Answer:
The part of the bridge that opens is 50 ft.
Step-by-step explanation:
The given parameters of the drawbridge are;
The entire length of the bridge = 100 feet
The height of the isosceles trapezoid formed = 25 feet
The angle at which the drawbridge meets the land ≈ 60°
Therefore, the part of the bridge that opens = The top narrow parallel side of the isosceles trapezoid
The length of each half of the bridge = (The entire length)/2 = 100 ft./2 = 50 ft.
Let 'x' represent the path of the waterway still partly blocked by each half of the bridge inclined
∴ x = 50 × cos(60°) = 25
x = 25 ft.
The path covered by both sides of the drawbridge = 2·x = 2 × 25 ft. = 50 ft.
The part of the bridge that opens = The entire length - 2·x
∴ The part of the bridge that opens = 100 ft. - 50 ft. = 50 ft.
The part of the bridge that opens = 50 ft.
A rod of length 30.0 cm has linear density (mass per length) given by
λ=50.0+20.0 x
where x is the distance from one end, measured in meters, and λ is in grams/ meter.
What is the mass of the rod?
The mass of the rod is 15.9 grams.
To find the mass of the rod, we need to integrate the linear density function over the entire length of the rod. The linear density function is given by λ = 50.0 + 20.0x, where x is the distance from one end measured in meters.
The mass of an infinitesimally small element of length dx is given by dm = λ*dx. Substituting the linear density function, we have dm = (50.0 + 20.0x)*dx.
Integrating both sides from x = 0 to x = 0.3 meters (corresponding to the length of the rod), we get:
∫dm = ∫(50.0 + 20.0x)dx
m = ∫(50.0 + 20.0x)dx
m = [50.0x + 10.0x^2] evaluated from x = 0 to x = 0.3
m = 50.00.3 + 10.0(0.3)^2
m = 15.0 + 0.9
m = 15.9 grams.
Therefore, the mass of the rod is 15.9 grams.
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Find the surface area (help me please ╥﹏╥ )
Answer:
100
Step-by-step explanation:
Add all of the inches together including the parts you don't see.
one side is 9 inches. there are 8 sides. so 9x8. One side in the box is 7 inches. there are 4 sides. so 7x4. 9x8 + 7x4 is equal to 72 + 28.
72 + 28=100
simplify -2+3(1-4)-2
Answer:
-13
Step-by-step explanation:
−2+3(1−4)−2
=−2+(3)(−3)−2
=−2+−9−2
=−11−2
=−13
hope it helped
please mark me as brainliest.
if a club has 20 members and 4 officers how many choices are there for a secretary
Answer:
20 x 4 = 60
Step-by-step explanation:
because it's says how many
Answer:
18 maybe
Step-by-step explanation:
it's either 20,19,or 18
but the secretary is the third to be elected so the answer is 18 maybe and if that doesn't work try one of the others trust me it's one of them.
hope this helps
What is the volume of this cylinder?
6 m
7 m
Round your answer to the nearest tenth.
Answer:
(Refer below:)
Step-by-step explanation:
Because there is no image, here's what I'm going to assume: there are multiple scenarios. Refer to each one below:
1) Where r = 6 and h = 7:
V = Bh
V = (π r²) (h)
V = (6² π) (7)
V = 36π (7)
V = 252π
2) Where r = 7 and h = 6:
V = Bh
V = (π r²) (h)
V = (7² π) (6)
V = 49π (6)
V = 294π
3) Where d = 6 and h = 7:
d = 2r = 6
r = 3
V = Bh
V = (π r²) (h)
V = (3² π) (7)
V = 9π (7)
V = 63π
4) Where d = 7 and h = 6:
d = 2r = 7
r = 3.5
V = Bh
V = (π r²) (h)
V = (3.5² π) (7)
V = 12.25π (7)
V = 87.75π ≈ 269.39
Write the word sentence as an equation.
12 less than a number m equals 20.
An equation that represents this word sentence is
Answer:
x - 12 = 20
Step-by-step explanation:
If I'm wrong do x = 12 - 20
The length of a rectangle is 3ft less than double the width, and the area of the rectangle is 14ft^2 find the dimensions of rectangle.
Answer: [tex]4\times 3.5\ ft^2[/tex]
Step-by-step explanation:
Given
area of the rectangle is [tex]A=14\ ft^2[/tex]
Suppose width is given by w
So, length is [tex]l=2w-3[/tex]
The area of a rectangle is [tex]A=l\times w[/tex]
putting values
[tex]\Rightarrow A=(2w-3)w\\\Rightarrow 14=2w^2-3w\\\Rightarrow 2w^2-3w-14=0\\\Rightarrow 2w^2-7w+4w-14=0\\\Rightarrow w(2w-7)+2(2w-7)=0\\\Rightarrow (2w-7)(w+2)=0\\\\\Rightarrow w=\dfrac{7}{2}\ ft[/tex]
length is [tex]l=4\ ft[/tex]
guys i need help ASAP!!!
Answer:
Q7 0.2
Q8 0.17
Step-by-step explanation:
Probability is the ratio of the number of possible outcome to the number of total outcome. The probability that an event will happen when added to the probability that it will not happen is 1
Given that the probability that the bulb will grow is 0.8, the probability it would not grow
= 1 - 0.8
= 0.2
A match may be won lost or drawn
Given that the probability of a win is 0.28 and that of a draw is 0.55, the probability of a loss
= 1 - (0.28 + 0.55)
= 0.17
Match the sides based on their relationship to A
PLEASE ANSWER ASAP
Answer:
13 hypotenuse
12 adjacent
5 opposite
a car can travel 174 miles in 4 hours how many miles can the car travel per hour
Answer:
43.5
divide 174 ÷ 4 and you get 43.5
4. verify the following identities 0 (a) 1 = 10 (x) + 2 (-1)"l2n(x) n=1 00 (b) e* = 10(x) +2 1. (x) = n=1 0 c) (c) e-* = 10(x) +2X(-1)"In(x) -X = n=1 0 (d) cosh x = 10(x) +2 Izn (x) X d n=1 00 (e) sinh x = 222n-1(x) - n=1
The given identities can be verified using basic rules of exponentials and algebra. Here are the steps to verify the given identities:
(a) 1 = ∑_(n=1) ^∞▒〖10^(x)+2(-1) ^nln(x)〗0
Rewrite the sum to obtain two series, one for even values of n, and one for odd values of n. ∑_(n=1)^∞▒10^(x) = 10^x+10^x+...= (2/3) (10^x) (odd terms only)∑_(n=1)^∞▒〖(-1)^nln(x)〗= ln(x)-ln(x)+ln(x)-ln(x)+...= (0) (even terms only)
Thus, we have 1= (2/3) (10^x) + (0) = (2/3) (10^x) (b) e^x = ∑_(n=1) ^∞▒〖10^x+2n(x)〗
Rewrite the sum to obtain two series, one for even values of n, and one for odd values of n.
∑_(n=1) ^∞▒10^(x) = 10^x+10^x+...= (1/2) (10^x) (even terms only) ∑_(n=1) ^∞▒〖2n(x)〗= 2(x)+2(2x) +2(3x) +...= 2x (1+2+3+...) = -x/(-1) ^2= -x
Thus, we have e^x= (1/2) (10^x) - x(c) e^(-x) = ∑_(n=1) ^∞▒〖10^x+2(-1) ^nln(x)〗0
We can use the same series from part (a) with x replaced by -x.
Thus, we have e^(-x) = (2/3) (10^(-x)) + (0) = (2/3) (1/10^x)
Similarly, e^x= (2/3) (10^x) Subtracting these two equations, we get: e^x - e^(-x) = (2/3) (10^x + 1/10^x) (answer) (d)
Cosh x = ∑_(n=0) ^∞▒〖10^x+2n(x)〗
Similar to part (b), we have two series, one for even values of n, and one for odd values of n.∑_(n=0)^∞▒10^(x) = 1+10^x+10^x+...= (1/2) (10^x) (even terms only)∑_(n=0)^∞▒〖2n(x)〗= 0+2x+2(2x)+2(3x)+...= 2x (1+2+3+...)= 2x(1/(-1)^2)= 2xThus, we have Cosh(x) = 1 + (1/2) (10^x) + 2x (e^x)(e^x - e^(-x)) / 2= 1 + (1/2) (10^x) + 2x (1 + (2/3) (10^x + 1/10^x)) (answer)(e) Sinh x = ∑_(n=1)^∞▒〖2^(2n-1)(x)〗
Rewrite the sum to obtain two series, one for even values of n, and one for odd values of n.∑_(n=1)^∞▒〖2^(2n-1)(x)〗= 2x+2^3x+2^5x+...= 2x(1+2^2+2^4+...)= 2x(2^0+2^2+2^4+...)= 2x(1/ (1-2^2))= -2x/3Thus, we have Sinh(x) = ∑_(n=1)^∞▒〖2^(2n-1)(x)〗= 2x/3 (answer)
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Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not exact, enter NOT.) dy/ dx = 9xe^x – y + 6x2
The given differential equation is not exact. To determine if a differential equation is exact, we need to check if its partial derivatives satisfy a specific condition.
In this case, the given equation is dy/dx = 9xe^x – y + 6x^2. Let's find the partial derivatives of the expression on the right-hand side with respect to y and x.∂/∂y (9xe^x – y + 6x^2) = -1∂/∂x (9xe^x – y + 6x^2) = 9e^x + 12x
The condition for exactness is that these partial derivatives are equal: ∂/∂y (∂/∂x) = ∂/∂x (∂/∂y). However, in this case, we have -1 ≠ 9e^x + 12x, which means the equation is not exact.As the equation is not exact, we cannot directly solve it by finding a potential function. Other methods, such as using integrating factors or applying specific techniques for solving non-exact equations, may be required.
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What is the simple interest earned on an $4,350 investment for 5 years at a rate of 2%?
Hey!
A = $4,785.00
I = A - P = $435.00
Equation:
A = P(1 + rt)
Calculation:
First, converting R percent to r a decimal
r = R/100 = 2%/100 = 0.02 per year.
Solving our equation:
A = 4350(1 + (0.02 × 5)) = 4785
A = $4,785.00
The total amount accrued, principal plus interest, from simple interest on a principal of $4,350.00 at a rate of 2% per year for 5 years is $4,785.00.
--------------------------------------------------
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ODE solutions using Laplace transforms
Solve the following initial value problem using Laplace transforms:
y" - 2y = e^x, y(0) = 0, y'(0) = 0.
The solution of the given differential equation using the Laplace transform is y(t) = 1 − [tex]e^{2t}[/tex] + 2 [tex]e^{-t}[/tex].
Given differential equation is y″−2y = eˣ, y(0) = 0, y′(0) = 0. We will solve it using Laplace transforms.
To solve the given differential equation using the Laplace transform, take the Laplace transform of each term of the differential equation. Then solve for Y(s) and find y(t) by taking the inverse Laplace transform.
Here, we take L{y} for Y(s) and L{y''} and L{y'} for s²Y(s) and sY(s) respectively.
L[y′′] − 2L[y] = L[eˣ] s²Y(s) − s⋅y(0) − y′(0) − 2Y(s)
= 1s − 1.0 − 0 − 2Y(s)
= 1s − 1
We have to rearrange the terms of the above equation in order to get Y(s) on one side.
Y(s) = 1s(s−2)(s−1) = As+Bs−2+Cs−1.
Using partial fraction expansion, A=1, B=1, and C=−2.
So,Y(s) = 1s+(1s−2)−2s−1.
We can write Y(s) as follows.Y(s) = 1s−(1s−2)+2s−1.
Then find the inverse Laplace transform of Y(s) to get the solution y(t).
y(t) = L − 1{Y(s)} = L − 1{1s} − L − 1{1s−2} + L − 1{2s−1}
= 1 − [tex]e^{2t}[/tex] + 2 [tex]e^{-t}[/tex].
Therefore, the solution of the given differential equation using Laplace transform is y(t) = 1 − [tex]e^{2t}[/tex] + 2 [tex]e^{-t}[/tex].
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A 13 foot ladder is leaning against the wall of a house. The ladder is 5 feet away from th
base of the house. How high up the house does the ladder reach?
Answer:
12 feet
Step-by-step explanation:
In Canada, the rate of inflation (i.E. How much things cost) is about 2.0%/year. In other words, the real value of your money is worth 2.0% less each year. Imagine you have $2250 in savings under your mattress
Answer:
Step-by-step explanation:
If you have $2250 as against an inflation rate of 2% every year, this then means that after the first year, the value of your money becomes
2250 * 2% =
2250 * 0.02 = 45
2250 - 45 = $2205
At the end second year
$2205 * 2% =
$2205 * 0.02 = 44.1
$2205 - 44.1 = 2160.9
At end of the third year
$2160.9 - 2% =
$2160.9 * 0.02 = 43.218
$2117.682
And so on, and so forth
if f(5) = 11, f ′ is continuous, and 6 5 f ′(x) dx = 19, what is the value of f(6)?
If f(5) = 11, f ′ is cοntinuοus, and 6 5 f ′(x) dx = 19, then f(6) = 30.
What is Fundamental Theοrem οf Calculus?Tο find the value οf f(6), we can use the Fundamental Theοrem οf Calculus. Accοrding tο the theοrem, if f(x) is cοntinuοus οn an interval [a, b] and F(x) is an antiderivative οf f(x) οn that interval, then the definite integral οf f(x) frοm a tο b is equal tο F(b) - F(a).
Given that f'(x) is cοntinuοus, we can apply the theοrem tο the integral:
∫₅₆ f'(x) dx = f(6) - f(5)
We are given that ∫₅₆ f'(x) dx = 19, and f(5) = 11. Plugging in these values, we have:
19 = f(6) - 11
Tο sοlve fοr f(6), we add 11 tο bοth sides:
f(6) = 19 + 11
f(6) = 30
Therefοre, the value οf f(6) is 30.
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i light is faster then anything how did dark get there first
hello there enjoy 30 points on da house
Answer:
this just confused me so much
Step-by-step explanation:
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4
Select the correct answer.
Solve the following equation for x.
x2 - 9x+ 18 = 0
O A.
X = -3; x = 6
ОВ.
X= 3; x = 6
OC.
x= -3; x = -6
OD.
x= 3; x = -6
(行
Reset
Next
Answer:
B
Step-by-step explanation:
Given
x² - 9x + 18 = 0 ← in standard form
(x - 3)(x - 6) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
x - 6 = 0 ⇒ x = 6
solution is x = 3, x = 6 → B
can anyone help me on this question but explain? What’s the difference between gross and net income
Answer & Explanation:
Gross income is the total pay you earn before any reduction and adjustments (taxes, mortgage, etc.).
Net income is the amount of pay you get after taxes and other reductions are taken out of your gross income; it's the money that you "actually get to take home in your pocket with" on the payday.
A spherical globe has a diameter of 10 inches. What is the approximate volume of the globe?
Answer:
523.33 in^3
Step-by-step explanation:
A sphere is a 3-dimensional version of a circle. An example of a sphere is a ball
Volume of a sphere = [tex]\frac{4}{3}[/tex]π[tex]r^{3}[/tex]
Where
π = 3.14
r = radius
the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.
A radius is half of the diameter
diameter = 2r
Radius = 10 in / 2 = 5 inches
[tex]\frac{4}{3}[/tex] × 3.14 ×[tex]5^{3}[/tex] = 523.33 [tex]in^{3}[/tex]
Andre has a summer job selling magazine subscriptions he earned $25 per week plus $3 for every subscription he sells.Andre hopes to make at least enough money to buy a new pair of soccer cleats
Answer:
Step-by-step explanation:
That Would be 43/3
The length of a rectangle is three times its width. If the perimeter is 120 inches, what is the length? The width?
Answer:
Length=45 inches, width=15 inches
Step-by-step explanation:
Length=3w
Width=w
Can be written as 3w+w+3w+w
Combine like terms to get 8w
120/8=15
w=15
Width=15 inches
Length=3(15)=45
Length=45 inches
1 The legs of a triangle are 6 cm and 8 cm. The hypotenuse is 14 cm. Is it a right triangle?
Answer:
this is not a right triangle
Step-by-step explanation:
^ = squared
The formula forthe Pythagorean theorem is a^+ b^ = c^
If this is a right triangle this must be true
6^ + 8^ = 14^
36 + 64 = 196
100 is not equal to 196
So this is not a right triangle
What is the area of the triangle in square yards?
6 yd.
15 3/4 yd.
hurry plss
Answer:
im guessing 6 is your base and your height is 15 3/4.
Formula of a triangle we must remember:
BH x 1/2 (basically dividing by 2)
94.5 (fraction form will be: 94 1/2)
94.5 divided by 2 = 47.25 <---------- decimal form
94 1/2 divided by 2 = 47 1/4 <------- fraction form
200% of what number is 350?
Answer:
The answer is 175
will give yall brainliest if yall answer this question
The probability of a vanilla taffy is given as follows:
P(vanilla) = 0.31.
Hence the probability of a vanilla or banana taffy is given as follows:
P(vanilla or banana) = 0.52.
How to calculate a probability?The two parameters that are needed to calculate a probability are listed as follows:
Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.Then the probability is then calculated as the division of the number of desired outcomes by the number of total outcomes.
When we are given the relative frequencies, we must simply identify the desired outcomes, as follows:
P(banana) = 0.21.P(vanilla) = 0.31.Hence the probability is given as follows:
P(vanilla or banana) = P(vanilla) + P(banana) = 0.52.
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What is the mean:4,3,5,4,8,0 IXL
Help me really please asp
Answer:
y1=4
x2=7
y2=-3
A carpet cleaner charges $50.97 to travel to the customers house and $15.11 per room cleaned. In the carpet cleaner charged $96.97 how many rooms did he clean?