What is the amplitude of the function graphed?

[tex]\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)= 2x^2-1\qquad \begin{cases} x_1=0\\ x_2=5 \end{cases}\implies \cfrac{f(5)-f(0)}{5-0} \\\\\\ \cfrac{[2(5)^2-1]~~-~~[2(0)^2-1]}{5}\implies \cfrac{50-(-1)}{5}\implies \cfrac{50+1}{5}\implies \cfrac{51}{5}\implies 10\frac{1}{5}[/tex]

Answer:

A

Step-by-step explanation:

Answer:

29.4

Step-by-step explanation:

29.4444 rounded to the nearest tenth is 29.4

the other answerer forgot to round to the tenths place

To  answer this question, we should make use of spherical coordinates.

Solution is:

S = (  4×cosθ ×sinΦ , 4 ×sinθ× sinΦ, 4 × cosΦ)

0 ≤ θ ≤ 2×π     ;  π/2  ≤ Ф ≤ (3/2)×π

In Analitic Geometry we have different way of determine, and identify  the position of objects, we have rectangular coordinates, cylindrical coordinates and spherical coordinates. The use of each of these system depends on de geometry of the problem.

In this particular case and according to the problem statement we should use spherical coordinates

x = ρ×cosθ ×sinΦ           y = ρ ×sinθ× sinΦ         z = ρ× cosΦ

In our particular case

ρ = 4   then   x = 4×cosθ ×sinΦ     y = 4 ×sinθ× sinΦ   z = 4 × cosΦ

0 ≤ θ ≤ 2×π     ;   π/2  ≤ Ф ≤ ( 3/2)×π

So the solution in terms of θ and/or  Φ

S = (  4×cosθ ×sinΦ , 4 ×sinθ× sinΦ, 4 × cosΦ)

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To find a parametric representation for the surface of the part of the sphere x² + y² + z² = 16 between the planes z = -2 and z = 2, use spherical coordinates with r = 4, θ ranging from 0 to π, and ϕ ranging from 0 to 2π.

To find a parametric representation for the surface of the part of the sphere x² + y² + z² = 16 that lies between the planes z = -2 and z = 2, we can use spherical coordinates.

Letting x = r sinθ cosϕ, y = r sinθ sinϕ, and z = r cosθ, where r is the radius of the sphere, θ is the polar angle, and ϕ is the azimuthal angle, we can rewrite the equation of the sphere as r² = 16.

Simplifying, we have r = 4.

Now we can write the parametric equations as x = 4 sinθ cosϕ, y = 4 sinθ sinϕ, and z = 4 cosθ, where θ ranges from 0 to π, and ϕ ranges from 0 to 2π.

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Answer: D) 60x-45y = - 1 where A = 60 , B = -45 , and c = - 1

Step-by-step explanation: Clear it : 45y=60x+1

Step 2: Isolate the constant on one side: ( -1 = -45y +60x)

step 3: A= 60 , B= - 45 , C= - 1

Answer:

60x-45y = - 1 where A = 60 , B = -45 , and c = - 1

Step-by-step explanation:

Answer:

The zeros of the function are;

x = 0 and x = 1

Step-by-step explanation:

The zeroes of the function simply imply that we find the values of x for which the corresponding value of y is 0.

We let y be 0 in the given equation;

y = x^3 - 2x^2 + x

x^3 - 2x^2 + x = 0

We factor out x since x appears in each term on the Left Hand Side;

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

This implies that either;

x = 0 or

x^2 - 2x + 1 = 0

We can factorize the equation on the Left Hand Side by determining two numbers whose product is 1 and whose sum is -2. The two numbers by trial and error are found to be -1 and -1. We then replace the middle term by these two numbers;

x^2 -x -x +1 = 0

x(x-1) -1(x-1) = 0

(x-1)(x-1) = 0

x-1 = 0

x = 1

Therefore, the zeros of the function are;

x = 0 and x = 1

The graph of the function is as shown in the attachment below;

As you can see there are two triangles but it can be done calculating just for one. First we must understand how formula for area of triangle works.

[tex]A=\frac{1}{2}bh[/tex]

Where [tex]b[/tex] represents base (hypotenuse) and [tex]h[/tex] as height of the triangle.

We know that:

[tex]

b=13cm \\

h=4cm

[/tex]

Using this data we fill the formula.

[tex]A=\frac{1}{2}\cdot13\cdot4=\frac{13\cdot4}{2}=13\cdot2=\boxed{26cm^2}[/tex]

Hope this helps.

r3t40

Answer:

Area of the triangle = 26 cm²

Step-by-step explanation:

The given triangle has the measure of height h = 4 cm

and base of the triangle = 13 cm

We know the formula of the area of a triangle = [tex]\frac{1}{2}(Base)(height)[/tex]

By putting the values in the formula

Area of the triangle = [tex]\frac{1}{2}(4)(13)[/tex]

                                = 2×13

                                = 26 cm²

Therefore, area of the given triangle is 26 cm².

Answer:

B. 0.43, -0.43

Step-by-step explanation:

The given equation is

[tex]-2=3-7\sqrt[5]{x^2}[/tex]

Combine similar terms to get:

[tex]-2-3=-7\sqrt[5]{x^2}[/tex]

[tex]-5=-7\sqrt[5]{x^2}[/tex]

[tex]\sqrt[5]{x^2}=\frac{5}{7}[/tex]

[tex]x^2=(\frac{5}{7})^5[/tex]

[tex]x^2=\frac{3125}{16807}[/tex]

[tex]x=\pm \sqrt{\frac{3125}{16807}}[/tex]

[tex]x=\pm 0.43[/tex]

[tex]x=0.43[/tex] or [tex]x=-0.43[/tex]

The correct answer is B.

Answer:

B

Step-by-step explanation:

First subtract 3 from the equation:

[tex]-2-3=3-7\sqrt[5]{x^2}-3\\ \\-5=-7\sqrt[5]{x^2}[/tex]

Now divide the equation by -7:

[tex]\sqrt[5]{x^2}=\dfrac{5}{7}[/tex]

Now raise the equation to the 5th power:

[tex]x^2=\left(\dfrac{5}{7}\right)^5[/tex]

Take square root:

[tex]x=\pm \sqrt{\left(\dfrac{5}{7}\right)^5} =\pm \dfrac{25}{49}\sqrt{\dfrac{5}{7}} \\ \\x_1\approx 0.43\\ \\x_2\approx -0.43[/tex]

Answer:

  D. -2a-b

Step-by-step explanation:

The additive inverse is found by multiplying the expression by -1.

  -1(2a+b) = -2a -b . . . . matches selection D

Answer:

75

Step-by-step explanation:

"given that it's a junior" means to only look at juniors.

From the table, under junior, there are 2  males and 6 females. 2 + 6 = 8. The total number of juniors is 8.

p(female given junior) = 6/8 = 3/4 = 0.75 = 75%

Answer: 75

Answer:

75

Step-by-step explanation:

"given that it's a junior" means to only look at juniors.

From the table, under junior, there are 2  males and 6 females. 2 + 6 = 8. The total number of juniors is 8.

p(female given junior) = 6/8 = 3/4 = 0.75 = 75%

Answer: 75

Answer:

Given: 175 g/L

1 gram/liter  =  0.06242796 pound/cubic foot

175 g/L * 0.06242796 pound/cubic foot= 10.924893 lb/ft3

So, a foam material has a density of 10.924893 lb/ft3 in units of lb/ft3

Step-by-step explanation:

Answer:

The correct answer option is D. 81.

Step-by-step explanation:

We are given the following expression and we are to find the value of x:

[tex] log _ 3 x = 4 [/tex]

We can inverse [tex] log _ 3 x [/tex] and re-write it as [tex]3^x[/tex].

Doing that, we will raise both the sides of the equation to the power of 3 to get:

[tex] 3 ^ { log 3 x } = 3 ^ 4 [/tex]

x = 81

the scale has a persicion of 2 and it reads high.

1. 2 is the precision of this old bathroom scale.
2. Since 135 lbs of the old scale is higher than 126 lbs of a better-maintained scale at the doctor's office.

Given that,
An old bathroom scale,
You step on the scale, and it reads 135 lb. You step off and step back on, and it reads 134 lb. You do this three more times and get readings of 135 lb, 136 lb, and 135 lb.

In mathematics, it deals with numbers of operations according to the statements.

Here,
a). What is the precision of this old bathroom scale,
= higher reading - the lower reading
= 136 - 134
= 2

b. The much more carefully constructed and better-maintained scale at the doctor's office reads 126 lb.
Since measured weight by the old scale is 135 lbs which is higher than 126 lbs measured by the scale at the doctor's office.

Thus,
1. 2 is the precision of this old bathroom scale.
2. Since 135 lbs of the old scale is higher than 126 lbs of a better-maintained scale at the doctor's office.

Learn more about arithmetic here:

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For [tex]180^\circ<\theta<270^\circ[/tex], we expect to have [tex]\cos\theta<0[/tex]. Then if [tex]\sin\theta=-\dfrac{15}{17}[/tex], we have

[tex]cos^2\theta+\sin^2\theta=1\implies\cos\theta=-\sqrt{1-\sin^2\theta}=-\dfrac8{17}[/tex]

[tex]\implies\sec\theta=\boxed{-\dfrac{17}8}[/tex]

Answer:

Step-by-step explanation:

Formula

abs(a + b) + abs(c)

Givens

a = - 3

b = - 7

c = - 15

Solution

abs(-3 - 7) + abs(-15)

abs(-10) + abs(-15)

10 + 15

25

Answer:

  150π in³ ≈ 471.24 in³

Step-by-step explanation:

The formula for the volume of a cylinder is ...

  V = πr²h

The radius is half the diameter, so you have a volume of ...

  V = π(5 in)²(6 in) = 150π in³ ≈ 471.24 in³

Answer:

Option B is correct answer.

Step-by-step explanation:

We need to solve the expression sec2xcot2x.

We know sec x = 1/ cos x and cot x = 1/ tan x and tan x = sin x/cos x and 1/tanx = cosx /sinx

Since in question we 2x instead of x so, replacing x with 2x and Putting values:

[tex]sec2x\,\, cot2x\\=\frac{1}{cos 2x} * \frac{1}{tan 2x} \\=\frac{1}{cos 2x} * \frac{cos2x}{sin2x}\\=\frac{1}{sin 2x}\\=csc2x[/tex]

So, Option B is correct answer.

Answer:

b

Step-by-step explanation:

Answer:

(−∞,−2) and (0,4)

Step-by-step explanation:

The function is positive when it is above the x-axis.  This is when x is less than -2 and when x is between 0 and 4.

This question is asking about the intervals in which a given function is positive. Without knowing the exact function, one would typically evaluate the function in the given intervals to decide whether the result is positive or negative.

The question is asking in which intervals a given mathematical function is positive. Without more specific information about the function, it is impossible to definitively say which of the intervals the function is positive in. Normally, you would evaluate the function at multiple points within the given intervals and analyze the output to determine if the function is positive or negative within those ranges.

For example, if you had the function f(x) = x^2 - 3x + 2, you could plug in a couple of values in the intervals (−∞,−2), (0,4), (4,∞), (−1.5,−1), (2,2.5), (−2, 0) and see whether the output is positive.

Again, without the specific function this exercise is theoretical and is based on your understanding of intervals and their relationship with function values.

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The answer for your question is A,D.

Answer:

D. supply curve shifts to the left

C. price increases and quantity decreases

Step-by-step explanation:

Since the number of sellers decreases, the quantity available at the same price decreases. This shifts the supply curve to the left.

When the supply curve shifts to the left, the equilibrium point shifts to the left (and up the demand curve). Hence the price increases and the quantity decreases.

Answer:

  (2 +4i)(5 -6i) . . . or . . . (4 -2i)(6 +5i)

Step-by-step explanation:

The product of two complex numbers is ...

  (a +bi)(c +di) = (ac -bd) +(bc +ad)i

So, we're looking for pairs of numbers that can be combined in different ways to give 34 and 8. The numbers we found (by trial and error) are ...

  2, 4, 5, 6

where 4*6 +2*5 = 34 and 4*5 -2*6 = 8. Because of the effect if i^2 on the sign, we need to have the imaginary parts have opposite signs.

Each of the solutions shown above is representative of 4 solutions. For example, for the first one, you could have ...

  (2 +4i)(5 -6i) = (2·5 +4·6) + (4·5 +2(-6))i = 34 +8i

  (5 -6i)(2 +4i) = (5·2 +6·4) + (-6·2 +5·4) = 34 +8i . . . . . order of factors swapped

  (-2 -4i)(-5 +6i) = ((-2)(-5) -(-4)(6)) + ((-4)(-5) +(-2)(6))i = 34 +8i . . . . both factors in the first solution negated

  (-5 +6i)(-2 -4i) = ((-5)(-2) -(6)(-4)) +(6(-2) +(-5)(-4))i = 34 +8i . . . . factors swapped and negated

___

Likewise, the second shown solution above is representative of 4 solutions.

Possible solutions are ...

with sign and order variations.

_____

Comment on trial and error

Actually, we did an exhaustive search of the 441 products of single-digit numbers [-9, 9] to see which pairs of them differed by 34. Then, among those, we looked for product pairs that added to 8. In the end, we found the 8 solutions described above.

Answer:

Range = {2,1,4,5}

Step-by-step explanation:

When a function is given in the form if a relation. i.e. ordered pairs.

When the function is given in the form of ordered pairs then the set of first elements i.e. x-coordinates of all ordered pairs forms domain while the set of second elements i.e. y-coordinate of all ordered pair is called range.

So in the given function:

Range = {2,1,4,5}

The repeating values are only written once..

ANSWER

A=16

EXPLANATION

The radius of the circle is r=4 units.

The area of a triangle is

[tex] \frac{1}{2} bh[/tex]

Both the height and the base of the triangle are radii, which is 4 units.

The area of the two isosceles right triangle is

[tex] 2(\frac{1}{2} \times 4 \times 4) = 16[/tex]

Answer:

Area of combined triangle = 2 * 8 = 16 square units

Step-by-step explanation:

Points to remember

Area of triangle = bh/2

b - Base and h - Height

From the figure we can see that a circle and two right angled triangles.

To find the combined area of triangles

Here base and height of two triangles is equals to radius of circle

Therefore b = 4 and h = 4

Area of one triangle = bh/2

 = (4 * 4)/2 = 8 square units

Area of combined triangle = 2 * 8 = 16 square units

8 students know Spanish since 12 students know French and 7 students know Italian

Answer:

8 students learn Spanish.

Step-by-step explanation:

In a class total number of students are 30.

Students who know Italian = 15

Students who know French = 10

Students who know both = 3

Rest all students know Spanish.

By Venn diagram attached number of students who know Spanish

= [ 30 - (12 + 3 + 7 )]

= 30 - (22)

= 8 students.

8 students learn Spanish.

Answer:

6.25

Step-by-step explanation:

I find it convenient to use technology to compute the mean absolute deviation. (see below)

Answer:

(MAD) Mean Absolute Deviation: 6.25

Step-by-step explanation:

Mean: 23 + 28 + 16 + 25 + 18 + 31 + 14 + 37 = 192/8 = 24

24 - 23 = 1

24 - 28 = 4

24 - 16 = 8

24 - 25 = 1

24 - 18 = 6

24 - 31 = 7

24 - 14 = 10

24 - 37 = 13

Mean Absolute Deviation (MAD): 1 + 4 + 8 + 1 + 6 + 7 + 10 + 13 = 50/8 = 6.25

(r^-7)^6 = r^-1 = 1/r

Therefore the answer is D. 1/r

Let me know if you have any questions.

Answer:

B. 1/r^42

Step-by-step explanation:

(r^-7)^6= r^-7*6= r^-42.

As a positive exponent: 1/r^42

Answer:

(-5,2)

Step-by-step explanation:

The given system is

1st equation: y = 4x + 22

2nd equation:  4x – 6y = –32

We plug in the first equation into the second equation to obtain:

4x – 6(4x + 22) = –32

We expand the parenthesis to obtain:

4x – 24x -132= –32

Group similar terms;

4x – 24x = –32+132

Combine similar terms

-20x =100

Divide both sides by -20

x =-5

Put x=-5 into the 1st equation

y = 4(-5) + 22

y=-20+22

y=2

The solution is:

(-5,2)

The value of f(-3) for the function f(x) = -6x + 3 is 21. The value of g(3) for the function g(x) = 3x + 21x - 3 is 66.

To find the value of f(-3), you substitute -3 in place of x in the function f(x) = -6x + 3. You get f(-3) = -6(-3) + 3 = 18 + 3 = 21.

To find the value of g(3), we substitute 3 in place of x in the function g(x) = 3x + 21x - 3. This gives g(3)= 3(3) + 21*(3)-3 = 9 + 57 = 66.

So, f(-3) = 21 and g(3) = 66.

To find the value of f(–3) and g(3), we need to substitute the given values into the respective functions.

For f(x) = –6x + 3, substituting x = –3 into the function, we get:

f(–3) = –6(–3) + 3 = 18 + 3 = 21

For g(x) = 3x + 21x – 3, substituting x = 3 into the function, we get:

g(3) = 3(3) + 21(3) – 3 = 9 + 63 – 3 = 69

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Answer:

12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

[tex] {9}^{2} + {x}^{2} = {15}^{2} \\ \\ 81 + {x}^{2} = 225 \\ \\ {x}^{2} = 144 \\ \\ {12}^{2} = 144 \\ \\ [/tex]

Answer: 311.25

Step-by-step explanation: Take 52.50 and multiply by 4.5. Then add the $75 service fee.

Answer:

$311.25

Step-by-step explanation:

This is your correct answer because 52.50 x 4.5 plus 75 equals 311.25.

To find the points where the tangent is horizontal or vertical on the given curve, we find the slope, set it equal to zero or undefined, and solve for t. Then substitute the values of t in the equations to find the corresponding points on the curve.

To find the points on the curve where the tangent is horizontal or vertical, we need to find the slope of the curve and determine when it is zero or undefined. For the given curve x = t^3 - 3t, y = t^2 - 4, we can find the slope dy/dx, set it equal to zero or undefined, and solve for t. Once we have the values of t, we can substitute them back into the equations x = t^3 - 3t and y = t^2 - 4 to find the corresponding points on the curve.

To find the horizontal tangent, we set dy/dx equal to zero:

dy/dx = (dy/dt) / (dx/dt) = (2t) / (3t^2 - 3) = 0

Setting the numerator equal to zero, 2t = 0, we find t = 0. Substituting t = 0 back into the equations x = t^3 - 3t and y = t^2 - 4, we get the point (0, -4).

To find the vertical tangent, we set dx/dt equal to zero:

dx/dt = 3t^2 - 3 = 0

Solving for t, we find t = ±1. Substituting t = 1 and t = -1 back into the equations x = t^3 - 3t and y = t^2 - 4, we get the points (2, -3) and (-2, -3) respectively.

Therefore, the points on the curve where the tangent is horizontal or vertical are (0, -4), (2, -3), and (-2, -3).

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The points on the curve defined by x = t^3 - 3t and y = t^2 - 4 where the tangent is horizontal or vertical are (-2, 3), (0, -4), and (2, 3).

In the subject of Mathematics, specifically calculus, the question is seeking the points on the curve defined by the parametric equations x = t^3 - 3t and y = t^2 - 4 where the tangent is horizontal or vertical. This means we are looking for the values of t where the derivative dy/dx equals 0 (horizontal tangent) or is undefined (vertical tangent).

First, we need to calculate the derivatives dx/dt and dy/dt. dx/dt = 3t^2 - 3 and dy/dt = 2t. Then we can find the overall derivative dy/dx = (dy/dt)/(dx/dt).

For a horizontal tangent, dy/dx = 0, meaning the numerator of our derivative equation must be zero: dy/dt = 2t = 0. This gives us t = 0.

For a vertical tangent, dy/dx is undefined, meaning the denominator of our derivative equation must be zero: dx/dt = 3t^2 - 3 =0. Solving this equation gives us t = -1, 1.

Substitute t = -1, 0, and 1 into x = t^3 - 3t and y = t^2 - 4 to get the points in the (x, y) format. This results in the points: (-2, 3), (0, -4), and (2, 3).

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