Answers
a) The height of the stone 5 seconds later is: 90 feet
b) The time at which the stone hits the ground is: 7.66 secs
c) The velocity of the stone when it hits the ground is: 227 ft/sec
How to solve Projectile Motion Problems?We are given:
Height above ground: h = 800 feet
Initial speed: u = 18 feet per second
(A.) Height of the stone at t = 5 seconds.
g = -32feet/sec²
t = 5 sec.
Since the stone is thrown vertically upward from some height X = 800 feet, so the total height will be:
h = X + ut + 1/2at²
h = 800 + (18*5) + ¹/₂ * (-32) * (5²)
h = 90 feet
(B.) At what time did the stone hit the ground, that means height, h = 0.
0 = 800 + (18t) + ¹/₂ * (-32) * (t²)
16t² - 18t - 800 = 0
t = 18 ± √-18² - 4 * 16 * (-800)/2*16
t = 7.66 sec
So at t = 7.66 secs, the stone hits the ground.
(C.) The velocity when the stone hits the ground.
Using the energy conservation theorem,
Initial total energy = Final total energy.
¹/₂mu² + mgh = ¹/₂mv² + 0
u² + 2gh = v²
v² = 18² + 2*32*800
v=√18² + 2*32*800
v = 227 ft/sec
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Related Questions
A ribbon is lining the outside of a circular object. If the object has a radius of 7 cm, then how long should the ribbon be?
Answers
Answer:
Length= 43.98 cm
Step-by-step explanation:
Circumference=2πr
r=7cm
C=2π(7)
C=43.98 cm
circumference is equal to the length of ribbon along the outside of the circular object
write an equivilant fractions for 3 3/4 and 1 2/3 using a common denominator iready
Answers
The requried equivalent fraction for the equivalent fraction to 3 3/4 and 1 2/3, is 45/12, and 20/12.
To find a common denominator for 4 and 3, we can multiply them together to get 12.
So, we can convert 3 3/4 as:
3 3/4 = 12/4 + 3/4 = 15/4
Similarly, we can convert 1 2/3 as:
1 2/3 = 5/3
Therefore, the equivalent fractions for 3 3/4 and 1 2/3 using a common denominator of 12 are:
15/4 = 45/12 and 5/3 = 20/12
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which parent functions have a y-intercept at (0,0)? select all that apply
Answers
Answer: A,E or F.
Step-by-step explanation: That's the only ones that have X's and then x is 0
2. The ramp above connects two vertical supports,
forming two similar triangles: AADE~ AABC. Side AC corresponds to which side in the other triangle?
Answer:
3. What is the length of side BC?
Answers
The side AC corresponds to the side AC in the other triangle and the length of BC is 15 units
Side AC corresponds to which sideFor two triangles to be similar, the corresponding sides of the triangles must be in proportion
Having said that
The side AC corresponds to the side AC in the other triangle
What is the length of side BC?The length BC is calculated as
BC/9 = 25/15
Express as products
So, we have
BC = 9 * 25/15
Evaluate the products
BC = 15
Hence, the length of BC is 15 units
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Find P U (Q n R).........................
Answers
Q n R = {5, 11} (common numbers)
P U (Q n R) = {5, 7, 10, 11, 13, 14} (Q n R common numbers + all the numbers from P)
Quadrilateral ABCD is inscribed in a circle such that:
Answers
Answer:
∠ C = 84°
Step-by-step explanation:
A quadrilateral inscribed in a circle is a cyclic quadrilateral.
the opposite angles sum to 180° , that is
∠ A + ∠ C = 180 , then
x² + 60 + 8x + 36 = 180
x² + 8x + 96 = 180 ( subtract 180 from both sides )
x² + 8x - 84 = 0 ← in standard form
(x + 14)(x - 6) = 0 ← in factored form
equate each factor to zero and solve for x
x + 14 = 0 ⇒ x = - 14
x - 6 = 0 ⇒ x = 6
x > 0 , then x = 6 , so
∠ C = 8x + 36 = 8(6) + 36 = 48 + 36 = 84°
PLEASE HELP ME! I will give brainliest answer! Please please!!
Answers
Answer:
12/2
Step-by-step explanation:
(x - h)^2 + (y - k)^2 = r^2
where (h,k) is the center of the circle and r is the radius.
Comparing this to the given equation, we see that the center of the circle is (-10,0) and the radius is sqrt(9) = 3.
The diameter of the circle is twice the radius, so:
diameter = 2(radius) = 2(3) = 6
Therefore, the diameter of the circle is 6.
We can write this in simplified, rationalized form as:
diameter = 6 = 6/1 = 12/2
*Image attached below with steps
b. Allison went to the bakery and spent $3.75 for each cookie she bought and $1.50 for
a cup of lemonade. She spent a total of $24.00. What was the cost of each cookie?
Equation:
Answer:
Answers
Answer: each cookie costs $6.00
OR
x=6
URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answers
Answer:
The second scatterplot does not suggest a linear relationship between x and y.
In the figure below, the segments HI and HJ are tangent to the circle centered at O. Given that OI = 3.9 and OH= 6.5, find HJ.
H
6.5
9
O
HJ = 0
X
Answers
Based on the figure, we can see that triangles OHJ and OIX are similar because they share the same angle at O and HI and HJ are tangent to the circle. Thus, we can set up the following proportion:
OH / OI = HJ / (HJ + 9)
Substituting the given values:
6.5 / 3.9 = HJ / (HJ + 9)
Cross-multiplying:
6.5(HJ + 9) = 3.9HJ
Distributing:
6.5HJ + 58.5 = 3.9HJ
Simplifying:
2.6HJ = -58.5
HJ = -22.5
However, this answer doesn't make sense in the context of the problem. Since HJ represents a length, it cannot be negative. Therefore, we need to re-examine our work.
Looking back at our proportion, we can see that the ratio of OH to OI is greater than 1, which implies that HJ is greater than 9. This makes sense since HJ is a chord of the circle and thus must be longer than the radius.
Let's try the problem again, but this time we'll rearrange the proportion to solve for HJ:
HJ / (HJ + 9) = OI / OH
Substituting the given values:
HJ / (HJ + 9) = 3.9 / 6.5
Cross-multiplying:
6.5HJ = 3.9HJ + 35.1
Simplifying:
2.6HJ = 35.1
HJ = 13.5
Therefore, HJ is equal to 13.5.
Solve for W.
w² + 7w = 0
Answers
Answer:
w=0,
w=-7
Step-by-step explanation:
MODELING REAL LIFE A hemisphere-shaped mole has a diameter of 5.7 millimeters and a surface area of about
51 square millimeters. The radius of the mole doubles. Estimate the new surface area of the mole. Round your
answer to the nearest whole number.
The new surface area is square millimeters.
Answers
The new surface area of the hemisphere-shaped mole would be = 102mm².
How to calculate the new surface area for the hemisphere-shaped mole?A hemisphere-shaped mole has a shape that has one surface that is curved and the other surface a flat circular base.
Since the surface area of one hemisphere has been given, the second hemisphere can be determined.
To calculate the new surface area of the hemisphere-shaped moles the following is carried out;
Radius of the initial mole = 5.7/2 = 2.85 mm
If 2.85mm radius = 51 mm²
2(2.85mm) radius = x
Make X the subject of formula;
X = 2×2.85 × 51/2.85
= 102 mm²
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Danielle deposited $300.00 into a new savings account that earns interest compounded continuously. After 8 years, the balance in the account
was $907.00. What was the interest rate on the account?
O 13.8%
O 12.5%
O 14.5%
O 10.1%
Answers
In this case, A = $907, P = $300, and t = 8 years. We need to find r.
907 = 300 * e^(8r)
Now, we'll solve for r:
(907/300) = e^(8r)
3.0233 = e^(8r)
To isolate r, take the natural logarithm of both sides:
ln(3.0233) = 8r
Now, divide by 8:
(ln(3.0233))/8 = r
r ≈ 0.125
To express the interest rate as a percentage, multiply by 100:
0.125 * 100 = 12.5%
So, the interest rate on the account is approximately 12.5%.
which statement about odd functions is correct?
Answers
Answer: C
Step-by-step explanation:
Think about y=[tex]x^{3}[/tex] This is an odd function because the highest exponent(degree) is odd
A. is wrong. Symmetry is where you can fold it and it would be the same. If i folded y=[tex]x^{3}[/tex] along the y- axis it would not be the same.
B is wrong. Transformations are where has it moved, which has nothing to do with odd functions in general
C. is correct. It is folded along y=x and flipped.
D. is wrong. If folded y=x it's in the same quadrant but it's not the same, its' reversed.
This graph represents the flight path of a model rocket launched in a park.
What do the key features of the curve represent in terms of the flight path of the rocket?
Chose from the drop-down to match each situation.
ill give brainlyest to the first to correctly answer this
Answers
The drop down menu is used to match each situation as below.
1. The rocket reached its maximum the x-value of the vertex
height in 5 s.
2. ground level the y-intercept
3. The rocket launcher was the y-value of the point containing
on the ground. the x-intercept on the right
4. The rocket was in the air 10 the x-intercept on the right
5. The maximum height of the the y-value of the vertex
rocket is 50 ft.
6. the time the rocket was the x-value of the point containing the
launched y-intercept
What is the key feature of the curveThe key features of the curve such as the x intercept is the point the launcher and the rocket were on ground.
The vertex is the point the rocket had the maximum and height.
Generally, the curve traces a parabolic path
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Find (fog)(2).
f(x) = 3x + 2
g(x) = x²
(fog)(2)=
Answers
Answer:
(f·g)(2) = 14----------------------------
Find the composition of the functions f(x) and g(x), which is written as f(g(x)).
Given functions:
f(x) = 3x + 2,g(x) = x² .Find f(g(x)):
f(g(x)) = f(x²) = 3(x²) + 2Evaluate f(g(2)):
f(g(2)) = 3(2²) + 2 = 3(4) + 2 = 12 + 2 = 14So, (f·g)(2) = 14.
Select an association attribute in each box to complete the sentence
Answers
Answer:
The pattern of association between time and distance is positive and linear.
Find the interest earned and the future value of an annuity with monthly payments of $200 for two years into an account that pays 6% interest per year compounded monthly.
Answers
The interest earned and the future value of an annuity with monthly payments of $200 for two years that pays 6% interest per year compounded monthly is $25.43 and $225.43
What is the interest earned?Principal,P = $200
Time, t = 6%
Number of periods, n = 12
Interest rate, r = 6%
= 6/100
= 0.06 rate per year,
FV = P(1 + r/n)^nt
FV = 200.00(1 + 0.06/12)^(12)(2)
FV = 200.00(1 + 0.005)^(24)
FV = $225.43
Therefore,
Principal = $200.00
Interest = $25.43
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Find the sum of 3√5 and 4√25 in simplest form. Also, determine whether the result is rational or irrational and explain your answer.
Answers
The sum of 3√5 and 4√25 is an irrational number.
First, simplify the expressions inside the square roots:
3√5 = 3√(5×1) = 3√5
4√25 = 4√(25×1) = 4×5 = 20
Now, we add them together:
3√5 + 4√25 = 3√5 + 20
This is the simplest form since 20 is already a rational number and we cannot simplify the square root of 5 any further.
To determine whether the result is rational or irrational.
Since 3√5 is irrational and cannot be simplified any further, the expression as a whole is also irrational.
Therefore, the sum of 3√5 and 4√25 is an irrational number.
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Given P( A) =0.12 P (B) = 0.12 P(A)=0.12, = 0.3 P(B)=0.3 and P(A ∪ B) = 0.334 P(A∪B)=0.334, find the value of P(A∩B), rounding to the nearest thousandth, if necessary.
Answers
The value of P(A∩B) rounding to the nearest thousandth, if necessary is: 0.086
How to solve probability problems?The parameters given are:
P(A) = 0.12
P(B) = 0.3
P(A ∪ B) = 0.334
We want to find the probability P(A∩B)
The P(A∪B) probability formula is given as:
P(A∪B) = P(A) + P(B) - P(A∩B)
where:
P(A) is Probability of event A happening
P(B) is Probability of event B happening
P(A∩B) is Probability of happening of both A and B.
Thus:
0.334 = 0.12 + 0.3 - P(A∩B)
P(A∩B) = 0.12 + 0.3 - 0.334
P(A∩B) = 0.086
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Use the binomial theorem to find specified term of the given power of binomial ( remember that r starts at 0 in the binomial theorem so finding say the second term means that r=1)
Answers
The fourth term in the expanded form of (x - 1)⁶ is -20x³.
What is the fourth term in the expanded form of (x - 1)⁶?The fourth term in the expanded form of (x - 1)⁶ using the binomial theorem is calculated as follows;
The expanded form of (x - 1)⁶ using the binomial theorem is;
(x - 1)⁶ = 1x⁶ + (-6)x⁵ + 15x⁴ + (-20)x³ + 15x² + (-6)x + 1
(x - 1)⁶ = x⁶ -6x⁵ + 15x⁴ -20x³ + 15x² -6x + 1
To find the fourth term, we look for the fourth term from the left side to right side, which is -20x³.
Therefore, the fourth term in the expanded form of (x - 1)⁶ is -20x³.
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Help: (It is just one question.)
Answers
The bearing of the cruise ship displacement from its initial position is 15.06°, which makes the second option correct
What is bearing?Bearing is usually measured in degrees, with 0° indicating the reference direction (usually North), and increasing clockwise to 360°. It refers to the direction or angle between a reference direction and a point or object.
We will get a right triangle from travels of the ship, such that we can call the initial position A, the point after 8 miles B and the point after 30 miles C
angle B = 30° + 60° = 90°
AB = 8
BC = 30
by Pythagoras rule;
AC = √(8² + 30²) = 31.04
using sine rule;
30/sinA = 31.04/sin90
A = sin⁻¹[(30 × sin90)/31.04]
A = 75.06°
bearing from initial position = (30° + 75.06°) - 90°
bearing from initial position = 105.06 - 90°
bearing from initial position = 15.06°
Therefore, the bearing of the cruise ship displacement from its initial position is 15.06°
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A cube has volume 3375 cubic inches. Determine the area of one face of the cube.
Answers
The area of one face of the cube that has a volume of 3375 cubic inches is: 225 square inches.
What is the Volume of a Cube?A cube has equal edge length, and therefore has faces with the same area. The formula for finding the volume of a cube is given as:
Volume of cube = s³, where s is the side length of the cube.
Also, to find the area of one face of a cube, we would use the formula below:
Area of one face of a cube = s².
Given the following:
Volume of a cube = 3375 cubic inches
Find s as shown below:
s = ∛3375
s = 15 inches.
Therefore, we have:
Area of one face of a cube = 15² = 225 square inches.
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If I have 100 tiles and 98 are letters and 2 are blank I randomly drawl 2 title the first is a consonant and the 2 nd is a vowel what is the probability that both events will occur
Answers
The probability that both events will occur is 23.76%.
Given that, you have 100 tiles and 98 are letters and 2 are blank you randomly drawl 2 title the first is a consonant and the 2nd is a vowel.
Consonants (A) = 56
Vowels (B) = 42
Blank = 2
Total letters = 100
Two letters are drawn with replacement.
P(A) = 56/100 = 0.56
P(B) = 42/ (100-1) = 0.424
P(A).P(B) = 0.56*0.424 = 0.2376
Hence, the probability that both events will occur is 23.76%.
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Complete question is attached.
Michel-Eugène Chevreul found that the greatest intensity came from placing ________colors next to each other.
tertirary
analogous
complementary
arbitrary
Answers
Michel-Eugène Chevreul found that the greatest intensity came from placing complementary colors next to each other. The Option C is correct.
Which colors create the greatest intensity?Chevreul made great contributions to the field of color theory as he made key findings was that placing complementary colors next to each other creates the greatest intensity.
These colors are opposite to each other on the color wheel such as red & green, blue & orange or yellow & purple. When these color are placed next to each other, these colors create a visual contrast that makes them appear brighter and more intense.
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given the expression (2^-3)(2^5)/2^7), select the three equivalent numerical expressions
Answers
The three equivalent numerical expressions are 1/32, 0.03125, 3.125 x 10^-2
How to simplify the numerical expressionsUsing the exponential rules, we can simplify the expressions as:
(2^-3)(2^5)/2^7)
= 2^(5-3)/2^7
= 2^2/2^7
= 1/2^(7-2)
= 1/2^5
= 1/32
Therefore, three equivalent numerical expressions for the given expression are: 1/32, 0.03125, 3.125 x 10^-2
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5- Solve the following expression and write the answers in the lowest term possible. [1
point]
a.
(m-8)²
m-4
n²-12m+32
2m
X
2m²-16m
m²-8m+161
Answers
The solutions to the expressions are (m-8)² = m² - 16m + 64 and 2m²-16m + m²-8m+161 = 3m²- 24m + 161
Solving the expressionsFrom the question, we have the following parameters that can be used in our computation:
(m-8)²
Expand
So, we have
m² - 16m + 64
Next, we have
2m²-16m + m²-8m+161
Evaluate the like terms
3m²- 24m + 161
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(Scatterplots/Line of Best Fit) Jason designed an electronic system for a class
project. He recorded the temperature of the system over several minutes of
usage, shown in the table below. If the temperature is approximately 48 degrees,
how many minutes of usage did he record?
Answers
The most likely number of minutes of usage recorded by Jason is A . approximately 50.
How to find the minutes of usage ?We can see that initially, the temperature of the electronic system began to increase as the time increased. It then began to decrease from the 20 minute and ketp decreasing till the 40th minute.
Assuming that the temperature keeps decreasing, it would mean that at 50 minutes, the temperature would be more than the temperature at 40 minutes and so would most likely be 48 degrees.
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Calculate the area of the square
Answers
The area of the given rectangle is 83.6cm²
How to find the area of the shape?We know that the area of a rectangle is equal to the product between the dimensions, here we can see that:
b = 11cm
h = 7.6cm
The formula for the area is:
A = b*h
Replacing the values we will get:
A = 11cm*7.6cm = 83.6cm²
that is the area.
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Answer appreciated! :D
Answers
Answer:
5/2
Step-by-step explanation:
Slope is rise over run, or how far it goes in the y direction over how far it goes in the x direction. In this case, y increases by a value of 5 at the same time x is increasing by a value of 2. This makes the slope 5/2, and it is positive since the values are increasing. If there is a problem your stuck on like this try graphing the points, desmos has a good graphing calculator :)