Given:
The difference between 7 and the sum of 1.0006 and 4.06.
To find:
The mathematical expression for given statement and it value.
Solution:
Sum of 1.0006 and 4.06 = [tex](1.0006+4.06)[/tex]
The expression for the difference between 7 and the sum of 1.0006 and 4.06 is
[tex]7-(1.0006+4.06)[/tex]
On simplification, we get
[tex]7-(1.0006+4.06)=7-5.0606[/tex]
[tex]7-(1.0006+4.06)=1.9394[/tex]
Therefore, the difference between 7 and the sum of 1.0006 and 4.06 is 1.9394.
Consider the following. (A computer algebra system is recommended.) y'' + 3y' = 2t4 + t2e−3t + sin 3t (a) Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. Y(t) = t(A0t4 + A1t3 + A2t2 + A3t + A4) + (B0t2 + B1t + B2)e−t + C sin 3t + D cos 3t Y(t) = t(A1t3 + A2t2 + A3t + A4) + t(B0t3 + B1t2 + B2t + B3)e−3t + C sin 3t + D cos 3t Y(t) = (A0t4 + A1t3 + A2t2 + A3t + A4) + t(B0t2 + B1t + B2)e−3t + C sin t + D cos t Y(t) = t(A0t4 + A1t3 + A2t2 + A3t + A4) + t(B1t + B2)e−3t + C sin 3t + D cos 3t Y(t) = t(A0t4 + A1t3 + A2t2 + A3t + A4) + t(B0t2 + B1t + B2)e−3t + C sin 3t + D cos 3t (b) Use a computer algebra system to find a particular solution of the given equation. Y(t) =
First look for the fundamental solutions by solving the homogeneous version of the ODE:
[tex]y''+3y'=0[/tex]
The characteristic equation is
[tex]r^2+3r=r(r+3)=0[/tex]
with roots [tex]r=0[/tex] and [tex]r=-3[/tex], giving the two solutions [tex]C_1[/tex] and [tex]C_2e^{-3t}[/tex].
For the non-homogeneous version, you can exploit the superposition principle and consider one term from the right side at a time.
[tex]y''+3y'=2t^4[/tex]
Assume the ansatz solution,
[tex]{y_p}=at^5+bt^4+ct^3+dt^2+et[/tex]
[tex]\implies {y_p}'=5at^4+4bt^3+3ct^2+2dt+e[/tex]
[tex]\implies {y_p}''=20at^3+12bt^2+6ct+2d[/tex]
(You could include a constant term f here, but it would get absorbed by the first solution [tex]C_1[/tex] anyway.)
Substitute these into the ODE:
[tex](20at^3+12bt^2+6ct+2d)+3(5at^4+4bt^3+3ct^2+2dt+e)=2t^4[/tex]
[tex]15at^4+(20a+12b)t^3+(12b+9c)t^2+(6c+6d)t+(2d+e)=2t^4[/tex]
[tex]\implies\begin{cases}15a=2\\20a+12b=0\\12b+9c=0\\6c+6d=0\\2d+e=0\end{cases}\implies a=\dfrac2{15},b=-\dfrac29,c=\dfrac8{27},d=-\dfrac8{27},e=\dfrac{16}{81}[/tex]
[tex]y''+3y'=t^2e^{-3t}[/tex]
[tex]e^{-3t}[/tex] is already accounted for, so assume an ansatz of the form
[tex]y_p=(at^3+bt^2+ct)e^{-3t}[/tex]
[tex]\implies {y_p}'=(-3at^3+(3a-3b)t^2+(2b-3c)t+c)e^{-3t}[/tex]
[tex]\implies {y_p}''=(9at^3+(9b-18a)t^2+(9c-12b+6a)t+2b-6c)e^{-3t}[/tex]
Substitute into the ODE:
[tex](9at^3+(9b-18a)t^2+(9c-12b+6a)t+2b-6c)e^{-3t}+3(-3at^3+(3a-3b)t^2+(2b-3c)t+c)e^{-3t}=t^2e^{-3t}[/tex]
[tex]9at^3+(9b-18a)t^2+(9c-12b+6a)t+2b-6c-9at^3+(9a-9b)t^2+(6b-9c)t+3c=t^2[/tex]
[tex]-9at^2+(6a-6b)t+2b-3c=t^2[/tex]
[tex]\implies\begin{cases}-9a=1\\6a-6b=0\\2b-3c=0\end{cases}\implies a=-\dfrac19,b=-\dfrac19,c=-\dfrac2{27}[/tex]
[tex]y''+3y'=\sin(3t)[/tex]
Assume an ansatz solution
[tex]y_p=a\sin(3t)+b\cos(3t)[/tex]
[tex]\implies {y_p}'=3a\cos(3t)-3b\sin(3t)[/tex]
[tex]\implies {y_p}''=-9a\sin(3t)-9b\cos(3t)[/tex]
Substitute into the ODE:
[tex](-9a\sin(3t)-9b\cos(3t))+3(3a\cos(3t)-3b\sin(3t))=\sin(3t)[/tex]
[tex](-9a-9b)\sin(3t)+(9a-9b)\cos(3t)=\sin(3t)[/tex]
[tex]\implies\begin{cases}-9a-9b=1\\9a-9b=0\end{cases}\implies a=-\dfrac1{18},b=-\dfrac1{18}[/tex]
So, the general solution of the original ODE is
[tex]y(t)=\dfrac{54t^5 - 90t^4 + 120t^3 - 120t^2 + 80t}{405}\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,-\dfrac{3t^3+3t^2+2t}{27}e^{-3t}-\dfrac{\sin(3t)+\cos(3t)}{18}[/tex]
What is the value of 17^0
Answer:
1
Step-by-step explanation:
Anything to the exponent of 0 is 1.
2/5×6/7= in simplist or mixed form
Answer:
2/5x6/7 = 12/35
Step-by-step explanation:
when we multiply fractions we multiply the denominators together and the numerators as well, so 2 x 6 = 12. and 5 x 7 =35
12/35
The order of the first term more than 100 in the sequence (Tn)=(2+5n) is ……
Answer:
20
Step-by-step explanation:
T19 = 97
T20 = 102
The 20th term is the first term more than 100.
__
You can find the value of n from ...
2 +5n > 100
5n > 98
n > 19.6
The 20th term is the first term more than 100.
Help me with this please I gave you 30 points
Answer:
a reflection over the vertical axis, the coordinates would be (-2,5) the first number being the horizontal, second vertical
Find the slant height of this square pyramid Round to the neatest 10th
Answer: 21.9
Step-by-step explanation:
-Use Pythagoras theorem-
To find hypotenuse: square root 15 squared plus 16 squared
= 21.9
What is the value of x in this triangle?
Enter your answer as a decimal in the box. Round only your final
answer to the nearest hundredth. 5, 20, x
Answer:
[tex]\sf x= 14.04^{\circ \:}[/tex]
using tan rule:
[tex]\sf tan(x)= \dfrac{opposite}{adjacent}[/tex]
solve:
[tex]\rightarrow \sf tan(x)= \dfrac{5}{20}[/tex]
[tex]\rightarrow \sf x= tan^{-1}(\dfrac{5}{20})[/tex]
[tex]\rightarrow \sf x= 14.04^{\circ \:}[/tex]
Answer:
x = 14.04° (nearest hundredth)
Step-by-step explanation:
Use the tan trig ratio:
[tex]\mathsf{\tan(\theta)=\dfrac{O}{A}}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleGiven:
[tex]\theta=x[/tex]O = 5A = 20[tex]\implies \mathsf{\tan(x)=\dfrac{5}{20}}[/tex]
[tex]\implies \mathsf{x=\arctan\left(\dfrac{5}{20}\right)}[/tex]
[tex]\implies \mathsf{x=14.04\textdegree \ (nearest \ hundredth)}[/tex]
An angle measures 70° more than the measure of its complementary angle. What is the measure of each angle?
Step-by-step explanation:
Let an angle = x
x= 70+(90-x)
x= 160-x
2x=160
x=80
So angle is 80 and it's complementary angle would be 10
Answer:
55∘ and 125∘
Step-by-step explanation:
Supplementary angles sum to
180∘
let one angle be [tex]x[/tex]
then the other angle is [tex]x+70[/tex]
summing the 2 angles gives
[tex]x+x+7=180[/tex]
[tex]2x+70=180[/tex]
subtract 70 from both sides
[tex]2x=180 -70=110[/tex]
divide both sides by
[tex]2x=\frac{110}{2} =55[/tex]
thus the angles are
55∘ and 55 + 70= 125∘
Arc length and sector area question
Answer:
<aob=1/2(can + ab)
<aob=1/2(25+46)
<aob=1/2(71)
<aob=35.5
area of a trapezoid 6 mm 2 mm 4 mm
Answer:48 mm
Step-by-step explanation:
6 x 2 x 4= 48mm
HELPPP PLS
Find the value of the variable.
Answer:
y = 90[tex]\sqrt{2}[/tex]
Step-by-step explanation:
using the sine ratio in the right triangle and the exact value
sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then using the 45° angle on the lower left
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{90}{y}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
y = 90[tex]\sqrt{2}[/tex]
The sum of the measures of the three interior angles of any triangle is always 180°. The unmarked angles of the triangle below total 150°. angle A triangle.gif What is the measure of an angle that would be complementary to ∠ A ? A. 30° B. 60° C. 90° D. 150°
As rest angles have sum 150°
Using angle sum property
x+150=180x=30°Now
Complementary angles have sum 90°
So the complementary angle is 90-30=60°
Option B
A very large gardening business grows rose bushes for sale to garden stores around the world. The most popular colors are red, pink, and white. The business decides on 50% red roses, 30% pink, and 20% white. A gardener orders 10 rose bushes selected randomly from a huge field. Her primary interest is in pink roses. A good model for the number of bushes with pink roses is given by the binomial distribution. Probability calculations are quicker when using the Normal approximation to the binomial distribution. Which of the following is false
a. The approximation requires np 10 and n(1 â p) 10.
b. The sample size here is too small to use the Normal approximation to the binomial.
c. The approximation requires np 30.
d. The Normal approximation works better if the success probability p is close to p = 0.5.
Complete options are;
a. The approximation requires np > 10 and n(1 - p) > 10.
b. The sample size here is too small to use the Normal approximation to the binomial.
c. The approximation requires np > 30.
d. The Normal approximation works better if the success probability p is close to p = 0.5.
Answer:
Option C is false
Step-by-step explanation:
Looking at the options,
In normal approximation to the binomial,
n is the sample size,
p is the given probability.
q = 1 - p
Now, one of the conditions for using normal approximation to the binomial is that; np and nq or n(1 - p) must be greater than 10.
This means that option A is true because we require np or n(1 - p) to be greater than 10.
From Central limit theorem, the sample size needs to be more than 30 for us to use normal approximation. Our sample is 10. Thus, option B is true.
The approximation doesn't require np > 30. Rather it's the sample size that needs to be more than 30. Thus, option C is false.
Generally, when the value of p in a binomial is close to 0.5, the normal approximations will work better than when the value of p is closer to either 0 or 1. The reason is that: for p = 0.5, the binomial distribution will be symmetrical. Thus, option D is correct.
Find the slope of -5x+4Y=-16
Given parameters:
Find the slope of the line;
-5x + 4y = -16
To find the slope of this line, we must express it in linear form according to the equation below;
y = mx + c
Where x and y are the coordinates
m is the slope
c is the intercept
Now let us write the given equation in this form;
-5x + 4y = -16
Take add +5x to both sides;
-5x + 4y + 5x = 5x - 16
4y = 5x - 16
Now, divide through by 4;
[tex]\frac{4y}{4}[/tex] = [tex]\frac{5x}{4}[/tex] - [tex]\frac{16}{4}[/tex]
y = [tex]\frac{5x}{4} - 4[/tex]
So the slope of the line is [tex]\frac{5}{4}[/tex]
At Ariel's family reunion, Ariel hands out watermelon for the annual seed-spitting contest.
She gives a watermelon slice to each kid at the reunion. She also gives a slice to 40 adults.
Ariel hands out 90 watermelon slices in all.
Which equation can you use to find how many kids k are at the reunion?
k
90
K-40 = 90
k + 40 = 90
40k = 90
40
Solve this equation for k to find how many kids are at the reunion.
kids
Could you please help me on this
Answer:
-x^2 +10x + 7
[tex]-x^2 +10x + 7[/tex]
Step-by-step explanation:
its the gray shaded area [(x+1)*(x+7)] minus the white area [(x-1)*(2x)]
AKA: [(x+1)*(x+7)] - [(x-1)*(2x)]
so first you foil to get both areas
gray region: (x+1)*(x+7) = x^2 + 8x + 7
white region: (x-1)*(2x) = 2x^2 - 2x
and then you subtract the white from the gray
[tex](x^2 + 8x + 7) - (2x^2 - 2x)[/tex]
-x^2 +10x + 7
The area of a baseball field bounded by home plate, first base, second base, and third base is a square. If a player at first base throws the ball to a player at third base, what is the distance the player has to throw? 90 feet is first base 90 feet at third base
Answer:
ta side from one base to next has length of x. so we know each side has length x and the shape they make is a square. This means we are only searching for the diagonal of a square. remember that a diagonal forms and isoscoles right triangle with the 2 sides being equal and the diagonal as the hypotenuse. Using pythagoream theorem we can say
a^2 + b^2 = c^2 all side lengths are x so we can put x in for a and b to get
x^2 + x^2 = c^2
2x^2 = c^2
c = x * squareroot(2)
so if the length between bases is 90 ft
c = 90 ft * squareroot(2)
c = 127.28 ft
Step-by-step explanation:
Answer: C 16,200 squared
Step-by-step explanation:
Question 1 OT TU
A clothing store sells T-shirts, t, for $8 a shirt, shorts, s, for $12, and hats, h, for
$10 each. The store earned $464 revenue last month. The store sold three
times as many T-shirts than hats, and twice as many shorts as hats. Using the
substitution method, how many T-shirts, shorts, and hats did the store sell?
A. t=84; s = 12; h = 10
B. t = 24; s = 8; h= 16
C. t= 8; s = 16; h = 24
D. t = 24; s = 16; h=8
SUBMIT
The circular floor of a teepee has a diameter of 9 yards. What is the circumference of the floor?
30 points pls show ur work thank u so much!!! :)
Answer:
28.26
Step-by-step explanation:
[tex]3.14\times9[/tex]
Calculate the product or quotient
[tex]28.26[/tex]
I hope this helps you
:)
Please answer quickly
The inequality below is equivalent to which of the following? 7−23x 9 B.x>−35 C.x<9 D.x<−35
WORTH ALL MY POINTS
If answers right i will give Brainliest
Answer:
?
Step-by-step explanation:
Lucy invested for 15 years at 2.8%, compounded annually and ended with an account balance of $2250. What was her initial deposit?
Answer:1244
Step-by-step explanation:
Answer:
Step-by-step explanation:
Use the formula for calculating compound interest PN=P0(1+rk)Nk where N is the unknown, PN=2250, k=1, N=15, and r=0.028. Substitute the values into the formula and simplify.
2250=P(1+0.0281)1⋅15
2250=P(1.028)15
2250=P(1.5132...)
1486.91=P
Rounded to the nearest dollar, Lucy's initial deposit was $1487.
Find the length of cable 1 in the diagram below
Answer:
cable 1 ≈ 54.63 ft
Step-by-step explanation:
using Pythagoras' identity in the right triangle having cable 1 as its hypotenuse.
let cable 1 be x , then
x² = 22² + 50² = 484 + 2500 = 2984 ( take square root of both sides )
x = [tex]\sqrt{2984}[/tex] ≈ 54.63 ft ( to 2 dec. places )
Which table of ordered pairs represents a proportional relationship?
Whoever answers correctly and first-will be marked brainiest :)
does anyone know the answer?
Answer:
£0.60
Step-by-step explanation:
If each pack costs £1.59 and Nadia orders 15 packs,
then the total order before discount = 1.59 x 15 = £23.85
From the table given, we can see that for an order of £23.85 a 2.5% discount will be applied.
Divide £23.85 by 100 to get 1%: £23.85 ÷ 100 = £0.2385
Now multiply by 2.5 to get 2.5%: £0.2385 × 2.5 = £0.59625 = £0.60
Alternatively, the calculation in one expression is:
(1.59 × 15) × 0.025 = 0.59625
Sarah wants to know if there is a difference in the time it takes her to run the high trestle trail from Madrid to Woodward based on the type of her running shoes her Hokas or her Asics.
write and solve and equation to find ABE
Answer:
77
Step-by-step explanation:
<DBE and <ABE are supplementary angles so their sum is equal to 180
<DBE is given as 103
103 + <ABE = 180 subtract 103 from both sides
<ABE = 77
1 Suppose that $61,000 is invested at 55% interest, compounded quarterly. a) Find the function for the amount to which the investment grows after t years b) Find the amount of money in the account at t=0.3.7, and 10 years. 12 %
a) The function for the amount to which the investment grows after t years is A(t) = (Simplify your answer. Type an expression using t as the variable )
Answer:
i think its a
Step-by-step explanation:
The function f is defined by f(x)=x-2 . Find f(z-5) .
f(z-5)=z-5-2
f(z-5)=z-9
Which one is it?
A, B, C, or D?
Answer: I'd go with C
Step-by-step explanation:
I need help with this math question
Answer:
-1/4x+3/4
or
-0.25x+0.75
Step-by-step explanation:
g(x) = mx + b
m = slope
b = initial value
m = -1/4
b = 3/4
g(x) = -1/4x+3/4
Hope this helped, let me know if you need more help!