A rifle is aimed horizontally at a target on a screen some distance away. The bullet hits the target 2.8 cm below the aim point. The initial velocity of the bullet is 750.0 m/s.

Find the flight time?

Answer:

Step-by-step explanation:

NOTE : we have 6×6=36 possible outcome.

we can resume the set of outcomes in the table below :

Then

the probability that the sum is not divisible

by 2 and not divisible by 4 :

= 18/36

= 1/2

Answer:

a=2

Step-by-step explanation:

[tex]area=2\int\limits^a_b {y} \, dx =2\int\limits^a_b {\sqrt{4ax} } \, dx \\=2 \times 2\sqrt{a} \frac{x^{\frac{3}{2} } }{\frac{3}{2} } ~from~~b~to~a\\=\frac{8}{3}\sqrt{a} (a^{\frac{3}{2} } -b^{\frac{3}{2} } )\\=\frac{8}{3} \sqrt{a}( (4a)^{\frac{3}{2} } -0)\\=\frac{8}{3} \sqrt{a} ((4a)\sqrt{4a} -0)\\=\frac{32 a}{3} \times 2a\\=\frac{64}{3} a^2[/tex]

[tex]\frac{64}{3} a^2=\frac{256}{3} \\a^2=\frac{256}{3} \times \frac{3}{64} =4\\a=2 (a > 0)[/tex]

the curve is a right parabola.

here b=0,and a=4a for x

we are finding the area between x-axis and x from 0 t0 4a.

curve is symmetrical about x-axis so we multiply by 2.

If the area of the region bounded by the curve [tex]y^2 =4ax[/tex]  and the line [tex]x= 4a[/tex]  is [tex]\frac{256}{3}[/tex] Sq units, then the value of  [tex]a[/tex] will be [tex]2[/tex] .

An area bounded by two curves is the area under the smaller curve subtracted from the area under the larger curve. This will get you the difference, or the area between the two curves.

Area bounded by the curve  [tex]=\int\limits^a_b {x} \, dx[/tex]

We have,

[tex]y^2 =4ax[/tex]  

⇒ [tex]y=\sqrt{4ax}[/tex]

[tex]x= 4a[/tex],

Area of the region  [tex]=\frac{256}{3}[/tex]  Sq units

Now comparing both given equation to get the intersection between points;

[tex]y^2=16a^2[/tex]

[tex]y=4a[/tex]

So,

Area bounded by the curve  [tex]= \[ \int_{0}^{4a} y \,dx \][/tex] ​

 [tex]\frac{256}{3} =\[ \int_{0}^{4a} \sqrt{4ax} \,dx \][/tex]

[tex]\frac{256}{3}= \[\sqrt{4a} \int_{0}^{4a} \sqrt{x} \,dx \][/tex]

 [tex]\frac{256}{3}= \[2\sqrt{a} \int_{0}^{4a} x^{\frac{1}{2} } \,dx \][/tex]                                            

[tex]\frac{256}{3}= 2\sqrt{a} \left[\begin{array}{ccc}\frac{(x)^{\frac{1}{2}+1 } }{\frac{1}{2}+1 }\end{array}\right] _{0}^{4a}[/tex]

[tex]\frac{256}{3}= 2\sqrt{a} \left[\begin{array}{ccc}\frac{(x)^{\frac{3}{2} } }{\frac{3}{2} }\end{array}\right] _{0}^{4a}[/tex]

[tex]\frac{256}{3}= 2\sqrt{a} *\frac{2}{3} \left[\begin{array}{ccc}(x)^{\frac{3}{2}\end{array}\right] _{0}^{4a}[/tex]

On applying the limits we get;

[tex]\frac{256}{3}= \frac{4}{3} \sqrt{a} \left[\begin{array}{ccc}(4a)^{\frac{3}{2} \end{array}\right][/tex]

[tex]\frac{256}{3}= \frac{4}{3} \sqrt{a} *\sqrt{(4a)^{3} }[/tex]

[tex]\frac{256}{3}= \frac{4}{3} \sqrt{a} * 8 *a^{2} \sqrt{a}[/tex]

[tex]\frac{256}{3}= \frac{4}{3} * 8 *a^{3}[/tex]

⇒ [tex]a^{3} =8[/tex]

[tex]a=2[/tex]

Hence, we can say that if the area of the region bounded by the curve [tex]y^2 =4ax[/tex]  and the line [tex]x= 4a[/tex]  is [tex]\frac{256}{3}[/tex] Sq units, then the value of  [tex]a[/tex] will be [tex]2[/tex] .

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Answer:

B

Step-by-step explanation:

Total money spent = 25 + 30 + 10 + 8 = 73

Per week = 73 / 4 = 18.25

The equation of line is y = -3x + 8

Slope is the ratio of the change in the y coordinates to the change in the x coordinates.

Analysis:

slope (m) = y2 - y1 / x2 - x1

m = 14 -5 / -2-1  = 9/-3 = -3

when y = 5, x = 1

y = mx + c

5 = -3(1) + c

5 = -3 + c

c = 5+3 = 8

Y = -3x + 8

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The most basic and common reason to use parentheses, brackets, and braces is to control the order of operations.

In mathematics, parenthesis is used to arrange numbers in the sequence of operations, clarify numbers, and denote multiplication.

Suppose you have an expression as:-

E = { ( 5-2 )8} 6

In this case, you would calculate 5 minus 2 first (parentheses), then multiply by 8 (brackets), then complete the part inside the curly braces, and finally multiply by 6.

Therefore the most basic and common reason to use parentheses, brackets, and braces is to control the order of operations.

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Based on the table, a conclusion which can be drawn about f(x) and g(x) is that: B. the functions f(x) and g(x) are reflections over the y-axis.

In Mathematics, two functions are considered to be reflections over the y-axis under the following condition:

If, f(-x) = g(x).

Evaluating the given functions, we have:

f(x) = 2ˣ

f(-x) = 2⁻ˣ = ½ˣ = g(x).

Similarly, two functions are considered to be reflections over the x-axis under the following condition:

If, -f(x) = g(x).

Evaluating the given functions, we have:

f(x) = 2ˣ

-f(x) = -2ˣ ≠ g(x).

Therefore, we can logically conclude that the two functions f(x) and g(x) are considered to be reflections over the y-axis but not the x-axis.

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Answer:

???

Step-by-step explanation:

Step-by-step explanation:

X^2 +4X +4=12 subtract the 12 from both sides

X^2 +4x-8= 0

now factor if possible since this equation is not factorable you can use the quadratic formula

Answer:

it is 3rd option C. -4, 5

Step-by-step explanation:

all the elements are associated with only one second element except -4

for -4 there are two second elements 3 and 5 from the ordered pairs (-4, 3) and (-4, 5)

so we can remove one of them to make R a function

since (-4, 3) is not in the options so the correct option is (-4, 5)

so c is the right one

Hope This Helped

As per defination of function

Every domain has an unique range

or

Here

One point need to be removed to get it function

Hence the point is (-4,5)

Answer:

b

Step-by-step explanation:

The statements true about the slopes and lines are

a) Line TV has a slope of 0.

b) Lines RS and TV are parallel.

c) Line SW has an undefined slope.

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be S ( 2 , 6 )

Let the second point be R ( -8 , 6 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 6 - 6 ) / ( -8 - 2 ) = 0

So , the slope of line RS = 0

Let the point T = T ( -6 , -4 )

Let the point V = V ( 8 , -4 )

Slope m = ( -4 - (-4) ) / ( 8 - (-6) ) = 0

So , the slope of line TV = 0

And , the lines RS and TV are parallel as they have the same slope

Now , the x coordinate of the point S and W does not change

So , it has an undefined slope

Hence , the equation of line is solved

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The complete question is attached below :

Lines RS, TV, and SW are shown.

Which statements are true about these lines? Select

three options.

Line RS has a slope of 6.

Line SW has an undefined slope.

Line TV has a slope of 0.

Lines RS and TV are parallel.

Line SW is perpendicular to line RS, but not to line TV.

In the diagram, the area of the given shape is 102 cm²

From the question question, we are to determine the area of the given shape

The given shape is a kite

The area of a kite is given by the formula,

[tex]A =\frac{pq}{2}[/tex]

Where A is the area

p and q are the diagonals

In the given diagram,

p = 6cm + 6 cm = 12 cm

q = 3 cm + 14 cm = 17 cm

Thus,

Area of the kite = [tex]\frac{12 \times 17}{2}[/tex]

Area of the kite = 6 × 17

Area of the kite = 102 cm²

Hence, the area of the given shape is 102 cm²

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Answer:

215

Step-by-step explanation:

1/6 chance to roll a 6

1/6 * 1290

The answer to the given question is as below:-

Polynomials:-

x³-7x²+9x-5x⁴-20

x⁵-5x⁴+4x³+2x-1

3x²-5x⁴+2x-12

Non-polynomial:-

x⁻5-5x⁻⁴+4x⁻³+2x⁻1-1

[tex]\dfrac{4}{x^4}+ \dfrac{3}{x^3}-\dfrac{2}{x^4}-1[/tex]

[tex]\sqrt[4]{x} -\sqrt[3]{x} 4+\sqrt{x}-8x+16[/tex]

A polynomial is a mathematical equation made up of indeterminates and coefficients and involves only addition, subtraction, multiplication, and non-negative integer exponentiation of variables. The exponents of the polynomials can not be irrational.

So the table will be formed as:-

Polynomials:-                            Non-polynomial:-        

x³-7x²+9x-5x⁴-20                     x⁻5-5x⁻⁴+4x⁻³+2x⁻1-1        

x⁵-5x⁴+4x³+2x-1                        [tex]\dfrac{4}{x^4}+ \dfrac{3}{x^3}-\dfrac{2}{x^4}-1[/tex]

3x²-5x⁴+2x-12                           [tex]\sqrt[4]{x} -\sqrt[3]{x} 4+\sqrt{x}-8x+16[/tex]

Therefore the polynomials and non-polynomials are shown in the table above.

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Answer:

v = √(LT/m)

Step-by-step explanation:

Given :

Multiply both sides with L :

Divide both sides by m :

Take the square root on each side :

Answer:

[tex]v = \sqrt{ \frac{tl}{m} } [/tex]

Step-by-step explanation:

[tex]t = \frac{mv {}^{2} }{l} \\ making \: v \: the \: subject \\ t \times l = mv {}^{2} \\ dividing \: bothsides \: by \: m \\ \frac{tl}{m} = \frac{mv {}^{2} }{m} \\ v {}^{2} = \frac{tl}{m} \\ finally \\ v = \sqrt{ \frac{tl}{m} } [/tex]

Step-by-step explanation:

Answer:

-204kk+3+32k/4k

Hope this helps!!

Answer:

perpendicular

Step-by-step explanation:

x = -2    is a vertical line at   x   =  -2

y is a horizontal line          the two lines are perpindicular

the lines  x=−2, y=10 are perpendicular to each other.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Here, The given equations are :

x=−2 and y=10

First, consider x = -2 equation :

equation x = -2 is a vertical line, parallel to x = 0 line and perpendicular to line y = 0.

Consider second line y = 10 :

line y = 10 is horizontal line and is parallel to line y = 0 and is perpendicular to line x = 0.

Therefore, the lines  x=−2, y=10 are perpendicular to each other.

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Answer:

Nominal wages, prices, and perceptions adjust upward to this new price level

Step-by-step explanation:

Answer:

B) 52

Bodmas rule:

Solving Steps:

⇒ 2 × (3 - 1)⁴ + 5 × 4

⇒ 2 × (2)⁴ + 5 × 4

⇒ 2 × 16 + 5 × 4

⇒ 32 + 20

⇒ 52

Option B

Equation of the function: f(x) = 4 sin (x/2) + 6.

The term sinusoidal is used to describe a curve, referred to as a sine wave or a sinusoid, that exhibits smooth, periodic oscillation. It is named based on the function y=sin(x).

Given: max value= 6, min value= -2, y-intercept= 6.

As, standard form f(x) = A sin (ωx +φ) + k,

where A is the amplitude, ω is the angular velocity with ω=2πf.

Now,

A = |6- (-2)/2|

A = |6 +2/2| = 8/2

A = 4

Also, ω:

The period of a sinusoidal is T = 1/f

so, f = 1 / T

ω = 2πf

ω = 2π ( 1/T) with T = 4π

ω = 2π (1/(4π) = 2π (2)

ω = 1/2

The y-intercept k = 6

So, equation with values A =4, ω = 1/2, k = 6, φ = 0.

f(x) = A f(x)

f(x) = A sin (ωx +φ) + k

f(x) = 4 sin (x/2) + 6.

Hence, equation of the function f(x) = 4 sin (x/2) + 6.

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Answer:

goto gauth maths and ask again

The height of the wall would be x - 1 and the perimeter of the wall is 32 feet

The area of the window is given as:

A = x^2 - 4x + 3

Expand

A = x^2 - 3x - x + 3

Factorize

A = x(x - 3) - 1(x - 3)

Factor out x - 3

A = (x - 1)(x - 3)

The width of the wall is given as: x - 3

So, the height of the wall would be x - 1

How to determine the perimeter?

The perimeter is calculated using:

P = 2 *(Width + Height)

This gives

P = 2 * (x - 1 + x - 3)

When x = 10, we have:

P = 2 * (10 - 1 + 10 - 3)

Evaluate

P = 32

Hence, the perimeter of the wall is 32 feet

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The height of the tree is 1.95 meters.

At 11 AM, we have

Savannah = 1.75 m

Tree Shadow = 43.75 m

Savannah Shadow = 39.2 m

So, we make use of the equivalent ratio

Savannah :Tree::Savannah Shadow:Tree Shadow

Now, 1.75:Tree::39.2:43.75

In fraction Tree/1.75 = 43.75/39.2

Multiply both sides by 1.75

Tree =43.75/39.2 ×1.75

Tree=1.95

Therefore, the height of the tree is 1.95 meters.

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Answer:

The answers are in the picture. Remember that first is x and then y when you see those coordinated again. (10,11) X=10 and Y=11.

Step-by-step explanation:

Answer:

162.5

Step-by-step explanation:

25=height

13=base

to find the area of a triangle you do (h(b)b)/2

Answer:

2/3(cx+1/2)-1/4=5/2. CX=29/8

The option first is correct because  y= 2√x and y= √2x have same domain which is x ≥ 0.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

y= 2√x

From the above function the domain should be:

x ≥ 0 (because square root of negative values does not exist)

The function:

y = √(2x)

2x ≥ 0

x ≥ 0

Thus, the option first is correct because  y= 2√x and y= √2x have same domain which is x ≥ 0.

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The interval notation that defines this set is: (-∞, -5]

And the graph can be seen below.

Here we want to graph the inequality:

x ≤ -5

This refers to all the values of x equal or smaller than -5.

To graph this, we need to graph a closed circle at -5, and we need to draw an arrow that points to the left (values smaller than -5). The graph is the one that you can see below.

The interval notation that defines this set is: (-∞, -5]

The first end is open, and the second is closed (because of the symbol ≤).

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