How can I solve this?

a) The work done is 3.3 J

b) The new force would  stretch it  1.9 cm beyond its natural length.

Hooke's law states that, the force of elasticity that tends to stretch a spring is directly proportional to the extension that is caused by the force as long as we do not by any means exceed the elastic limit of the material. This implies that the Hooke's law can only be found to hold when the elastic limit of the material has not been exceeded and the material has not become plastic.

Now;

F = Ke

W =1/2 Fe

F = 2W/e

W = work done

F = force exerted

e = extension

F = 2 * 23 /(44 - 30) * 10^-2

F = 328.6 N

a) To stretch  34 cm to 36 cm;

W = 1/2 *  328.6 N * 2 * 10^-2

W = 3.3 J

The work done is 3.3 J

b) F = Ke

328.6 N/(44 - 30) * 10^-2 = K

K = 2347 N/m

Then;

45 N =  2347 N/m * e

e = 45 N/ 2347 N/m

e = 0.019 m or 1.9 cm

New length = 30 cm + 1.9 cm = 31.9 cm

The new force would stretch it to a distance of 31.9 cm or 1.9 cm beyond its natural length.

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Answer: 35/4

Step-by-step explanation:

7/11 ÷ 4/5 》7/11 × 5/4 = 35/44

The evaluation of the subtraction operation using the number line is 2/3. The correct option is the last option 2/3

From the question, we are to evaluate the subtraction operation using the number line

From the number line we can observe that the magnitude of the distance between two successive mark is 1/3

Now, we are subtract

-2/3 - (-1 1/3)

If we count from - 1 1/3 to -2/3, we will observe that there are two marks.

Thus,

1/3 + 1/3 = 2/3

Hence, the evaluation of the subtraction operation using the number line is 2/3. The correct option is the last option 2/3

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Answer:Cylinder B has the radius r and the height as h. The lateral surface area of cone is. The lateral surface area of cylinder is. 1/2 × lateral surface area of cylinder B, ⇒. ⇒ = lateral surface area of cone A. Hence we can conclude that the lateral surface area of cone A is exactly 1/2 the lateral surface area of cylinder B is option (A) true.

Hope this helped you :)

False, the statement that: The lateral surface area of cone A is equal to the lateral surface area of cylinder B. is not true.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Since, Lateral area of cone is given by: πrl

where r is the radius and l is the slant height

Here r = r and l = h

Hence, lateral area of cone A= π × r × h

                                           = πrh

And, Lateral area of cylinder is given by:

= 2πrh

where r is the radius and h is the height

Hence, Lateral area of cylinder B=2πrh

Clearly, both the lateral areas are not equal.

Hence, the statement that: The lateral surface area of cone A is equal to the lateral surface area of cylinder B. is not true.

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The reflection of the triangle gives the co-ordinates A'(5, 2) B'(0, -3) C'(-4,-1) .

In mathematics, a reflection is a mapping from a Euclidean space to itself that is an isometry with a set of fixed points known as the hyperplane; this set is also known as plane of reflection or the axis. The mirror image of a figure in the axis or plane of reflection is the image produced by a reflection.

When an object is reflected across the x -axis , the image will be at same distance from the x axis as the object or point is on the cartesian plane.

So if a point P has the co-ordinates (x , y) .  When reflected across the x-axis the the reflection has the co-ordinates P'(x , -y ) .

The co-ordinates of the 3 points are A(5,-2) B(0, 3) C(-4,1).

When reflected across the x-axis the co-ordinates become :

A(5,-2) →A'(5,2)

B(0, 3)→B'(0,-3)

C(-4,1)→C'(-4,-1)

Hence the second option is correct, the reflected image of the triangle has the coordinates  A'(5, 2) B'(0, -3) C'(-4,-1) .

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Hi there,

I hope you and your family are staying safe and healthy!

[tex]-9 (y-13) = 16[/tex]

This is called a linear equation. Let's distribute:

[tex]-9y + 117 = 16[/tex]

Now we need to subtract 117 from both sides

[tex]-9y +117-117=16-117[/tex]

[tex]-9y = -101[/tex]

Now divide both sides by -9

[tex]\frac{-9y}{-9} = \frac{-101}{-9}[/tex]

[tex]y = \frac{101}{9}[/tex]

Happy to help! All the best this semester!

Answer:

0.06(50h)

Step-by-step explanation:

Tax is usually computed by taking a percentage of the cost of a good or service. In the expression, we see that h represents the number of hours worked that are being paid for. Naturally, the cost of a service is the price times the hours worked. Therefore, 50 must represent the number of hours worked, and 50h represents the price Deborah must pay before tax. Knowing all this, we can deduce that the expression 0.06(50h) represents the tax that she must pay as it is a tax rate (6%) being multiplied by the cost before tax.

Answer:

3.69

Step-by-step explanation:

Answer:

3.69

Step-by-step explanation:

when the nearest number from the right side is lower than 5 it just disappears and all of the numbers after that will disappear as well.

Answer:

True statements are 4 and 5

Step-by-step explanation:

This s basically using set theory to evaluate line segments

The union of two(or more) sets is the set of elements that are in either or both sets.

Here is an example
If set A = {1, 2, 3, 4} and set B = {3, 4, 5, 6} then
A ∪ B = (1, 2, 3, 4, 5, 6}
Note that there cannot be any duplicates in a set

We have to treat the line segments as sets  to solve this problem.

For easier explanation, I am going to view each segment as having points which I am labeling 1, 2, 3 etc.

The individual independent line segments are JL, LM, MN, and NT, basically each is a set of the points that comprise each segment

You have to visualize each of these line segments as being comprised of these points.

Note that these are distinct sets ie there is  no common point when we consider the above 4 sets

Let set
JL have the points {1, 2, 3} we say JL = {1, 2, 3}

LM = {4, 5}

MN = {6, 7}

NT = {8, 9}

We see that there are no common points between each of the four sets below

1. JL ∪ MN = set of points that lie in JL or MN or both. Since JL and MN are distinct sets, the union of these two sets is s
JL U MN = {1, 2, 3} U {5, 6} = {1, 2, 3, 5, 6} . However, JM contains all the points from J to M which is {1, 2, 3, 4, 5} which is not the same as JL U MN

So Statement 1 is false

2. JL U MN = {1, 2, 3} U {6, 7} = {1, 2, 3, 6, 7} so it contains more points than MN{6, 7} and therefore Statement 2 is false

3. LM U LN
We can see that LN contains all the points in LM and MN = {4, 5, 6, 7}. LM U LN = {4, 5} U { 4, 5, 6, 7} = {4, 5, 6, 7}. But LM is only a subset of LN and has fewer points {4, 5}  so Statement 3 is false

4. LM U LN
LM = {4, 5}, LN = {4, 5, 6, 7} so LM U LN = {4, 5, 6, 7} = LN. Remember sets don't duplicate. So Statement 4 is True

5. NT U JT
NT = {8, 9} and JT = set of all points in the segment from J to T which is all the points. So JT = {1, 2, 3, 4, 5, 6, 7, 8, 9} and NT U JT = {1, 2, 3, 4, 5, 6, 7, 8, 9} which is the set of all points in JT. Therefore Statement 5 is True

The figure below shows a graphical representation of what I wrote above. If you look at LN for instance, it has 4 points {4, 5, 6, 7} and therefore represents all the points in LM and LN (without duplication of points). This is Statement 4, by the way

The ratio of area of the ball bearings will be equal to 4 / 9.

We are given the volume of the ball bearings as:

Volume 1 = 1.6 cm³

Volume 2 = 5.4 cm³

Now, the ratio of their volumes will be equal to:

r = 1.6 / 5.4

r = 16 / 54

r = 8 / 27

Now, we know that, the scale factor will be:

k = ∛8 / 27

k = 2 / 3

Also, we know that, the ratio of their areas is the square of their scale factor.

So, the ratio of area will be equal to:

R = (2 / 3)²

R = 4 / 9

Therefore, we get that, the ratio of area of the ball bearings will be equal to 4 / 9.

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The ratio of their areas is 4 / 9.

The scale factor for the linear dimensions of the ball bearings will be the cube root of the volume scale factor:

[tex]$$k=\sqrt[3]{(1.6 / 5.4)}=2 / 3$$[/tex]

Then the scale factor for the areas will be the square of this scale factor: ratio of surface area =(2 / 3)^2=4 / 9

The area is the product of two linear dimensions, so its scale factor is the product of the linear dimension scale factors. That is, the scale factor for area is the square of the linear dimension scale factor.

Similarly, volume is the product of three linear dimensions, so its scale factor is the cube of the linear dimension scale factor.

To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilized. It is employed to change the size of an item.

If the original figure's dimensions and the dilated (increased or lowered) figure's dimensions are known, the scale factor can be determined. A rectangle, for instance, has dimensions of 5 units in length and 2 units in breadth.

The sides of this rectangle will change to 10 units and 4 units, respectively, if the size of the rectangle is increased by a scale factor of two. Therefore, we may use the scale factor to determine the modified figures' dimensions.

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Answer: All the answers you need are attached in the file.

Step-by-step explanation: Hope it helps!

Answer:

339.15

Step-by-step explanation:

5% is equal to 1/20, so we can use 1/20 in place of 5%. All that needs to be done is to determine 1/20 of 357 and subtract the result (we subtract because Tapiwa raked more than Adam)

357 x 1/20 = 17.85

357 - 17.85
339.15

Step-by-step explanation:

2 × 7 × 7.................

Answer:

124.59

Step-by-step explanation:

Answer:

the answer would be 20,313,04

Step-by-step explanation:

last place = 8 rounds up makes the thousandth place 5 which rounds up and makes the hundreth place 0 which doesnt change tyhe 4 giving us our aanswer. PLEASE MARK BRAINLIEST.

Answer:

15.6 in² (nearest tenth)

Step-by-step explanation:

Circumference of a circle

[tex]\large\boxed{C=2\pi r}[/tex]

Where r is the radius of the circle.

Given:

Substitute the given value into the equation for the circumference and solve for r:

[tex]\begin{aligned}\implies 14 & = 2 \pi r\\\\ r & = \dfrac{14}{2 \pi}\\\\ r & = \dfrac{7}{ \pi}\end{aligned}[/tex]

Area of a circle

[tex]\large\boxed{A=\pi r^2}[/tex]

Where r is the radius.

Substitute the found radius into the equation for area and solve for A:

[tex]\begin{aligned}\implies A&=\pi \left(\dfrac{7}{\pi}\right)^2\\\\ A&=\pi \cdot \dfrac{7^2}{\pi^2}\\\\ A&=\dfrac{49\pi}{\pi^2}\\\\ A&=\dfrac{49}{\pi}\\\\A & = 15.6\;\sf in^2\;(nearest\:tenth)\end{aligned}[/tex]

Therefore, the area of the circle with a circumference of 14 in is 15.6 in².

Answer:

Step-by-step explanation:

The value is 102.

Here the expression is 2x² - 5x.

We have to find the value of the algebraic expression for x = -6.

Expression = 2x² - 5x

Now put the value of x = -6 in the expression, we get

2x² - 5x = 2(-6)² - 5(-6)

             = 2×36 + 30

             = 72 + 30

             = 102

Therefore the value of an algebraic expression is 102.

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Equation f (x) = |x| represent the Absolute Value Functions.

Parent functions are the simplest form of a given family of functions. A family of functions is a group of functions that share the same highest degree and, consequently, the same shape for their graphs.

Absolute Value Functions :

The parent function of absolute value functions is y = |x|. Absolute value functions are expected to return V-shaped graphs.

The vertex of y = |x| is found at the origin as well. Since it extends on both ends of the x-axis, y= |x| has a domain at (-∞, ∞).  Absolute values can never be negative, so the parent function has a range of [0, ∞].

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Applying the triangle proportionality theorem, the value of x and the value of y are:

C. y = 5, x = 10.

Since lines m and n are said to be parallel lines, therefore, according to the triangle proportionality theorem, the ratios below can be created.

4/12 = y/15 [proportional sides]

Cross multiply

(y)(12) = (4)(15)

12y = 60

Divide both sides by 12

12y/12 = 60/12

y = 5

x = 15 - y

Plug in the value of y

x = 15 - 5

x = 10

Thus, applying the triangle proportionality theorem, the value of x and the value of y are:

C. y = 5, x = 10.

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Answer:

80 percent

Step-by-step explanation:

4/5 = 80 percent (4/5 = .8, .8*100= 80)

Answer:

  9.2

Step-by-step explanation:

You want the distance between A(2, 0) and B(0, 9).

The distance formula is based on the Pythagorean theorem. It tells you the distance between (x1, y1) and (x2, y2) is ...

  d = √((x2 -x1)² +(y2 -y1)²)

For the given points, this becomes ...

  d = √((0 -2)² +(9 -0)²) = √(4+81) = √85

  d ≈ 9.2

The distance between A and B is about 9.2 units.

Answer:

x - 4

Step-by-step explanation:

The quickest way to do this is to Factor and "cancel". (Cancelling is not a mathematical term--it really is dividing)

x^2 - 16 is the difference of two squares. Its super-beneficial to recognize a difference of two squares and its factored form:

(x - 4)(x + 4)

Now you have:

(x - 4 )(x + 4) / x+4

The x+4 term "cancels" and you end up with x-4 as your answer.

You could also do this division problem using long division or synthetic division. You will get the same answer.

Answer: B

Step-by-step explanation:

f(2) = 2, and is defined/exists. Holes (and asymptotes) like the hole at (2, -2) ruins continuity. The limit exists, but is not equal to f(2) which is why continuity is ruined at x=2

Answer: B

Step-by-step explanation:

f(2) = 2 and exists/is defined Holes (and asymptotes) such as the one at (2, -2) destroy continuity. The limit exists, but it is not equal to f(2), hence continuity is broken at x=2.

Answer:

Yes si true

Step-by-step explanation:

If you analyze the figures you will realize that they are the same, the size differentiates it but they have the same angles.

Reason:

It is impossible to pass a single vertical line through more than one point on the graph. This relation passes the vertical line test.

The other graphs fail the vertical line test. For instance, in the upper right corner we have a vertical line through x = -1 which passes through more than one point. The input x = -1 leads to multiple outputs y = -1 and y = 3 at the same time.

A function is only possible when each input leads to exactly one output.

The meaning of the point (378,9) is with 9 yards of yarn, Paula can knit 378 knot hats.

Given that:-

The number of hats h she can knit varies directly with the amount of yarn y in yards she has.

Also, the constant of proportionality is 42.

Hence, we can write,

h ∝ y

h = ky

where, k is the constant of proportionality, hence,

h = 42y

We have to interpret the meaning of  (378, 9).

From, the equation, h = 42y

We can observe that,

When y = 9

h = 42*9 = 378.

Hence, we can write that, the meaning of the point (378,9) is with 9 yards of yarn, Paula can knit 378 knot hats.

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The solution of the equation for y is y = 5 - 2x and the values of y are 9, 5 and -1

The equation is given as

y + 2x = 5

Subtract 2x from both sides of the equation

So, we have

y + 2x - 2x = 5 - 2x

Evaluate the like terms

y = 5 - 2x

Next, we solve the function for the values of x

When x = -2, we have:

y = 5 - 2 * -2

Evaluate

y = 9

When x = 0, we have:

y = 5 - 2 * 0

Evaluate

y = 5

When x = 3, we have:

y = 5 - 2 * 3

Evaluate

y = -1

Hence, the solution of the equation for y is y = 5 - 2x and the values of y are 9, 5 and -1

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The value of y when x = -2 , 0 , 3 are 9, 5 and -1 respectively.

Given the equation;

y + 2x = 5

Make 'y' the subject of formula

y = 5 - 2x    (1)

When x = -2

Let's substitute the value of x as -2 in equation (1)

y = 5 - 2(-2)

expand the bracket

y = 5 + 4

y = 9

When x = 0

Substitute the value of x = 0

y = 5 -2(0)

y = 5 - 0

y = 5

When x = 3

Substitute the value of x = 3

y = 5 - 2(3)

y = 5 - 6

y = -1

Thus, the value of y when x = -2 , 0 , 3 are 9, 5 and -1 respectively.

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The slope of the line passing through the coordinates (0, 0) and (6, 3) is 1/2

The formula for calculating the slope of a line is expressed according to the equations:

Slope = y₂-y₁/x₂-x₁

Using the coordinate points (0, 0) and (6, 3) on the line. On substituting, we will have;

Slope = 3-0/6-0

Slope = 3/6

Simplify

Slope =1/2

Hence the slope of the line passing through the coordinates (0, 0) and (6, 3) is 1/2

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