Answers
Answer:
640 m
Step-by-step explanation:
We can consider 4 seconds to be 1 time unit. Then 8 more seconds is 2 more time units, for a total of 3 time units.
The distance is proportional to the square of the number of time units. After 1 time unit, the distance is 1² × 80 m. Then after 3 time units, the distance will be 3² × 80 m = 720 m.
In the additional 2 time units (8 seconds), the ball dropped an additional
... (720 -80) m = 640 m
_____
Alternate solution
You can write the equation for the proportionality and find the constant that goes into it. If we use seconds (not 4-second intervals) as the time unit, then we can say ...
... d = kt²
Filling in the information related to the first 4 seconds, we have ...
... 80 = k(4)²
... 80/16 = k = 5
Then the distance equation becomes ...
... d = 5t²
After 12 seconds (the first 4 plus the next 8), the distance will be ...
... d = 5×12² = 5×144 = 720 . . . meters
That is, the ball dropped an additional 720 -80 = 640 meters in the 12 -4 = 8 seconds after the first data point.
Related Questions
What expression represents "one third of the difference between fifteen and some number"?
Possible Answers:
Answers
difference between fifteen and some number = 15 - p
1(15 - p)/3 should be your best answer
hope this helps
For 3x2- 4x+ 1, match the following:
x Degree
3 Variable
1 Algebraic expression
3x2-4x+ 1 Coefficient
. 2 Constant
Answers
x = variable
expression = 3x^2-4x+1
coefficients = 3 and -4
constant = 1
For this case we have the following definitions:
Algebraic expression: It is one that contains terms of different degrees with their respective coefficients. Degree of the polynomial: is the largest exponent of the polynomial. Variabe: is the independent term of the polynomial Coefficient: They are the constant numerical values that accompany the variables of the polynomial. Constant: It is a term of the polynomial that does not accompany the variable.Answer:
x ----------------> Variable
3 ----------------> Coefficient
1 ----------------> Constant
[tex]3x ^ 2-4x + 1[/tex] -----------> Algebraic expression
2 ----------------> Degree
Marcy bought 1/4 pound of chocolate covered caramels at $2.69 a pound and 1/4 pound of coffee at $3.50 a pound how much did the candy cost
Answers
The sale price of an item is $15 after a 70% discount is applied. What is the original price of the item?
Answers
Make a table showing the probability distribution for the possible sums when tossing two four-sided dice (the sides are numbered 1-4 on each die). (give the probabilities as decimals rounded to four decimal places.)
Answers
(1, 1), (1, 2), (1, 3), (1, 4)
(2, 1), (2, 2), (2, 3), (2, 4)
(3, 1), (3, 2), (3, 3), (3, 4)
(4, 1), (4, 2), (4, 3), (4, 4)
Those give us these sums:
2, 3, 4, 5
3, 4, 5, 6
4, 5, 6, 7
5, 6, 7, 8
P(sum of 2) = 1/16 =0.0625
P(sum of 3) = 2/16 = 0.125
P(sum of 4) = 3/16 = 0.1875
P(sum of 5) = 4/16 = 0.25
P(sum of 6) = 3/16 = 0.1875
P(sum of 7) = 2/16 = 0.125
P(sum of 8) = 1/16 = 0.0625
What’s the sum of 2/5 and 2/4
Answers
5 x 4 = 20
2 x 4 = 8
2 x 5 = 10
8/20 + 10/20 = 18/20
18/20, or 9/10 simplified, is your answer
Hope this helps
the area of a rectangle is 95 square yard. if the perimeter is 48 yards find the length and width of rectangle
Answers
according to the condition w+l=48 and w*l=95.
Using these two equation:
[tex] \left \{ {{l+w=48} \atop {lw=95}} \right. \ =\ \textgreater \ \ \left[\begin{array}{ccc}l=24- \sqrt{481};w=24+ \sqrt{481}\\ \\l=24+ \sqrt{481};w=24- \sqrt{481}\end{array}[/tex]
A partially eaten bag of grape weighs 5/8 of a pound. The bag of grapes weighed 4 times this amount before any were eaten. What was the original weight of the bag of grapes?
Answers
4 * 5/8
That is 5/2, or 2 1/2, or 2.5
Hope this helps
To find the original weight of a bag of grapes before some were eaten, you divide the current weight of 5/8 lb by 4. The calculation reveals that the bag's original weight was 5 pounds.
The question asks us to calculate the original weight of a bag of grapes before it was partially eaten. After eating some of the grapes, the bag now weighs 5/8 of a pound. To find the original weight, we need to determine what weight, when multiplied by 4, would equal 5/8 of a pound. We do this by dividing the current weight by 4 to reverse the multiplication. Using the formula:
Original Weight = Current Weight / 4
So:
Original Weight = (5/8) lb / 4
When we do the calculation:
Original Weight = (5/8) lb / (4/1)
Original Weight = (5/8) lb \(1/4)
Original Weight = (5/32) lb
Since (5/32) lb is equivalent to 5 pounds (when multiplied by 4, it gives 20/32 lb, which simplifies to 5/8 lb), the original weight of the bag of grapes was 5 pounds.
The blue shape is a dilation of the black shape. What is the scale factor of the dilation?
Answers
blue shape:
(-5.10)
black shape:
(-1,2)
As one figure is the dilatation of another then:
k (-1,2) = (- 5,10)
From here we know:
-k = -5
Equivalently:
2k = 10
Where we conclude:
k = 5
Answer:
The scale factor of the dilation is:
k = 5
Answer:
the asnwer is 5
Step-by-step explanation:
i did this question
A rectangular prism has a length of 114 centimeters, a width of 4 centimeters, and a height of 314 centimeters.
What is the volume of the prism?
Enter your answer in the box as a simplified mixed number or a decimal.
cm³
Answers
----------
The volume of the prism is 143184 cm^3
----------
WORK: 114*4=456*314=143184
----------
Have a great day!
what is 6.345 divided by 0.09
Answers
I really hope this is right lol
write an equation in slope intercept: 6x+5y=30
Answers
5y = 6x + 30
This is the correct equation for slope-intercept form.
I hope this helps!
Choose an even number between 24 and 35. Draw a picture and explain why it is an even number.
Answers
when the figure below is rotated 90 degrees counterclockwise about the origin what would be the new coordinates of point c?
a (-5,3)
b (3,-5)
c (5,-3)
d (5,3)
Answers
When a point is rotated 90 degrees counterclockwise about the origin, its new coordinates can be found by swapping the x and y coordinates and changing the sign of the new y coordinate. In this case, the new coordinates of point C would be (-3,-5).
Explanation:When a point is rotated 90 degrees counterclockwise about the origin, its new coordinates can be found by swapping the x and y coordinates and changing the sign of the new y coordinate.
In this case, point C has coordinates (5,-3). When we rotate it, the new x coordinate becomes -3 and the new y coordinate becomes -5. Therefore, the new coordinates of point C would be (-3,-5).
A central angle measuring 150° intercepts an arc in a circle whose radius is 6. What is the area of the sector of the circle formed by this central angle? 15π 24π 30π 36π
Answers
Answer: 15
Step-by-step explanation: its 15
what is -20 divide it by -2
Answers
when you divide two negative numbers, the answer becomes positive:
-20/-2 = 10
10 is your answer
Note for multiplying and dividing:
two positive numbers will give you a positive answer
one negative numbers and one positive number will give you a negative answer
two negative numbers will give you a positive answer
hope this helps
Write the formula for a function d(x) that describes the distance between the point p and a point (x,y) on the line.
Answers
determine which statement is true about the zeros of the function graphed below
Answers
Answer:
B
Step-by-step explanation:
What are the solution(s) to the quadratic equation 50 – x2 = 0? x = ±2 x = ±6 x = ±5 no real solution btw i just clicked the last choice on accident
Answers
Move the x^2 to the other side
x^2=50
Now take the square root of both sides
x=+_(50)^1/2 (^1/2 means square root)(+_ is plus or minus. Sorry XD)
Now simplify the square root
X=+_5(2)^1/2
Voila. The answer is C
Answer:
Option C
Step-by-step explanation:
we need to find the solution(s) to the quadratic equation 50 – x^2 = 0
50 – x^2 = 0
Subtract 50 from both sides
– x^2 = -50
Now divide by -1 from both sides
x^2 = 50
To remove square , take square root on both sides
[tex]x=+-\sqrt{50}[/tex]
[tex]x=+-\sqrt{25*2}[/tex]
[tex]x=+-5\sqrt{2}[/tex]
Option C is the answer
If cos(3x)=sin(x+18degrees) what is the value of x
Answers
1. rule: cosα=sin(90°-α), it means that cos 3x=sin(90°-3x);
2. sin(90°-3x)=sin(x+18°); ⇔ 90°-3x=18°+x; ⇔ x=18°.
Answer: x=18°.
a bin size of __ is most appropriate for the data set shown above??
Answers
D) 10.
Hope I helped :-)
caculate the distances tarryn if she drives 7/8 mile each way to and from work, 5 days a week
Answers
She will cover 35/8 miles.
What is Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
total distance in miles = 7/8 miles per day
So, in 5 days in a week.
She will cover
=5*7/8
=35/8 miles.
Hence, She will cover 35/8 miles.
Learn more about unitary method here:
https://brainly.com/question/22056199
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How many 5-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, if repetition of digits is not allowed? a.119 b.16,807 c.2520 d.120
Answers
c. 2520
Explanation:
Repetition is not allowed, therefore:
1st digit can be any of the given 7 numbers
2nd digit can be any of the remaining 6 numbers
3rd digit can be any of the remaining 5 numbers
4th digit can be any of the remaining 4 numbers
5th digit can be any of the remaining 3 numbers
This means that:
number of possible combinations = 7 * 6 * 5 * 4 * 3 = 2520 numbers
Hope this helps :)
The arithmetic sequence 2, 4, 6, 8, 10, . . . represents the set of even natural numbers. What is the 100th even natural number? a100 =
Answers
Answer: The 100th even natural number is 200.
Step-by-step explanation: Given that the following arithmetic sequence represents the set of natural numbers :
2, 4, 6, 8, 10, . . ..
We are given to find the 100th even natural number, i.e., the 100-th term of the sequence.
We know that
the n-th term of an arithmetic sequence with first term a and common difference d is given by
[tex]a_n=a+(n-1)d.[/tex]
For the given sequence, we have
a = 2 and d = 4 - 2 = 6 - 4 = . . . =2.
Therefore, the 100-th term of the sequence will be
[tex]a_{100}=a+(100-1)d=2+99\times2=2+198=200.[/tex]
Thus, the 100th even natural number is 200.
Geoff planted dahlias in his garden. Dahlias have bulbs that divide and reproduce underground. In the first year, Geoff’s garden produced 6 bulbs. In the second year, it produced 12 bulbs, and in the third year, it produced 24 bulbs. If this pattern continues, how many bulbs should Geoff expect in the eighth year?
Answers
x---------------> number of bulbs produced per year
n--------------> number of years
we know that
the pattern can be modeled through the following equation
x=6*[2^(n-1)]
for n=1 year
x=6*[2^(1-1)]----------> 6 bulbs
for n=2 year
x=6*[2^(2-1)]----------> 12 bulbs
for n=3 year
x=6*[2^(3-1)]----------> 24 bulbs
for n=8 year
x=6*[2^(8-1)]----------> 6*128=768 bulbs
the answer is 768 bulbs
Final answer:
Geoff's garden exhibits exponential growth of dahlia bulbs, doubling each year. By following this pattern, Geoff should expect to have 768 bulbs in the eighth year.
Explanation:
Geoff’s dahlia bulbs are showing a pattern of doubling in quantity each year. This is an example of exponential growth, a concept commonly explored in mathematics. To determine the number of bulbs Geoff can expect in the eighth year, we need to continue this pattern.
In the first year, there are 6 bulbs. The second year has 12 bulbs which is 6 multiplied by 2. The third year has 24 bulbs, which is 12 multiplied by 2. This pattern suggests that every year, the number of bulbs is the previous year's total multiplied by 2.
By following this pattern, to find the number of bulbs in the eighth year, we calculate:
Fourth year: 24 bulbs × 2 = 48 bulbs
Fifth year: 48 bulbs × 2 = 96 bulbs
Sixth year: 96 bulbs × 2 = 192 bulbs
Seventh year: 192 bulbs × 2 = 384 bulbs
Eighth year: 384 bulbs × 2 = 768 bulbs
Therefore, Geoff should expect to have 768 bulbs in his garden in the eighth year if the pattern of doubling the number of bulbs each year continues.
There are 5.28 cups of pudding to be put into 6 dishes.How much pudding should be put into each dish to make it equal?
Answers
Note: In order to divide decimals, you move the decimal in the divisor (the number the other nimber is being divided by) by whatever amount to make it whole, and then do the same to the dividend by moving the decimal places of that number. Add 0's to the empty spots, and then divide like you would regular numbers. You may not need this now, but if you get questions like this and you can't use a calculator, it will really help.
factor a^2b^2-7ab+10
Answers
The factored form of −7ab+10 is (ab−5)(ab−2).
Explanation:To factor the expression −7ab+10, we look for two binomials whose product gives the original expression. In this case, the factors are
(ab−5)(ab−2).
Expanding
(ab−5)(ab−2) using the distributive property, we get:
(ab−5)(ab−2)=(ab)(ab)−(ab)(2)−(5)(ab)+(5)(2)
Simplifying each term, we get:
−2ab−5ab+10
Combining like terms, we have:
−7ab+10
Therefore, the factored form of −7ab+10 is (ab−5)(ab−2).
What is the length of line segment XZ
Answers
The line segment XZ has a length of 16 units. Hence, the 3rd option is the correct choice. Computed using the tangent to the circle and the Pythagoras Theorem.
How is a tangent inclined to the circle?A tangent to a circle is always perpendicular to it, that is, the radius drawn from the center of the circle to the tangent, is always perpendicular to it.
What is the Pythagoras Theorem?According to the Pythagoras Theorem, in a right triangle, the square of the hypotenuse, that is, the side opposite to the right angle, is equal to the sum of the squares of the legs, that is, the other two sides.
How to solve the question?In the question, we are asked to find the length of the line segment XZ.
Firstly, we name the center of the circle O.
The diameter of the circle is given to be 12 units.
Thus, its radius = 12/2 = 6 units,
Joining the radius OW, we get a right triangle OWZ, as the radius from the center of the circle to the tangent is always perpendicular.
In the right triangle OWZ, by Pythagoras Theorem, we can write:
OZ² = OW² + WZ² {Since, OZ is the hypotenuse},
or, (k + 6)² = 6² + (k + 4)² {Since, OZ = OY + YZ = Radius + k = 6 + k, and OW = Radius = 6},
or, k² + 12k + 36 = 36 + k² + 8k + 16 {Using the formula (a + b)² = a² + 2ab + b²},
or, k² + 12k - k² - 8k = 36 + 16 - 36 {Rearranging},
or, 4k = 16 {Simplifying},
or, k = 4 {Simplifying}.
Now, XZ = XY + YZ = Diameter + k = 12 + 4 = 16 units.
Thus, line segment XZ has a length of 16 units. Hence, the 3rd option is the correct choice. Computed using the tangent to the circle and the Pythagoras Theorem.
Learn more about the tangent to the circle and the Pythagoras Theorem at
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for the simple harmonic motion equation d=2sin(pi/3t), what is the frequency?
Answers
1/6
Answer:
Frequency of [tex]d=2\sin (\frac{\pi t}{3})[/tex] is [tex]\frac{1}{6}[/tex].
Step-by-step explanation:
We have the harmonic equation as, [tex]d=2\sin (\frac{\pi t}{3})[/tex].
It is known that,
If a function f(x) has a period P, then the function cf(bx) has period [tex]\frac{P}{|b|}[/tex].
So, we have,
As the function [tex]\sin t[/tex] has [tex]2\pi[/tex], then [tex]d=2\sin (\frac{\pi t}{3})[/tex] will have period [tex]\frac{2\pi}{\frac{\pi}{3}}[/tex] = 6
Further, the frequency of a function is the reciprocal of its period.
Thus, the frequency of [tex]d=2\sin (\frac{\pi t}{3})[/tex] is [tex]\frac{1}{6}[/tex].
The mode of a set is the number that occurs the most in a set.
True False