The multiplication shows that the total steps for the ramp will be 28 inches.
How to calculate the steps for the ramp?From the information given, the school has 4 steps to the front door and each step is 7 inches tall.
In this case, the total steps of the ramp will be gotten by multiplying the values. This will be:
= 4 × 7 = 28 inches.
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The strength of an electrical current x flowing through the electric circuit shown is expressed as a function of time t and satisfies the following differential equation:
[tex]\displaystyle \large{L \frac{dx}{dt} + Rx = V}[/tex]
Find the strength of the electrical current x after switch S is closed at time t = 0. Assume that L, R and V are positive constants, and also that x = 0 when t = 0. Then, find [tex]\displaystyle \large{ \lim_{t \to \infty} x}[/tex]
Topic: Application of Differential Equation Reviews
Answer:
The current of the circuit at t = 0 is equal to 0.
If we take the limit as t approaches infinity, the current is equal to ε/R or V/R.
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]:
[tex]\displaystyle (cu)' = cu'[/tex]
Derivative Property [Addition/Subtraction]:
[tex]\displaystyle (u + v)' = u' + v'[/tex]
Derivative Rule [Basic Power Rule]:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Slope Fields
Separation of VariablesIntegration
IntegralsIntegration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Method: U-Substitution
Electricity
Ohm's Law: V = IR
V is voltage (in Volts)I is current (in Amps)R is resistance (in Ohms)Circuits
Circuit SymbolsKirchhoff's Laws (Loop and Junction Rule)InductorsStep-by-step explanation:
*Note:
In the given equation, our variable of differentiation is x. I will rewrite this as current I for physics notation purposes.
Step 1: Define
Identify given.
[tex]\displaystyle L \frac{dI}{dt} + RI = V[/tex]
[Assuming switch S is closed] Recall that an inductor is used in a circuit to resist change. After a long period of time, when it hits steady-state equilibrium, we expect to see the inductor act like a wire.
Step 2: Find Current Expression Pt. 1
[Kirchhoff's Law] Rewrite expression:Step 3: Find Current Expression Pt. 2
Identify variables for u-substitution.
Set u:Step 4: Find Current Expression Pt. 3
[Kirchhoff's Law] Apply U-Substitution:Recall that our initial condition is when t = 0, denoted as u₀, and we go to whatever position u we are trying to find. Also recall that time t always ranges from t = 0 (time can't be negative) and to whatever t we are trying to find.
[Kirchhoff's Law] Integrate both sides:Recall that our initial condition u₀ (derived from Ohm's Law) contains only the voltage across resistor R, where voltage is supplied by the given battery. This is because the current is stopped once it reaches the inductor in the circuit since it resists change.
Back-Substitute in u and u₀:Step 5: Solve
If we are trying to find the strength of the electrical current I at t = 0, we simply substitute t = 0 into our current function:
[tex]\displaystyle\begin{aligned}I(t) & = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}t} \\I(0) & = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}(0)} \\& = \boxed{\bold{0}}\end{aligned}[/tex]
If we are taking the limit as t approaches infinity of the current function I(t), we are simply just trying to find the current after a long period of time, which then would just be steady-state equilibrium:
[tex]\displaystyle\begin{aligned}I(t) & = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}t} \\\lim_{t \to \infty} I(t) & = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}(\infty)} \\& = \boxed{\bold{\frac{\mathcal E}{R}}}\end{aligned}[/tex]
∴ we have found the current I at t = 0 and the current I after a long period of time and proved that an inductor resists current running through it in the beginning and acts like a wire when in electrical equilibrium.
---
Topic: AP Physics C - EMAG
Unit: Induction
Math Practices and Problem Sol
17. Number Sense Using three different
numerators, write an equation in which
three fractions, when added, have a
sum of 1.
Answer:
First choose a common denominator, here i picked 11 then we think of 3 diffrent numbers so that their sum is 11 such as 2+4+5=11 so a possible equasion would be
Step-by-step explanation:
Ethan donated $15.00 of the $50.00 he received as a gift.
Which decimal represents the fraction of $50.00 Ethan
donated?
A. 0.15
B. 0.3
C. 0.35
D. 0.5
(WILL MARK BRAINLIEST*
Answer:
0.3
Step-by-step explanation:
15/50=0.3
OR
(15*2)/(50*2)
30/100=0.3
Emily and Jennifer are playing a game with dice. Each one has a die. If each one rolls one and the sum of the numbers are 7 or 11 they win. If the sum is 2, 3 or 12 they lose. If it is any other number there is no winner or loser.
Find the sample space by either creating a tree or a chart/table. (remember, each die has the numbers 1-6 on it).
Then find:
P (they win - if the sum is 7 or 11)
P (they lose - if the sum is 2, 3 or 12)
The total sample space. HINT: How many total possible combinations?
This experiment has 36 possible combinations, and we will see that:
P(they win) = 0.22P(they loose) = 0.11How to get the probabilities?
First, we need to find the total number of outcomes.
We have two dice with 6 outcomes each, so the total number of outcomes of the experiment of tossing the two dice is:
C = 6*6 = 36
Such that the sample space is all the numbers between 2 and 12 (because our variable is the sum of the two values).
Now, to get the probability of winning we need to count the number of outcomes that add to 7 or 11, these are:
(Add to 7)
dice 1 dice 2
1 6
2 5
6 1
5 2
4 3
3 4
(Add to 11)
dice 1 dice 2
5 6
6 5
So there are 8 outcomes, then the probability of winning is:
P = 8/36 =0.22
The probability of losing is when the sum adds to 2, 3, or 12.
The outcomes that add to that:
(Add to 2)
dice 1 dice 2
1 1
(Add to 3)
dice 1 dice 2
1 2
2 1
(Add to 12)
dice 1 dice 2
6 6
There are 4 outcomes that add to these values, so the probability of losing is:
P = 4/36 = 0.11
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A researcher is interested in whether blind Braille readers could be taught to read faster using the same techniques as sighted readers. He has blind adults complete a reading speed test before and after a six-week speed-reading course. In the beginning of the study, a randomly selected group of 121 blind Braille readers scored an average of 261 words per minute on the reading speed test. Since the sample size is larger than 30, the researcher can assume that the sampling distribution of MD is normal. He plans to use a repeated-measures t test. The researcher identifies the null and alternative hypotheses as:
A company makes concrete bricks that are shaped like rectangular prisms. Each brick is 5inches long, 4inches wide, and 2inches tall. How much concrete will they need to make 1600 bricks?
Answer:
The answer would be 64,000.
Step-by-step explanation:
To find the area of one concrete block you will multiple length x width x height. Using the measurements provided, one block will equal 40. You will then multiple this by 1,600 to equal 64,000.
If x = 18, evaluate the following expression:
12 + 3
The ages of the people in attendance at the showing of an award-winning foreign film are shown below. a graph shows age of attendees (in years) labeled 0 to 20 thru 61 to 80 on the horizontal axis and frequency on the vertical axis. 0 to 20 years at frequency 15. 20 to 40 years at frequency 40. 41 to 60 years at frequency 40. 61 to 80 years at frequency 15. which statement must be true according to the histogram? the data is symmetrical, showing that the majority of the attendees were between the ages of 30 and 50. the data is symmetrical, showing that the majority of the attendees were between the ages of 21 and 60. the data is skewed, showing that the majority of the attendees were between the ages of 30 and 50. the data is skewed, showing that the majority of the attendees were between the ages of 21 and 60.
Answer:
B
Step-by-step explanation:
i got it right on edge
Answer:
It is B
Step-by-step explanation:
What’s The Answer Of This? Please HELP FAST
Answer:
those are corrisponding angles which means they equal each other making <H and <G both 57 degrees
What is the equation of a line that passes through the hypotenuse of the right triangle in the graph?
A. 1/5x
B. y=5x
C. y=-5x
D. y=2/5x
Answer:
y = 5x
Step-by-step explanation:
Hey there!
To start with the hypotenuse of a triangle is the longest side of it
and to get an equation of a line you would use
y = mx + b
where m is the slope
and b is the y-intercept
to get the slope you would do rise over run
rise/run
take 2 points and see how much it rises and runs to the next point
you would then get 5
then we figure out the y-intercept where the line intercepts the y-axis
in this case 0
In conclusion the answer is y = 5x + 0
we can also remove the 0 because it is unnecessary
y = 5x
Help!! Khan academy geomtry practice
Answer:
33.51 units³
Step-by-step explanation:
Volume of a sphere is given by the formula :
V = [tex]\frac{4}{3} \pi r^{3}[/tex]
Because we have the radius we can plug it into the equation to give us :
V = (4/3)×π×(2)³
V = 4/3×8π
V ≈ 33.51
Units will be units³ since no measurement is given but it to the power of 3 since it is volume.
When placed near each other, blocks of metal A and B are magnetically attracted to each other, while blocks B and Care repelled by
each other.
Therefore, blocks A and C will be
A)
repelled by each other.
B)
attracted to each other.
C)
unaffected by each other.
D)
Not enough information given
Answer:
A) repelled by each other, I did this on usa testprep
Step-by-step explanation:
Answer:
b atracted to each other
Step-by-step explanation:
got it right on usatestprep
use an equation to find the value of k so that the line that passes through (1,3) and (5,k) has a slope of m=2.
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{k}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{k}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{1}}}~~ = ~~\stackrel{\stackrel{m}{\downarrow }}{2} \\\\\\ \cfrac{k-3}{4}=2\implies k-3=8\implies k=11[/tex]
f(3) if f(x) = 2x + 5 =
Answer:
11
Step-by-step explanation: Uh- if X=3 then it would be 2(3) +5. 2x3 is 6, and 6+5 is 11.
Answer:
11
Step-by-step explanation:
2(3) + 5
simplify
6 + 5 = 11
hope this helps
Solve 196x2 + 25 = 0 by using square roots.
show how to rewrite 1/5 with the denominator of 10
Answer:
2/10
Step-by-step explanation:
Since the denominator is 10, we must find what the numerator is so that the fraction can be equal to 1/5. Since 10 is twice of 5, we multiply 2 by 2 as well. With that, we get a final answer of 2/10.
please help me, thank you if you do
Answer:
Step-by-step explanation:
1. The sequence is not arithmetic.
2. d=-30
A radioactive element decays at a rate of 5.25% annually. There are 35 grams of the substance
present. How much of the substance remains after 12 years (Round to the nearest hundredth)?
TEKS A2.5(B)(D)
Answer:
18.32 gm
Step-by-step explanation:
= 35 ( 1-.0525)^12 = 18.32 gm remain
What are the solutions of 12 - x2 =0?
O x=2/3 and x = -2/3
O x= 3, and x = -373
O x= 4,3 and x = -4/3
O x=6 and x = -6
Factor each polynomial. 20 points
5a^2b^2 + 10ab +25a
8m^2n^2 - 24mn^3 +16mn
9xz^3 + 18yz^2 + 24z^2
16x^6y + 16x^2y^4 + 32x^3y^2
So, here we are to factor the polynomials :
[tex]\\ 1. \sf \qquad5a^2b^2 + 10ab +25a\\ \\[/tex]
[tex] \longrightarrow\sf \qquad5a(ab^2 + 2b +5)\\ \\[/tex]
[tex]\\ 2. \sf \qquad 8m^2n^2 - 24mn^3 +16mn\\ \\[/tex]
[tex] \longrightarrow\sf \qquad 8mn(mn - 3n^2 +2)\\ \\[/tex]
[tex]\\ 3. \sf \qquad 9xz^3 + 18yz^2 + 24z^2\\ \\[/tex]
[tex]\longrightarrow \sf \qquad 3z(3xz^2 + 6yz+ 8z)\\ \\[/tex]
[tex]\\ 4. \sf \qquad 16x^6y + 16x^2y^4 + 32x^3y^2\\ \\[/tex]
[tex] \longrightarrow \sf \qquad 16 {x}^{2} y(x^4 + y^3 + 2xy)\\ \\[/tex]
Some points to know :
Factorisation is the reverse process of multiplucation.The Factorisation is the process of finding two or more expressions such that their product is the given expression.Sue says the expressions for 4y and y⁴ are Equivalent when y = 5. Is She Correct? Please Justify Your Answer.
Answer:
Sue is incorrect
Step-by-step explanation:
Just substitute in the values[tex]4\times 5=20\\5^{4}=625[/tex]Since 20 does NOT equal 625, Sue is incorrectIn a group, more than 1/2 are boys, but they are less than 2/3 of the group. Can there be:(In each case, if your answer is “yes”, find out how many boys there were. Explore all possible cases). Could there be 5 kids
Using proportions, it is found that Yes, there could be 5 kids, with 3 boys and 2 girls.
What is a proportion?A proportion is a fraction of a total amount.
In this problem, supposing a total of 5 kids:
More than 1/2 = 50% are boys, hence there are more than 2.5 boys, as 0.5 x 5 = 2.5.Less than 2/3 = 66.67% are boys, hence there are less than 3.33 boys, as 0.6667 x 5 = 3.33.Hence, Yes, there could be 5 kids, with 3 boys and 2 girls.
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Use the regression equation to predict the sales of skin diving and scuba equipment in the year 2008
Answer:c
Step-by-step explanation:
If a baseball card appreciates exponentially in value by 50% over 10 years, what is its annual appreciation (growth) rate? Please use a calculator, and answer to the nearest whole percent.
we can use hmmm any value per se for the card, hmmm say let's use $2, if the baseball card was initially 2 bucks, and after 10 years it went up in value by 50%, well 50% of 2 is 1, so the new value is 3 bucks, then
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill &3\\ P=\textit{initial amount}\dotfill &2\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &10\\ \end{cases} \\\\\\ 3=2(1 + \frac{r}{100})^{10}\implies \cfrac{3}{2}=(1 + \frac{r}{100})^{10}\implies \cfrac{3}{2}=(\frac{100+r}{100})^{10} \\\\\\ \sqrt[10]{\cfrac{3}{2}}=\cfrac{100+r}{100}\implies 100\sqrt[10]{\cfrac{3}{2}}=100+r \\\\\\ 100\sqrt[10]{\cfrac{3}{2}}-100=r\implies 4\approx r[/tex]
A baseball field in the shape of a square is shown. the corners are labeled home plate, first base, second base, and third base. the distance between home plate and first base is 90 feet. a baseball field is in the shape of a square. the distance between each pair of bases along the edge of the square is 90 feet. what is the distance between home plate and second base? startroot 2 endroot feet
Answer:
90√2 feet
Step-by-step explanation:
The geometry of the problem can be modeled by a right triangle with sides 90 feet. The length of the hypotenuse is the distance from home plate to 2nd base. The Pythagorean theorem tells you that distance (c) is ...
c² = a² +b²
c² = (90 ft)² +(90 ft)² = 8100 ft² +8100 ft²
c² = 16200 ft²
c = √16200 ft = 90√2 ft
The distance between home plate and second base is 90√2 feet.
Answer:
A baseball field is in the shape of a square. The distance between each pair of bases along the edge of the square is 90 feet. What is the distance between home plate and second base?
(90) StartRoot 2 EndRoot feet
Step-by-step explanation:
There are 100 students in a band. Forty percent are 12 years old, 1/2 are 13 years old, and the rest are 14 years old. Write the portion of the band for each age
Answer:
40x 12 year olds
50x 13 year olds
10x 14 year olds
Step-by-step explanation:
40% of 100 is 40
50% of 100 is 50
100%-90%=10%, 10% of 100 = 10
Students of 12 years are 40%, students of 13 years are 50% and students of 14 years are 10%.
What is percent?A percentage is a figure or ratio that can be stated as a fraction of 100. If we need to calculate the percentage of a number, we must divide it by its full value and then multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." It is represented by the symbol "%".
Given, total students in band = 100
40% are of 12 years
40% of 100 = 0.4 x 100 = 40
12 years student = 40 = 40%
1/2 of 13 years
1/2 of 100 = 1/2 x 100 = 50 =50%
13 years of student = 50
and rest are 14 years
100 - 50 - 40 = 10
14 years student = 10 = 10%
Hence 40% students are 12 years, 50% are of 13 years and 10% of students are of 14 years.
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What was one of the main causes of the Great Depression?
a. The overuse of credit
b. The under-utilization of money
c. WWII
d. Excessive government borrowing
Answer:
B
Step-by-step explanation:
4/9÷1/2 as a fraction (simplest form)
Answer:
8/9
Step-by-step explanation:
4/9 ÷ 1/2 = dividing by 1/2 is the same as multiplying by its reciprocal 2/1
4/9 × 2/1 = (4×2)/(9×1) multiply numerators (top numbers) and multiply denominators (bottom numbers)
The price of a game console that regularly sells for $800 is reduced to $616. By what percentage is the price reduced?
Answer:23%
Step-by-step explanation: 800-616= 184
Discount is 184
percentage is 184/800 ×100/1 =23%