HELP LAST ATTEMPT !?!!

Answer:

.7314

Step-by-step explanation:

I plugged this number into the calculator and got .7313537016, and then rounded it to the fourth decimal place, which gave me my answer

Functions can be used to model real life scenarios

The function is given as:

[tex]\mathbf{V(t) = -t^3 + t^2 + 12t}[/tex]

(a) Sketch V(t)

See attachment for the graph of [tex]\mathbf{V(t) = -t^3 + t^2 + 12t}[/tex]

(b) The reasonable domain

t represents the number of weeks.

This means that: t cannot be negative.

So, the reasonable domain is: [tex]\mathbf{[0,\infty)}[/tex]

(c) Average rate of change from t = 0 to 2

This is calculated as:

[tex]\mathbf{m = \frac{V(a) - V(b)}{a - b}}[/tex]

So, we have:

[tex]\mathbf{m = \frac{V(2) - V(0)}{2 - 0}}[/tex]

[tex]\mathbf{m = \frac{V(2) - V(0)}{2}}[/tex]

Calculate V(2) and V(0)

[tex]\mathbf{V(2) = (-2)^3 + (2)^2 + 12 \times 2 = 20}[/tex]

[tex]\mathbf{V(0) = (0)^3 + (0)^2 + 12 \times 0 = 0}[/tex]

So, we have:

[tex]\mathbf{m = \frac{20 - 0}{2}}[/tex]

[tex]\mathbf{m = \frac{20}{2}}[/tex]

[tex]\mathbf{m = 10}[/tex]

Hence, the average rate of change from t = 0 to 2 is 20

(d) The instantaneous rate of change using limits

[tex]\mathbf{V(t) = -t^3 + t^2 + 12t}[/tex]

The instantaneous rate of change is calculated as:

[tex]\mathbf{V'(t) = \lim_{h \to \infty} \frac{V(t + h) - V(t)}{h}}[/tex]

So, we have:

[tex]\mathbf{V(t + h) = (-(t + h))^3 + (t + h)^2 + 12(t + h)}[/tex]

[tex]\mathbf{V(t + h) = (-t - h)^3 + (t + h)^2 + 12(t + h)}[/tex]

Expand

[tex]\mathbf{V(t + h) = (-t)^3 +3(-t)^2(-h) +3(-t)(-h)^2 + (-h)^3 + t^2 + 2th+ h^2 + 12t + 12h}[/tex][tex]\mathbf{V(t + h) = -t^3 -3t^2h -3th^2 - h^3 + t^2 + 2th+ h^2 + 12t + 12h}[/tex]

Subtract V(t) from both sides

[tex]\mathbf{V(t + h) - V(t)= -t^3 -3t^2h -3th^2 - h^3 + t^2 + 2th+ h^2 + 12t + 12h - V(t)}[/tex]

Substitute [tex]\mathbf{V(t) = -t^3 + t^2 + 12t}[/tex]

[tex]\mathbf{V(t + h) - V(t)= -t^3 -3t^2h -3th^2 - h^3 + t^2 + 2th+ h^2 + 12t + 12h +t^3 - t^2 - 12t}[/tex]

Cancel out common terms

[tex]\mathbf{V(t + h) - V(t)= -3t^2h -3th^2 - h^3 + 2th+ h^2 + 12h}[/tex]

[tex]\mathbf{V'(t) = \lim_{h \to \infty} \frac{V(t + h) - V(t)}{h}}[/tex] becomes

[tex]\mathbf{V'(t) = \lim_{h \to \infty} \frac{ -3t^2h -3th^2 - h^3 + 2th+ h^2 + 12h}{h}}[/tex]

[tex]\mathbf{V'(t) = \lim_{h \to \infty} -3t^2 -3th - h^2 + 2t+ h + 12}[/tex]

Limit h to 0

[tex]\mathbf{V'(t) = -3t^2 -3t\times 0 - 0^2 + 2t+ 0 + 12}[/tex]

[tex]\mathbf{V'(t) = -3t^2 + 2t + 12}[/tex]

(e) V(2) and V'(2)

Substitute 2 for t in V(t) and V'(t)

So, we have:

[tex]\mathbf{V(2) = (-2)^3 + (2)^2 + 12 \times 2 = 20}[/tex]

[tex]\mathbf{V'(2) = -3 \times 2^2 + 2 \times 2 + 12 = 4}[/tex]

Interpretation

V(2) means that, 20 people were infected after 2 weeks of the virus spread

V'(2) means that, the rate of infection of the virus after 2 weeks is 4 people per week

(f) Sketch the tangent line at (2,V(2))

See attachment for the tangent line

The slope of this line is:

[tex]\mathbf{m = \frac{V(2)}{2}}[/tex]

[tex]\mathbf{m = \frac{20}{2}}[/tex]

[tex]\mathbf{m = 10}[/tex]

The slope of the tangent line is 10

(g) Estimate V(2.1)

The value of 2.1 is

[tex]\mathbf{V(2.1) = (-2.1)^3 + (2.1)^2 + 12 \times 2.1}[/tex]

[tex]\mathbf{V(2.1) = 20.35}[/tex]

(h) The maximum number of people infected at the same time

Using the graph, the maximum point on the graph is:

[tex]\mathbf{(t,V(t) = (2.361,20.745)}[/tex]

This means that:

The maximum number of people infected at the same time is approximately 21.

The rate of infection at this point is:

[tex]\mathbf{m = \frac{V(t)}{t}}[/tex]

[tex]\mathbf{m = \frac{20.745}{2.361}}[/tex]

[tex]\mathbf{m = 8.79}[/tex]

The rate of infection is 8.79 people per week

Read more about graphs and functions at:

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Answer:

180 kids chose French

Step-by-step explanation:

40/100 = x/450

4/10 = x/450

10•45= 450

4•45= 180

Answer:

5 would be the dependent variable.

Step-by-step explanation:

5 would be the dependent variable because that is the number that is that depends on the others in the equation for it to be the final answer.

Answer:

180

Step-by-step explanation:

k = 72/2=36

y =kx

y =36(5)

y = 180

Answer:

$600

Equation:

(Base) x (percent as a decimal) x (years) = interest

(B x .16 x 7.5 = 720)

Steps:

(Base) x (percent as a decimal) = (interest) / (years)

(B x .16 = 96)

Base = (interest / years) / (percent as a decimal)

(B = 600)

9514 1404 393

Answer:

  D.  J(x) = 1/4(-x)^3

Step-by-step explanation:

Reflection across the y-axis replaces x with -x. Then if Fr(x) represents the reflected function, we have ...

  Fr(x) = (-x)^3.

Compression by a factor of c < 1 multiplies the function value by c. Then ...

  J(x) = 1/4·Fr(x)

  J(x) = (1/4)(-x)^3

The only set of side lengths that can form a triangle is 9, 4, 8.

Option A is the correct answer.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Let's check if each of the given sets of side lengths satisfies this condition:

A.

9, 4, 8

9 + 4 > 8 ✓

9 + 8 > 4 ✓

4 + 8 > 9 ✓

All three inequalities are true, so these side lengths can form a triangle.

B.

14, 7, 6

14 + 7 > 6 ✓

14 + 6 > 7 ✓

7 + 6 > 14 ✗

The last inequality is false, so these side lengths cannot form a triangle.

C.

3, 8, 1

3 + 8 > 1 ✓

3 + 1 > 8 ✗

8 + 1 > 3 ✓

The second inequality is false, so these side lengths cannot form a triangle.

Therefore,

The only set of side lengths that can form a triangle is A. 9, 4, 8.

Learn more about triangles here:

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Answer:

6 ang

Step-by-step explanation:

mark me as brainliest

Answer:

no

Step-by-step explanation:

Answer:

38 meters below sea level.

Step-by-step explanation:

if the sub dives 155 BELOW sea level, this equals -155.

then it RISES 117 meters, which equals +117.

we can make this into an  equation

-155+117=-38!

the location of the sub is 38 meters below sea level.

Answer:

A. 17 feet

Step-by-step explanation:

We can't find volume through given information.

Lets find the area

[tex]\\ \sf\longmapsto Area=LB[/tex]

[tex]\\ \sf\longmapsto Area=\dfrac{7}{2}\times \dfrac{9}{4}[/tex]

[tex]\\ \sf\longmapsto Area=\dfrac{63}{6}[/tex]

Simplify the expression:

7 + -10c² + 100

collect like terms:

7+100-10c²

107-10c²

If you meant, 7+ -10c² + 10c, then it can't be simplified further as there are no like terms.

Answer:

64.2857

Step-by-step explanation:

take the distance traveled divided by the distance which will give you the speed traveling multiplying the distance and the speed will give you the time ot takes

Answer:

correct

Step-by-step explanation:

Answer:

221

Step-by-step explanation:

109×2+3=221, pattern is x2+3

--

4×2+3=11

11×2+3=25

25×2+3=53

53×2+3=109

Answer:

A= 5.6 x 5.6 = 31.36

P= 5.6 × 4 = 22.4

Step-by-step explanation:

to find the area of a square, just take the length of 1 side and square it (A= length^ 2)

to find the perimeter of a square multiply length by 4 sides.

*these formulas only hold true for squares bc the length of each side is the same.

Answer:

40i²-5i+45

Step-by-step explanation:

Answer: 0.2

happy learning

Answer:

$8,704

Step-by-step explanation:

Answer:

Quadratic equation in vertex form: y = 2(x + 3)²+ 0

Step-by-step explanation:

The vertex form of a quadratic equation is:

y = a (x - h)² + k  where:

The value of a determines that the graph opens up or down.  If a is positive, the graph opens up. The value of a also makes the parent function wider or narrower.  

The vertex of the given parabola occurs at point (h, k) where the parabola intersects the axis of symmetry, x = h. It is also determines whether it is either the maximum or minimum point on the graph.

The quadratic equation of the graph in vertex form is: y = 2(x + 3)²+ 0

where:

a = 2

vertex (minimum point) = (-3, 0)

axis of symmetry: x = -3

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Answer:

C

Step-by-step explanation:

To write the equation of line when slope and one point is given

[tex]y2 - y1 = m(x2 - x1)[/tex]

here m = 3/4

(x1,y1) = 3,-2

Substitute all the values in Formula

[tex]y + 2 = \frac{3}{4} (x - 3) \\ y + 2 = \frac{3}{4} x - \frac{9}{4} \\ y = \frac{3}{4} x - \frac{9}{4} - 2 \\ = \frac{3}{4} x - \frac{17}{4} \\ 4y = 3x - 17 \\ - 3x + 4y = - 17[/tex]

multiply by 4 on both sides

[tex]4y = 3x - 17 \\ - 3x + 4y = - 17[/tex]

Answer:

5+5+9+9 = 28 cm

Step-by-step explanation:

to determine perimeter add the length of each side (2 sides = 5cm and two sides = 9cm.)

Answer:

[tex]\sf\longmapsto \: x = 4[/tex]

Step-by-step explanation:

[tex]\sf\longmapsto \: 4x = 16[/tex]

[tex]\sf\longmapsto \: x = \frac{16}{4} [/tex]

[tex]\sf\longmapsto \: x = 4[/tex]