A baseball diamond is a square with sides 90 ft long. A batter is at bat, with runners at first and second base. At the moment the ball is hit, the runner at first base runs to second base at 25 ft/s. Simultaneously, the runner on second base runs to third base at 15 ft/s. How fast is the distance between these two runners changing 2 s after the ball is hit?
Answers
Answer:
It is changing at -11 ft
Step-by-step explanation:
The distance d is given by
d = √x²+(90-y)²
We have to differentiate
dy/st = 25ft
dx/dt = -15ft
The question says after 2 seconds
Y = 25x2 = 50ft
X = -15x2 = -30ft
Then we calculate rate of change of distance. From the calculations I did, I arrived at
(1/2√900+1600).[900-2000]
= -1100/2x50
= -1100/100
= -11ft
Please check attachment to help you understand the answer better as it is more detailed.
The distance between these two runners changing 2 s after the ball is hit 11 ft
What is differentiation?The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.
A baseball diamond is a square with sides 90 ft long.
A batter is at bat, with runners at first and second base.
At the moment the ball is hit, the runner at first base runs to second base at 25 ft/s.
Simultaneously, the runner on second base runs to third base at 15 ft/s.
The distance d is given by
[tex]\rm d = \sqrt{x^{2} +(90-y)^2}[/tex]
We have to differentiate
[tex]\rm \dfrac{dy}{st} = 25 \ ft\\\\\dfrac{dx}{dt} = -15 \ ft[/tex]
The question says after 2 seconds
[tex]\rm Y = 25x ^2 = 50 \ ft\\\\X = -15x^2 = -30 \ ft[/tex]
Then we calculate the rate of change of distance will be
[tex]\rm \dfrac{1 }{2\sqrt{900 + 1600}} * (900 - 2000) = \dfrac{-1100}{2*50} = \dfrac{-1100}{100} = -11\ ft[/tex]
More about the differentiation link is given below.
https://brainly.com/question/24062595
Related Questions
Plizzz helppp I don't know how to do it helpp
Answers
Answer:
Lol I'll help you. So for the 1st problem, you need to subtract 7x from 4x but if your looking for and answer then x=2. For the 2nd problem subtract 3x-5x and 7 + 9 which brings you to -2x - 16 which means you would have to find x in this problem which means x has to be a negative. The negative answer is x= -32 since a negative x a negative is a positive. Which brings you to 16-16 and then 0. For the third one, you need to change the problem. Turn it into 5x - x = 4 + 8 which brings you to 4x = 12 making x =3. and for number 4 you need do the same as we just did and do 11x - 6x - 3x and then do 20 - 6 which brings you to 2x = 14 which makes x=7.
Step-by-step explanation:
Suppose that IQ scores have a bell-shaped distribution with a mean of
96 and a standard deviation of
17. Using the empirical rule, what percentage of IQ scores are between
79 and
113?
Ta
Answer
How to enter your answer
%
Answers
Answer:
68 %
Step-by-step explanation:
The Empirical rule formula states that:
• 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.
• 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.
• 99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.
Mean of 96 and a Standard deviation of 17
Applying , the first empirical rule for 1 standard deviation from the mean, we have:
μ - σ
96 - 17
= 79
μ + σ
96 + 17
= 113
Therefore, the percentage of IQ scores that are between 79 and 113 is 68%
Please help if you know how to do this, thanks
Answers
9514 1404 393
Answer:
4) y = -3(x+2)^2 +4; y = -3x^2-12x-8; ABC=(-3, -12, -8)
5) y = 0.5(x-1)^2-2; y = 0.5x^2-x-1.5; (h,k) = (1, -2)
6) y = -0.3(x+2)^2-6; y = -0.3x^2-1.2x-7.2; (h,k) = (-2, -6)
Step-by-step explanation:
Writing a quadratic equation through a set of points is most easily done using the regression function of a graphing calculator or spreadsheet.
4) see the first attachment
y = -3(x+2)^2 +4 . . . vertex form
y = -3x^2 -12x -8 . . . standard form (A, B, C) = (-3, -12, -8)
__
5) see the second attachment
y = 0.5(x -1)^2 -2 . . . vertex form; vertex = (1, -2)
y = 0.5x^2 -x -1.5 . . . standard form
__
6) see the third attachment
y = -0.3(x +2)^2 -6 . . . vertex form; vertex = (-2, -6)
y = -0.3x^2 -1.2x -7.2 . . . standard form
_____
Doing this without machine help requires you pick a form of the equation you want, fill in the x- and y-values for three of the given points, then solve the resulting equations for the unknown parameters. Usually, we use the form ...
y = ax^2 +bx +c
which will result in three linear equations for a, b, c. Those can be solved by any of the usual methods.
Find the unknown angle measure.
Answers
<A + <B + <C = 180 degrees
<A + 72 + x = 180 degrees
<A + x = 180 - 72
<A = 108 degrees.
x = 180 - 108
x = 72
Mr. Thompson sold 4 vacuum cleaners in the first month. In the second month, he sold 3 times as many vacuum cleaners as the first month. In the third
month, he sold 5 times as many vacuum cleaners as the first month.
a. How many vacuum cleaners did Mr. Thompson sell in the three months?
bers
Mr. Thompson sold ____
vacuum cleaners in the three months.
b. He sold the vacuum cleaners for $435 each. How much money did Mr. Thompson earn? (Be sure to put a comma in your answer.)
bers
Mr. Thompson earned $ ________
Answers
A salesperson gets a commission of $1600 for the first $10,000 of sales, and then $800 for each additional $10,000 or partial of sales, let s(x) represent the commission on x dollars of sales. Find the value of A(45000)
Answers
Answer:
s(55000)=400+200(45000/10000)
""=400+200(5)=400+1000=$1400 total commission
Step-by-step explanation:
HOPE THIS HELPS :)
PLZZZZ HELP IM BEING TIMED AND I DONT GET THIS PROBLEM
Answers
Answer:
C) 11/8
Step-by-step explanation:
Answer:
Its 11/8 (c)
Step-by-step explanation:
subtract first the numerators then apply the absolite value.
After that find the lcm= 8
30/8 (15/4) - 19/8
Use the number line to answer the question. Each tick represents 1 unit.
Which of the following points are neither negative nor positive? Select all that apply.
H
M
L
J
P
K
N
Please help
Answers
Answer:
M is niether Negitive or positive
Step-by-step explanation:
Because it is on the zero
mark me brainliest plz
Answer:
Answer:
M is niether Negitive or positive
Step-by-step explanation:
Because it is on the zero
Step-by-step explanation:
Determine the intercepts of the line.
Y-intercept(__ , __)
X-intercept(__,__)
Answers
Answer:
Y-intercepts: (0,6)
X-intercepts: (8,0)
Answer:
Y-intercept: (0,-6)
X-intercept: (-8,0)
Step-by-step explanation:
In order to find an intercept, you have to know the difference in the two axis. The intercept is just where the plot line hits the axis. On the top, left side, you can see that the blue line his the black x-axis at -8 over to the right but it doesn't mover down. This means the x-intercept hits at (-8,0). On the upper, right side, you can see that the blue line his the black y-axis by not moving sideways, but it does go -6 down. This means that the y-intercept would be (0,-6).
What is the answer for number 12
Answers
Use integers to represent the values in the statement. The highest elevation in a country is Mt. Snowy with an altitude of 17,311 feet. The lowest elevation in the country is Green Valley with an altitude of 237 feet below sea level.
Answers
Answer:
A)+17311 represent the value in the statement.
B)-237 represent the value in the statement.
Step-by-step explanation:
A) The highest elevation in a country is Mt. Snowy with an altitude of 17,311 feet.
Elevation is in the positive direction
So, the positive integer will represent the given situation
So, The highest elevation in a country is Mt. Snowy with an altitude of +17311
Thus +17311 represent the value in the statement.
B)The lowest elevation in the country is Green Valley with an altitude of 237 feet below sea level.
Below the sea level means negative direction
So, the negative integer will represent the given situation
So, The lowest elevation in the country is Green Valley with an altitude of - 237 feet below sea level.
Thus -237 represent the value in the statement.
Tickets for a drumline competition cost $5 at the gate and $3 in advance. One hundred more tickets were sold in advance than at the gate. The total revenue from ticket sales was $1990. How many tickets were sold in advance?
Answers
Answer:
The number of tickets sold at the gate is [tex] G = 211.25[/tex]
The number of tickets sold in advance is [tex] A = 311.25 [/tex]
Step-by-step explanation:
From the question we are told that
The cost of a tickets at the gate is [tex]a = \$ 5[/tex]
The cost of a ticket in advance is [tex]b = \$ 3[/tex]
Let the number of ticket sold in the gate be G
Let the number of ticket sold in advance be A
From the question we are told that
One hundred more tickets were sold in advance than at the gate and this can be mathematically represented as
[tex]G + 100 = A[/tex]
From the question we are told that
The total revenue from ticket sales was $1990 and this can be mathematically represented as
[tex]5 G + 3A = 1990[/tex]
substituting for A in the equation above
[tex]5 G + 3[G + 100]= 1990[/tex]
[tex]5 G + 3G + 300= 1990[/tex]
[tex] 8G + 300= 1990[/tex]
[tex] 8G = 1690[/tex]
=> [tex] G = 211.25[/tex]
Substituting this for G in the above equation
[tex]5 [211.25] + 3A = 1990[/tex]
=> [tex] 3A = 1990 - 1056.25[/tex]
=> [tex] A = 311.25 [/tex]
The population of a small country is 2.279 million and its national debt is $6.03 billion. What is the amount of debt per person? Round to the nearest whole number.
Answers
Answer:
$2,646 per person
Step-by-step explanation:
In this scenario, we are given the ratio of debt:population size of roughly 6.03billion (numerator) for every 2.279million people (denominator). Therefore in order to find the amount of debt per person we simply divide the debt by the population in order to reduce the population to 1 and see how much debt every individual would have. Like so...
6,030,000,000 dollars / 2,279,000 people = x
2,645.89 dollars / 1 person = x
Rounding this value up to the nearest dollar would mean that every individual has an estimated debt of 2,646 dollars.
–h2 – 4h + 5 = 0 solve quadratic equation
Answers
Answer:
[tex]x=-5, 1[/tex]
General Formulas and Concepts:
Order of Operations: BPEMDAS
Standard Form: ax² + bx + c = 0
Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
Step-by-step explanation:
Step 1: Define
-h² - 4h + 5 = 0
a = -1
b = -4
c = 5
Step 2: Solve for x
Substitute: [tex]x=\frac{-(-4)\pm\sqrt{(-4)^2-4(-1)(5)} }{2(-1)}[/tex]Simplify: [tex]x=\frac{4\pm\sqrt{(-4)^2-4(-1)(5)} }{2(-1)}[/tex]Exponents: [tex]x=\frac{4\pm\sqrt{16-4(-1)(5)} }{2(-1)}[/tex]Multiply: [tex]x=\frac{4\pm\sqrt{16+20} }{-2}[/tex]Add: [tex]x=\frac{4\pm\sqrt{36} }{-2}[/tex]Evaluate: [tex]x=\frac{4\pm6 }{-2}[/tex]Evaluate: [tex]x=-5, 1[/tex]there are 5,280 feet in 1 mile. if Riley ran 26,400 feet how many miles did she run
Answers
Pls hurry
Use the Order of Operations to simplify the problems below. Number your answers with the same number as the problem.
1) −23+(−2)3
2) 4−2(3)+8
3) 3(4)2+7(2)
Answers
Answer:
1) -23+(-2)3
-23-2×3
-23-6
-29
2)4-2(3)+8
4-2×3+8
4-6+8
-2+8
6
3) 3(4)2+7(2)
3×4×2+7×2
24+14
38
Using the equation y=(1/2)x, when x=0 what is the value y ?
Answers
Answer:
.
Step-by-step explanation:
The price of a technology stock was $9.71 yesterday today the price rose to $9.84 find the percentage increase round your answer to the nearest 10th of a percent
Answers
Answer:
1.34%
Step-by-step explanation:
In order to find the percentage increase between these two prices, we must first find the difference in price. We calculate this by subtracting the final price by the initial price like so...
$9.84 - 9.71 = 0.13
Now we divide the difference by the initial price to find what percentage of the initial price this difference is, since this percentage difference was added to the initial price to get the new and final price point.
0.13 / 9.71 = 0.013388 ... multiply by 100 to get percent value
0.013388 * 100 = 1.3388% or 1.34% rounded.
Each step in a procedure to solve this equation is shown.
Equation: 5x−7=3(x+1)
Step 1: 5x−7=3x+3
Step 2: 2x−7=3
Step 3: 2x=−4
Step 4: x=−2
In which step is the first error made?
a. from the original equation to step 1
b. from step 1 to step 2
c. from step 2 to step 3
d. from step 3 to step 4
Answers
Answer:
from step 3 to step 4
Step-by-step explanation:
because 2x-7=3 is equal to 2x=3+7=10
not 2x=-4 so 3 is false so even four is incorrect
The surface area of a cube may be found using the formula A=6s2.
What is the edge length of a cube with a surface area of 81 cm2?
Round your answer to the nearest tenth.
Answers
81=6s2
S2= 81/6
S= 3.67cm
3 5 of students at a school are boys. If there are 2610 students at the school, how many are girls?
Answers
Answer:
1044 girls in the school
Step-by-step explanation:
3/5*2610=1566 boys
2610-1566-1044 girls
it should be 1044 because
3/5=.6 or 60%boys and 40% girls
2610 * 60% or .6 = 1566 boys
2610 - 1566boys = 1044 girls
or
2610 * 40% or .4 = 1044 girls
so there are 1044 girls at the school
Help me with this question quick PLZz
Answers
Answer:7 to 3
Step-by-step explanation:
Answer:
3:10
Step-by-step explanation:
3 Parrots
Total Number of Birds: 3+7=10
The sum of two squares of two consecutive numbers is 145. What are those two numbers?
Answers
Answer:
8 and 9
Step-by-step explanation:
Answer:
Think!
72 + 82 = 49 + 64 = 113
82 + 92 = 64 + 81 = 145
Step-by-step explanation:
Found the answer by simple experimentation.
hope this helps
12x^4 divided by 3x^2
Answers
Answer:
12x^4 divided by 3x^2 is 4x^2
Step-by-step explanation:
So what you basically do is 12 divided by 3 which is 4.
When you divide exponents, its basically subtracting the exponent while leaving the coefficient of x or whatever the same.
When you multiply exponents, you are literally adding the exponent while leaving the coefficient alone.
When you add exponents, you gotta have the same exponent and you can't add something like x^3 + x^7 because they don't have the same unit of the exponent, but you can only do that with multiplication or division.
So, since you are dividing, you "subtract" the exponent of x^4 by x^2 so you get x^2 since 4-2 equals 2.
I hope this is at a point where you can understand!
Hope this helps!
Answer:
4x^2 beep beep
Suppose that $4500 is placed in an account that pays 19% interest compounded each year.
Assume that no withdrawals are made from the account.
(a) Find the amount in the account at the end of 1 year.
(b) Find the amount in the account at the end of 2 years.
Answers
Answer:
a) 5355
b) 6372.45
Step-by-step explanation:
4500 * 1.19 = 5355
5355 * 1.19 = 6372.45
he cost of manufacturing a particular videotape is C(x)90009x, where x is the number of tapes produced. The average cost per tape, denoted by , is found by dividing by x. Find .
Answers
Answer:
The average cost per tape is 10.
Step-by-step explanation:
The cost of manufacturing a particular videotape is :
C(x) = 9000+9x
Where
x is the number of tapes produced.
We need to find the value of average per tape i.e. [tex]\lim_{x \to 9000} \bar C(x)[/tex]
[tex]\bar C(x)=\dfrac{9000+9x}{x}\\\\=\dfrac{9000}{x}+9\\\\ \lim_{n \to 9000} \bar C(x)=\dfrac{9000}{9000}+9\\\\=1+9\\\\=10[/tex]
So, the average cost per tape is 10.
The probability that an employee at a company uses illegal drugs is 0.08. The probability that an employee is male is 0.62. Assuming that these events are independent, what is the probability that a randomly chosen employee is a male drug user?
Answers
Answer: 0.0496
Step-by-step explanation:
If events are said to be independent it means that the probability of one happening does not affect the probability of the other.
In calculating the probability that an employee is both male and a drug user using independent events, multiply the probabilities of the individual events to find the probability of the the events happening together.
P(A) * P(B) = P(A and B)
0.08 * 0.62 = 0.0496
Probabilities are used to determine the chances of events.
The probability that a randomly chosen employee is a male drug user is 0.0496
Represent the two events as A and B, such that:
[tex]P(A) = 0.08[/tex]
[tex]P(B) =0.62[/tex]
So, the probability that a randomly chosen employee is a male drug user is calculated as:
[tex]P(A\ and\ B) =P(A) \times P(B)[/tex]
This gives
[tex]P(A\ and\ B) =0.08 \times 0.62[/tex]
Multiply
[tex]P(A\ and\ B) =0.0496[/tex]
Hence, the probability that a randomly chosen employee is a male drug user is 0.0496
Read more about probabilities at:
https://brainly.com/question/20227629
the measure of an angle is 79.7 what is the measure of its complementary angle
Answers
Answer:
10.3
Step-by-step explanation:
Answer:
10.3°
Step-by-step explanation:
complementary angles are angles that sum up to 90°.
Therefore the complement of 79.7
= 90-79.7
=10.3°
karen is an accountant. she finds she spends two fifths of her work day answering emails. if she spent 3.6 hours answering e mails, how many hours was her work day?
Answers
HELP ASAP IT'S AN EMERGENCY