Explain how to determine the zeros of the function below, and also
identify the zeros of this function

Answer:

a) 0 seconds.

b) The stunt diver is in the air for 2.81 seconds.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]

[tex]\Delta = b^{2} - 4ac[/tex]

Height of the diver after t seconds:

[tex]h(t) = -4.9t^2 + 12t + 5[/tex]

a) How long is the stunt diver above 15 m?

Quadratic equation with [tex]a < 0[/tex], so the parabola is concave down, and it will be above 15m between the two roots that we found for [tex]h(t) = 15[/tex]. So

[tex]h(t) = -4.9t^2 + 12t + 5[/tex]

[tex]15 = -4.9t^2 + 12t + 5[/tex]

[tex]-4.9t^2 + 12t - 10 = 0[/tex]

Quadratic equation with [tex]a = -4.9, b = 12, c = -10[/tex]. Then

[tex]\Delta = 12^{2} - 4(-4.9)(-10) = -52[/tex]

Negative [tex]\Delta[/tex], which means that the stunt diver is never above 15m, so 0 seconds.

b) How long is the stunt diver in the air?

We have to find how long it takes for the diver to hit the ground, that is, t for which [tex]h(t) = 0[/tex]. So

[tex]h(t) = -4.9t^2 + 12t + 5[/tex]

[tex]0 = -4.9t^2 + 12t + 5[/tex]

[tex]-4.9t^2 + 12t + 5 = 0[/tex]

Quadratic equation with [tex]a = -4.9, b = 12, c = 5[/tex]. Then

[tex]\Delta = 12^{2} - 4(-4.9)(5) = 242[/tex]

[tex]x_{1} = \frac{-12 + \sqrt{242}}{2*(-4.9)} = -0.36[/tex]

[tex]x_{2} = \frac{-12 - \sqrt{242}}{2*(4.9)} = 2.81[/tex]

Time is a positive measure, so we take 2.81.

The stunt diver is in the air for 2.81 seconds.

Answer:

a. add the equations to eliminate x

Step-by-step explanation:

this is called process of elimination

- 9 3 x 7 5

To get the combination that would yield the greatest result if the true number are multiplied,

i. multiply each given combination

73 x 95 = 6935

79 x 53 = 4187

97 x 35 = 3395

93 x 75 = 6975

ii. get the largest result from the results calculated above in (i)

The greatest of the results is 6975, therefore the digits should be placed like so;

9   3

7   5

Answer:  378y^3

Step-by-step explanation:

the formula for volume is V = L * w * h , where V=volume, L=length, W=width, and H=height

if we plug the numbers from the picture in, the formula would look like this:

V = 9y * 7y * 6y

to solve you just multiply them together

V = 378 y^3

Answer:

The one on the right

Step-by-step explanation:

Because it is 4 then 3

Answer:

the second one (the one to the right)

Step-by-step explanation:

Answer:

Presently; Veeru is 15 and Neeru is 20

Step-by-step explanation:

Given

See comment for proper format of question

Let their present ages be x and y

So:

[tex]x : y = 3 : 4[/tex]

5 years time, the ratio will be:

[tex]x + 5: y + 5= 4 : 5[/tex]

Required

Their present ages

Express both ratios as fractions

[tex]x : y = 3 : 4[/tex] becomes

[tex]\frac{x}{y} = \frac{3}{4}[/tex]

and

[tex]x + 5: y + 5= 4 : 5[/tex] becomes

[tex]\frac{x+5}{y+5} = \frac{4}{5}[/tex]

Make x the subject in: [tex]\frac{x}{y} = \frac{3}{4}[/tex]

[tex]x = \frac{3}{4}y[/tex]

[tex]x = 0.75y[/tex]

Cross multiply in [tex]\frac{x+5}{y+5} = \frac{4}{5}[/tex]

[tex]5(x + 5) = 4(y + 5)[/tex]

Substitute [tex]x = 0.75y[/tex]

[tex]5(0.75y + 5) = 4(y + 5)[/tex]

Open brackets

[tex]3.75y + 25 = 4y + 20[/tex]

Collect like terms

[tex]3.75y -4y = -25 + 20[/tex]

[tex]-0.25y = -5[/tex]

Divide by -0.25

[tex]y = 20[/tex]

Substitute [tex]y = 20[/tex] in [tex]x = 0.75y[/tex]

[tex]x = 0.75 * 20[/tex]

[tex]x = 15[/tex]

Answer:

i had the exact same question as this, dm me on discord so i can screenshare my answer

Step-by-step explanation:

jey0001 is my discord

Answer:

12 hours

Step-by-step explanation:

pages total = pages written + pages per hour * number of hour

47 = 11 + 3*h

Subtract 11 from each side

47 -11 = 11 +3h -11

36 = 3h

Divide by 3

36/3 = 3h/3

12 = h

Answer:

Michelle invested $ 6,400 at 8% and $ 3,600 at 12%.

Step-by-step explanation:

Given that Michelle invested $ 10,000 for one year, part at 8% interest and the rest at 12% annual interest, and her total interest for the year was $ 944, to determine how much money did she invest at 12% interest, the following calculation must be done:

10,000 x 0.08 + 0 x 0.12 = 800

8,000 x 0.08 + 2,000 x 0.12 = 880

4,500 x 0.08 + 5,500 x 0.12 = 1,020

6,000 x 0.08 + 4,000 x 0.12 = 960

6,500 x 0.08 + 3,500 x 0.12 = 940

6,400 x 0.08 + 3,600 x 0.12 = 944

Therefore, Michelle invested $ 6,400 at 8% and $ 3,600 at 12%.

Answer:

B. (8, -54)

Step-by-step explanation:

y = -7x + 2

Check to see if the point makes the equation true

A. (1,2)  2 = -7(1)+2 = -7+2 = 5   False

B. (8, -54) -54 = -7(8)+2 = -56+2 = -54  True

C. (5, -35)  -35 = -7(5) +2 = -35+2 = -33 False

D. (1, -7)  -7 =-7(1)+2 = --7+2 = -5  False

Answer:

a- x = 5/3, or x = -7/2

b- 675

c - 5·x + 2

Step-by-step explanation:

The polynomial representing the capital of the two partners = 6·x² + 11·x - 35

a. The total share is the capital of the two partners together = 6·x² + 11·x - 35

∴ When their total share is equal to 0, we have;

6·x² + 11·x - 35 = 0

Factorizing the above equation with a graphing calculator gives;

(3·x - 5)·(2·x + 7)

Therefore;

x = 5/3, or x = -7/2

b- The total expenditure, when x = 10 is given by substituting the value of x in the polynomial 6·x² + 11·x - 35, as follows;

When x = 10

6·x² + 11·x - 35 = 6 × 10² + 11 × 10 - 35 = 675

The total expenditure of Vicky and Micky when x = 10 is 675

c - The sum of their expenditure is (3·x - 5) + (2·x + 7) = 5·x + 2

Answer:

Explanation:

Hey there!

Please see your required solution in picture.

Quotient Q(X) = 3x²-x+4

Hope it helps!

Answer:

see image

Step-by-step explanation:

Plato/Edmentum

Answer:

a

Step-by-step explanation:

The first four terms of the sequence are 3, 7, 15, and 31. This sequence is represented using an explicit geometric formula.

A rule is defined such that its definition includes itself.

Example:

F(x) = F(x-1) + c

is one such recursive rule.

PART A:

State the first four terms of this sequence.

[tex]a_1 = 3\\\\a_n = 1+ 2a_{n-1}[/tex]

[tex]a_2 = 1+ 2a_{2-1}\\\\a_2 = 1+ 2a_{1}\\\\a_2 = 7\\\\a_3 = 1+ 2a_{2}\\\\a_3 = 15\\\\a_4 = 1+ 2a_{3}\\\\a_4 = 31\\[/tex]

PART B:

This sequence is represented using an explicit geometric formula.

Learn more about the recursive rule and explicit rule here:

https://brainly.com/question/12620593

#SPJ2

i wonder this is math problem or code word for treasure

Answer:

Step-by-step explanation:

(2x-15) = 45

Step-by-step explanation:

When two angles lie on a straight line, they are supplementary

what this mean is that the add up to equal 180 degrees

Mathematically, we have this as:

(2x-15) + 135 = 180

(2x-15) = 180-135

(2x-15) = 45

Answer:

metals or metalloids

Step-by-step explanation:

I'm built different i dont know if im right about the question. im just not sure if i understood the question correctly

Answer:

[tex]\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}}} \, dx = \infty[/tex]

General Formulas and Concepts:

Algebra I

Calculus

Limits

Limit Rule [Variable Direct Substitution]:                                                             [tex]\displaystyle \lim_{x \to c} x = c[/tex]

Derivatives

Derivative Notation

Basic Power Rule:

Integrals

Integration Constant C

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]

U-Substitution

U-Solve

Improper Integrals

Exponential Integral Function:                                                                              [tex]\displaystyle \int {\frac{e^x}{x}} \, dx = Ei(x) + C[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx[/tex]

Step 2: Integrate Pt. 1

Step 3: Integrate Pt. 2

Identify variables for u-substitution.

Rewrite u-substitution to format u-solve.

Step 4: Integrate Pt. 3

∴  [tex]\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx[/tex]  diverges.

Topic: Multivariable Calculus

Answer:

Step-by-step explanation:544

Answer:

total weight of wheat and rice is 8 kg

Step-by-step explanation:

rice = [tex]3\frac{3}{2}[/tex]

=3*2+3/2

=9/2

wheat = [tex]2\frac{1}{2}[/tex]

=2*2+1/2

=5/2

total weight of wheat and rice = [tex]\frac{7}{2} + \frac{9}{2}[/tex]

since their denominator are same u can add numerators.

=7 +9/2

=16/2

=8

Answer: True

Through the change of base formula, we can say,

[tex]\log_{2}(1) = \frac{\log(1)}{\log(2)} = \frac{0}{\log(2)} = 0[/tex]

So in short,

[tex]\log_{2}(1)=0[/tex]

It turns out that

[tex]\log_{b}(1) = 0[/tex]

for real numbers b such that b > 0 and [tex]b \ne 1[/tex]

Answer:

[tex]10\frac{7}{18}[/tex]

Step-by-step explanation:

First revert it to improper fraction.

[tex]\frac{13}{2} +\frac{35}{9} \\\\[/tex]

Now put them to a common denominator.

[tex]\frac{187}{18}[/tex]

=> [tex]10\frac{7}{18}[/tex]

Answer:

=−4√2​

I got this when simplified.

Answer:

[tex]8x3+24x2+10x+30= 2[(4x^2+5)(x+3)][/tex]

Step-by-step explanation:

Given

[tex]8x3+24x2+10x+30= 2(4x^3+12x^2+5x+15)[/tex]

[tex]8x3+24x2+10x+30= 2[4x^2(x+3)+5(x+3)][/tex]

Required

The complete factored form

We have:

[tex]8x3+24x2+10x+30= 2[4x^2(x+3)+5(x+3)][/tex]

Factor out x + 3

[tex]8x3+24x2+10x+30= 2[(4x^2+5)(x+3)][/tex]

The above represents the completely factored form

Answer:

C on edge

Step-by-step explanation:

I took the test

Answer:

-5/2

Step-by-step explanation:

Perpendicular slope is always the negative reciprical. This basically means the opposite sign and the nubers are flipped.

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