The velocity (v metres per second) of a body is known to be proportional to the square root of its kinetic energy (e joules). When the velocity of a body is 120 m/s, its kinetic energy is 1600 J.
a) Write down a relationship between v and e, using k as the constant of proportionality.
b) Calculate the value of k.
c) If v = 21, calculate the kinetic energy of the body in joules.​

The amount of blood that a cylindrical tube hold will be 0.23 cubic dm.

Let r be the radius and h be the height of the cylinder. Then the volume of the cylinder will be

V = π r²h cubic units

A cylindrical tube 14.5 cm high and 4.5 cm in diameter is used to collect blood samples. Then the radius of the cylinder will be

r = d / 2

r = 4.5 / 2

Then the volume of the cylinder will be

V = π r²h

V = 3.14 (4.5 / 2)² × 14.5

V = 3.14 × 20.25 × 14.5 / 4

V = 921.98 / 4

V = 230.5 cubic cm

V = 0.23 cubic dm

The amount of blood that a cylindrical tube hold will be 0.23 cubic dm.

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Answer:

0.84

4.48

5.32

Step-by-step explanation:

Answer:

x = 64

Step-by-step explanation:

The interior angles of a triangle add up to 180 degrees, so the missing angle in the triangle on the right has an angle measurement of 180 - 47 - 81 = 52 degrees.

Since the angle and the rightmost angle in the triangle on the right are vertical angles. They are congruent.

Finally, since the triangle on the left is an isosceles triangle and the base angles, the angles on the top left and bottom left, are congruent and therefore their angle measures are both x degrees. So, 2x + 52 = 180 and x = 64.

The value of x in the angles is 17

The angles are given as

3x + 10 and 2x - 5

These angles are complementary angles

So, we have

3x + 10 + 2x - 5 = 90

Collect the like terms

So, we have

3x + 2x + 10 - 5 = 90

Evaluate the like terms

So, we have

5x = 85

Divide both sides by 5

x = 17

Hence, the value of x in the angles is 17

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Answer:

Perimeter=16cm

Area=16cm

Step-by-step explanation:

we know that all 4 sides of square are equal. So,

Length of 4 sides of square= 16cm

Length of 1 side of square= 16/4cm=4cm

Now that we have found the length of single side of square, by using the formula of area and perimeter we can get of square like this:

Perimeter= 4 times the length of square

or,Perimeter= 4*4

Therefore,Perimeter=16 cm

Now,

Area=square of length of side

or,Area=4^2

Therefore, Area=16 cm

Answer: 5.2

Step-by-step explanation:

If we put both points on a grid, Jordan's house would be 4 points above and 3 points to the left of Ca'Miyah's. We can plug these two amounts into the pythagorean theorem to find the distance between the houses: 4^2 + 3^2 = x^2. If we solve this equation, we get 5.196, which rounds to 5.2.

Hope this helps!

Answer:

y-intercept : 3

x-intercepts are 1 and 2

Vertex is at (2,-1)

Axis of symmetry is at x = 2

Step-by-step explanation:

See attached graph.

The equation y = x² – 4x + 3 represents a parabola

y-intercept at is at B(0,3); y-intercept is 3

x-intercept points at C(1,0) and D(3,0) so x-intercepts are 1 and 3

The vertex is the lowest point on this parabola (2-1)

Axis of symmetry is a line passing through the vertex and dividing the parabola into two equal halves. This is the vertical line x = 2

The width and length of the field are 160ft and 200ft respectively

When both the given variables are related to each other, we are required to consider one variable as x and the other as a function of x to solve accordingly

Let the width of the football field be 'x' ft.

then according to given data,

length= 200 ft more than width= (x+200)ft

According to given,

Perimeter of the given field =2L+2W=1040

where L is length and W is the width

Now putting the values of length and width earlier derived, we get:

2(x)+2(x+200) =1040

2x+2x+400=1040

4x+400=1040

4x=1040-400

4x=640

x=160ft

Now, the width of the field= x=160ft

length of the field= x+200=160+200=360ft

Hence the length and the width of the field are 160ft and 360ft

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Answer:

n - 4 = - 15

Step-by-step explanation:

Hope this helps :)

All real numbers x more than 2 units from 0 will be |x - 2| ≤ 0.

What does "real number" mean?

All real numbers x at most 2 units from 0

This means if x is centered at 2 then it can move at the max 2 units on either side (i.e. 4 units after 2 and 0 units before 2)

This will be |x - 2| ≤ 0

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The annual interest rate is 6.69%  for 3 years at compound interest.

What does the term "compound interest" mean?

[tex]A = P.( 1 + \frac{r}{n} )^{n.t}[/tex]

p = 5600

t = 3

I = 1200

n = 1

The interest  earned I is

I = [tex]P. ( 1 + \frac{r}{n} )^{n.t} - P[/tex]

1200 = [tex]5600 . ( 1 + \frac{r}{1} )^{1.3} - 5600[/tex]

[tex]1200 = 5600 .( 1 + r )^{3} - 5600[/tex]

[tex]\frac{1200}{5600} = ( 1 + r)^{3} - 1[/tex]

[tex]\frac{3}{14} = ( 1 + r )^{3} - 1\\[/tex]

[tex]\frac{17}{14} = ( 1 + r)^{3}[/tex]

Take the log base 10 of both sides

log17 - log14 = 3.log( 1 + r)

1.23045 - 1.14613 = 3.log( 1 + r)

3.log( 1 + r) = 0.084322

log( 1 + r) = 0.028107

1 + r = [tex]10^{0.28107}[/tex]

1 + r = 1.06686

r = 0.06686

The annual interest rate is 6.69%.

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The equation of the line shown in the diagram is y = 0.5x+0.5.

A line is a mark connecting two points.

To calculate the equation of the line, we use the formula below

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, the equation of the line shown in the diagram is y = 0.5x+0.5.

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MBND is a parallelogram as BN=MD and BN║MD.

A parallelogram is a quadrilateral whose both pair of opposite side are equal and parallel. Few examples of parallelograms are square, Rhombus  and rectangle.

Given ABCD is a parallelogram and ∠A=90°

Now we have to prove that MBND is a parallelogram

Given BN⊥AC and DM⊥AC

Since BN and DM are both perpendicular to the same straight line AC then we cam say that BN║DM.

Again we know  from the properties of parallelogram that the diagonal divides a parallelogram into two equal triangles.

Therefore the diagonal AC divides the parallelogram into two equal triangles ΔABC and ΔADC.

Now we know that the area of a triangle is given by [tex]\frac{1}{2}[/tex] ×base ×height .

Area of  ΔABC =Area of ΔADC

Since BN⊥AC and DM⊥AC

∴[tex]\frac{1}{2}[/tex]×BN×AC=[tex]\frac{1}{2}[/tex]×DM×AC

This above equation can be simplified as

BN=MD

Hence BMND is a parallelogram as we know from the properties of parallelogram that when a pair of opposite sides are equal and parallel in a quadrilateral it is a parallelogram.

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Answer:

C

Step-by-step explanation:

539/3 = 179.666

85/3 =28.3333

9285/ 3 = 3095

640/3=213.3333

Answer:

C

Hope this helps :)

Step-by-step explanation:

All the others numbers equal a decimal when divided by 3. However, C equals a whole number so it's C.

9,285 ÷ 3 = 3,095

Answer:

SHOWN BELOW!!!!

Step-by-step explanation:

KEEP IN MIND ----> *Square root of a number is a value, which on multiplication by itself gives the original number. The square root is an inverse method of squaring a number.*

Alright so the first equation C^2 - 49 = 0

Step 1 : Add 49 to both sides

C^2 - 49 + 49 = 0 + 49

C^2 = 49

Step 2 : Take the square root

(squ root) C^2 = (squ root)49

C = +/- (squ root) 49

Final answer ---> C = 7 OR C = -7

2.) 4S^2 - 100 = 0

Step 1 : Add 100 to both sides

4S^2 - 100 + 100 = 0 + 100

4S^2 = 100

Step 2 : Divide both sides by 4

4S^2/4    =   100/4

S^2 = 25

Step 3 : Take the square root

(squ root) S^2 = (squ root) 25

S =  +/- (squ root) 25

Final answer ---> S = 5 OR S = -5

3.) 9x^2 = 324

Step 1: Divide both sides by 9.

9x^2/9 = 324/9

x^2 = 36

Step 2: Take the square root

squ root) x^2 = (squ root) 36

x = +/- (squ root) 36

Final answer ---> x = 6 OR x = -6

Answer:

-4/7, 1/19, 7/4

Step-by-step explanation:

-4/7 is less then zero, and the only negative number so it is first

1/19 is the second lowest

7/4 is the highest because it is the only one that is greater then 1. (simplified, 7/4= 1 3/4)

A triangle is a 2-dimensional shape that has 3sides and 3 interior angles. The height of the isosceles triangle is approximately 49.5cm

The theorem states that the square of the hypotenuse is equal to the sum of the square of other two sides.

From the given question, the hypotenuse is 50cm and the base of the triangle is 14cm

Determine the height using the expression

h² = 50² - (14/2)²

h² = 2500 - 7²

h² = 2500 - 49

h = √2451

h = 49.5cm

Hence the height of the triangle is approximately 49.5cm

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Answer:

1 and 1/6 or 7/6

Step-by-step explanation:

Answer:

7/6

Step-by-step explanation:

=5/6+2/6

=5/6+1/3

7/6

Answer:

$1,820

Step-by-step explanation:

The math problem is $35 times 52 weeks

An angle is denoted by the angle symbol ∠ and the three letters representing the name of the angle.

An angle is denoted by the angle symbol ∠ which is then being followed by three letters that will represent the points that form an angle.

Lets say for example, the expression ∠ABC will mean that “the angle is formed by the points A, B and C”

where the vertex of the angle is at the point B as it is in the middle.

Angles can also be of different types like:

An Acute Angle which means an angle is less than 90 degrees.

A Right Angle which means an angle which is exactly 90 degrees.

An Obtuse Angle which is an angle more than 90 degrees and less than 180 degrees.

A Straight Angle which is an angle that is exactly 180 degrees.

And a Reflex Angle which is an angle greater than 180 degrees and less than 360 degrees.

Therefore, an angle is denoted by the angle symbol ∠ and the three letters representing the name of the angle.

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The perpendicular slope is expressed as the negative reciprocal of the slope or − 1 m. In this scenario, the slope, or m, is −4 so the slope of the perpendicular line is − 1 −4 which simplifies to 1 4

Answer:

Where exactly is the "the following" you are talkibg about.

Answer:40 miles

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

[tex]5\cdot \:5+7[/tex]

Answer:

it's x+3

Step-by-step explanation:

it seems to go up by one so if you go down by you the input of 1 would be the output of 4 also known as (1,4)

and go again down by 1 and get (0,3)

so we know we have to add 3 each time so it is x+3

Answer:

a

Step-by-step explanation:

the unknown value is n then 3 less than this value is

n - 3

Answer:

answer is C

because other equations normally n>3 but C equation normally is n<3

so answer is C

Answer: A=-2

Step-by-step explanation:

AB=11

B=9

B-11=A

9-11=A

A=-2