what are the impact test, and the types of impact test explain in details with drawing

Find the solutions to (-1+x^2)y''+4xy'+2y=0

y_1=?

y_2=?

Consider the equation xln(x)= 1 for x≥1. In this problem, you are asked to show that this equation has a unique solution 1≤x <∞by completing both parts below. Note that you are not asked to find this solution, just to show that it exists and that it is unique!

(a) Show that the equation has at least one solution x such that 1≤x <∞.

(b) Show that the equation has at most one solution x such that 1≤x <∞.

1. List the possible rational zeros of the the polynomial function. Do not find the zeros.

f ( x ) = 3 x 5 − 5 x 2 + 6 x − 1

A) ± 1 , ± 3

B) ± 1 , ± 1 3

C) ± 1 , ± 1 3 , ± 3

D) ± 3 , ± 1 3

Group of answer choices

A

B

C

D

2. Find zeros and write the polynomial in factored form.

P ( x ) = 4 x 3 − 11 x 2 − 6 x + 9

A) − 1 , 3 4 , 3 ; P ( x ) = ( 4 x − 3 ) ( x − 3 ) ( x + 1 )

B)− 1 , 4 3 , − 3 ; f ( x ) = ( 4 x − 3 ) ( x − 3 ) ( x + 1 )

C) − 3 , 3 4 , 1 ; f ( x ) = ( 4 x − 3 ) ( x − 1 ) ( x + 3 )

D) 1 , 4 3 , − 3 ; f ( x ) = ( 4 x − 3 ) ( x − 1 ) ( x + 3 )

Group of answer choices

A

B

C

D

3. Find a polynomial P ( x ) of degree 3 that has integer coefficients and zeros 1 + i and 8

A) P ( x ) = x 3 + 6 x 2 + 16 x − 14

B)  P ( x ) = x 3 + x 2 − 14 x + 16

C)  P ( x ) = x 3 − 8 x 2 − 14 x − 12

D)  P ( x ) = x 3 + 6 x 2 − 14 x + 16

Group of answer choices

A

B

C

D

4. Given f ( x ) = 2 x + 6and  g ( x ) = 4 x 2 + 1. Find  ( g ∘ f ) ( 1 ).

5. The function f is one-to-one. Find its inverse.

f ( x ) = ( x + 2 ) 3 − 8

A) f − 1 ( x ) = x + 8 3 − 2

B) f − 1 ( x ) = x + 10 3

C)  f − 1 ( x ) = x + 6 3

D)  f − 1 ( x ) = x − 2 3 + 8

Group of answer choices

A

B

C

D

7. Find the domain of the function.

f ( x ) = log 7 ⁡ ( 9 − x 2 )

A) ( − ∞ , − 2 ) ∪ ( 2 , ∞ )

B) ( − 2 , 2 )

C) ( − 4 , 4 )

D) [ − 2 , 2 ]

Group of answer choices

A

B

C

D

10. Find the amount in a savings account at the end of 9 years if the amount originally deposited is $9000 and the interest rate is 7% compounded semiannually. Round your answer in two decimal places.

Group of answer choices

A) $12,266.08

B) $18,389.14

C) $167,670.00

D) 16,717.40

11. Find out how long it takes a $2900 investment to double if it is invested at 7% compounded semiannually. Round to the nearest tenth of a year.

Group of answer choices

A) 10.3 yr

B) 10.1 yr

C) 9.9 yr

D) 10.5 yr

Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(t) = 2 cos(t),    −3π/2 ≤ t ≤ 3π/2

Find the absolute maximum and absolute minimum values of f on the given interval.

f(x) = x³ − 5x + 8,    [0, 3]

Let {an} be a sequence defined recursively by a1 = 1 and an+1 = 2√ 1 + an where n ∈ N

(b) Does {an} converge or diverge? Justify your answer, making sure to cite appropriate hypotheses/theorem(s) used. Hint : Try BMCT [WHY?].

(c) (Challenge) If {an} converges then find its limit. Make sure to fully justify your answer.

1. Find an equation of the tangent line to the graph of x^2 + 4xy + y^2 =13 at point (2,1), by using implicit differentiation.

1.) Find the local maximum and minimum values and saddle point(s) (x,y,f) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f (x, y) = xy − 5x − 5y − x2 − y2

2.)Find the local maximum and minimum values and saddle point(s)(x,y,f) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x, y) = x3 + y3 − 3x2 − 9y2 − 9x

3.)Find the local maximum and minimum values and saddle point(s)(x,y,f) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x, y) = 5y cos(x), 0 ≤ x ≤ 2π

Consider the following figure. A hexagon has six labeled vertices and a dashed line segment which divides the hexagon into a trapezoid and rectangle. The first side is horizontal, starts at vertex R, goes to the right, and ends at vertex S. The second side is vertical, starts at vertex S, goes up, and ends at vertex T. The third side starts at vertex T, goes up and to the right, and ends at vertex V. The fourth side is horizontal, starts at vertex V, goes to the left, and ends at vertex W. The fifth side starts at vertex W, goes down and to the right, and ends at vertex X. The sixth side is vertical, starts at vertex X, goes down, and ends at vertex R. ∠R and ∠S are right angles. A dashed line segment connects vertex X to vertex T. The trapezoid is created above the segment and the rectangle below the segment. Given: hexagon RSTVWX with WV ∥ XT ∥ RS RS = 10 ST = 6 TV = 10 WV = 22 WX ≅ VT Find: ARSTVWX in square units

Solve the given system of differential equations by systematic elimination.

I had this as my answer and webassign rejected it:

(x(t), y(t)) = c_1e^t+e^{-\left(\frac{t}{2}\right)}\left(c_2\cos \left(\frac{\sqrt{3}}{2}t\right)+c_3\sin \left(\frac{\sqrt{3}}{2}t\right)\right),e^{-\left(\frac{t}{2}\right)}\left(\left(-\frac{3}{2}c_2-\frac{3\sqrt{3}.}{4}c_3\right)\cos \left(\frac{\sqrt{3}}{2}t\right)+\left(\frac{-3}{2}c_3+\frac{3\sqrt{3}}{4}c_2\right)\sin \left(\frac{\sqrt{3}}{2}t\right)\right)

An isosceles right triangle, whose hypotenuse is 12 ft long, is submerged vertically so that the hypotenuse is parallel to the surface of the water. If its vertex is 3 ft above the surface, find the total force on one side of the plate?

The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find lower and upper estimates for the distance that she traveled during these three seconds.

Part 1 of 5

We will use either L₆ or R₆ for the upper and lower estimates.

Since the runner's speed is an increasing function, then  

will give the lower estimate, and

will give the upper estimate.

1. What is the difference between the Riemann integral and the Darboux Integral?

2. Give the same characteristics between Riemann integrals and Darboux integrals !.