Find the slope of the tangent line to the parabola y=4x-x^2 at the point (1,3)
In model trains, O scale means the models are made using a 1:48 scale. In the U.S., real train tracks have rails that are 4 ft 8 in apart.
a. If miniature train track was made using O scale, how far apart should the rails be? Round to the nearest hundredth of an inch.
b. The word gauge refers to how far apart the model rails are. For some reason, O gauge track does not exactly use O scale, and O gauge rails are 1.25 inches apart. Find the relative difference of the rail spacing on O gauge track compared to what it should be if it followed O scale. Round to the nearest tenth of a percent.
Final answer:
The correct O scale model train track spacing should be 1.17 inches. However, the actual O gauge spacing is 1.25 inches. The relative difference in the rail spacing is approximately 6.8%.
Explanation:
To solve for the correct O scale model train track spacing:
Convert the real train track gauge to inches: 4 feet x 12 inches/foot + 8 inches = 56 inches.
Divide the real gauge by the scale factor of 48 to find the model gauge: 56 inches / 48 = 1.1667 inches.
Round the result to the nearest hundredth of an inch: 1.17 inches.
Now to calculate the relative difference between O scale and the actual O gauge:
Determine the actual O gauge spacing: 1.25 inches.
Calculate the difference in spacing: 1.25 inches - 1.17 inches = 0.08 inches.
Find the relative difference by dividing the spacing difference by the O scale spacing and then multiply by 100 to get the percentage: (0.08 inches / 1.17 inches) x 100 = 6.8%.
Round the result to the nearest tenth of a percent: 6.8%.
At Travis's Hats, 60% of the 25 hats are baseball caps. How many baseball caps are there?
The planet Mercury has a diameter of 4,878 km whereas the Moon has a radius of 1736.5 km. Which object is larger and why?
The planet Mercury is larger than the Moon, because the radius of Mercury is greater than the Moon.
Here,
Given that;
The planet Mercury has a diameter of 4,878 km.
And, The Moon has a radius of 1736.5 km.
We have to find the larger planet.
What is the relation between radius and diameter?
The radius is half or the diameter of the object.
Now,
The planet Mercury has a diameter of 4,878 km.
Hence, The radius of Mercury = 4,878/2 = 2,439 km
And, The radius of the Moon = 1736.5 km
Clearly, 2,439 > 1,736.5
So, The planet Mercury is larger than the Moon, because the radius of Mercury is greater than the Moon.
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What is the sum and classification of 3/20 + sqrt of 10
A. 3.31227766..., irrational
B. 3.31227766..., rational
C.18.16227766..., irrational
D.18.16227766..., rational
Answer:
a
Step-by-step explanation:
Answer:
A. 3.31227766..., irrational
Step-by-step explanation:
We have been given two numbers. We are asked to find sum of given numbers and classify the type of number after addition.
[tex]\frac{3}{20}+\sqrt{10}[/tex]
[tex]0.15+3.1622776601683793[/tex]
[tex]3.3122776601683793[/tex]
We can see that [tex]\frac{3}{20}[/tex] is a rational number, while [tex]\sqrt{10}[/tex] is an irrational number as its digits are repeating infinitely after decimal.
We know that sum of a rational and irrational number is irrational, therefore the sum of given numbers is irrational and option A is the correct choice.
Dale cut a wire into 7 equal pieces. The wire was originally 7.84 meters long. How long is each piece?
Find the laplace transform of f(t)={0,(t−4),0≤t<4t≥4
The Laplace transform of f(t) is [tex]\( \frac{4}{s}e^{-4s} \)[/tex].
Sure, let's find the Laplace transform of the piecewise function [tex]\( f(t) = \begin{cases} 0, & 0 \leq t < 4 \\ t - 4, & t \geq 4 \end{cases} \).[/tex]
Define the function for all ( t ):
[tex]\[ f(t) = \begin{cases} 0, & 0 \leq t < 4 \\ t - 4, & t \geq 4 \end{cases} = (t - 4)u(t-4) \][/tex]
where u(t) is the unit step function.
Use the definition of the Laplace transform:
[tex]\[ \mathcal{L}\{f(t)\} = \int_0^\infty f(t)e^{-st} dt \][/tex]
Break the integral into two parts based on the piecewise definition of f(t) :
[tex]\[ \mathcal{L}\{f(t)\} = \int_0^4 0 \cdot e^{-st} dt + \int_4^\infty (t - 4)e^{-st} dt \][/tex]
Solve each integral separately:
[tex]\[ \int_0^4 0 \cdot e^{-st} dt = 0 \][/tex]
[tex]\[ \int_4^\infty (t - 4)e^{-st} dt = \int_4^\infty te^{-st} dt - 4\int_4^\infty e^{-st} dt \][/tex]
Integrate:
[tex]\[ = \left[ -\frac{1}{s}te^{-st} \right]_4^\infty - \left[ -\frac{4}{s}e^{-st} \right]_4^\infty \][/tex]
[tex]\[ = \left(0 - \left(-\frac{4}{s}e^{-4s}\right)\right) - \left(0 - \left(-\frac{4}{s}e^{-4s}\right)\right) \][/tex]
[tex]\[ = \frac{4}{s}e^{-4s} \][/tex]
Combine the results:
[tex]\[ \mathcal{L}\{f(t)\} = \frac{4}{s}e^{-4s} \][/tex]
So, the Laplace transform of f(t) is [tex]\( \frac{4}{s}e^{-4s} \)[/tex].
The Laplace transform of the given piecewise function f(t) is found using the Heaviside step function and shifting theorem, yielding[tex]\[ \mathcal{L}\{f(t)\} = \frac{6}{s^4} \][/tex]
To find the Laplace transform of the function f(t), we'll break it down into two parts: one for t < 4 and another for [tex]\( t \geq 4 \).[/tex]
For t < 4 , f(t) = 0 , so its Laplace transform is simply 0.
For [tex]\( t \geq 4 \), \( f(t) = (t - 4)^3 \)[/tex]. We'll use the property of the Laplace transform that states [tex]\( \mathcal{L}\{t^n\} = \frac{n!}{s^{n+1}} \). So, for \( f(t) = (t - 4)^3 \)[/tex], we get:
[tex]\[ \mathcal{L}\{(t - 4)^3\} = \frac{3!}{s^{3+1}} \\\[ = \frac{6}{s^4} \][/tex]
Now, we can combine both parts:
[tex]\[ \mathcal{L}\{f(t)\} = 0 \quad \text{for } t < 4 \\\[ \mathcal{L}\{f(t)\} = \frac{6}{s^4} \quad \text{for } t \geq 4 \\\text{Therefore, the Laplace transform of}\; \( f(t) \) is:\[ \mathcal{L}\{f(t)\} = \frac{6}{s^4} \][/tex]
Trey has answered 15 E-mails.This is 20% of E-mails he must answer.How many E-mails does he need to answer?
Help for C if anyone knows, thanks
Earth's radius is about 261.4% of Mercury's radius.(2,440 km.)
what is the radius of Earth?
Earth's radius is approximately 6,378.96 km.
Explanation:To find the radius of Earth, we can use the information given in the question. We know that Earth's radius is approximately 261.4% of Mercury's radius, which is given as 2,440 km.
Let's set up an equation to solve for Earth's radius. Let x represent Earth's radius:
x = 261.4% * 2,440 km
Converting 261.4% to decimal form, we get 2.614. Multiplying this by 2,440 km, we find that Earth's radius is approximately 6,378.96 km.
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What number is the solution to n over 3 is negative 12
A -36
B -4
C 4
D 36
you have n/3 = -12
to solve for n, multiply both sides by 3
n = -12 * 3 = -36
answer is A. -36
Darius and Matthew have three fruit bars. They are both hungry after playing football and decide to split the fruit bars evenly.
Samuel filled the glasses shown below completely with water. The total amount of water that Samuel poured into the glasses is 60 cubic centimeters. What is the height of glass 1? Round your answer to the nearest tenth. (Use π = 3.14.) Note that all measurements are in centimeters and images are not drawn to scale.
The possible answers are 0.2, 1.7, 3.9 or 5.6. When googled the answer always comes up 3.9. I always get 1.6527 which rounds up to 1.7. How about you?
volume of glass 2 = pi*r^2*h/3= 3.14 *2.5^2*6/3 = 39.25 cubic cm
60-39.25 = 20.75 cu cm was in 1st cup
volume of cylinder = pi *r^2 *h
20.75 = 3.14 *2^2 *h
20.75 = 3.14*4*h
20.75 = 12.56*h
h = 20.75 /12.56 = 1.652 round to 1.7
Answer:
The height of glass 1 is 1.7 cm.
Step-by-step explanation:
We are given the following information in the question:
The total amount of water that Samuel poured into the glasses is 60 cubic centimeters.
Volume of glass 2 = Volume of cone =
[tex]\displaystyle\frac{1}{3}\pi r^2h\\\\\text{Putting value of r and h}\\\\= \frac{1}{3}\times 3.14\times \frac{5}{2}\times \frac{5}{2}\times 6 = 39.25\text{ cubic cm}[/tex]
Volume of glass 1 =
[tex]\text{ Total Volume } - \text{Volume of glass 2}\\= 60 - 39.25\\= 20.75\text{ cubic cm}[/tex]
Volume of glass 1 = Volume of cylinder =
[tex]20.75 = \pi r^2h\\\text{where r is the radius of cylinder and h is the height of cylinder}\\\\\text{Putting the values of r}\\\\ 20.75 = 3.14\times \displaystyle\frac{4}{2}\times \frac{4}{2}\times h\\\\h = \frac{20.75}{3.14\times 2\times 2} 1.656 \approx 1.7[/tex]
Thus, the height of glass 1 is 1.7 cm.
In how many ways can you receive four cards of the same face value and one card from the other 48 available cards?
Towing charge 30$ plus $3 per mile if I paid $117 how far was the car towed
Brenda has a balance of d dollars in her piggy bank. Explain what value(s) d may have if d = 28
Identify the binomial A. x2 −4x + 2 B. x2 C. x2 − 4 D. 2x2 + 3x −1 + y
What is the value of x?
Enter your answer in the box.
x =
3x + 50 = 6x -10
add 10 to each side
3x +60 = 6x
subtract 3x from each side
60 = 3x
x = 60/3 = 20
x = 20
HELP I WILL GIVE BRAINLIEST!
what value of x makes the equation true? 9x - 15 - 2x = -60 + 9x
What is Kaycie's net income?
Answer:
Net income of Kaycie is $1,195
Step-by-step explanation:
We are given a monthly Income statement of September 2013.
First we count total income of Kaycie's
Income = Wages
Total Income = $2,700
Now we calculate total expenses
Kaycie's expenses are on food, rent clothing, transportation, medical and Insurance.
Expenses = Food+Rent+Clothing+Transportation+Medical+Insurance
Expenses=210+975+90+120+60+50
Total Expenses = $1,505
Net Income = Total Income - Total Expenses
Net Income = 2700 - 1505
Net Income = $1,195
Thus, Net income of Kaycie is $1,195.
Answer:
In so many words its "1,195"
Step-by-step explanation:
What is the selling price if the actual cost is $720 and 43% markup on selling price
in the diagram below,point O is the center of the given circle.
Love them or hate them, they do be spitting straight facts
In the accompanying diagram angle 1 and angle 2 are supplementary what is m angle 3
P: grass is green or Q: 3 is the square root of 10 (P ∨ Q)
Answer:
TFT
Step-by-step explanation:
Simplify three to the negative ninth divided by three to the negative twelfth.
Answer:
3^3
Step-by-step explanation:
What is 25.4067 to the nearest hundredth
For children between the ages of 18 months and 29 months, there is approximately a linear relationship between height and age. the relationship can be represented by ŷ = 63.80 + 0.61x where y represents height (in centimeters) and x represents age (in months). joseph is 23.5 months old and is 80 centimeters tall. what is joseph's residual?
a.78.135
b.112.600
c.5.865
d.1.865
e.-32.600 f) none of the above
Answer: Joseph's residual is 1.86 (option d).
Step-by-step explanation:
Hi, to answer this question we have to replace the variable "x" for Joseph’s age (23.5 months) in the equation given:
y = 63.80 + 0.61x.
y = 63.80 + 0.61 (23.5)
y = 63.80 + 14.335 = 78.135
Now, we subtract the amount obtained to Joseph's height ( 80 centimeters).
Mathematically speaking:
80 - 78.135 = 1.865
So, Joseph’s residual is 1.86 (option d).
Ben is 8 years older than Sarah 10 years ago Ben was twice as old as Sarah how old are Ben and Sarah today
3/4x+5/6=5x-125/3 solve for x
Final answer:
To solve the equation 3/4x + 5/6 = 5x - 125/3 for x, you can start by getting rid of the fractions. Multiply every term in the equation by the least common multiple (LCM) of the denominators, which in this case is 12. Combine like terms and solve for x.
Explanation:
To solve the equation 3/4x + 5/6 = 5x - 125/3 for x, you can start by getting rid of the fractions. To do this, multiply every term in the equation by the least common multiple (LCM) of the denominators, which in this case is 12. This gives you:
9x + 10 = 60x - 500
Next, combine like terms by subtracting 9x from both sides of the equation:
10 = 51x - 500
Then, add 500 to both sides of the equation:
510 = 51x
Finally, divide both sides of the equation by 51 to solve for x:
x = 10
What is the value of ▲ in the equation shown?
8 x 4 = ( ▲ x 7) - (▲ x 3)
= _____
Answer:
8
Step-by-step explanation: