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
Read more about projectile at: https://brainly.com/question/31525894
#SPJ1
can someone help me with this question?
Find area of a circle whose diameter 21cm
The area of the circle is approximately 346.36 square centimeters.
What is area?Area is a mathematical concept that refers to the amount of space that is inside a two-dimensional shape or surface. It is typically measured in square units, such as square meters (m² or square centimeters (cm²).
What is a diameter?The diameter of a circle is the distance across the circle passing through its center. It is twice the length of the circle's radius.If you know the diameter of a circle, you can calculate its radius by dividing the diameter by 2: radius = diameter/2
In the given question,
The diameter (d) of a circle is the distance across the circle passing through the center.
If the diameter of the circle is 21 cm, then the radius (r) of the circle (which is half of the diameter) is:
r = d/2 = 21/2 = 10.5 cm
The formula for the area (A) of a circle is:
A = πr²
where π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter, approximately equal to 3.14159.
Substituting the value of r into the formula, we get:
A = π(10.5)² A = 346.36 cm² (rounded to two decimal places)
Therefore, the area of the circle is approximately 346.36 square centimeters.
To know more about area of circle, visit:
https://brainly.com/question/28642423
#SPJ1
Write v as the sum of two vector components if v = -5i+6j and w = 3i+4j
Vector v can be written as the sum of two vector components, \(v_x = -5i\) and \(v_y = 6j\)
To write vector v as the sum of two vector components, we need to decompose it into two vectors along different directions.
v = -5i + 6j
w = 3i + 4j
We can decompose vector v into two components, one along the x-axis and the other along the y-axis.
Let's denote the component along the x-axis as \(v_x\) and the component along the y-axis as \(v_y.\)
The x-component, \(v_x,\) represents the projection of vector v onto the x-axis and can be found using the dot product of v and the unit vector i:
\(v_x = v . i = (-5i + 6j) . i = -5i . i + 6j . i = -5\)
Similarly, the y-component, \(v_y,\) represents the projection of vector v onto the y-axis and can be found using the dot product of v and the unit vector j:
\(v_y = v . j = (-5i + 6j) . j = -5i . j + 6j . j = 6\)
Now, we can write vector v as the sum of its components:
\(v = v_x + v_y = -5i + 6j\)
So, vector v can be written as the sum of two vector components: -5i along the x-axis and 6j along the y-axis.
For similar question on components.
https://brainly.com/question/28351472
#SPJ11
find x.
8
2radius3
8
8radius3
(hurry plz, will give brainliest) -15pts-
Answer:
Answere is X= 8
Step-by-step explanation:
Use sine law
Sin(angle) = Opposite/ Hypotenuse
Sin (30) = 4 /X
X = 4 / sin (30)
X = 8
Write the number in Scientific notation form.
0.0755
Answer:
The scientific notation will be 7.55 x 10^-2
Step-by-step explanation:
You need to make the number at least 1 but below 10 so you would move the decimal over 2 places to the right
Hope this helps :)
Answer:
7.55 x 10⁻²
Step-by-step explanation:
0.0755
As we move the decimal two spaces to the right it will be a negative integer.
7.55 x 10⁻²
Look at attached image.
Goldie Gold Jewelry uses direct labor hours to apply overhead and estimated total overhead costs at $52,500 and direct labor hours at 12,500 for the second quarter. The direct labor quantity standard is 1.75 direct labor hours per unit, and the company produced 5,250 units in the second month of the second quarter. This required 2,625 direct labor hours. What was the overhead rate for the second quarter?
In the case above, the value of the overhead rate for the second quarter is $17,640.
What is the overhead rate about?Note that:
In the case above, for one to be able to calculate the predetermined overhead rate, a person need to divide the value of the estimated overhead costs which is $52,500 by that of the estimated direct labor hours .
Predetermined overhead rate=Estimated overhead costs/ estimated direct labor hours
Predetermined overhead rate=$52,500/ 12,500
Predetermined overhead rate=$4.20/DLH overhead rate
Hence: $52,500/ 12,500 = $4.20/DLH overhead rate.
Since the Overhead that was applied at standard hours was said to be allowed, then:
= $4.2 x 2,400 x 1.75
= $17,640.
Therefore, In the case above, the value of the overhead rate for the second quarter is $17,640.
Learn more about overhead rate from
https://brainly.com/question/16256360
#SPJ1
water and food are products of?
Which of the following explains the relationship between angles A and D
Answer:
I believe they are vertical angles
Step-by-step explanation:
Vertical angles are angles that are across from each other. They are also equal to each other.
For each pair of functions f, g below, find f(g(x)) and g(f(x))
Then, determine whether and are inverses of each other.
Simplify your answers as much as possible.
(Assume that your expressions are defined for all in the domain of the composition.
You do not have to indicate the domain.)
Answer:
See below
Step-by-step explanation:
Part A
\(f(g(x))=f(\frac{x}{3})=3(\frac{x}{3})=x\\g(f(x))=g(3x)=\frac{3x}{3}=x\)
Since BOTH \(f(g(x))=x\) and \(g(f(x))=x\), then \(f\) and \(g\) are inverses of each other
Part B
\(f(g(x))=f(\frac{x+1}{2})=2(\frac{x+1}{2})+1=x+1+1=x+2\\g(f(x))=g(2x+1)=\frac{(2x+1)+1}{2}=\frac{2x+2}{2}=x+1\)
Since BOTH \(f(g(x))\neq x\) and \(g(f(x))\neq x\), then \(f\) and \(g\) are NOT inverses of each other
x-4=2(y-3) in slope intercept form?
Answer:
y = x/2 + 1
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Step 1: Write equation
x - 4 = 2(y - 3)
Step 2: Solve for slope-intercept form
Distribute 2: x - 4 = 2y - 6Add 6 to both sides: x + 2 = 2yDivide both sides by 2: x/2 + 1 = yRewrite: y = x/2 + 1Find two numbers that multiply to be -12 and add up to be -1.
Answer:
(-4)(3) = -12
(-4+3) = -1
Hope this helps :) Please mark as brianliest!!
Hii please answer i would appreciate it thankssss
Answer:
Just some background:
Congruent means that a triangle has the same angle measures and side lengths of another triangle.
SAS congruence theorem: If two sides and the angle between these two sides are congruent to the corresponding sides and angle of another triangle, then the two triangles are congruent. Congruent triangles: When two triangles have the same shape and size, they are congruent.
Let's look at A first.
The triangle on left, we know 40 and 30 degree angles. So 3 all angles together = 180, so the 3rd angle = 180-30-40 = 110.
Now look at the triangle on the right. The angle shown is 110! This angle is between the sides marked with || and ||| marks, indicating that those two sides are the same length between both triangles.
Therefore both triangles are the same by Side-Angle-Side or SAS.
Now look at B.
It's a right triangle. We are missing 1 side of each triangle.
Let's solve for the missing "leg" of the triangle on the right. The pythagorean theorem says that a^2 + b^2 = c^2 where a and b are the 'legs' or sides of the triangle and c is the hypotenuse (always the longest length opposite the right angle).
so 2^2 + b^2 = 4^2
4 + b^2 = 16
b^2 = 16-4
b^2 = 12
That missing side is the \(\sqrt{12}\).
This does NOT match the triangle on the left.
Theses two triangles are NOT congruent.
What questions do you still have about what we’ve learned
Amanda created a table to help her represent the sample space of spinning a spinner and flipping a coin.
What is the probability that the result of the spin is blue and the coin lands heads up?
Group of answer choices
1/8
4/8
2/8
3/8
Find the equation of a line that passes through the points (-2, -1) and (0, -5)
Answer:
Step-by-step explanation:
slope = (-5-(-1))/(0-(-2)) = (-4)/2 = -2
y+5 = -2(x-0)
y = -2x - 5
Answer:
-2x - 5
Step-by-step explanation:
Simplify the following expression:
√-36+√-100+ 7
O A. 7+ 16i
OB. 7+√136i
O C. 16
C. 16 - 7i
O D. 23 + 0i
Translate this phrase into an algebraic expression.
72 decreased by twice a number
Use the variable n to represent the unknown number.
Hey there!
The answer is 72 - 2n.
"twice a number" represents a number multiplied by 2. So we have "2n"
"decreased by twice a number" would mean subtracting twice a number, or subtracting "2n".
"72 decreased by" means that we are subtracting the number FROM 72, so we get "72 - 2n".
Have a super awesome day! :)
Two rooms in a house need to be painted. Each room can be painted either white or yellow
Answer:
I recommend white, If you do a yellow do a light base yellow like Cornsilk, Creamy Corn, or Pale Peach!
Step-by-step explanation:
A recipe requires 1/4 of a cup of cranberries for 1 batch of scones how many batches of scones can be made using 6 1/2
Answer:
26
Step-by-step explanation:
6 times 4 =24 then 4/1 times 1/2 = 4/2 equals 2 and then you add 2 to 24 and that is 26.
Answer:
26
Step-by-step explanation:
If 1/4 of a cup of cranberries and make 1 batch, and there are four 1/4 cups in a whole cup, then 1 cup of cranberries can make 4 batches of scones.
By that same logic, there are two 1/4 cups in 1/2 a cup, so 1/2 cup of cranberries can make 2 batches of scones.
So, with the knowledge that 1 cup of cranberries makes 4 batches of scones, 6 cups of cranberries can make 6 x 4 = 24 batches, and adding on 1/2 cup gives us 2 more batches for a total of 24 + 2 = 26 batches.
What is 30x2? Id love to know
The planet Uranus has a radius of 25,362 km, and planet Mars has a radius of 3,390 km. How many times bigger is the volume of Uranus than Mars? Assume that both planets are spheres.
Round your answer to one decimal place.
Answer:
ranus is a large planet with a volume of 6.833 x 1013 cubic kilometers. You could fit a little more than 63 Earths inside of Uranus, but like the other gas giants, it is not very dense. Comprised mostly of gas, the planet is only about 14.5 times more massive than Earth is.
Step-by-step explanation:
^
-2, -4, -8,-16, ... Find the explicit formula
Answer:
it is multiplying by 2 every time. so it would be x(2)
x would be the numbers like -2....etc
hope this is what you were asking!!
its times 2 each time so -2×2=-4 and so on and so on
There are 200 kids in the 7th grade at smith middle school. If 25% of them purchase a school t-shirt that costs $20, how much money did the 7th grade spend on t-shirts?
Answer:
$1,000.
Step-by-step explanation:
200 kids divided by 25% or 4 = 50 then 50 x 20 = 1,000.
how can you make the number 2 using the digits 1984 and using any equation?
Answer:
See below, there might be more than one answer
Step-by-step explanation:
4-(9-8)-1=2
What is the circumference of this circle? Use π ≈ 3.14. Round your answer to the nearest tenth of a centimeter.
the diameter is 13
The circumference of the given circle is 41 cm
What is a circle?A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.
The circumference of a circle is the boundary length of the circle, it is basically the perimeter of the circle, in degree measure it can not exceed by 360°
Given that, a circle, with diameter, 13 cm, we need to find it circumference.
We know that, the circumference of a circle is given by,
Circumference of the circle = π × diameter
= 3.14 × 13
= 40.82
≈ 41 cm
Hence, the circumference of the given circle is 41 cm
Learn more about circles, click;
https://brainly.com/question/29142813
#SPJ9
Mrs. Okafor had $475 in her savings account. Each year, the value of the savings account increases
by 4%. How much money does she have in her account after 1 year?
Write an equation to represent the problem. Use b to represent the amount Mrs.
Okafor has in her account after 1 year.
Answer:
$475 + 4% (19 percent) = $494 a year.
Step-by-step explanation:
Question 2 (15 points )
Determine the scale factor from circle A to circle B.
O
Scale factor =
B
30
Thus, the scale factor from circle A to circle B is found to be 2.
Explain about the scale factor:The ratio between comparable measurements of just an element and a portrayal of that element is known as a scale factor in mathematics. The copy will be larger if the scaling factor is a whole number. A fractional scaling factor means that the duplicate will be smaller.
You must first choose which direction we are scaling in order to determine the scale factor:
Scale Up = larger measurement / smaller measurement (smaller to larger).Smaller measurement equals greater measurement when scaling down.The radius of circle A = 2 units
The radius of circle B = 4 units.
So, there is a dilation with the scale factor of 2 units as 2*2 = 4 units.
Thus, the scale factor from circle A to circle B is found to be 2.
know more about the scale factor:
https://brainly.com/question/25722260
#SPJ1
please at least someone help me with this question .so I don't have nightmares !Class A has 11 pupils and class B has 15 pupils.
Both classes sit the same maths test.
The mean score for class A is 77.
The mean score for both classes is 49.
What is the mean score (rounded to 2 DP) in the maths test for class B?
Answer:
28.47
Step-by-step explanation:
The mean score is given by the formula (Total Score) /(Number of Students)
or
Total Score = (Mean Score) x (Number of students)
Total number of students = 11 + 15 = 26
Class A Total Score = 77 x 11 = 847
Total score for both classes = 49 x 26 = 1,274
Total Score for Class B = Total score for both classes - Class A Total Score
= 1,274 - 847 = 427
Mean Score for class B = 427/15 = 28.47
Round to the nearest 10.
18 eggs
eggs
34p
p
55 cm
cm
At the fast food restaurant, an order of fries costs $1.09 and a drink costs $1.18. How much would it cost to get 3 orders of fries and 2 drinks? How much would it cost to get ff orders of fries and d drinks?
Answer:
5.63 Happy to Help :)
Step-by-step explanation: