x(t) = t^3 - 12t^2 + 36t
Velocity = x'(t) = 3y^3 - 24t + 36 = 0
x'(t) = t^2 - 8t + 12 = 0
x'(t) = t^2 - 6t - 2t + 12 = 0
x'(t) = t(t - 6) - 2(t - 6) = 0
x'(t) = (t - 2)(t - 6) = 0
t = 2 and t = 6 must be the roots.

Is my answer of D "2 and 6" correct based on this work?

Answer:

mean is 578.3 deviation 261.9

Step-by-step explanation:

Answer with Step-by-step explanation:

As we can see the venn diagram:

number of bird+fish=6

number of bird+not fish=8

number of fish+not bird=19

and number of not fish and not bird=22

Hence, we get the following table

                        Fish           Not Fish            Total

Bird                6                    8                       14

Not Bird         19                  22                       41

Total               25                 30                       55

                Fish    Not Fish   Total

Bird            6            18           14

Not Bird    19           22          41

Total          25           30         55

Answer:

Option B is correct.

add 4 times the second equation to 3 times the first equation

Step-by-step explanation:

Given the system of equation:

[tex]2x - 4y = 6[/tex]                         ......[1]

[tex]-3x + 3y =12[/tex]                       .....[2]

Multiply equation [1] by 3 we get;

[tex]3(2x-4y) = 3 \cdot 6[/tex]

Using distributive property; [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]

6x - 12y = 18                                   .......[3]

Multiply equation [2] by 4 we get;

[tex]4(-3x+3y) = 4 \cdot 12[/tex]

Using distributive property we get;

-12x + 12y = 48                                   ......[4]

Add equation [3] and [4] to eliminate y and solve for x;

(6x -12y) + ( -12x +12y ) = 18 + 48

6x - 12y -12x + 12y = 66

Combine like terms;

6x - 12x = 66

or

-6x = 66

Simplify:

x = -11

Therefore, the operation which could be used to eliminate the y-variable and find the value of x is;

add 4 times the second equation to 3 times the first equation.

Answer:

Option B

Step-by-step explanation:

Given is a system of two equations as

[tex]2x − 4y = 6 \\−3x + 3y = 12[/tex]

To solve them using elimination:

Elimination method is the method of making coefficients of one variable numerically equal

IN the given system we have -4 as coefficient for y in I equation and 3 for y in II equation.

To make them numerically equal with opposite signs we can multiply I equation by 3 and II by 4

WE get

[tex]6x-12y =18\\-12x+12y=48[/tex]

Now if we add these two we are able to eliminate y from the system

Adding gives

[tex]-6x=66\\x=-11[/tex]

So option B is right

Answer:

2b - 3 = 5

Step-by-step explanation:

If her brother read b number of books last summer, twice the number of books her brother read

= 2b

three less than twice as many books as her brother read

= 2b - 3

If haley read five books and it is same as three less than twice as many books as her brother last summer, then

2b - 3 = 5

Answer:

The new length of the enlarged figure will 18 cm.

Step-by-step explanation:

A scale factor is a number which scales, or multiplies the original figure by some quantity.

In the equation [tex]y = Cx[/tex], C is a scale factor for x. It is called the constant of proportionality or scale factor of y to x.

As the given length is 3 cm, so with a scale factor of 6, the length of the enlarged figure will be [tex]3\times 6=18[/tex] cm

Therefore, the new length of the enlarged figure will 18 cm.

By using basic property of inverse function we got that if f(x) and it’s inverse function are both plotted on the same coordinate plane, then their point of intersection is (3,3)

Function is relation between a set to another set with a property that every element of first set has a unique image in second set.

Here graph of f(x) is given and we have to find the point of intersection of function and it's inverse function

We know that a function and it's inverse function are mirror image of each other with respect to line y=x hence they intersect only at y=x line

By drawing y=x line with the given graph we got that f(x) intersect y=x line at (3,3) hence inverse function will intersect at (3,3)

By using basic property of inverse function we got that if f(x) and it’s inverse function are both plotted on the same coordinate plane, then their point of intersection is (3,3)

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When the graph of a function and its inverse function are plotted on the same coordinate plane, the point of intersection is the point where the two graphs intersect. Therefore, the point of intersection is (x, y).

When the graph of a function and its inverse function are plotted on the same coordinate plane, the point of intersection is the point where the two graphs intersect.

Let's say the point of intersection is (x, y).

This means that both f(x) and f-1(x) have the same x-coordinate, which is x, and the same y-coordinate, which is y.

Therefore, the point of intersection is (x, y).

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The student's conversion calculation of speed units from kilometers per minute to miles per hour yields a speed of 2.4 miles/hour, so the answer is choice A.

The question is a conversion exercise in speed units from kilometers per minute to miles per hour. We have the following information: 3.2 km in 50 min, and we know that 1 mile is equivalent to 1.6 km and 60 min is equivalent to 1 hour. Thus, the conversion is as follows:

3.2 km ÷ 50 min. = 0.064 km/min.

Converting km/min to mi/hr involves multiplying by 60 (minutes in an hour) and dividing by 1.6 (km in a mile), and we get:

(0.064 km/min x 60 min/hr) ÷ 1.6 km/mi. = 2.4 mi/hr.

Hence, the correct answer is (A) 2.4 miles/hour.

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[tex] \displaystyle
|\Omega|=\binom{30}{2}=\dfrac{30!}{2!28!}=\dfrac{29\cdot30}{2}=435\\
|A|=\binom{12}{2}=\dfrac{12!}{2!10!}=\dfrac{11\cdot12}{2}=66\\\\
P(A)=\dfrac{66}{435}=\dfrac{22}{145}\approx15\% [/tex]

The measure of side a is 14.

We have,

We use the trigonometric identites:

Sin function

Now,

Sin A = Perpendicular / Hypotenuse

Sin 34 = a / 25

0.56 = a / 25

a = 0.56 x 25

a =  14

Thus,

The measure of side a is 14.

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The height of cylinder is,

⇒ h = 2.4 inches

We have to given that,

In a cylinder,

Volume = 271.4 inches³

And, Radius = 6 inch

Since, We know that,

Volume of cylinder is,

⇒ V = πr²h

Where, V is volume , r is radius and h is height.

Substitute all the values, we get;

⇒ 271.4 = 3.14 × 6² × h

⇒ 271.4 = 3.14 × 36 × h

⇒ 271.4 = 113.04 × h

⇒ h = 2.4 inches

Thus, The height of cylinder is,

⇒ h = 2.4 inches

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