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4=∣−3a+4∣ Solve for all values of a in simplest form. Answer Attempt 2 out of 2
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1، a. Identify all possible zeros of the function P(x)=3+x2−8x+4.
b. Use a graphing calculator to prove one of the zeros. SHOW ALL WORK!!!
c. Use factoring to find the remaining zeros. SHOW ALL WORK!!!
Verifica di Matematica, dicembre 2024 A) Dati i punti A(2k;1), B(k+3;k−3) e C(4−k,k)
Si determini per quali valori del parametro reale k: 1)il punto medio di AB appartiene all'asse x (1 punto)
2)il segmento AC non interseca l'asse y (1 punto)
3)il baricentro del triangolo ABC si trova sulla retta di equazione y=1−x (1 punto)
The position of a body at time tsec is s=t3−9t2+24tm. Find the body's acceleration each time the velocity is zero. The body's acceleration each time the velocity is zero is □m/s2
(Simplify your answer. Use a comma to separate answers as needed.)
Solve for x and graph the solution on the number line below. If possible, resolve your answer to a single inequality. In case of no solution ( ∅ ), leave the number line blank.
3x−2≤−26 and 3x−2<31
For the given functions, f(x)=x2+3 and g(x)=5x−3, find the indicated composition. Write your answer by filling-in the blanks. a. (f∘g)(x)= b. (f∘g)(4)= Moving to another question will save this response. Question 21 of 23
Solve for x and graph the solution on the number line below. If possible, resolve your answer to a single inequality. In case of no solution ( ∅ ), leave the number line blank.
2x+10≥30 or 2x+10>34
Divide using long division.
x−43x4+3x3+3x−5
Enter the quotient (without the remainder). Quotient: Enter the remainder. For example, if the remainder is 10, enter 10. If there is no remainder, enter 0. Remainder:
Return the question paper and blue book at the
(b) Approximate ∫00.41+x of f(x)=ln(3−x) at a=0 and its radius of convergence.
x4dx correct to 5 decimal places.
the series 1+π+2!π2+3!π3+4!π4+…
the curve x=3cost−cos3t,y=3sint−sin3t,0≤t≤3π/2.
gion bounded by y=2−x2 and y=x. 6. Evaluate the integral or show that it is divergent.
(a) ∫2∞xlnxdx
(b) ∫−∞∞4x2+4x+5dx 7. A force of 6x−2 newtons moves an object along a straight line when it is x meters from the origin. Calculate the work done in moving the object from x=4m to x=8m. 8. Fine the area of the surface obtained by rotating y=5−x about the x-axis for 3≤x≤5. 9. Find the volume generated by y=ex,y=e−x,x=1, about the y-axis. Hint: It may be easier to use the method of cylindrical shells, but you are free to use other methods, provided that you clearly show your work.
Find all values of m for which the equation has two complex (non-real) solutions. 4v+(m+3)=−5v2 Write your answer starting with m, followed by an equals sign or inequality symbol (for example, m<5). Reduce all fractions.
Question
Given f(x)=x−4−2x2−6x+20, which of the following statements are true? Select the correct answer below:
f(x) has a removable discontinuity at x=4.
f(x) has a jump discontinuity at x=4f(x) has an infinite discontinuity at x=4.
f(x) is continuous at x=4
For the polynomial function f(x)=x2(x−2)3(x+4), answer parts a through e. a. Use the Leading Coefficient Test to determine the graph's end behavior.
Which of the following is the correct statement about the end behavior of the given function? A. The graph falls to the left and to the right.
B. The graph rises to the left and to the right.
C. The graph rises to the left and falls to the right.
D. The graph falls to the left and rises to the right.
Two roots of the polynomial function
f(x)=x3−7x−6 are −2 and 3 Use the fundamental theorem of algebra and the complex conjugate theorem to determine the number and nature of the remaining root(s). Explain your thinking.
DONE
A)1−21x2−31x3B)1−21x2−34x3C)1−21x2+32x3D)1−21x2−31x3E)1−21x+32x2 6. Déterminez les trois premiers termes non nuls de la série de Maclaurin de (1−x)ex.
Verify that the origin is a regular singularity of each of the equations 2−6 and that the roots of the indicial equation (40.38) do not differ by an integer. Find, by the method of Frobenius, two independent solutions of each equation and intervals of convergence. 2. x2y′′+x(x+21)y′+xy=0.
Compare the amplitudes and periods of the functions y=21cosx and y=3cos2x. The amplitude of y=21cosx is □ and the amplitude of y=3cos2x is □ . The period of y=21cosx is and the period of y=3cos2x is □ .
For the functions f(x)=x+1x and g(x)=x11, find the composition f∘g and simplify your answer as much as possible. Write the dor notation.
(f∘g)(x)=□ Domain of f∘g : □
Determine the location of each local extremum of the function.
f(x)=x3+7x2+8x+3
A. Local maximum at −34; local minimum at -2
B. Local maximum at 2 ; local minimum at 34
C. Local maximum at 32; local minimum at 4
D. Local maximum at -4 ; local minimum at 3−2
Quadratic Equations Unit Test Part 1 Which of the following quadratic equations is not solvable by grouping? 2x2−2x−10=0 2x2+14x+12=0 x2−2x+1=0 x2−12x+35=0
Calculate the distance between the points L=(−3,−1) and K=(5,−7) in the coordinate plane.
Give an exact answer (not a decimal approximation). Distance: □ □□□
Suppose that the functions g and h are defined as follows.
g(x)=x+7h(x)=(x−6)(x+6)
(a) Find (hg) (2).
(b) Find all values that are NOT in the domain of hg. If there is more than one value, separate them with commas.
(a) (hg)(2)=□
(b) Value(s) that are NOT in the domain of hg :