Answer:
a) a = -3, b = 18, c = 48; s(t) = -3t²+18t+48b) 48mc) 8secsStep-by-step explanation:
The question is incomplete. Here is the complete question.
'A rock was thrown from the top of a cliff such that its distance above sea level was given by s(t)=at²+bt+c, where t is the time in seconds after the rock was released. After 1 second the rock was 63 m above sea level, after 2 seconds 72 m, and after 7 seconds 27 m. a. Find a, b and c and hence an expression for s(t). b. Find the height of the cliff. c. Find the time taken for the rock to reach sea level.'
Given the equation of the distance modelled as s(t)=at²+bt+c
If after 1 second the rock was 63 m, then 63 = a+b+c
If after 2 seconds, the distance was 72 m then 72 = 4a+2b+c
Also if after 7 seconds, the distance is 27 m, then 27 = 49a+7b+c
i) Solving the 3 equations simultaneously to get a, b and c we have;
a+b+c = 63 ... 1
4a+2b+c = 72 ...2
49a+7b+c = 27 ...3
Subtracting 2 from 1 and 3 from 2 we will generate 2 new equations as shown;
eqn 2- eqn1: 3a + b = 9...4
eqn 3- eqn 2: 45a + 5b = -45
eqn 3- eqn 2: 9a+b = -9 ... 5
solving 4 and 5 simultaneously
3a + b = 9 ...4
9a+b = -9 ... 5
Taking the difference of 4 and 5 we have
6a - -9-9
6a = -18
a = -3
substituting a = -3 into equation 4 to get b we have;
3(-3)+b = 9
-9 + b = 9
b = 9+9
b = 18
substituting a = -3 and b = 18 into equation 1 to get c we have;
-3+18+c = 63
15+c = 63
c = 48
a = -3, b= 18 and c = 48
The distance function will be s(t) = -3t²+18t+48
ii) If the height of the cliff is modelled by the equation s(t)=at²+bt+c
The height of the cliff is at when t = 0
s(0) = -3(0)²+18(0)+48
s(0) = 48m
The height of the cliff is 48m
iii) At the sea level, the height of the rock will be 0m, substituting this into the modeled equation for the height to get the time we have;
s(t)=at²+bt+c
0 = -3t²+18t+48
3t²-18t-48 = 0
t² - 6t - 16 =0
t² - 8t+2t - 16 = 0
t(t-8)+2(t-8) = 0
(t+2)(t-8) = 0
t = -2 or 8
Taking the positive value of the time, t = 8secs
Time taken for the rock to reach sea level is 8secs
Factor completely 5x2 - 20.
Answer:
[tex]5(x-2)(x+2)[/tex]
Step-by-step explanation:
Factor out 5:
[tex]5(x^2-4)[/tex]
Use difference of squares formula for the inside:
[tex]5(x-2)(x+2)[/tex]
click here if your good t math it ez
Write three fractions that are equivalent to 1/2
Use a diagram to show how you know you are right.
Answer:2/4 3/6 4/8
Step-by-step explanation:
Donnie deli man delivered 595 box lunches for the robotics convention. There were 20 more turkey sandwiches then roast beef. There were twice as many roast beef has PB&J. How many of each type of BoxLunch did Donnie delivered?
Answer:
250 turkey sandwiches were delivered.
There were 230 roast beef delivered.
115 PB&J were delivered.
Step-by-step explanation:
This question is solved using a system of equations.
I am going to say that:
x is the number of turkey sandwiches.
y is the number of roast beef.
z is the number of PB&J.
Donnie delivered 595 box lunches
This means that [tex]x + y + z = 595[/tex]
There were 20 more turkey sandwiches then roast beef.
This means that [tex]x = y + 20[/tex]
There were twice as many roast beef has PB&J.
This means that [tex]y = 2z[/tex].
So in the second equation, we have that [tex]x = 2z + 20[/tex]
Replacing this in the first equation:
[tex]x + y + z = 595[/tex]
[tex]2z + 20 + 2z + z = 595[/tex]
[tex]5z = 575[/tex]
[tex]z = \frac{575}{5}[/tex]
[tex]z = 115[/tex]
115 PB&J were delivered.
[tex]x = 2z + 20 = 2*115 + 20 = 250[/tex]
250 turkey sandwiches were delivered.
[tex]x = y + 20[/tex]
So
[tex]y = x - 20 = 250 - 20 = 230[/tex]
There were 230 roast beef delivered.
Find the value of u. If the volume is 560
Answer:
10 ft
Step-by-step explanation:
V = l*w*h
560 = 7*8 *u
560 = 56u
divide each side by 56
560/56 = 56u/56
10 =u
Peter's grandma has a trapezoidal garden, as in the picture.
a) What is the length of the fence of that garden?
b) What is the area of the garden?
The word in the top left corner in the picture is not linked to this task.
Length of fence = perimeter of trapezoid
= 12 + 6 + 5 + 5
= 28 meters
Area of garden = [tex]h (\frac{base 1 + base2}{2} )[/tex]
= 4([tex]\frac{12+6}{2}[/tex])
= 4 x 9
= 36 sq. meters
A car traveled 360 miles in 4 hours. If its speed were to be 15 mph slower, how long would it take to travel the same distance?
Answer: 4.8 hours.
Step-by-step explanation:
To find how long it would take to travel the same distance at a slower speed, find the speed the car is currently driving at.
Speed is distance over time, or in this case, miles per hour.
360 / 4 = 90 miles per hour.
The car is travelling 15 miles per hour slower, so the new speed is 90 - 15, or 75 miles per hour.
You can now use the same equation to find the time travelled:
360 / x = 75
360 = 75x
Divide both sides by 75 to get your answer:
4.8 = x
It would take the car 4.8 hours to travel the same distance.
What type of function is represented in the table?
x 0 1 2 3 4 5
y -7 -2 3 8 13 18
a.quadratic
b.exponential
c.logarithmic
d.linear
The type of function represented in the table is linear.
How to find the type of function represented in a table ?Let's check the type of function represented in the table.
You can tell if a table is linear by looking at how x and y change. If, as x increases by 1, y increases by a constant rate, then a table is linear. You can find the constant rate by finding the first difference.
It can also be found by using the linear equation,
y = mx + b
where
m = slopeb = y-interceptTherefore,
The x increases by y and the y increase by a constant rate of 5.
-2 - (-7) = 53 - (-2) = 58 - 3 = 5Therefore, the function represented in the table is linear.
learn more function here: https://brainly.com/question/14252853
#SPJ1
Express the fraction StartFraction 6 Over 22 EndFraction as a percent. Round the answer to the nearest whole percent.
the answer would be 27% :3
Answer:
27%
Step-by-step explanation:
What number is in the hundreds place in 500?
Answer:
The 5!
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
because it is the 3rd number from the ones place
Westin is comparing the triangles below.
Triangle F G H. Side G H is 4 centimeters, angle G is 117 degrees, and angle H is 27 degrees. Triangle J L K. Side J L is 8 centimeters, angle J is 27 degrees, and angle L is 117 degrees.
He uses the similarity statement Triangle H G F is similar to triangle L J K. Which best describes the accuracy of Westin’s statement?
Accurate. HG and LJ are proportional.
Inaccurate. HG and LJ are not corresponding sides.
Inaccurate. The sides are not proportional. There is no common ratio between the sides.
Inaccurate. The angles in the order listed do not correspond.
Answer:
It is Inaccurate: The angles in the order listed do not correspond. I just took the test
Answer:
Inaccurate. The angles in the order listed do not correspond.
Step-by-step explanation:
I am doing the test rn and I think this is the right answer
what do u have to do???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
Step-by-step explanation:
Step 1: Answer the question
They are independent because the cards are always going to stay the same. If each card that was picked and discarded, that would alter the future which would make it dependent. But... since it doesn't change the cards, it is independent.
Answer: independent
Answer:
Independent
Step-by-step explanation:
Since the second selection is made after replacement, the options are exactly the same as the first selection. Therefore the second selection doesn't depend on the first one. Hence, they are independent
If it was without replacement, they would have been dependent
can someone help me please I'm doing this for math Olympics
A contractor is asked to build a new set of townhouses in attached clusters of
different sizes. He created plans for one-, two-, and three-house clusters, as shown in the diagram below. The builder used computer software to draw the line segments used to represent the houses. How many line segments are needed to draw 4 houses? 10 houses? 47 houses? n houses? Explain your strategy.
A)Greg
B)tony
C)Robert
D)John
Answer:
C
Step-by-step explanation:
Let's compare 3/7 and 3/4 first. These two fractions have the same numerator but not the same denominator, so the fraction with the smaller denominator will be larger. Therefore, 3/4 is larger, so we can eliminate A.
4/9 is less than 1/2, and 3/4 is greater than 1/2, so 3/4 is greater than 4/9 and we can eliminate B. The same goes for D.
Therefore, our answer is C) Robert. Hope this helps!
If Two-thirds = StartFraction x over 12 EndFraction, what is the value of x? 4 8 18 24
Answer:
8
Step-by-step explanation:
[tex] \frac{2}{3} = \frac{x}{12} \\ x = \frac{2 \times 12}{3} \\ x = 2 \times 4 \\ x = 8[/tex]
Answer:
B) 8
Step-by-step explanation:
2\3= X/123X=2424÷3=8The answer is 8Angle relationships with parallel lines can someone answer please help
Answer:
x°= 34°
m<x and angle measuring 34° are corresponding angles since two lines are parallel with a third line intersecting them.
Correct answers only please! I keep losing points...
Quincy has $6,000 in a savings account that earns 4% interest, compounded annually.
To the nearest cent, how much interest will he earn in 5 years?
Use the formula B = p(1 + r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answer:
A = $ 7,299.92
A = P + I where
P (principal) = $ 6,000.00
I (interest) = $ 1,299.92
Step-by-step explanation:
A = P(1 + r/n)nt
Where:
A = Accrued Amount (principal + interest)
P = Principal Amount
I = Interest Amount
R = Annual Nominal Interest Rate in percent
r = Annual Nominal Interest Rate as a decimal
r = R/100
t = Time Involved in years, 0.5 years is calculated as 6 months, etc.
n = number of compounding periods per unit t; at the END of each period
Question is in the picture
Answer:
y = 2x - 7
Step-by-step explanation:
When x is equal to 0, then the y value is your y-intercept. So, your y-intercept is -7.
Now, pick two points. Let's pick (-1,-9) and (0,-7). We can add these into the slope formula.
[tex]Slope(m)=\frac{y2-y1}{x2-x1}[/tex]
[tex]m=\frac{-7-(-9)}{0-(-1)}[/tex]
[tex]m=\frac{2}{1}[/tex]
[tex]m=2[/tex]
Now, we can use the slope and the y-intercept and put them into a slope-intercept equation.
[tex]y=mx+b[/tex]
[tex]y=2x-7[/tex]
How do I find the perimeter for a square and a triangle?
Answer: 24 inches.
Step-by-step explanation:
You can find the perimeter of the polygon by adding the side lengths.
First, find the missing side lengths.
There is a short space between the right side of the square above the triangle. The triangle is 3 inches tall, and the square is 4 inches tall, so that space is 1 inch long.
We can then add the sides to find the perimeter:
4 + 9 + 5 + 1 + 5 = 24 inches long.
Keep in mind that the three inches of the triangle is not included in the sum because it is not on the outside of the polygon. The perimeter only includes the lengths of the exterior sides.
PLEASE HELP!!
Use the Triangle Inequality Theorem to determine which set of numbers CANNOT form the side lengths of a triangle.
A. 7, 9, 20
B. 6, 14, 17
C. 8, 24, 30
D. 2, 2, 3
E. 12, 22, 32
Answer:A
Step-by-step explanation:
Side lengths do not adhere to the triangle inequality theorem.
In 2015, about 895.5 million passengers traveled by plane in the United States. Which value is the BEST estimate of the number of passengers?
A. 9 x 10°
B. 9 x 108
C. 8 x 108
D. 8 x 10°
Find a monic quartic polynomial f(x) with rational coefficents whose roots include
x=1-sqrt2, and x=2+sqrt5. Give your answer in expanded form.
Answer:
The polynomial hose roots are :
x = 1 - √2 and
x = 2 + √5
Is
x² - (3 + √5 + √2)x + 2 + √5 - 2√2 -√10 = 0
Step-by-step explanation:
The roots of the equation are
x = 1 - √2 and
x = 2 + √5
(x - 1 + √2)(x - 2 - √5) = 0
x²- 2x - x√5 - x + 2 + √5 + x√2 - 2√2 - √10 = 0
x² - (3 + √5 + √2)x + 2 + √5 - 2√2 -√10 = 0
This is the expanded form
Write the word sentence as an equation.
The quotient of 36 and a number g is 9.
Answer:
[tex]\frac{36}{g}[/tex]=9
Items for a fundraiser are packaged in small boxes shaped like rectangular prisms that are inches long, inches wide, and 8 inches tall. To transport the items to an event, you want to know how many of the small boxes will fit in larger boxes. The larger boxes are available in two sizes. Large Box 1 is inches long, 18 inches wide, and 24 inches tall. Large Box 2 is inches long, inches wide, and 24 inches tall. Both the small and large boxes must remain upright.
Answer:
- The number of small boxes that will fill the large box 1 = 64
- The number of small boxes that will fill the large box 2 = 56
Step-by-step explanation:
Complete Question
Items for a fundraiser are packaged in small boxes shaped like rectangular prisms that are 4.5 inches long, 4.5 inches wide, and 8 inches tall. To transport the items to an event, you want to know how many of the small boxes will fit in larger boxes. The larger boxes are available in two sizes. Large Box 1 is 24.25 inches long, 18 inches wide, and 24 inches tall. Large Box 2 is 20.5 inches long, 18.5 inches wide, and 24 inches tall. Both the small and large boxes must remain upright.
Solution
To know how many of the small boxes will fit in larger boxes, we need to obtain the volumes of the small box, large box 1 and large box 2.
Volume of a cuboid = L × W × H
For the small box,
Length = L = 4.5 inches
Width = W = 4.5 inches
Height = H = 8 inches
Volume of the small box = 4.5 × 4.5 × 8 = 162 in³
For large box 1,
Length = L = 24.25 inches
Width = W = 18 inches
Height = H = 24 inches
Volume of the large box 1 = 24.25 × 18 × 24 = 10,476 in³
For large box 2
Length = L = 20.5 inches
Width = W = 18.5 inches
Height = H = 24 inches
Volume of the large box 2 = 20.5 × 18.5 × 24 = 9,102 in³
The number of small boxes that'll fill the large box 1 = (10,476/162) = 64.667 = 64 small boxes (rounded down because the fraction cannot be forced into the large box 1.
The number of small boxes that will fill the large box 2 = (9,102/162) = 56.185 = 56 small boxes.
Hope this Helps!!!
Find the mean for each data set. Number of Flowers . . . . . . <-----I-----I-----I-----I-----I-----I-----I-----I-----I-----> 10 11 12 13 14 15 16 17 18
Answer:
Well to find the mean of the above
take £ as sigma
therefore,
mean= £fx/£f
This simply means the sum of all the numbers divided by the number of members
therefore,
10 + 11+12+13+14+15+16+17+18= 126
And the number of figure present on the number line are 9, therefore 126 divided by 9
giving you a result of 14
Therefore the mean of the above numbers is 14.
If f(x)=2x+3, find the following value of f(x)=11.
Please help me understand this problem and the answer please.
Please check 1, 2, 4, and 5 for me and please help me with question 3.
Thank you!
Answer:
n = 7
Step-by-step explanation:
Your answers are correct.
For problem 3, we use error estimation:
| (-2)ⁿ⁺¹ / (n+1)! | < 0.01
(2)ⁿ⁺¹ / (n+1)! < 0.01
By trial and error:
If n = 3, (2)ⁿ⁺¹ / (n+1)! = 0.667
If n = 5, (2)ⁿ⁺¹ / (n+1)! = 0.089
If n = 7, (2)ⁿ⁺¹ / (n+1)! = 0.006
Solve the equation by doing the inverse operation to work backwards
x+13=25
Answer:
x = 12
Step-by-step explanation:
x+13=25
Subtract 13 from each side
x+13-13=25-13
x = 12
PLEASE HURRY !!!!!
Step- by- step
Solve the equation for x:
4x - 4 = 6x + 8
Solve the equation for x:
1/3x + 4 = 10
Find the sum of the interior angles
of a polygon with 35 sides.
What is the formula for the circumference of a circle in terms of r
Answer:
C = 2πr
Step-by-step explanation:
The formula for the circumference of a circle is C = πd, and since the diameter, d, is equal to double the radius, 2r, we can replace 2r for d. Giving us C = 2πr