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?
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.
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Help me plz
8th grade math
Answer
I would say the 3rd one.
Step-by-step explanation:
I do not really remember this but I am in 8th grade math to (Algebra)
Find the remainder when
f(x) = 8x^3 + 4x^2 – 13x + 3
is divided by 2x + 5.
A. 1241/125
B. -129/2
C. 69/125
D. 183
Dividing f(x) by 2x + 5 leaves the same remainder as division by x + 5/2. By the remainder theorem, it is equal to f (-5/2), so the remainder here is
f (-5/2) = 8 (-5/2)³ + 4 (-5/2)² - 13 (-5/2) + 3 = -129/2
Samantha estimates the product of 925 x 38 as 36,000. Without computing the exact answer, is her estimate reasonable? Explain
Please help ASAP
Based only on the given information, it is guaranteed that AD = DB
Answer: True
Step-by-step explanation:
Answer:
true
Step-by-step explanation:
What are the values for a and b?
Answer:
a= 10 b= 6
Step-by-step explanation:
When multiplying exponents they should be added together and when dividing they should be subtracted from each other.
2+8=10 & 10-4= 6
You are creating bracelets and then selling them to your friends at a 85% markup rate. If it costs you $1.80 to create the bracelet, how much of a markup will you add to the bracelet?
Answer:
you will add $1.53 to every bracelet you make
Step-by-step explanation:
figure out what 85 percent of 1.80 is and then add that to 1.80 for the total price
85% x 1.8 = 1.53 (markup ammount)
1.80 + 1.53 = 3.33 (total cost)
$75 dinner; 18% tip
Explained step by step pls
Answer: $13.50
Step-by-step explanation:
Answer:
$13.5
Step-by-step explanation:
Everything you do is multiply 75 by 0.18 ( 0.18 represents 18%)
which gives you 13.5, so the tip would be $13.50
34 full. He uses 16 of a full tank’s gas per day driving to and from work.
How many days can Drew drive to work with the gas he has in the tank?
Determine the intercepts of the line.
Y-intercept(__ , __)
X-intercept(__,__)
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).
Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 9 percent, has a YTM of 7 percent, and has 13 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 7 percent, has a YTM of 9 percent, and also has 13 years to maturity. The bonds have a $1,000 par value.
What is the price of each bond today? If interest rates remain unchanged, what do you expect the price of these bonds to be one year from now? In three years? In eight years? In 12 years? In 13 years?
Answer:
Bond Xcurrent market price:
PV of face value = $1,000 / (1 + 3.5%)²⁶ = $
PV of coupon payments = $45 x 16.89035 (PV annuity factor, 3.5%, 26 periods) = $760.07
current market price = $408.84 + $760.07 = $1,168.91
price in 1 year:
PV of face value = $1,000 / (1 + 3.5%)²⁴ = $437.96
PV of coupon payments = $45 x 16.05837 (PV annuity factor, 3.5%, 24 periods) = $722.63
market price = $437.96 + $722.63 = $1,160.59
price in 3 years:
PV of face value = $1,000 / (1 + 3.5%)²⁰ = $502.57
PV of coupon payments = $45 x 14.2124 (PV annuity factor, 3.5%, 20 periods) = $639.56
market price = $502.57+ $639.56 = $1,142.13
price in 8 years:
PV of face value = $1,000 / (1 + 3.5%)¹⁰ = $708.92
PV of coupon payments = $45 x 8.31661 (PV annuity factor, 3.5%, 10 periods) = $374.25
market price = $708.92 + $374.25 = $1,083.17
price in 12 years:
PV of face value = $1,000 / (1 + 3.5%)² = $933.51
PV of coupon payments = $45 x 1.89969 (PV annuity factor, 3.5%, 2 periods) = $85.49
market price = $933.51 + $85.49 = $1,019
price in 13 years:
market price = $1,000 + $45 = $1,045
Bond Ycurrent market price:
PV of face value = $1,000 / (1 + 4.5%)²⁶ = $318.40
PV of coupon payments = $35 x 15.14661 (PV annuity factor, 4.5%, 26 periods) = $530.13
current market price = $318.40 + $530.13 = $847.53
price in 1 year:
PV of face value = $1,000 / (1 + 4.5%)²⁴ = $347.70
PV of coupon payments = $35 x 14.49548 (PV annuity factor, 4.5%, 24 periods) = $507.34
market price = $347.70 + $507.34 = $855.04
price in 3 years:
PV of face value = $1,000 / (1 + 4.5%)²⁰ = $414.64
PV of coupon payments = $35 x 13.00794 (PV annuity factor, 4.5%, 20 periods) = $455.28
market price = $414.64+ $455.28 = $869.92
price in 8 years:
PV of face value = $1,000 / (1 + 4.5%)¹⁰ = $643.93
PV of coupon payments = $35 x 7.91272 (PV annuity factor, 4.5%, 10 periods) = $276.95
market price = $643.93 + $276.95 = $920.88
price in 12 years:
PV of face value = $1,000 / (1 + 4.5%)² = $915.73
PV of coupon payments = $35 x 1.87267 (PV annuity factor, 4.5%, 2 periods) = $65.54
market price = $915.73 + $65.54 = $981.27
price in 13 years:
market price = $1,000 + $35 = $1,035
Point A is located at negative 6 over 8 and point B is located at negative 1 over 8. What is the distance between points A and B? negative 6 over 8 plus negative 1 over 8 = negative 7 over 8; therefore, the distance from A to B is absolute value of negative 7 over 8 equals negative 7 over 8 units negative 6 over 8 plus negative 1 over 8 = negative 7 over 8; therefore, the distance from A to B is absolute value of negative 7 over 8 equals 7 over 8 units negative 6 over 8 minus negative 1 over 8 = negative 5 over 8; therefore, the distance from A to B is absolute value of negative 5 over 8 equals negative 5 over 8 units negative 6 over 8 minus negative 1 over 8 = negative 5 over 8; therefore, the distance from A to B is absolute value of negative 5 over 8 equals 5 over 8 units
Given:
Point A is located at [tex]-\dfrac{6}{8}[/tex].
Point B is located at [tex]-\dfrac{1}{8}[/tex].
To find:
The distance between points A and B.
Solution:
We know that,
Distance between points A and B = Location of A - Location of B
Using this given values, we get
Distance between points A and B [tex]=-\dfrac{6}{8}-\left(-\dfrac{1}{8}\right)[/tex]
[tex]=-\dfrac{6}{8}+\dfrac{1}{8}[/tex]
[tex]=\dfrac{-6+1}{8}[/tex]
[tex]=-\dfrac{5}{8}[/tex]
Distance cannot be negative. So, we need to find the absolute value of [tex]-\dfrac{5}{8}[/tex].
[tex]|-\dfrac{5}{8}|=\dfrac{5}{8}[/tex]
The distance between A and B is [tex]\dfrac{5}{8}[/tex].
Therefore, the correct option is D.
The base area of a right circular cone is 1/4 of its total surface area. What is the ratio of the radius
to the slant height?
Given:
The base area of a right circular cone is [tex]\dfrac{1}{4}[/tex] of its total surface area.
To find:
The ratio of the radius to the slant height.
Solution:
We know that,
Area of base of a right circular cone = [tex]\pi r^2[/tex]
Total surface area of a right circular cone = [tex]\pi rl+\pi r^2[/tex]
where, r is radius and l is slant height.
According to the question,
[tex]\pi r^2=\dfrac{1}{4}(\pi rl+\pi r^2)[/tex]
Multiply both sides by.
[tex]4\pi r^2=\pi rl+\pi r^2[/tex]
[tex]4\pi r^2-\pi r^2=\pi rl[/tex]
[tex]3\pi r^2=\pi rl[/tex]
Cancel out the common factors from both sides.
[tex]3r=l[/tex]
Now, ratio of the radius to the slant height is
[tex]\dfrac{r}{l}=\dfrac{r}{3r}[/tex]
[tex]\dfrac{r}{l}=\dfrac{1}{3}[/tex]
Therefore, the ratio of the radius to the slant height is 1:3.
There are 3,785 milliliters in 1 gallon, and there are 4 quarts in 1 gallon.
How many milliliters are in 3 gallons? Explain.
there are 11356.2 milliliters in 3 us gallons
pls help:( i’ll mark brainlest!
Answer:
[tex]\sqrt{26}[/tex]
Step-by-step explanation:
Based only on the given information, it is guaranteed that Ac = bc
Answer:
True
Step-by-step explanation:
True because if AC = BC, then the triangles are the same.
The side AC is congruent to the side BC the statement is true.
What is congruency?The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one are congruent to the included angle and corresponding two sides of the other triangle.
In the given figure we can see that the ∠ACD ≅ ∠BCD and AB ⊥ CD mean that the line CD is dividing the line AB into two equal parts.
Therefore, the side AC is congruent to the side BC the statement is true.
Learn more about congruency at
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The Sweet Shoppe sells a half-dozen cupcakes for $16.50. The Cupcake Factory sells a dozen cupcakes for $30.00. Jameska purchases two cupcakes from each shop. What is the difference in the purchases?
The difference in the purchases is $
.
Answer:
$1.50
Step-by-step explanation:
The cost of half of dozen of cupcakes at Sweet Shoppe = $16.50.
The cost of a dozen cupcakes at Cupcake factory = $30.00. Therefore the cost of half a dozen cupcakes at Cupcake factory = $30.00 / 2 = $15.00
The difference in purchases = cost of half a dozen cupcakes at Sweet Shoppe - cost of half of dozen of cupcakes at cupcake factory
The difference in purchases = $16.50 - $15.00 = $1.50
This means that their is a difference of $1.50 for half a dozen cupcakes between the Sweet Shoppe and cupcake factory.
A manufacturer has designed a process to produce pipes that are 10 feet long. The distribution of the pipe length, however, is actually Uniform on the interval 10 feet to 10.57 feet. Assume that the lengths of individual pipes produced by the process are independent. Let X and Y represent the lengths of two different pipes produced by the process. h)What is the probability that the second pipe (with length Y) is more than 0.11 feet longer than the first pipe (with length X)
The probability that the second pipe (with length Y) is more than 0.11 feet longer than the first pipe (with length X) is approximately 2.6092%.
Here,
Since the length of the pipes follows a uniform distribution on the interval [10 feet, 10.57 feet], the probability density function (PDF) for each pipe is:
f(x) = 1 / (10.57 - 10) = 1 / 0.57 ≈ 1.7544 for 10 ≤ x ≤ 10.57
Since the lengths of the pipes are independent, the joint probability density function (PDF) of X and Y is the product of their individual PDFs:
f(x, y) = f(x) * f(y) = 1.7544 * 1.7544 = 3.0805 for 10 ≤ x ≤ 10.57 and 10 ≤ y ≤ 10.57
Now, we want to find the probability that the second pipe (Y) is more than 0.11 feet longer than the first pipe (X).
Mathematically, we want to find P(Y > X + 0.11).
Let's set up the integral to calculate this probability:
P(Y > X + 0.11) = ∬[10 ≤ x ≤ 10.57] [y > x + 0.11] f(x, y) dx dy
We integrate with respect to x first and then with respect to y:
P(Y > X + 0.11) = ∫[10 ≤ y ≤ 10.57] ∫[10 ≤ x ≤ y - 0.11] f(x, y) dx dy
P(Y > X + 0.11) = ∫[10 ≤ y ≤ 10.57] [∫[10 ≤ x ≤ y - 0.11] 3.0805 dx] dy
P(Y > X + 0.11) = ∫[10 ≤ y ≤ 10.57] [3.0805 * (x)] from x = 10 to x = y - 0.11 dy
P(Y > X + 0.11) = ∫[10 ≤ y ≤ 10.57] [3.0805 * (y - (10 - 0.11))] dy
P(Y > X + 0.11) = 3.0805 * ∫[10 ≤ y ≤ 10.57] (y - 9.89) dy
P(Y > X + 0.11) = 3.0805 * [(y² / 2) - 9.89y] from y = 10 to y = 10.57
P(Y > X + 0.11) = 3.0805 * [((10.57)² / 2) - 9.89 * 10.57 - (((10)² / 2) - 9.89 * 10)]
P(Y > X + 0.11) = 3.0805 * [((111.7249 / 2) - 104.9135 - (50 / 2 - 98.9)]
P(Y > X + 0.11) = 3.0805 * [(55.86245 - 104.9135 + 49.9)]
P(Y > X + 0.11) = 3.0805 * [0.84895]
P(Y > X + 0.11) ≈ 2.6092
Therefore, the probability that the second pipe (with length Y) is more than 0.11 feet longer than the first pipe (with length X) is approximately 2.6092%.
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Can you help me i wil give you a branlist and please help me
Answer:
i love free points dont you
A rectangular piece of land has an area of 3/4 square mile.The land is 2 1/2 miles long what is its width
Answer:
width = 3/10 mi
Step-by-step explanation:
area = length * width
width = area/length
width = (3/4 mi^2)/(2 1/2 mi)
width = (3/4 mi^2)/(5/2 mi)
width = 3/4 * 2/5 mi
width = 6/20 mi
width = 3/10 mi
Video games made up 77.8% of the total revenue for a small specialty store.
A) 0.0778 B) 7.78 C) 77.8
D) 0.778
Timod at home while attending classes
Answer:
D
Step-by-step explanation:
This is saying 77.8% percent out of 100, therefore we right it like D
I hope this helped, please mark Brainliest, thank you!
What is 3/100 - 1/50 equal?
Answer:
0.01?
Step-by-step explanation:
0.8 kg is more or less than 0.6 kg
Answer:
More than
Step-by-step explanation:
Answer:
More
Step-by-step explanation:
COLLE
past d
see co
A boat capsized and sank in a lake Based on an assumption of a mean weight of 131 lb, the boat was rated to carry 60 assengers (s the load lin was 7,860 lb).
After the boat sank, the assumed mean weight for similar boats was changed from 131 lb to 173 lb Complete parts a and below.
a. Assume that a similar boat is loaded with 60 passengers, and assume that the weights of people are normally distributed with a mea of 176 1 lb end a standard
deviation of 40.2 lb. Find the probability that the boat is overloaded because the 60 passengers have a mean weight greater than 131 ||
The probability is
(Round to four decimal places as needed)
b. The boat was later rated to carry only 17 passengers, and the load limit was changed to 2,941 lb. Find the probability t at the boat is erloaded bause the
mean weight of the passengers is greater than 173 (so that their total weight is greater than the maximum capacity of 29 1 lb)
The probability is
(Round to four decimal places as needed)
Do the new ratings appear to be safe when the boat is loaded with 17 passengers? Choose the correct answer below.
sees o
ents
see sc
see sco
past do
O A. Because the probability of overloading is lower with the new ratings than with the old ratings, the new ratings appes to be safe
OB. Because there is a high probability of overloading, the new ratings appear to be safe when the boat is loaded with passengers
OC. Because there is a high probability of overloading, the new ratings do not appear to be safe when the boat is loaded with 17 passe ers:
Click to select your answer(s)
past due
If sqrt 16 = x, then x2 =
Answer:
The square root of 16=4, 4x2=8, x2=8.
Step-by-step explanation:
find the value of each missing variable?
Step-by-step explanation:
9x - 2 = 5x + 54 because these angles are corresponding
9x - 5x = 54 + 2 add/subtract like terms
4x = 56 and this divided by 4
x = 14
9x - 2 + 10y + 6 = 180° because these two angles makes a straight line
9×14 - 2 + 10y + 6 = 180°
126 - 2 + 10y + 6 = 180° add like terms
130 + 10y = 180° subtract 130 from both sides
10y = 50 divide by 10
y = 10
How much smaller is x−3 than x+4?
Answer: bsf google
Step-by-step explanation: go to google look it up and find the answer
Answer:
x-3
Step-by-step explanation:
It's x-3 because if you put 12-3 it will be 9 but if you add x+4 it will be 16
help needed please answer asap
A line passes through (2, 7) and has a slope of -4. What is its equation in point-slope form?
Sorry I'm bad
Answer:
y= (-4/1)x -1
Step-by-step explanation:
Since there are no exponents in this problem, the next step is
✔ (- 2)2.2
.
Simplify the previous step and you get
.
The final answer is
Anwers:
22 is the answer