective time intervals are;
[6, 6.01]. 192.16
[6, 6.001]. 192.016
[6, 6.0001]. 192.0016
[5.9999, 6]. 191.9984
[5.999, 6]. 191.984
[5.99, 6]. 191.84
The instantaneous velocity at t = 6 is v(6) = 192 ft/s
What are the average and instantaneous velocities of the ball?The distance traveled as a function of time is s(t) = 16•t² ft.
(a) The distance traveled during the time interval [6, 6.5] is found as follows;
s(6) = 16 × 6² = 576
s(6.5) = 16 × 6.5² = 676
The distance traveled in the interval, [6, 6.5], ∆s(t) = 676 - 576 = 100
The distance traveled during the time interval [6, 6.5] = 100 feet
(b) Average velocity = ∆s(t)/∆t
∆t = 6.5 - 6 = 0.5
Therefore;
∆s(t)/∆t = 100/0.5 = 200
The average velocity = 200 ft./s
(c) The average velocities over the given time intervals, obtained using a graphing calculator, are;
Interval. Average velocity
[6, 6.01]. 192.16
[6, 6.001]. 192.016
[6, 6.0001]. 192.0016
[5.9999, 6]. 191.9984
[5.999, 6]. 191.984
[5.99, 6]. 191.84
Given that at t = 6, as the time interval approaches zero from the right and from the left, the average velocity approaches 192 ft./s, the instantaneous velocity at t = 6, v(6) is 192 ft./s
v(6) = 192 ft./s
Using calculus, differentiation, we have;
v(t) = ds/dt = 2×16 × t = 32•t
v(6) = 32 × 6 = 192
Therefore;
v(6) = 192 ft./s
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I need to solve this problem using the he quadratic formula
Answer:
the quadratic formula is
-b + {the square root of} b^2 - 4ac / 2a
-
or just
(-b±√(b²-4ac))/(2a)
Step-by-step explanation:
yh
twenty more than a number is less than twice the same number
Answer:
x+20<2x
Step-by-step explanation:
20 more than a number implies that twenty must be added to the variable. Then, because it says less than you add a less than symbol. Finally, twice the same number tells you to use x again but since it’s being multiplied by 2, typing 2x makes it easier to understand.
Is 5x+3y=0 linear or nonlinear
Answer:
3.33333
Step-by-step explanation:
It is a Linear
HELP QUICK!
Which rectangle is not an enlargement of rectangle A?
A
B
C
D
Answer:
The answer is D.
Find the scale of each dimension:
B: 6/3 = 2 and 10/5 = 2, both dimensions have the same scale factor of 2.
C: 15/3 = 5 and 25/5 = 5, both dimensions have the same scale factor of 5.
D: 60/3 = 20 and 90/5 = 18, each dimension has a different scale factor so is not an enlargement.
hope it helped:)!
Answer: answer a is wrong answer b is right answer c is wrong answer d is right
Step-by-step explanation:
d and b are right why? bc b saids this; 6 ft for b; 10 ft d; 60 ft and 90 ft
2x+5-19 division property of equality
Answer:
Step-by-step explanation:
it is the steps to get to that certain step
some of the steps are out of order
I'm going to assign letters
the order is
A: 2x+5=19
B: 2x+5-5=19-5
C: 2x=14
D: 2x/2=14/2
E: x=7
A: given
B: we subtracted 5 from both sides so subtraction property of equality
C: subtract
D: divison property of equality (we divide both side by 2)
E: divide
Y over 5 + 6 = 21, what is y?
Answer:
y=231
Step-by-step explanation:
to solve for y simplify both sides of the equation by isolating the variable
Area Model Multiplication
Timothy saves $176 a month. Timothy saves $29 less each month than Camden. How much will
Camden save in 3 years?
Find seven ordered pairs to the equation y=x²-2. Then determine its graph.
X
-3
The graph of y = x² -2 is a parabola
To find the seven ordered pairs of the equation y = x²-2, we have to find out the value of y by assuming the different values of x that are 0,1,-1,2,-2,3 and -3which gives us seven different coordinates
Let put x=0, y= -2
Let put x=1, y= -1
Let put x=-1, y= -1
Let put x=2, y= 2
Let put x=-2, y= 2
Let put x=3, y= 7
Let put x=-3, y= -7
If we plot all the coordinates for the value of x and y (0,-2),(1,-1),(-1,1),(2,2),(-2,2)(3,-7),(-3,7) and connect all the dots we will get a upward facing parabola
Hence, The graph of y = x² -2 is a parabola
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Simplify 15^5/ -5^-6
Answer:
Step-by-step explanation:
Factor 15^5: 5^5 x 3^3
[tex]\frac{5^5*3^5}{-5^-6} = 5^1^1\\ \\ \frac{5^1^1*3^5}{-1} =-5^1^1*3^5\\ \\ =-11865234375[/tex]
Either: -5^11(3^5) or -11865234375
(depending on how you're supposed to write it)
I think at least
Which of the following shows examples of things that convert light energy to electrical energy? (5 points)
•Fan and wind turbine
•Light bulb and blender
•Airplane and human body
•Solar panels and solar cells.
The electrical device which shows an example of the conversion of light energy into electrical energy is: D. solar panels and solar cells.
What is a PV panel system?A PV panel system is an abbreviation for photovoltaic (PV) panel system and it is also referred to as a photovoltaic module, solar cell panel, or solar electric panel.
In Electrical engineering, the photovoltaic (PV) panel system are typically designed and developed to convert the light energy received from the Sun into electrical energy, which can be used specific electrical devices and home appliances.
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Find the value of y. (7x-7) 63 (3x + 45) (-6)
Answer:
b
Step-by-step explanation:
just did the test like 20 mins ago good look
Can someone help with this question?✨
X = 13 is length of Hypotenuse by use of Pythagoras's Theorem.
What is the Pythagorean theorem ?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.In this triangle use Pythagoras theorem
Let Hypotenuse is x .
x² = 12² + 5²
x² = 144 + 25
x = √169
x = 13
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In ΔABC, what is the value of cos B?
In right-angled triangle (ΔABC), the value of cos(B) is equal to 12/13.
What is a right angle?A right angle can be defined as a type of angle that is formed by the intersection of two (2) straight lines at 90 degrees. This ultimately implies that, a right angle has a measure of 90 degrees.
How to calculate the magnitude of cos θ?In order to determine the magnitude of cos θ, we would apply the law of cosine because the given side lengths represent the adjacent side and hypotenuse of a right-angled triangle.
cos(θ) = Adj/Hyp
Where:
Adj represents the adjacent side of a right-angled triangle.Hyp represents the hypotenuse of a right-angled triangle.θ represents the angle.Substituting the parameters into the formula, we have;
cos(B) = 12/13
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You want to buy an item that costs $100. Which of these is the most cost-effective choice for buying the item?
The most cost-effective choice for buying the item is buying it at a 10 percent discount without sales tax.
A percent discount on a product means that the price of the product is reduced by that percentage.
The full question is that, You want to buy an item that costs $100. Which of these is the most cost-effective choice for buying the item?.
a. using a paid membership card to buy it at a 10 percent discount.
b. buying it online at a 10 percent discount with a $5 shipping charge.
c. buying it at a 10 percent discount without sales tax.
we will calculate the final price in each case to analyze the most cost-effective choice,
In in first case, when using a paid membership card to buy it at a 10 percent discount. we get,
10% of $100 = 10/100×100 = $10
cost = $100 - $10 = $90
On top of this $90 there is the charges of the membership card, therefore the price increases. ( price in first case)
In second case, when buying it online at a 10 percent discount with a $5 shipping charge.
100%-10% = 90%
90% of 100 = $90
Cost: $90 + $5 = $95 ( price in second case)
In third case, when buying it at a 10 percent discount without sales tax.
100% - 10% = 90%
90/100 × 100 = $90. ( price in third case which is minimum as compared to rest of the cases)
Therefore, buying the item at a 10 percent discount without sales tax is the most cost effective method since there is no other cost involved.
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A plant is 7 cm tall on June 1. On September 1, the plant is 46.9 cm tall. What is the scale factor of the growth of the plant if all parts grew proportionally?
The scale factor will be equal to 6.7. The correct option is B.
What is the scale factor?The scale factor is defined as the proportion of the new image's size to that of the previous image.
Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.
Given that a plant is 7 cm tall on June 1. On September 1, the plant is 46.9 cm tall.
The scale factor will be calculated as:-
Scale factor = 46.9 / 7
Scale factor = 6.7
Therefore, the scale factor will be equal to 6.7. The correct option is B.
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1. Write a function that describes the area of the water puddle on the floor as a function of its
radius. Use function notation.
The area of the floor water puddle as a function of radius is 6860. The function notation is mgt∆x = (20 0.5t)g4∆t.
What is meant by function notation?Function notation is a method for writing functions that are simple to read and understand. When we use function notation, the independent variable is typically x, and the dependent variable is F. (x).
Therefore,
The bucket moves upward at a rate of 40/10 = 4 meters per minute. If time is measured in minutes, the bucket is x = 4t meters above the ground at time t. Water is dripping out at a rate of 5/10 kg/minute. Because there is initially 20 kg of water in the bucket, there is m = 20 0.5t kg remaining at time t.
Consider the interval of time between t and t + t. During this time, the bucket moves ∆x = 4∆t meters. So the work performed during this interval is
mgt∆x = (20 0.5t)g4∆t,
The bucket is x = 4t meters
and the integral for the total work performed is
[tex]4 g \int_0^{10}(20-0.5 \cdot t) d t \\[/tex]
= [tex]4 g\left(20 t-\left.0.25 t^2\right|_0 ^{10}=700 g=700 \cdot(9.8)=6860\right. \text { joules. }[/tex]
Hence, The area of the floor water puddle as a function of radius is 6860.
The complete question is:
A bucket of water of mass 20 kg is pulled at constant velocity up to a platform 40 meters above the ground. This takes ten minutes during which time 5 kg of water drips out at a steady rate through a hole in the bottom of the bucket. Find the work needed to raise the bucket to the platform
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ill give brainly and 10 points hurry please
Answer:
B
Step-by-step explanation:
it cant be a or c because if it is a negative then there is no need to put a + sign or add another - sign
Answer:
A
Step-by-step explanation:
Let's get the answer.
Suppose the question was the distance between 12 and 1. You would write it as 12 - 1 = 11. So you have to pick an answer that looks like this example.
B: is actually 11 12 -1 = 11
C: is 12 +(-1) = 12 - 1 which also gives 11
D: -1 -12 = -13. You are not really really with a distance here. You are combining 2 negative numbers.
So the answer is A.
-12 - (-1) = -12 + 1 = - 11
Family Flowers employs 17 people, of whom 14 earn gross pay of $660.00 each and 3 earn gross pay of $740.00 each on a weekly basis. What is the
employer's share of total Social Security and Medicare taxes for the first quarter of the year? (Social security tax is 6.2% of wages up to $128,400. Medicare
tax is 1.45% of all wages.)
o $660.00
o $740.00
o $890.68
o $11,396.97
Based on the gross pay to the employees of Family Flowers, the employer's share of total Social Security and Medicare taxes for the first quarter is $11,396.97
How to find the social security and medicare tax?First, find the gross pay for all 17 people in the first quarter:
= ( (660 x 14) + (740 x 3)) x 12 weeks in quarter
= (9,240 + 2,220) x 12
= $137,520
The social security tax is paid up to $128,400:
= 6.2% x 128,400
= $7,960.80
The Medicare tax is:
= 1.45% x 137,520
= $1,994.04
The total Social Security and Medicare taxes:
= 7,960.80 + 1,994.04
= $11,396.97
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16.
A quote you received from a local restaurant is $625 for a business luncheon. The restaurant owner tells you the price with gratuity is $720. How
much did the owner add for gratuity?
A. $75
B. $105
C. $85
O D. $95
Given m || n, find the value of x and y.
X=
(5y+19)
(2x+1)
y =
(3x-19)
m2
72
uyfgwu wfweiufw wuifhw ifew iuf iuf 7gi
A rectangular board is 1100 millimeters long and 700 millimeters wide. What is the area of the board in square meters?
Answer:
its 300000000
Step-by-step explanation:
the 5th dimensions negate your father out of existence
please help me please dont ignore
Answer:
2
Step-by-step explanation:
Given a graph of an original object and its image after dilation, you want to know the scale factor of the dilation.
DilationThe scale factor multiplies each of the coordinates.
The original coordinates of point A are (0, 1).
The coordinates of dilated point A' are (0, 2).
The factor that multiplies 1 to make it be 2 is 2/1 = 2.
The dilation scale factor is 2.
__
Additional comment
As a check, you can consider another point:
C(4, 3) × 2 = C'(8, 6) . . . . matches the point on the graph
The circumference of a circle is 16π ft. What is the area, in square feet? Express your answer in terms of \piπ.
Answer: A≈20.37
Step-by-step explanation:
There's brainly
A=C2
4π=162
4·π≈20.37183
Write the decimal as a fraction or a mixed number in simplest form
-0.8
Answer:
-4/5 this is because 5 can't be simplified and 4/5 is like 8 out 10 but simpler and has a negative.
|16-4t|+ 5 = 0 please help me
Answer:
No solution
Step-by-step explanation:
Absolute values may not be less than 0.
[tex]\left|16-4t\right|+5-5=0-5\\\left|16-4t\right|=-5\\\mathrm{if~x~ > ~0,true}\\\mathrm{if~x~ < ~0,false}\\\mathrm{x < 0}\\\mathrm{No~Solution}[/tex]
x is the result of the equation.
When traveling to Great Britain, Bethany exchanged $635 US dollars into £580 British pounds. How many pounds did she receive for each US dollar?
After the exchange from the U.S dollar to British pounds, Bethany received £0.91 for each U.S. dollar.
What is an exchange rate?An exchange rate is a rate or a price of one country's currency in terms of another.
The exchange rate describes how much each currency can be obtained when converting one currency to another.
In this instance, the exchange rate between the U.S. dollar and the British pound is $1 = £0.91.
Data and Calculations:Total US dollars with Bethany = $635
The total British pounds received by Bethany after the exchange = £580
Exchange rate per U.S. dollar = £0.91 (£580/$635)
Exchange rate per British pound = $1.095 ($635/£580)
Thus, Bethany received £0.91 for each U.S. dollar.
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Which list shows these lengths in order greatest to least?
Using the conversion of fraction to decimal, the list that shows these lengths in order greatest to least is:
[tex]\frac{\sqrt{3}}{11}, \frac{\pi}{24}, \frac{3}{25}, \frac{9}{100}[/tex]
How a fraction is converted to decimal?A fraction is converted to decimal dividing the numerator by the denominator.
Hence the numbers in this problem are given as follows:
9/100 = 0.09.π/24 = 0.131.3/25 = 0.12.sqrt(3)/11 = 0.1575.Hence, considering the conversions to decimal above, the list that shows these lengths in order greatest to least is:
[tex]\frac{\sqrt{3}}{11}, \frac{\pi}{24}, \frac{3}{25}, \frac{9}{100}[/tex]
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Which list shows the runner's in order fastest to slowest.
Answer:
C
Step-by-step explanation:
First you need to convert the fractions into decimal form.
Joe-12 1/2 becomes 12.5
Ellen-12.09
Steve-12.4
Patty-12.8
Now put these in order from fastest to slowest
12.09,12.4,12.5,12.8
Answer:
12.8
12 1/2
12 2/5
12.09
is least from greatest
Water comes out of a pipe at a rate of 16 gallons per minute.
How many gallons have come out after 4 minutes?
Answer:64
Step-by-step explanation:16 × 4
According to the following table, what is the federal income tax due for Mr. and Mrs. Jones filing their federal income tax return jointly who make a combined $92,400 in taxable income?
Based on the fact that Mr. and Mrs. Jones are filling their federal tax return jointly, their federal income tax due is $11,737
How to find the federal income tax?There was no table included so I will use the federal income tax rates for those filing in April 2022.
For a married couple filing jointly like Mr. and Mrs. Jones with a combined $92,400 taxable income, the federal income tax due is:
= 9,328 + 22% of income over $81,050
= 9,328 + (22% x (92,000 - 81,050))
= 9,328 + (22% x 10,950))
= 9,328 + 2,409
= $11,737
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