A ball is hit vertically upwards from a cliff, which is 80 m above the sea. The displacement
from the edge of the cliff, s, measured upwards in metres, after t seconds is given by
S = 300 - 5t2. Calculate:
a the time it takes for the ball to land in the sea
b the time it takes to reach the highest point
c the total distance travelled during the motion.
Answers
Answer:
a) 8 seconds
b) 3 seconds
c) 170 meters
Step-by-step explanation:
a) When the ball lands in the sea, s = -80.
-80 = 30t − 5t²
5t² − 30t − 80 = 0
t² − 6t − 16 = 0
(t + 2) (t − 8) = 0
t = -2 or 8
t = 8 seconds
b) The ball reaches its highest point when the velocity is 0 (or at the vertex of the parabola).
t = -b / (2a)
t = -30 / (2 × -5)
t = 3 seconds
c) The highest point is:
s = 30(3) − 5(3)²
s = 45
So the ball rises 45 meters, falls 45 meters, then falls 80 meters.
The total distance traveled is 45 + 45 + 80 = 170 meters.
Related Questions
Yellow trapezoid equals to ________? not 2 or 3
Answers
Answer:
The yellow trapezoid equals to 6.
Step-by-step explanation:
Assuming that two green items equals to two purple items and one yellow trapezoid, we can make the equation 5+5=2+2+x. Simplifying both sides, we get 10=4+x. If we subtract 4 from both sides and isolate x, we get that x=6.
Answer:
yellow trapezoid = 6
Step-by-step explanation:
since the green crescent equals 5, and there are two on the left side, that would equal 10, so the right side also should equal 10 too. The purple teardrops equal two, and there are two on the right side, so the total of teardrops on the right side is equal to 4. Since both sides need to equal to 10, and we only have 4, we need to find the amount of the yellow trapezoid. To do that you need to subtract 4 from 10, to get 6, which is the amount of the yellow trapezoid.
Lydia graphed ΔLMN at the coordinates L (0, 0), M (2, 2), and N (2, −1). She thinks ΔLMN is a right triangle. Is Lydia's assertion correct? Yes; the slopes of segment LM and segment LN are opposite reciprocals. No; the slopes of segment LM and segment LN are not opposite reciprocals. Yes; the slopes of segment LM and segment LN are the same. No; the slopes of segment LM and segment LN are not the same.
Answers
Answer:
No; the slopes of segment LM and segment LN are not opposite reciprocals
Step-by-step explanation:
slope of LM: (2 - 0)/(2 - 0) = 1
slope of LN: (-1 - 0)/(2 - 0) = -1/2
Two lines are perpendicular when the multiplication of their slopes is equal to negative one, that is, they are opposite reciprocals. In this case:
slope of LM*slope of LN = 1*(-1/2) = -1/2
The correct option is
No; the slopes of segment LM and segment LN are not opposite reciprocals
The calculation is as follows:
slope of LM: [tex](2 - 0)\div (2 - 0)[/tex] = 1
And,
slope of LN: [tex](-1 - 0)\div (2 - 0)[/tex]= [tex]-1\div 2[/tex]
Here two lines should be perpendicular at the time when the multiplication of their slopes is equalivalent to negative one.
So,
= slope of LM × slope of LN
[tex]= 1\times (-1\div 2)\\\\ = -1\div 2[/tex]
Learn more: https://brainly.com/question/9122916?referrer=searchResults
True/False Worth
points)
(05.02 LC)
You can draw a quadrilateral with two sets of parallel lines and no right angles.
True
O False
Answers
Answer:
the answer is true
Step-by-step explanation:
Because a parallelogram would be the result.
Solve the following inequality
X-4
——- > - 5
5
Answers
X-4 /3 > -5
Multiply both sides by 3
X-4 > -15
Add 4 to both sides
X > -11
Answer:
[tex] \frac{x - 4}{3} > - 5[/tex]
[tex]x - 4 > 3 \times ( - 5)[/tex]
[tex]x - 4 > - 15[/tex]
[tex]x > - 15 + 4[/tex]
[tex]x > - 11[/tex]
Step-by-step explanation:
(
[tex]( {8x}^{2} + 4x + 4) - (7x + 9)[/tex]
solve
Answers
Answer:
[tex]8x^{2} -3x-5[/tex]
Step-by-step explanation:
[tex]8x^{2} +4x+4-7x-9[/tex]
[tex]8x^{2} +4x-7x+4-9[/tex]
[tex]8x^{2} -3x-5[/tex]
Which equation is quadratic in form
Answers
Answer:
The answer is A because the quadratic equation formula
Step-by-step explanation:
because the quadratic equation formula is
ax^2+bx+c=0
and when you sub A into it, you get it in the needed form
Answer:
The Answer is A
Step-by-step explanation:
I nedd help on this please
Answers
Answer:
c sqrt( ( x2-x1) ^2 + ( (y2-y1) ^2)
Step-by-step explanation:
The distance formula is
d = sqrt( ( x2-x1) ^2 + ( (y2-y1) ^2)
It is the difference between the coordinates. It is based on the Pythagorean theorem
Samantha can write 1 1⁄2 pages in 3 minutes. How many pages could she write in 12 minutes?
Answers
Answer:
[tex]6\:\mathrm{pages}[/tex]
Step-by-step explanation:
[tex]3 \times 4 = 12[/tex]
[tex]1\frac{1}{2} \times 4=6[/tex]
Answer:
6 pages
Step-by-step explanation:
1.5 pages x pages
--------------- = ------------
3 minutes 12 minutes
Using cross products
1.5 * 12 = 3x
Divide each side by 3
18 /3 = 3x/3
6 =x
6 pages
An electrician uses the function f(x) = 60 + 40x to calculate the total cost, in dollars, for a service call that takes x hours to
complete. What does the coefficient 40 represent?
A)
The electrician works 40 hours.
B)
The electrician charges $40 per hour.
Eliminate
The electrician drives 40 miles to work.
D)
The electrician charges a $40 trip charge.
Answers
Answer:
(B) The electrician charges $40 per hour.
Step-by-step explanation:
Total cost=fixed cost + variable cost
F(x)=60+40x
Fixed cost =60
Variable cost=40x
x=hours of service
40=40 dollar per hour charge
The coefficient 40 represent the electrician charge of $40 per hour
(B) The electrician charges $40 per hour.
Solve for x. 4x−4−3x2−16=6x+4 −112 372 −432 112
Answers
Answer:
Input interpretation:
solve x×4 x - 4 - 3 x^2 - 16 = 6 x + 4 - 112×372 - 432×112
Results:
x = 3 - i sqrt(90015)
x = 3 + i sqrt(90015)
Khan academy question
Answers
Step-by-step explanation:
There it is..................
Answer:
(2,5)
Step-by-step explanation:
A nurse collected data about the average birth weight of babies in the hospital that month. Her data is shown using the dot plot. Create a box plot to represent the data. dot plot titled Monthly Birth Weight and number line from 8 to 9 in increments of 1 tenth labeled Birth Weight (in pounds.) with zero dots over 8, zero dots over 8 and 1 tenth, 2 dots over 8 and 2 tenths, 2 dots over 8 and 3 tenths, 2 dots over 8 and 4 tenths, 3 dots over 8 and 5 tenths, zero dots over 8 and 6 tenths, 1 dot over 8 and 7 tenths, zero dots over 8 and 8 tenths, 1 dot over 8 and 9 tenths, and zero dots over 9 box plot with minimum value 8 and 3 tenths, lower quartile 8 and 4 tenths, median 8 and 5 tenths, upper quartile 8 and 6 tenths, and maximum value 8 and 9 tenths box plot with minimum value 8 and 2 tenths, lower quartile 8 and 3 tenths, median 8 and 4 tenths, upper quartile 8 and 5 tenths, and maximum value 8 and 9 tenths box plot with minimum value 8 and 3 tenths, lower quartile 8 and 5 tenths, median 8 and 6 tenths, upper quartile 8 and 7 tenths, and maximum value 8 and 9 tenths box plot with minimum value 8 and 2 tenths, lower quartile 8 and 3 tenths, median 8 and 4 tenths, upper quartile 8 and 6 tenths, and maximum value 8 and 9 tenths
Answers
Answer:
The values of the box-plot are: B = {8.2, 8.3, 8.4, 8.5 and 8.9}.
Step-by-step explanation:
The data provided is as follows:
X Frequency
8 0
8.1 0
8.2 2
8.3 2
8.4 2
8.5 3
8.6 0
8.7 1
8.8 0
8.9 1
9 0
So, the actual data is:
S = {8.2 , 8.2 , 8.3 , 8.3 , 8.4 , 8.4 , 8.5 , 8.5 , 8.5 , 8.7 , 8.9 }
A boxplot, also known as a box and whisker plot is a method to demonstrate the distribution of a data-set based on the following 5 number summary,
Minimum (shown at the bottom of the chart) First Quartile (shown by the bottom line of the box) Median (or the second quartile) (shown as a line in the center of the box) Third Quartile (shown by the top line of the box) Maximum (shown at the top of the chart).The data set is arranged in ascending order.
The minimum value is, Min. = 8.2
The lower quartile is,
[tex][\frac{n+1}{4}]^{th}\ obs.=[\frac{11+1}{4}]^{th}\ obs.=3^{rd }\ obs. =8.3[/tex],
Q₁ = 8.3.
The median value is,
[tex][\frac{n+1}{2}]^{th}\ obs.=[\frac{11+1}{2}]^{th}\ obs.=6^{th}\ obs.=8.4[/tex]
Median = 8.4
The upper quartile is,
[tex][\frac{3(n+1)}{4}]^{th}\ obs.=[\frac{3(11+1)}{4}]^{th}\ obs.=9^{th }\ obs. =8.5[/tex],
Q₃ = 8.5.
The maximum value is, Max. = 8.9.
So, the values of the box-plot are: B = {8.2, 8.3, 8.4, 8.5 and 8.9}.
Answer:
The values of the box-plot are: B = {8.2, 8.3, 8.4, 8.5 and 8.9}.
Step-by-step explanation:
I took the practice test
the students in Mrs. Kranger's class are holding a car wash to raise money for their end- of- year field trip. they washed 45 cars by noon, and their goal is to wash 110 cars by the end of the day. write and solve an addition equation to find c, the number of cars they still need to wash to meet their goal.
Answers
Answer:
45 + c = 110
c = 65
Step-by-step explanation:
110 - 45 = 65
Please mark as brainliest!
Answer:
They need to wash 65 more cars to reach their goal.
Step-by-step explanation:
45+c=110
subtract 45 from both sides
c=65
|7t|=35 solve the equation
Answers
Answer:
t = 5,-5
Step-by-step explanation:
35/7 = 5
because it is an absolute value, it will always be positive:
-35/7 = -5
Answer:
T = 5,
Step-by-step explanation:
7T = 35
divide 7 by both
T = 5
hope this helps
CA=2,AB=3, The angle of C=90 degrees what is the angle of B?
Answers
Answer:
m∠B ≈ 41.81°
Step-by-step explanation:
If we draw a picture, it would help a lot. Once we visualize the triangle, we can see that we have sin∅ = 2/3. So, plugging into your calc,
sin∅ = 2/3
∅ = sin^-1(2/3)
∅ = 41.8103
Please Help! ASAP C: :D
Answers
Answer:
C). Zero
Step-by-step explanation:
This is a pretty simple question.
Any number multiplied by zero will be zero, and zero cannot have a positive or negative sign, which is why zero has its own sign, which is known as the Sign of Zero.
The rule is you go left to right on an equation so the answer that you get from 4.3 (-3.2) you would have to multiply it by zero and anything multiplied by zero equals zero
Given that ƒ(x) = 4x + 5 and g(x) = x2 – 2x – 2, find (ƒ + g)(x). Question 11 options: A) (ƒ + g)(x) = x2 + 6x + 3 B) (ƒ + g)(x) = –x2 + 6x + 7 C) (ƒ + g)(x) = x2 + 2x + 3 D) (ƒ + g)(x) = –x2 + 2x – 7
Answers
Answer: C
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
Solve x/-4 - (-8)=12
16
80
-80
-16
Answers
Answer:
-80
Step-by-step explanation:
Solve for x for the x value.
So I’m not great in math at all I spent 15 min crying because I don’t get it so anyone pls help
Answers
Answer:
A
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
Here b = 13 and h = 4 , thus
A = [tex]\frac{1}{2}[/tex] × 13 × 4 = [tex]\frac{1}{2}[/tex] × 52 = 26 units² → A
Answer:
A, 26
Step-by-step explanation:
Since the area of a triangle is one half base times height, and we have our height as 4, and our base as 13, we get 1/2 * 13 * 4, which is equal to 13 times 2, which is 26. Thus, our answer is A, 26.
Simplify. 2u^2-2/ u^2-3u+2
Answers
The scale on a map is 1cm for every 400 km. If Maine and Japan are 22cm apart on the map, what is the distance between Maine and Japan? Please help!!!!!
Answers
Answer:
8800km
Step-by-step explanation:
If 1cm = 400km
then you have to substitute in 22cm instead of 1cm making it..
22x400=8800.
Hope this helps.
Evaluate the expression for
x = 8, y = 4:
x + 10/y+5
Answers
Answer:
2Solution,
X=8
y=4
Now,
[tex] \frac{x + 10}{y + 5} \\ = \frac{8 + 10}{4 + 5} \\ = \frac{18}{9} \\ = 2[/tex]
hope this helps...
Good luck on your assignment..
8+10/4+5
18/9
=2
Levi would like to use a credit card to make a $3000 purchase. He is considering two credit options. The first requires a down payment of $1000 followed by monthly payments of $125. The second requires a down payment of $1300 followed by monthly payments of $110. The two options accumulate the same amount of interest and require the same number of monthly payments. What is the amount of interest for this loan?
Answers
Answer: $500
Step-by-step explanation:
Hi, since both credit options accumulate the same amount of interest:
1000+125x=1300+110x
Solving for x(number of months)
125x-110x =1300-1000
15x = 300
x =300/15
x= 20 months
Replacing x =25 in one equation:
1000+125x =
1000+125(20)=
1000+2500= $3500
Finally, we have to subtract the amount of the purchase (3000) to the result obtained:
3500-3000=$500
Feel free to ask for more if needed or if you did not understand something.
Solve for x in the triangle. Round your answer to the nearest tenth.
Answers
Answer:
x ≈ 6.9
Step-by-step explanation:
We use tan∅ to solve this:
tan21° = x/18
18(tan21°) = x
x = 6.90955
Select the graph of the solution. Click until the correct graph appears.
Ixl < 3
Answers
Answer:
In the figure attached, the solution is shown.
Step-by-step explanation:
Given the inequality:
|x| < 3
There are 2 solutions:
x < 3 or x > -3
This can be rewritten as follows:
-3 < x < 3
On the number line, this represents all the point between -3 and 3. Notice that -3 and 3 are not included in the solution; that is why there are open circles at these points on the graph.
Use the relationship between the side lengths and the
angles opposite those sides. What are the smallest and
largest angles of ALMN?
The smallest angle of the triangle is
The largest angle of the triangle is
Answers
Answer:
Smallest angle - ∠M
Largest angle - ∠N
Step-by-step explanation:
In a triangle opposite side of a largest angle is largest and opposite side of a the smallest angle is smallest.
In the given triangle LMN,
Side lengths of the triangle have been given as,
LM = 27 in.
MN = 25 in.
LN = 24 in.
Relationship in these sides will be,
LM > MN > LN
Therefore, relationship in their opposite sides will be,
∠N > ∠L > ∠M
The smallest angle of the triangle is angle M.
And the largest angle of the triangle is angle N.
hi what is the answer for this
Answers
Step-by-step explanation:
first find the side length by
considering a triangle under
the square
[tex]l \: = \sqrt{ {3}^{2} + {1}^{2} } = \sqrt{10} \: cm \\ area \: = \: \sqrt{10} \times \sqrt{10} = 10 \: {cm}^{2} \: \: \: \: ans[/tex]
The Locust Points idea allows you to define geometric objects just by determining whether or not two distance are equal.
A.) True
B.) False
Answers
Answer:
A. True
Step-by-step explanation:
The locus of points idea allows you to define objects in terms of points and given distances.
Answer:
True
Step-by-step explanation:
Given area of a rectangle: 7x^2+57x+8
Find Perimeter:
Answers
Answer:
Perimeter of the rectangle is 16x+18 units.
Step-by-step explanation:
The area of rectangle is
[tex]7x^2+57x+8[/tex]
First we have to find the factor form of above expression.
Splitting the middle term, we get
[tex]7x^2+56x+x+8[/tex]
[tex]7x(x+8)+1(x+8)[/tex]
[tex](x+8)(7x+1)[/tex]
Area of a rectangle is the product of its dimensions. It means dimensions of the rectangle are (x+8) and (7x+1).
Perimeter of a rectangle is
[tex]Perimeter=2(l+b)[/tex]
[tex]Perimeter=2[(x+8)+(7x+1)][/tex]
[tex]Perimeter=2[8x+9][/tex]
[tex]Perimeter=16x+18[/tex]
Therefore, the perimeter of the rectangle is 16x+18 units.
Which diagram can be used to prove AABC – ADEC using similarity transformations?
А
E
B
D
А
D
В
С
Answers
The diagram that can be used to prove [tex]\triangle ABC \sim \triangle DEC[/tex] is (b)
Similar triangles may or may not have congruent corresponding sides, but the corresponding angles must be congruent.
The above means that,
All three angles of the two triangles must be congruentThe three sides must be in equivalent proportions.Using the above highlight, we can conclude that the diagram that can be used to prove [tex]\triangle ABC \sim \triangle DEC[/tex] is (b) see attachment
Read more about similar triangles at:
https://brainly.com/question/9166513