Answer:
[tex]\Huge \boxed{\mathrm{61.22 \ m}}[/tex]
Step-by-step explanation:
A stone is thrown downward straightly with the velocity of 20 m/s and it reaches the ground at the velocity of 40 m/s. What will be the height of building? (Question)
The initial velocity ⇒ 20 m/s
The final velocity ⇒ 40 m/s
We can apply a formula to solve for the height of the building.
[tex](V_f)2 - (V_i)^2 =2gh[/tex]
[tex]V_f = \sf final \ velocity \ (m/s)[/tex]
[tex]V_i = \sf initial \ velocity \ (m /s)[/tex]
[tex]g = \sf acceleration \ due \ to \ gravity \ (m/s^2 )[/tex]
[tex]h = \sf height \ (m)[/tex]
Plugging in the values.
Acceleration due to gravity is 9.8 m/s².
[tex](40)^2 - (20)^2 =2(9.8)h[/tex]
Solve for [tex]h[/tex].
[tex]1600 - 400 =19.6h[/tex]
[tex]1200 =19.6h[/tex]
[tex]\displaystyle h=\frac{1200}{19.6}[/tex]
[tex]h= 61.22449[/tex]
The height of the building is 61.22 meters.
Two angles form a
linear pair. The
measure of one
angle is three times
the measure of the
other. Find the
measure of each
Answer:
45° and 135°
Step-by-step explanation:
A linear pair of angles sum to 180°
let one angle be x , then the other is 3x ( 3 times the other ), thus
x + 3x = 180
4x = 180 ( divide both sides by 4 )
x = 45
Thus the 2 angles are
x = 45° and 3x = 3 × 45° = 135°
The measure of two angles are 135 and 45 degrees if the two angles form a linear pair. The measure of one angle is three times the measure of the other.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
It is given that:
Two angles form a linear pair. The measure of one angle is three times the measure of the other.
As we know,
If two angles form a linear pair it means the angle made by the pair is 180 degrees
Let the two angles are x and y
x + y = 180
x = 3y (one angle is three times the measure of the other)
Solving the two linear equations in two variable:
3y + y = 180
4y = 180
y = 180/4
y = 45 degrees
x = 3(45) = 135 degrees
Thus, the measure of two angles are 135 and 45 degrees if the two angles form a linear pair. The measure of one angle is three times the measure of the other.
Learn more about the angle here:
brainly.com/question/7116550
#SPJ2
Z varies directly as x/y² and y varies inversely as x,if z=⅓ when x =2 and y=¼. Express (a). Y interms of x and (b). Z interms of x
Answer:
Baba
Step-by-step explanation:
Booey
A zucchini plant in Darnell’s garden was 10 centimeters tall when it was first planted. Since then, it has grown approximately 0.5 centimeter per day. a. Write a rule to describe the function. b. After how many days will the zucchini plant be 18.5 centimeters tall?
Answer:The number of days it will grow to be 18.5 cm tall is 17 days.
Step-by-step explanation:
To find how many days it will grow until it reaches 18.5 centimeters, first find the difference of the new height by the old height.
So= 18.5-10= 8.5cm
8.5 is the centimeters it needs to grow to be 18.5 cm tall.
Then, divide it by the number of centimeters it will grow in one day, which is 0.5, to find the days it grew 8.5 cm.
So= 8.5÷0.5= 17
I hope this helps! Ask me if you're confused.
the length and breadth of a hall is two times its breadth and the breadth is two times its height if the cost of papering its wall at rs 25 per sq metre is rs 10800 find the cost of paving marbles on its floor at rs 250 per sq metre
any help pleaseeeee
Answer:
Rs 11250
Step By Step Explanation:
Because by increasing rs 225 in sq .m . You have to increase 225*2=450 in amount
10800+450 = 11250
Answer From Gauth Math
Answer:
mathematics photography
What is the value of the expression below when w = 6 and x = 2?
9w + 9x
a=v^2/r Solve the formula for r
Answer:
[tex]\Large \boxed{r =\frac{v^2 }{a}}[/tex]
Step-by-step explanation:
[tex]\displaystyle a=\frac{v^2 }{r}[/tex]
We need to rearrange and solve the formula for [tex]r[/tex].
Multiply both sides of the equation by [tex]r[/tex].
[tex]\displaystyle a \times r=\frac{v^2 }{r} \times r[/tex]
Simplify the equation.
[tex]ar=v^2[/tex]
Divide both sides of the equation by [tex]a[/tex].
[tex]\displaystyle \frac{ar}{a} =\frac{v^2 }{a}[/tex]
Simplify the equation.
[tex]\displaystyle r =\frac{v^2 }{a}[/tex]
Find the perimeter of rectangle whose length is 40 and the diagonal is 41 cm
Answer:
P = 98 cmStep-by-step explanation:
Given one side and diagonal of rectangle we can use Pythagorean theorem to calculate the other side of it.
[tex]L=40\, cm\\D=41\,cm\\W=\ ?\\\\W^2+L^2=D^2\\\\W^2+40^2=41^2\\\\W^2+1600=1681\\\\W^2=81\\\\W=9[/tex]
Perimeter:
P = 2W + 2L = 2•40 + 2•9 = 80 + 18 = 98
A study of parents of kindergarteners included 349 parents who were chosen at
random. Of these parents, 47% said they sent their children to pre-kindergarten. School
records show that only 31% of parents of kindergarteners sent their children to pre-
kindergarten. Identify the statistic and the parameter.
Three hundred forty-nine is the parameter and 47% is the statistic.
Three hundred forty-nine is the statistic and 47% is the parameter.
Three hundred forty-nine is the parameter and 31% is the statistic
Forty-seven percent is the parameter and 31% is the statistic
Forty-seven percent is the statistic and 31% is the parameter
Answer:
Forty-seven percent is the statistic and 31% is the parameter
Step-by-step explanation:
Various terms are used in mathematics when it comes to carrying out particular studies in statistics.
A) Parameter
A parameter when is comes to statistical studies can be defined as the term that tells us more about a group or population of people.
B) Statistic
Statistic is a measure that tells us about is a characteristic of a sample or part of a given population.
In the above question, we are told that: a study of parents of kindergarteners included 349 parents who were chosen at random. Of these parents, 47% said they sent their children to pre-kindergarten. School records show that only 31% of parents of kindergarteners sent their children to pre- kindergarten.
According to the definition of Parameter and Statistic that I explained above,
A) The Parameter is 31% . This is
because it tell us about percentage ( a sample) of parents whose children are in kindergarten that sent their children to prekindergarten first.
B) The Statistic is 47% . This is because, it tell us about the percentage of parents that sent their children to prekindergarten.
A population of size 3,624 grows at a rate of 3% per year, compounded continuously. How big will the population be in 2 years?
Answer:
Step-by-step explanation:
The continuous compound formula is
[tex]y=Pe^{rt[/tex] where P is the principle or starting value, r is the growth rate in decimal form, and t is the time in years. For us:
[tex]y=3624e^{(.03)(2)}\\y=3624e^{.06}\\y=3624(1.061836547)\\y=3848.09[/tex]
which would probably round to just 3848 people.
Please answer ASAP. The question is down below
Answer: A
Step-by-step explanation:
Notes: Dividing by a fraction means to multiply by its reciprocal.
The denominator cannot equal zero.
[tex]\dfrac{5a^3bc}{8ab^3}\div\dfrac{-ab^2}{6a^5b}\cdot \dfrac{2a^2b^3}{3b}\qquad \rightarrow a\neq 0,b\neq 0\\\\\\=\dfrac{5a^3bc}{8ab^3}\cdot\dfrac{6a^5b}{-ab^2}\cdot \dfrac{2a^2b^3}{3b}\\\\\\=\dfrac{5\cdot 6\cdot 2\quad a^3\cdot a^5\cdot a^2\quad b\cdot b\cdot b^3\quad c}{8\cdot -1 \cdot 3\quad a\cdot a\qquad b^3\cdot b^2\cdot b \quad}\\\\\\=\dfrac{-60a^{10}b^5c}{-24a^2b^6}\\\\\\=\dfrac{-5a^8c}{2b}[/tex]
A book cost Rs.950 is sold for Rs 980. find profit/loss%
Answer:
96.94%
Step-by-step explanation:
Steps to solve "what percent is 950 of 980?" If you are using a calculator, simply enter 950÷980×100 which will give you 96.94 as the answer.
Answer:
96.94%
Step-by-step explanation:
Could you help with maths please? All shown on the picture :)
Answer:
4 is tenths (a) and 5 is hundredths (b)
Step-by-step explanation:
Now, 0.45
0 indicates the ones place (it comes before the decimal)
0.45 can also be written as:
0.4+0.05
= 4/10+5/100
what can we conclude from this?
we can say that 4 is in the tenths whilst 5 is in the hundredths.
therefore, a is 4 and b is 5.
Hope this helps you! :)
How do you solve 23?
Problem 22
You have the correct answer since there are 9 non-white socks out of 15 total.
========================================================
Problem 23
Answer: A) 7/20------------------------
Explanation:
We have 10 blue marbles and 10+4+5+6 = 14+11 = 25 marbles total
This means there are 25-10 = 15 non-blue marbles.
The probability of selecting a non-blue marble is 15/25. I won't reduce this as we'll use this fraction to set up the next probability.
Because the marble is not replaced, this means we go from 15 non-blue marbles to 15-1 = 14 non-blue marbles. We also go from 25 total marbles to 25-1 = 24 total.
In short, the fraction 15/25 turns into 14/24 after subtracting 1 from each part.
--------------
Let's reduce each fraction mentioned
15/25 = (3*5)/(5*5) = 3/5
14/24 = (2*7)/(2*12) = 7/12
Then we'll multiply the two reduced fractions
(3/5)*(7/12) = (3*7)/(5*12) = 21/60
Lastly, we'll reduce that result
21/60 = (3*7)/(3*20) = 7/20
The probability of selecting two marbles that aren't blue is 7/20. This is done without replacement.
--------------
As a shortcut, we could say:
(15/25)*(14/24) = 7/20
Can anyone help idk how to do it
Answer:
Carl can type 450 words in 5 minutes at that rate.
Step-by-step explanation:
Every two minutes, carl can type 180 words. To find out how many words he can type in 1 minute, all we have to to is divide 180 by 2 to get 90wpm (words per minute)
if we multiply 90wpm by 5 Minutes, we get 450 words per minute
Ja'Von kicks a soccer ball into the air. The function f(x) = –16(x – 2)2 + 64 represents the height of the ball, in feet, as a function of time, x, in seconds. What is the maximum height the ball reaches?
Answer:
The maximum height the ball reaches is 64 feet
Step-by-step explanation:
The given function is f(x) = -16·(x - 2)² + 64
From the equation, the path described by the ball is an inverted n-shaped parabola
The maximum height is therefore, the tip of the parabola
At the maximum height, the slope = 0 because the tip is momentarily flat
Since the slope (y₂ - y₁)/(x₂ - x₁) = The derivative Δy/Δx, we find the derivative of the function and equate it to zero to find the coordinates at the maximum height
Δy/Δx = dy/dx = d(-16·(x - 2)² + 64)/dx = -32·(x - 2) = -32·x + 64
To check if it is a maximum, we have;
d²y/dx² = d(-32·x + 64)/dx = -32 which is negative, indicating that the slope is reducing and we at the maximum point of the slope
Therefore for the maximum height Δy/Δx = dy/dx = -32·x + 64 = 0
64 = 32·x
x = 64/32 = 2 seconds
We now have the x-value at the slope, the f(x) value, is therefore;
f(2) = -16·(2 - 2)² + 64 = 64 feet
Therefore, the maximum height the ball reaches is 64 feet.
Answer:
D: 6
Step-by-step explanation:
I got it right on the test Edge nuity
Stevens works at a large home appliance store . He earns a base salary of $20,000 plus commission which can be modeled by the equation y = 0.1x + 20,000. What is the meaning of the y-intercept in the equation ?
Answer:
it is b or 20,000 or it is the base salary, you can put all 3 to be safe since they are all technichaly the same.
Step-by-step explanation:
so y=mx+B is the equation right here m the slope which is rise over run or y/x=.1 and B is the y inercept and 20,000 it is the starting point on the graph. where it overlaps with the y axis, in this case 20,000 which as it says earlier is his base salary
Hi can someone help me with these 3 questions. Thanks :)
Answer:
a) 45° cause tan = sin/cos and sin 45 and cos 45 both give square root 2/2
b) 120°
c) sin = -1/2 = -30° or 330° both are same
Use the trig circle which i have included in the answer to better understand trig angles
hope that answers your question
I want to let you know that each angle has sets of coordinates the left number is cos and right is sin. Ex) sin of 30 is 1/2 and cos of 30 is square root 3/2 In case you dont fully understand dont hesitate to comment.
good luck!!
Find four rational number between 1/4 and 2/3.
Answer:
4/12, 5/12, 6/12, 7/12
Step-by-step explanation:
1/4 x 3/3 = 3/12
2/3 x 4/4 = 8/12
between 3/12 and 8/12
4/12, 5/12, 6/12, 7/12
you can simplify these if you wish
Hope that helped!!! k
What is the equation of a parabola that has a vertical axis passes through the point (-1,3) and has its vertex (3,2)
Answer:
Standard Form: y = 0.0625x²-0.375x+2.5625
Graphing Form: y = (1/16)(x-3)²+2
Step-by-step explanation:
19. the first side of a triangle measures 4in less than the second side, the third side is 3 in more than the first side, and the perimeter is 15 in. how long is the third side
please help it’s late and i already started the test and my head hurts
Answer:
the third side is 5 2/3 in.
s - 1
Step-by-step explanation:
a = side 1
b = side 2
c = side 3
a + b + c = 15
a = b - 4 => b = a + 4
c = a + 3
a + a + 4 + a + 3 = 15
3a + 7 = 15
3a = 8
a = 8/3 = 2 2/3 in
b = a + 4 = 6 2/3 in
c = a + 3 = 5 2/3 in
another one another one...........
Answer:
B
Hope it helped you out
Tysm
An emu that measures 45 inches in height is 60 inches less than 5 times the height of a kakapo.
What is the height of a kakapo in inches?
The kakapo is inches tall.
Pls help me
Answer:
21 inches tall
Step-by-step explanation:
Let x represent the height of the kakapo.
Create an equation to represent this situation, and solve for x:
45 = 5x - 60
105 = 5x
21 = x
So, the kakapo is 21 inches tall.
What is the values of x and y
Answer:
If you have given an equation, you see the x and y in it. Just taking second equation and think any common factor between x's variable. With common factor, multiply both and you will find the value of y and put it in any equation, you will find the value of X.
Answer:
Hey there!
I can't see the full problem, but if when x=0.5, y=4, then when x=4, y=32, and when x=9, y=72. You multiply by a common multiple to get from x to y.
Hope this helps :)
Mildred’s salary has increased from £24,600 to £25,338. By what percentage has her salary increase?
Answer:
The answer is 3%Step-by-step explanation:
To find the percentage increase we use the formula
[tex]Percentage \: change = \frac{ change}{original \: quantity} \times 100[/tex]
To find the change subtract the smaller quantity from the bigger one
From the question
original price = $24,600
Current price = $ 25,338
Change = $25,338 - $ 24,600
Change = $ 738
So the percentage increase is
[tex] \frac{738}{24600} \times 100[/tex]
[tex] = \frac{3}{100} \times 100[/tex]
We have the final answer as
Percentage increase = 3%Hope this helps you
The table shows the number of balls, by sport, in the gym. Select the true statements about the information in the table.
Answer:
Soccer you use the lease amount of balls and in tennis you use the most
The table below shows the number of cars Jing sold each month last year.
What is the median of the data in the table.
13
16
19
20.5
23.5
Other:
Answer:
The median of the data in the table is 19.
Step-by-step explanation:
We are given the following data that shows the number of cars Jing sold each month last year below;
Number of cars Jing sold: 13, 16, 19, 20.5, 23.5
For calculating the median, firstly we have to observe that the number of observations (n) in our data is even or odd because;
If n is odd, then the formula for calculating median is given by;Median = [tex](\frac{n+1}{2} )^{th} \text{ obs.}[/tex]
If n is even, then the formula for calculating median is given by;Median = [tex]\frac{(\frac{n}{2} )^{th} \text{ obs.} + (\frac{n}{2}+1 )^{th} \text{ obs.} }{2}[/tex]
Here, the number of observations in our data is odd, i.e. n = 5.
So, Median = [tex](\frac{n+1}{2} )^{th} \text{ obs.}[/tex]
= [tex](\frac{5+1}{2} )^{th} \text{ obs.}[/tex]
= [tex](\frac{6}{2} )^{th} \text{ obs.}[/tex]
= 3rd obs. = 19
Hence, the median of the data in the table is 19.
Simplify 4^2+6(.5)-2^
Please show step by step :)
———————
Simplify 10- (15/5+4)
Please show step by step :)
Answer:
4^2 + 6(5)-2^3
16+30-8
38
Solve for b. -11b+7 = 40 b=
Answer:
B= -3
Step-by-step explanation:
Move the terms that do not contain b to the right then solve. Hope this helps!
Answer:
[tex]\large \boxed{{b=-3}}[/tex]
Step-by-step explanation:
[tex]-11b +7=40[/tex]
Subtract 7 from both sides.
[tex]-11b +7-7=40-7[/tex]
[tex]-11b=33[/tex]
Divide both sides by -11.
[tex]\displaystyle \frac{-11b}{-11} =\frac{33}{-11}[/tex]
[tex]b=-3[/tex]
How many solutions exist for the given equation?
3(x-2)=22-x
O zero
Oone
Otwo
Oinfinitely many
Answer:
one solution
Step-by-step explanation:
3(x-2)=22-x
Distribute
3x -6 = 22-x
Add x to each side
3x-6+x = 22-x+x
4x-6 =22
Add 6 to each side
4x-6+6 = 22+6
4x = 28
Divide by 4
4x/4 = 28/4
x = 7
There is one solution
Answer:
It has only one solution
Step-by-step explanation:
[tex]3(x - 2) = 22 - x [/tex]
open the brackets:
[tex]3x - 6 = 22 - x[/tex]
collect like terms together:
[tex]3x + x = 22 + 6[/tex]
then solve:
[tex]4x = 28 \\ x = \frac{28}{4} \\ \\ x = 7[/tex]
A pendulum's height is modeled by the function h(t) = 4 cos(pi/4*t) + 8 where h is the
measure of the pendulum's height in feet and t is the number of seconds since the
maximum height. How many seconds does it take the pendulum to complete one
full swing?
===========================================================
Explanation:
The general cosine template is
y = A*cos(B(t - C)) + D
where in this case
A = 4B = pi/4C = 0D = 8We only really need to worry about the B value. To get the period T, we do the following
T = 2pi/B
T = (2pi)/(pi/4)
T = 2pi * (4/pi)
T = 8
Note how the pi terms canceled. The period is 8 seconds, which is the length of one full cycle. This is the time it takes for the pendulum to do one full swing (eg: start at the right, swing to the left all the way, then swing back to the right again).
The result of 8 we got has nothing to do with the D = 8 value (this D value could be any other number and T = 8 would still be the case as long as B doesn't change of course).