The mass of the part of a metal rod that lies between its left end and a point x meters to the right is 3x^2 kg. Find the linear density when is 1 m, Where is the density the highest? The lowest?

Answer:

[tex]\bold{y=2.5x^2+7x+3.3}[/tex]

Step-by-step explanation:

Given:

Parabola with

x − intercepts (−2.2, 0) and (−0.6, 0)

and

y − intercept (0,3.3)

To find:

Equation of parabola ?

Solution:

We can use factored form to find the equation of the parabola.

[tex]y=a(x-\alpha)(x-\beta)[/tex]

Where [tex]\alpha, \beta[/tex] are the x intercepts.

Let use put

[tex]\alpha = -2.2\\\beta = -0.6[/tex]

[tex]y=a(x-(-2.2))(x-(-0.6))\\\Rightarrow y =a(x+2.2)(x+0.6)[/tex]

Now, let us put y − intercept (0,3.3) in the above equation to find the value of a.

[tex]\Rightarrow 3.3 =a(0+2.2)(0+0.6)\\\Rightarrow 33 =a(22)(0.6)\\\Rightarrow 3 = 2a\times 0.6\\\Rightarrow a = 2.5[/tex]

So, the equation becomes:

[tex]\Rightarrow y =2.5(x+2.2)(x+0.6)\\\Rightarrow \bold{y=2.5x^2+7x+3.3}[/tex]

Answer: 9

Step-by-step explanation:

4+6x+5=7x

-6x -6x

=

4+5=1x

9=1x

X=9

Answer:

according to me

Step-by-step explanation:

yes u r correct

;]

Answer:

10% discounted

Step-by-step explanation:

500× X = 450

while X is the sale price

so we solve for X

(500X)÷500 = 450 ÷ 500

X = 0.9

then we turn that into percentage

0.9 × 100 = 90%

finding the discount percentage

100% - 90% = 10%

f(x) represents x-axis. So, for f(-1), look the point of -1. Then vertically, it reaches the point of -3 which is in the y-axis.

Answer is -3.

Answer:

Hey there!

p(x)=7x+25

7x+25=60

7x=35

x=5

Let me know if this helps :)

Answer:

price of vegetables= regular price-discount

p=r-discount

Step-by-step explanation:

discount = regular price- price of vegetables

discount= r-p

OR

price of vegetables= regular price-discount

p=r-discount

percentage discount

[(original price- discounted price)/original price]*100= percent discount

Answer:

P = r - 8

Step-by-step explanation:

Got it correct.

Answer:

yes

Step-by-step explanation:

A rational number is a number that can be written as a ratio of integers

-8/5 is a ratio of integers so it is rational

Answer:

Yes.

Step-by-step explanation:

Rational numbers you can solve. They have a solution.

Answer & Step-by-step explanation:

PEMDAS:

Parentheses

Exponents

Multiplication and Division left to right

Addition and Subtraction left to right

We have two forms of grouping in the expression. Do the inner-most one first, still following PEMDAS within the grouping symbol:

Simplify division:

[tex]6/4=1.5\\1.5-1=0.5\\[/tex]

Re-insert:

[tex]40/(19-1+0.5)[/tex]

Simplify subtraction and addition within parentheses:

[tex]19-1+0.5\\18+0.5\\18.5[/tex]

Re-insert:

[tex]40/18.5[/tex]

Simplify division:

[tex]40/18.5=2.162162162162162162.....[/tex]

:Done

Clear question is;

A ball is dropped from the top of a

building. The expression 4.9x² gives the distance in meters the ball

has fallen after x seconds. Write and simplify an expression that gives the

distance in meters the ball has fallen after x² seconds. after x³ seconds.

Answer:

A) Distance = 4.9x⁴

B) Distance = 4.9x^(6)

Step-by-step explanation:

We are given the expression 4.9x² which is the distance in meters the ball

has fallen after x seconds.

Thus,

A) after x² seconds, we have;

Distance = 4.9(x²)²

Distance = 4.9 * (x²) * (x²)

When we have to multiply 2 same numbers with the same power, the powers add up. Thus, we now have;

Distance = 4.9x⁴

B) after x³ seconds, we have;

Distance = 4.9(x³)²

Distance = 4.9 * (x³) * (x³)

When we have to multiply 2 same numbers with the same power, the powers add up. Thus, we now have;

Distance = 4.9x^(6)

Answer:

y = 15, 11, and -1 when x = -1, 0, and 3 (respectively).  Together, we have the points (-1, 15), (0, 11), and (3, -1).

Step-by-step explanation:

Assuming you want to find the values of y for each evaluated x, we will simply plug in the values into the equation.

y + 4x = 11

y = 11 - 4x

For x = -1

y = 11 - 4(-1)

y = 15

For x = 0

y = 11 - 4(0)

y = 11

For x = 3

y = 11 - 4(3)

y = -1

Thus, we have the points, (-1, 15), (0, 11), and (3, -1).

Cheers.

Answer:

180° angle is supplementry angle

Step-by-step explanation:

180°

Answer:

Option a) ∠RXZ & ∠YXZ

Step-by-step explanation:

If sum of two angles are 180°, then the two angles are called supplementary.

∠RXZ & ∠YXZ forms a straight line and sum of ∠RXZ & ∠YXZ

will be 180. So, they are supplementary

Answer:

E (-2, 4).

Step-by-step explanation:

(x/2 + 1)(x/2 - 2) = 0

x/2 = -1,  x/2 = 2

x = -2, 4.

The roots will be 2 times the roots of f(x).

Answer:

[tex]\Large \boxed{\mathrm{E. \ -2, \ 4}}[/tex]

Step-by-step explanation:

The zeros of f(x/2) will double the zeros of f(x).

x = -1 × 2 = -2

x = 2 × 2 = 4

Answer:

I GOT YOU!

Step-by-step explanation:

⛅️= 10

❄️= 5

x = 8

So,

10+10+10=30

10+5+5=20

5+8= 13

10+5+8=23

I hope I helped...

Answer: Option A & D are true statements.

Work:

For option A, it states 1 pound = 2.75. Now when we divide 16.50 by 6 we get 2.75, so option A is true.

Option B states 2.75 pounds = 1$. We already know this isn't true seeing as 2.75 pounds would equal 7.56, so option B is false.

Option C reads as 5 pounds equal 15.50. When we multiply 5 by 2.75, we get 13.75, so option C is also untrue.

Option D quotes 12 pounds equals 33. When we multiply 12 by 2.75, it equals 33, so this is a true statement!

Option E says the point 3,9 is on the graph, but its not. So this is not true.

Answer:

At 7 seconds the instantaneous rate of change of the function s(t) with time which is the velocity is -11.18 m/s

Step-by-step explanation:

The given information on the height can be written as follows;

s(t) = -2.72·t² + 26.9·t + 6

Where;

s = The height (displacement) of the golf ball

t = The time taken during the motion of the golf ball

The velocity is found by finding the derivative of the displacement s as follows;

v = d(s(t))/dt = d(-2.72·t² + 26.9·t + 6)/dt = 2×(-2.72)×t + 26.9

When t = 7, v = 2×(-2.72)×7 + 26.9 = -11.18 m/s

Therefore the ball is coming down with 11.18 m/s speed at 7 seconds.

Answer:

its a formulae

we know (sinx+cosx)^3= sin^3x +cos^3x+3sinxcosx(sinx+cosx)

(a+b)^3= a^3 +b^3+3ab(a+b)

Step-by-step explanation:

(sin^2x)^3 +cos^2x)^3+3sin^2x cos^2x(sin^2x+cos^2x)

according to formulae

(sin^2x+cos^2x)^3  {as we know sin^2x+cos^2x =1}

so the (1)^3= 1

{proved}

thank u

Answer:  see proof below

Step-by-step explanation:

Use the formula for factoring a cubic:   (a³ + b³) = (a + b)(a² - ab + b²)

and the formula for a perfect square:    a² + 2ab + b² = (a + b)²

and the Pythagorean Identity:               cos²x + sin²x = 1

Proof LHS →  RHS

Given:                     sin⁶x + cos⁶x       + 3sin²x cos²x

Regroup:            (sin²x)³ + (cos²x)³     + 3sin²x cos²x

Factor Cubic:     (sin²x + cos²x)(sin⁴x - sin²x cos²x +  cos⁴x)   + 3sin²x cos²x

Pythagorean Identity:             1(sin⁴x - sin²x cos²x +  cos⁴x)   + 3sin²x cos²x

Add like terms:                         sin⁴x + 2sin²x cos²x +  cos⁴x

Regroup:                               (sin²x)² + 2sin²x cos²x +  (cos²x)²

Factor Perfect Square:                      (sin²x + cos²x)²

Pythagorean Identity:                                 (1)²

Simplify:                                                        1

LHS = RHS:   1 = 1    [tex]\checkmark\\[/tex]

Answer:

x=3

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

8 - 5 = 3

(Checking v)

3 + 5 = 8

Answer:

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

The expression that completes the blank is A. 11  x  w * x 3 = 11  x 3  x  w.

The commutative property is a mathematical concept that states that the order in which we multiply the factors does not affect the product.

According to the commutative property, a mathematical principle, the product is unaffected by the order in which we multiply the integers.

According to the above, the example of a commutative property is:

11  x w x 3 = 11 x  3 x w

This expression is the one with the commutative property because it has the same factors on both sides of the equation in a different order and that does not affect the result.

Therefore, the correct answer is A.

This question is incomplete because you are missing the options, here are the options:

A. 11 x w x 3 = 11 x 3 x w

B. 11 x w x 3 = 11 x w x 3

C. (11 x w) x 3 = 11 x (w x 3)

D. 11 x (w x 3) = (11 x w) + (11 x 3)

To know more about cumulative property follow

https://brainly.com/question/2475734

#SPJ6

Answer:

1 to 2.

We can see that the figure starts at the bottom left, and then moves to the bottom right.

So the vertical position remains constant, and the horizontal position changed, this can be a reflection around the vertical axis.

2 to 3.

Now the figure goes from the bottom right and moves to the top right, not only that, in (2) the figure is facing up, and in (3) the figure is facing down, then we have a reflection around the horizontal axis.

3 to 4.

Similar to the first case, this is a reflection over the vertical axis.

4 to 5.

Similar to the second case, this is a reflection over the horizontal axis.

(Something to notice, the movements can be called "Rotations over the ___ axis". I used reflection because it is specific for this type of motion, while rotation can be used to describe really complex types of motion)

Answer:

New point (x+6, y-4)

Step-by-step explanation:

Given:

Points = (x , y)

Mapping

6 units to the right

4 units down

Find:

New point

Computation:

On line X, numbers are add on move right side

So,

x+6

On line Y, numbers are subtract on move down

So,

y-4

New point (x+6, y-4)

Answer:

[tex]\sqrt{26}[/tex]

Answer:

p/8

Step-by-step explanation:

Answer:

The calculation that will give us the estimated volume is the area of the base of the pyramid of Giza in square meters multiplied by the height of the pyramid of Giza in meters divided by 3 i.e A * h/3

Step-by-step explanation:

Here in this question, we are interested in giving the calculation that will give us the estimated volume of the Great pyramid of Giza in cubic meters.

Mathematically, from the first part of the question, the formula for this is obtainable.

We are told that the formula for calculating the volume of a pyramid is A times h/3 where A represents the area of the base of the pyramid and h represents the height of the pyramid.

In equation form;

V = A * h/3

From the question, we are told that the area of the base is 53,000 m^2 while the height is 150 m

Now, plugging these values into the equation above, we have

V = 53,000 * 150/3

V = 53,000 * 50 = 2,650,000 m^3

The estimated volume of the Great Pyramid of Giza in cubic meters is 2,650,000.

Given the following data:

To calculate the estimated volume of the Great Pyramid of Giza in cubic meters:

Mathematically, the volume of a pyramid is given by the formula:

[tex]Volume = \frac{1}{3} \times base \;area \times height[/tex]

Substituting the given parameters into the formula, we have;

[tex]Volume = \frac{1}{3} \times 53000 \times 150\\\\Volume = 17,666.667 \times 150\\\\Volume = 2,650,000[/tex]

Volume of the Great Pyramid of Giza = 2,650,000 cubic meters

Read more: https://brainly.com/question/11168779

Answer:

Hey there!

Slope: 7-3/1-(-1), which is equal to 4/2, or 2.

Point slope: y-7=2(x-1)

So choice B is correct.

Let me know if this helps , or if you have any more questions :)

Answer:

2/3= 0.666666666667

Step-by-step explanation:

Formula :-

[tex]\sf \: S.I \: = \frac{P.R.T}{100} \\ [/tex]

Given that :-

The interest received on Rs 5000 = interest received on Rs 6000 , when rate of interest on Rs 6000 is 8 % .

To Find :-

The rate of interest on rupees 5000 .

Solution :-

→ S.I = P.R.T/100

→ 5000.R. 1 / 100 = 6000 × 8 × 1 / 100

→ 50 R = 60×8

→ 50 R = 480

→ R = 480/ 50

→ Rate of interest = 9.6 %

So rate on Rs 5000 is 9.6 %

Answer:

(1) Reuse;  (2) Recycle ;  (3) Reduce

Step-by-step explanation:

The ideal sequence would be:

1) Use it again (reuse) if the object still serves its intended purpose/s

2) If not possible to the used again, send it to a recycling plant to extract from it items/parts/substance of utility for other new products

3) if it cannot be reused or recycled, the last option will be to reduce it completely.

Answer:

  10 minutes

Step-by-step explanation: