What would be the minimum value of the function for the graph shown if we consider the graph to be a sine function of the form y=a sin ⁡(x−c)?

2
0
-2
-4

The range of F(x) = logb x is the set of all real numbers.

TRUE

The range of F(x) = logb x is the set of all real numbers since the correct option is True.

The domain of this function is R+ or a positive real number For range if b>1  function will be an increasing function and the graph will be asymptotic to the negative y-axis. which implies if x goes to infinity f(x) goes to infinity and vice versa if 0<b<1 function will be a decreasing and graph will be asymptotic to the positive y-axis. which implies if x goes to infinity f(x) goes to 0 and vice-versa the range of the above function is all real numbers.

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Answer:

d = 7.071068

Step-by-step explanation:

Using the point slope formula (y-y1=m(x-x1)) it is found to be y=1/2x+2.

The answer is D. 36pi units^3

Hope this helps!

The formula for cylinder volume is: pi*r^2*h

For this case we have that the volume of the cylinder is given by:

[tex]V = \pi * r ^ 2 * h[/tex]

Where:

h: It is the height of the cylinder

A: It is the radius of the cylinder

We have to, according to the given data:[tex]h = 4\\r = 3[/tex]

Substituting:

[tex]V = \pi * (3) ^ 2 * 4\\V = \pi * 9 * 4\\V = 36 \ pi[/tex]

[tex]36 \pi \ units ^ 3[/tex]

ANswer:

Option D

[tex]36 \pi \ units ^ 3[/tex]

To estimate 47% of 77, multiply 77 by 0.47. The estimated value is approximately 36.19.

To estimate the percent of a number, we multiply the number by the percentage as a decimal. In this case, to estimate 47% of 77, we multiply 77 by 0.47. This gives us an estimated value of 36.19. Therefore, 47% of 77 is approximately 36.19.

Answer:

C and D

Step-by-step explanation:

3 is the base because its the number being multiplied repeatedly while the exponent would be the number of times its being multiplied.

hi there the answer is 7:30 see the picture

Answer:

Median

Step-by-step explanation:

This set of data has an extreme outlier, which will throw off the mean. The median, on the other hand, does not change or changes minimally whether or not the outlier is there.

By default, the mean is always better, but if an outlier, such as this one, is too large, the median is better.

Answer:

11.1 years

Step-by-step explanation:

The formula for interest compounding continuously is:

[tex]A(t)=Pe^{rt}[/tex]

Where A(t) is the amount after the compounding, P is the initial deposit, r is the interest rate in decimal form, and t is the time in years.  Filling in what we have looks like this:

[tex]2000=1150e^{{.05t}[/tex]

We will simplify this first a bit by dividing 2000 by 1150 to get

[tex]1.739130435=e^{.05t}[/tex]

To get that t out the exponential position it is currently in we have to take the natural log of both sides.  Since a natural log has a base of e, taking the natual log of e cancels both of them out.  They "undo" each other, for lack of a better way to explain it.  That leaves us with

ln(1.739130435)=.05t

Taking the natural log of that decimal on our calculator gives us

.5533852383=.05t

Now divide both sides by .05 to get t = 11.06770477 which rounds to 11.1 years.

Answer:

The length of the escalator ≈ 1088.8 ft ⇒ answer (b)

Step-by-step explanation:

* Lets explain the problem

- Consider the escalator and the vertical raise formed a right

 angle triangle

- The length of the escalator is the hypotenuse

- The vertical rise is on leg of the right triangle

- The angle of elevation is the angle between the hypotenuse

  and the horizontal

* Now lets solve the problem

∵ Angle of elevation = 10° 21' 36"

∵ Vertical distance = 195.8 feet

* The vertical is opposite to the angle of elevation

∴ sin angel of elevation= the vertical/the length of the escalator

∴ sin(10° 21' 36") = 195.8/the length of the escalator

- By using cross multiplication

∴ The length of the escalator = 195.8/sin(10° 21' 36") = 1088.8 feet

* The length of the escalator = 1088.8 ft

ANSWER

[tex]( \frac{3}{34} , \frac{501}{34} )[/tex]

EXPLANATION

The given parabola has equation;

[tex]y = 34 {x}^{2} - 6x + 15[/tex]

Comparing this equation to

[tex]y = a{x}^{2} + bx + c[/tex]

we have

a=34, b=-6 and c=15

The x-coordinate of the vertex is given by:

[tex]x = \frac{ - b}{2a} [/tex]

[tex]x = \frac{ - - 6}{2(34)} [/tex]

[tex]x = \frac{ 6}{2(34)} [/tex]

[tex]x = \frac{ 3}{34} [/tex]

The y-coordinates of the vertex is obtained by substituting the x-value of the vertex into the equation:

[tex]y = 34( { \frac{3}{34} })^{2} - 6( \frac{3}{34}) + 15[/tex]

[tex]y = { \frac{9}{34} } - \frac{18}{34}+ 15[/tex]

[tex]y = \frac{501}{34} [/tex]

The vertex is

[tex]( \frac{3}{34} , \frac{501}{34} )[/tex]

Answer: (4,3)

He meant 3/4 not 34

Answer:

option C

y = 2

Step-by-step explanation:

Given in the question,

a co-ordinate = (-2,2)

x = -2

y = 2

Equation of the straight line

y = mx + c

here m = gradient of the line

        c = y - intercept

plug value in the equation above

y = (0)x + 2

y = 2

Answer:

see explanation

Step-by-step explanation:

There are 2 possible positions for n, that is

- 2 - 1.5 = - 3.5

OR

- 2 + 1.5 = - 0.5

Both are 1.5 units distance from - 2

The possible values of n are -0.5 and -3.5

Step-by-step explanation:

Analyze two cases

1) n-(-2)=1.5

Solve for n

n+2=1.5

n=1.5-2

n=-0.5

2) -2-n=1.5

n=-2-1.5

n=-3.5

For this case we have that, by definition, the volume of the cylinder is given by:

[tex]V = \pi * r ^ 2 * h[/tex]

Where:

h: It's the height

A: It's the radio

We have to:

[tex]h = 15\\r = 12[/tex]

Substituting:

[tex]V = \pi * (12) ^ 2 * 15\\V = \pi * 144 * 15\\V = 2160 \pi \ units ^ 3[/tex]

Answer:

Option B

Answer: 2160

Step-by-step explanation:

apex

Answer: Option D.

Step-by-step explanation:

You can  observe that the dimensions of the bedroom in the scale drawing are:

[tex]length=2"\\width=1.5"[/tex]

You know that [tex]\frac{1}{2}"=3feet[/tex]

Then you need to convert these dimensions to the actual dimensions. So, you get:

[tex]actual\ lenght=\frac{(2")(3ft)}{\frac{1}{2}" }=12ft\\\\actual\ width=\frac{(1.5")(3ft)}{\frac{1}{2}" }=9ft[/tex]

Therefore, you can calculate the actual area of the bedroom. This is:

[tex]Area=(actual\ lenght)(actual\ width)\\Area=(12ft)(9ft)\\Area=108ft^2[/tex]

Answer:

Option D.

Step-by-step explanation:

From the given figure it is clear that

Length of the bedroom in scale drawing = 2''

Width of the bedroom in scale drawing = 1.5''

It is given that

Scale [tex]\frac{1}{2}''=3feet[/tex]

[tex]1''=6feet[/tex]

Using this conversion we get

[tex]2''=12feet[/tex]

[tex]1.5''=9feet[/tex]

Actual length of the bedroom = 12 feet

Actual width of the bedroom = 9 feet

Area of a rectangle is

[tex]Area=length\times width[/tex]

Actual area of the bedroom is

[tex]Area=12\times 9[/tex]

[tex]Area=108[/tex]

The actual area of the bedroom is 108 ft2.

Therefore, the correct option is D.

Answer:

The conic is ellipse of equation (x - 1)²/22 + (y + 4)²/44 = 1

Step-by-step explanation:

* Lets revise how to identify the type of the conic  

- Rewrite the equation in the general form,  

 Ax² + Bxy + Cy² + Dx + Ey + F = 0  

- Identify the values of A and C from the general form.  

- If A and C are nonzero, have the same sign, and are not equal  

 to each other, then the graph is an ellipse.  

- If A and C are equal and nonzero and have the same sign, then  

 the graph is a circle  

- If A and C are nonzero and have opposite signs, and are not equal  

then the graph is a hyperbola.  

- If either A or C is zero, then the graph is a parabola  

* Now lets solve the problem

The equation is 4x² + 2y² - 8x + 16y - 52 = 0

∴ A = 4 and C = 2 ⇒ same sign and different values

∴ The equation is ellipse

* The standard form of the ellipse is

  (x - h)²/a² + (y - k)²/b² = 1

- Lets try to make this form from the general form

- Group terms that contain the same variable, and move the

  constant to the opposite side of the equation

∴ (4x² - 8x) + (2y² + 16y) = 52

- Factorize the coefficients of the squared terms

∴ 4(x² - 2x) + 2(y² + 8y) = 52

- Complete the square for x and y

# To make completing square

- Divide the coefficient  of x (or y) by 2 and then square the answer

- Add and subtract this square number and form the bracket of

 the completing the square

# 2 ÷ 2 = 1 ⇒ (1)² = 1 ⇒ add and subtract 1

∴ 4[(x² - 2x + 1) - 1] = 4(x² - 2x + 1) - 4

- Rewrite as perfect squares ⇒ 4(x -1)² - 4

# 8 ÷ 2 = 4 ⇒ (4)² = 16 ⇒ add and subtract 16

∴ 2[(y² + 8y + 16) - 16] = 2(y² + 8y + 16)² - 32

- Rewrite as perfect squares ⇒ 2(y + 4)² - 32

∴ 4(x - 1)² - 4 + 2(y + 4)² - 32 = 52

∴ 4(x - 1)² - 4 + 2(y + 4)² = 32 + 4 + 52

∴ 4(x - 1)² + 2(y + 4)² = 88 ⇒ divide all terms by 88

∴ (x - 1)²/22 + (y + 4)²/44 = 1

Since tan is negative in the second quadrant, hence the direction angle for v is 98.13 degrees

The direction of a vector is the degree at which the vector is moving with respect to the horizontal.

Given the coordinate point (-3, 21), the direction is expressed as:

theta = arctan(y/x)

Substitute

theta = arctan(21/-3)
theta =arctan(-7)

theta = -81.7 degrees

Since tan is negative in the second quadrant, hence the direction angle for v is 98.13 degrees

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Answer:

Vol. of the composite figure is 189 m³

Step-by-step explanation:

Find the volume of the larger figure by mult. together its 3 dimensions:

V = (9 m)(8 m)(3 m) = 216 m³.

Next, find the volume of the "notch," which is (3 m)³, or 27 m³.

Finally, subtract the "notch" volume from the 216 m³ volume found earlier:

216 m³ - 27 m³ = 189 m³

Answer:

The lateral area is [tex]4,608\pi\ in^{2}[/tex]  or  [tex]32\pi\ ft^{2}[/tex]

Step-by-step explanation:

we know that

The lateral area of a cylinder (pillar) is equal to

[tex]LA=2\pi rh[/tex]

Remember that

1 ft=12 in

Find the lateral area in square inches

we have

[tex]r=8\ in[/tex]

[tex]h=24\ ft[/tex] ----> convert to inches

[tex]h=24*12=288\ in[/tex]

substitute the values

[tex]LA=2\pi (8)(288)[/tex]

[tex]LA=4,608\pi\ in^{2}[/tex]

Find the lateral area in square feet

we have

[tex]h=24\ ft[/tex]

[tex]r=8\ in[/tex] -----> convert to feet

[tex]r=8/12=(2/3)\ ft[/tex]

substitute the values

[tex]LA=2\pi (2/3)(24)[/tex]

[tex]LA=32\pi\ ft^{2}[/tex]

The reading program really improved some of the student's reaping speeds.

[tex]x < - 10.434462 \\ x > 0[/tex]

Answer:

D

Step-by-step explanation:

approximately 0.3 or 3/10 pizza was left for Julio to eat.

mind you some numbers were rounded. if you want the exact number then it's 9/28 which is equal to 0.32.

hope this helps

After accounting for the amounts of pizza eaten by Julio's family (parents, brothers, and sisters), you find that there was approximately 0.36 pizzas left for Julio to eat.

This question deals with some basic arithmetic and fractions. Start by counting how many pizzas Julio's family ate altogether. His parents ate 3/7 of one pizza, his brothers ate 2 3/4 pizzas, and his sisters ate 2 1/2 pizzas.

To add these amounts together, you might find it easiest to convert all the fractions to sevenths. The brothers ate 2 4/7 pizzas (as 4/7 is equivalent to 1/2) and the sisters ate 2 3.5/7 pizzas (as 3.5/7 is equivalent to 1/2). Add these to the 3/7 pizza the parents ate, you find the family ate a total of approximately 5.64 pizzas.

Since Julio's family ordered 6 pizzas in total, you then subtract the total amount eaten by the family from 6, which is approximately 0.36 pizzas. Therefore, Julio was left with 0.36 pizzas to eat.

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Answer:

She will receive [tex]\$5[/tex]

Step-by-step explanation:

step 1

Find the total cost

The total cost is equal to

[tex]5(\$6.00)+4(\$7.50)=\$60[/tex]

step 2

Find the difference

[tex]\$65-\$60=\$5[/tex]

Answer:

$5

Step-by-step explanation:

65-6x5-4x7.5=5

Answer:

i have provided some pictures to help you i cant post the graphs though cuz they dont allow me to but if you need them i can send link pictures  :)

i also love you're Naruto profile picture uwu

Jeanne can use a system of inequalities to make at least $75.

Let X represent babysitting hours = $6 per hour.

Y represent tutoring hours = $10 per hour.

If she will work more 7.5hours or more than 7.5 hours she can make $75 easily.

$10 per hour × 7 hours = $70

& $6 per hour × 1 hour = $6

so, $70 + $6 = $76.

In the above way she can make easily $75.

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Answer:

The equation of the curve is y = x² + 3x

Step-by-step explanation:

I get your drift, but wish you had stated specifically that you wanted to find the equation of this curve.

Slope of tangent line to curve is dy/dx = 2x + 3.

Integrating that with respect to x yields y = x² + 3x + C.

The point (-3, 0) must satisfy this equation:

0 = (-3)² + 3(-3) + C, so C = 0.

The equation of the curve is y = x² + 3x

The equation of the curve where the slope at any point is 2x + 3 and it passes through the point (-3, 0) is y = x² + 3x.

The student's question involves finding the equation of a curve given that at each point (x, y) on the curve, the slope is 2x + 3, and the curve passes through the point (-3, 0). This is a problem that involves differential equations, as it asks us to find a function y(x) whose derivative with respect to x is given.

To find the equation of the curve, we integrate the slope function. Since the slope at any point is 2x + 3, we have:
∂y/∂x = 2x + 3
Integrating both sides with respect to x gives:
y = x² + 3x + C

To find the constant of integration C, we use the fact that the curve passes through (-3, 0). Substituting these values into the equation gives:
0 = (-3)² + 3(-3) + C
0 = 9 - 9 + C
Thus, C = 0, and the equation of the curve is:
y = x² + 3x.

Answer: 12b

Step-by-step explanation: you multiply 4 by 3 but keep the b

Answer:

C ---> 12b

Step-by-step explanation:

First you would distribute the 4 to the 3b which will give you 12b.

4(3b)

4*3=12

12b

[tex]\vec r(t)=t^2\,\vec\imath+t^3\,\vec\jmath-2t\,\vec k[/tex]

[tex]\mathrm d\vec r=(2t\,\vec\imath+3t^2\,\vec\jmath-2\,\vec k)\,\mathrm dt[/tex]

[tex]\vec f(x,y,z)=(x+y^2)\,\vec\imath+xz\,\vec\jmath+(y+z)\,\vec k[/tex]

[tex]\vec f(x(t),y(t),z(t))=(t^2+t^6)\,\vec\imath-2t^3\,\vec\jmath+(t^3-2t)\,\vec k[/tex]

The line integral is

[tex]\displaystyle\int_C\vec f\cdot\mathrm d\vec r=\int_0^2\bigg((t^2+t^6)\,\vec\imath-2t^3\,\vec\jmath+(t^3-2t)\,\vec k\bigg)\cdot(2t\,\vec\imath+3t^2\,\vec\jmath-2\,\vec k)\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^2(2t^7-6t^5+4t)\,\mathrm dt=\boxed{8}[/tex]

Given:

[tex]\to \bold{\int_{c} \ F \cdot dx}[/tex]

Where

[tex]\to \bold{F(x,y,z)=(x+y^2)i+xzj+(y+z)K}[/tex] and C is given by the vector function [tex]\bold{r(t)}[/tex].

[tex]\to \bold{r(t)=t^2i+t^3j-2tk,\ \ 0\leq t\leq 2}\\\\\to \bold{dx=(2ti+3t^2j-2k)dt}\\\\[/tex]

therefore

[tex]\to \bold{x=t^2}\\\\ \to \bold{y=t^3}\\\\ \to \bold{z=2t}\\\\\to \bold{F(r)=(t^2+(t^3)^2)i+t^2(-2t)j+(t^3-2t)k}\\\\[/tex]

            [tex]\bold{=(t^2+t^6)i-2t^3j+(t^3-2t)k}\\\\[/tex]

[tex]\bold{\therefore}\\\\\bold{F(r).dx=((t^2+t^6)i-2t^3j+(t^3-2t)k).(2ti+3t^2j-2k)}\\\\[/tex]

             [tex]=\bold{((t^2+t^6)2t-2t^3(3t^2)+(t^3-2t)(-2)]dt}\\\\=\bold{(2t^3+2t^7-6t^5-2t^3+4t)dt}\\\\=\bold{(2t^7-6t^5+4t)dt}\\\\[/tex]

Calculating the line integral:

[tex]\bold{\int_{c}\ F .dx=\int^{2}_{t=0} (2t^7-6t^5+4t)dt}\\\\[/tex]

               [tex]=\bold{[\frac{t^8}{4}-t^6+2t^2]^{2}_{0}}\\\\=\bold{\frac{2^8}{4}-2^6+2(2)^2}\\\\=\bold{\frac{256}{4}-64+2(4)}\\\\=\bold{64-64+8}\\\\=\bold{8}[/tex]

Therefore the final answer "8".

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Answer:

8

Step-by-step explanation:

When you are told to find f(-5), that means that you are to sub in a -5 for every x you see.  That -5 could be any number or expression.  Subbing in a -5 looks like this:

[tex]7(-5)^5+35(-5)^4-2(-5)^3-4(-5)^2+30(-5)+8[/tex]

Be careful with all those negatives.  Doing the math on that gives you that f(-5) = 8

[tex]\vec F(x,y,z)=4x^2\,\vec\imath+4y^2\,\vec\jmath+3z^2\,\vec k\implies\nabla\cdot\vec F=8x+8y+6z[/tex]

Let [tex]S[/tex] be the surface of the rectangular prism bounded by the planes [tex]x=0[/tex], [tex]x=a[/tex], [tex]y=0[/tex], [tex]y=b[/tex], [tex]z=0[/tex], and [tex]z=c[/tex]. By the divergence theorem, the integral of [tex]\vec F[/tex] over [tex]S[/tex] is given by the integral of [tex]\nabla\cdot\vec F[/tex] over the interior of [tex]S[/tex] (call it [tex]R[/tex]):

[tex]\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\iiint_R(\nabla\cdot\vec F)\,\mathrm dV[/tex]

[tex]=\displaystyle\int_0^c\int_0^b\int_0^a(8x+8y+6z)\,\mathrm dx\,\mathrm dy\,\mathrm dz=\boxed{abc(4a+4b+3c)}[/tex]

Answer:

[tex]\displaystyle \iiint_D {\nabla \cdot \textbf{F}} \, dV = \boxed{6875}[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:
[tex]\displaystyle (cu)' = cu'[/tex]

Derivative Rule [Basic Power Rule]:

Integration

Integration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:
[tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Multivariable Calculus

Partial Derivatives

Vector Calculus (Line Integrals)

Del (Operator):
[tex]\displaystyle \nabla = \hat{\i} \frac{\partial}{\partial x} + \hat{\j} \frac{\partial}{\partial y} + \hat{\text{k}} \frac{\partial}{\partial z}[/tex]

Div and Curl:

Divergence Theorem:
[tex]\displaystyle \iint_S {\big( \nabla \times \textbf{F} \big) \cdot \textbf{n}} \, d\sigma = \iiint_D {\nabla \cdot \textbf{F}} \, dV[/tex]

Step-by-step explanation:

*Note:
Your question is incomplete, but I have defined the missing portions of the question below.

Step 1: Define

Identify given.

[tex]\displaystyle \textbf{F} (x, y, z) = 4x^2 \hat{\i} + 4y^2 \hat{\j} + 3z^2 \hat{\text{k}}[/tex]

[tex]\displaystyle \text{Region (Boundary de} \text{fined by rectangular prism):} \left\{ \begin{array}{ccc} 0 \leq x \leq 5 \\ 0 \leq y \leq 5 \\ 0 \leq z \leq 5 \end{array}[/tex]

Step 2: Find Flux Pt. 1

Step 3: Find Flux Pt. 2

We can evaluate the Flux integral (Divergence Theorem integral) using basic integration techniques listed under "Calculus":

[tex]\displaystyle \begin{aligned}\int\limits^5_0 \int\limits^5_0 \int\limits^5_0 {\big( 8x + 8y + 6z \big)} \, dx \, dy \, dz & = \int\limits^5_0 \int\limits^5_0 {4x^2 + x \big( 8y + 6z \big) \bigg| \limits^{x = 5}_{x = 0}} \, dy \, dz \\& = \int\limits^5_0 \int\limits^5_0 {\big( 40y + 30z + 100 \big)} \, dy \, dz \\& = \int\limits^5_0 {20y^2 + y \big( 30z + 100 \big) \bigg| \limits^{y = 5}_{y = 0}} \, dz \\\end{aligned}[/tex]

[tex]\displaystyle\begin{aligned}\int\limits^5_0 \int\limits^5_0 \int\limits^5_0 {\big( 8x + 8y + 6z \big)} \, dx \, dy \, dz & = \int\limits^5_0 {\big( 150z + 1000 \big)} \, dz \\& = \big( 75z^2 + 1000z \big) \bigg| \limits^{z = 5}_{z = 0} \\& = \boxed{6875} \\\end{aligned}[/tex]

∴  [tex]\displaystyle \Phi = \boxed{6875}[/tex]

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Topic: Multivariable Calculus

Unit: Stokes' Theorem and Divergence Theorem

Answer:

[tex]\boxed{\text{(v) and (viii)}}[/tex]

Step-by-step explanation:

The three step test for continuity states that a function ƒ(x) is continuous at a point x = a if three conditions are satisfied:

(i) Left-hand limit = right-hand limit.

Pass. The limit from either side is 8.

(ii) Left-hand limit = limit.  

Pass. If the limits from either direction exist, the limit exists.

(iii) Limit as x ⟶ ∞ is not part of the three-step test.

(iv) Limit as x ⟶ 1 exists. Pass.

(v)  f(1) is defined.

FAIL. f(1) is not defined.

(vi) Limit as x ⟶ ∞ is not part of the three-step test.

(vii) Passing the three-step test is not a step in the test.

(viii) The limit as x ⟶ 1 does not equal f(1).

FAIL. f(1) is undefined.

The steps in the three-step test for which the function fails are [tex]\boxed{\textbf{(v) and (viii)}}[/tex].