What ordered pair is closest to a local minimum of the function, f(x)?
A. (-1, -3)
B. (0, -2)
C. (1, 4)
D. (2, 1)​

Answer:

1 + 3 + 5 + A+9 divide by 5​

Step-by-step explanation:

The volume of the region R bounded by the x-axis is: [tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}[/tex]

The volume of a solid is the degree of space occupied by a solid object. If the axis of revolution is the planar region's border and the cross-sections are parallel to the line of revolution, we may use the polar coordinate approach to calculate the volume of the solid.

In the graph, the given straight line passes through two points (0,0) and (2,8).

Therefore, the equation of the straight line becomes:

[tex]\mathbf{y-y_1 = \dfrac{y_2-y_1}{x_2-x_1}(x-x_1)}[/tex]

where:

Thus, from the graph let assign (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 8), we have:

[tex]\mathbf{y-0 = \dfrac{8-0}{2-0}(x-0)}[/tex]

y = 4x

Now, our region bounded by the three lines are:

Similarly, the change in polar coordinates is:

where;

Now

Then:

[tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^2 (rdr d\theta )}[/tex]

[tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}[/tex]

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The given differential equation is not exact, if we convert it to an exact one, we get:

[tex]2ydx + 2*(x - sin(y)^{1/2})*dy = 0[/tex]

A differential equation:

[tex]Ndx + Mdy = C[/tex]

Is exact only if:

[tex]\frac{dM}{dy} = \frac{dN}{dx}[/tex]

In this case, we have:

[tex]2ydx + (x - sin(y)^{1/2})*dy = 0\\\\then:\\\\N = 2y\\M = x - sin(y)^{1/2}[/tex]

If we differentiate, we will get:

[tex]\frac{dN}{dy} = 2\\\\\frac{dM}{dx} = 1[/tex]

So, to convert this to an exact differential equation, we need to add a factor 2 to N, this will give:

[tex]2ydx + 2*(x - sin(y)^{1/2})*dy = 0[/tex]

This is, in fact, an exact differential equation.

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Answer:

[tex]f^{-1}(x)=\dfrac{1}{3}(\ln x +1)[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=e^{3x-1}[/tex]

Replace f(x) with y:

[tex]\implies y=e^{3x-1}[/tex]

Take natural logs of both sides:

[tex]\implies \ln y = \ln e^{3x-1}[/tex]

Apply the Power Log Law   [tex]\ln x^n=n\ln x[/tex] :

[tex]\implies \ln y = (3x-1)\ln e[/tex]

As [tex]\ln e=1[/tex] then:

[tex]\implies \ln y = 3x-1[/tex]

Rearrange to make x the subject:

[tex]\implies 3x=\ln y +1[/tex]

[tex]\implies x=\dfrac{1}{3}(\ln y +1)[/tex]

Swap x for [tex]f^{-1}(x)[/tex]  and y for x:

[tex]\implies f^{-1}(x)=\dfrac{1}{3}(\ln x +1)[/tex]

Answer:

67m²

Step-by-step explanation:

12m + 6m + 4m + 36 m 8m = 67m²

The time intervals when the riders could see Niagara falls are; 0.834 < t < 1.416 and (3.084, 3.666)

From the diagram attached, we can say that;

Period = 2π/k

where;

k = 2π/2.25

k = 8π/9

Thus;

h(t) = -(48/2) cos (8π/9)t + ((48/2) + 0.5)

h(t) = -24cos (8π/9)t + 24.5

Riders can see Niagara falls if they are higher than 41 meters above the ground. Thus;

41 = -24cos (8π/9)t + 24.5

41 - 24.5 = -24cos (8π/9)t

16.5 = -24cos (8π/9)t

-0.6875 = cos (8π/9)t

cos⁻¹0.6875 = (8π/9)t

t = 0.834 min

Thus, time interval is between;

0.834 < t < (2.25 - 0.834)

⇒ 0.834 < t < 1.416 and

(2.25 + 0.834) < t < (2.25 + 1.416)

⇒ (3.084, 3.666)

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The statements that are true about the dollhouses is: 1,4,5.

The space inside dollhouse 1 can be found using the equation V = 6 (6) (5) + one-half (6) (6) (4).

Space inside dollhouse 1:

V = 6 (6) (5) + 1/2 (6) (6) (4)

V=180+72

V=252 inches

The space inside dollhouse 2 can be found using the equation

V = 6 (6) (5) + 1/3 (6) (6) (4)

V=180+48

V=228

The space inside dollhouse 1 is 24 inches cubed greater than the space inside dollhouse 2.

V1=252

V2=228

Hence:

252-228=24 inches cubed

V1 ≥V2

Therefore the statements that are true about the dollhouses is: 1,4,5.

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The value of her investment after 8 years is  $8,293.81.

An interest rate tells you how high the cost of borrowing is, or high the rewards are for saving.

Given:

P= $5600

r= 5.4%

t= 8 years

Then solve the equation for A

A = P(1 + r/n)^nt

A = 5,400.00[tex](1 + 0.054/4)^{4/8}[/tex]

A = 5,400.00[tex](1 + 0.0135)^{32}[/tex]

A = $8,293.81

Hence, the value will be $8,293.81.

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Answer:

-15876

Step-by-step explanation:

|correct me if I'm not correct|

(Hope it's Help)

[keep safe]

The number is 15876

Number systems are systems in mathematics that are used to express numbers in various forms and are understood by computers. A number is a mathematical value used for counting and measuring objects, and for performing arithmetic calculations. Numbers have various categories like natural numbers, whole numbers, rational and irrational numbers, and so on. Similarly, there are various types of number systems that have different properties, like the binary number system, the octal number system, the decimal number system, and the hexadecimal number system.

A number system is a system representing numbers. It is also called the system of numeration and it defines a set of values to represent a quantity. These numbers are used as digits and the most common ones are 0 and 1, that are used to represent binary numbers. Digits from 0 to 9 are used to represent other types of number systems.

Given number:

10584

So, the number multiplied by the third of itself

x* 2/3 = 10584

x= 10584* 3/2

x= 15876

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The attached image represents the completed Venn diagrams

Diagram 1

We have:

Multiples of 3 and Multiples of 10

When the sets are populated, we have:

Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

Multiples of 10 = 10, 20, 30

Both = 30

Next, we complete the circles using the above data values

See attachment 1

Diagram 2

We have:

Multiples of 2, Multiples of 3 and Multiples of 5

When the sets are populated, we have:

Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30

Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

Multiples of 5 = 5, 10, 15, 20, 25, 30

Multiples of 2 and 3 = 6, 12, 18, 24 and 30

Multiples of 2 and 5 = 10, 20 and 30

Multiples of 3 and 5 = 15 and 30

All = 30

Next, we complete the circles using the above data values

See attachment 2

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The Pattern B is the twice of the Pattern A.  Then the correct option is C.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Item 11 In the table,

Pattern A uses the rule "add 5" and Pattern B uses the rule "add 10".

Pattern A   10  15  20  25  30

Pattern B   20 30 40  50  60

Then the Pattern B is the twice of the Pattern A.

Then the correct option is C.

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Answer:

=> Apply law of cosine

[tex]c^2=a^2+b^2-2abcos\left(C\right)[/tex]

=> input value

[tex]z^2=6.5^2 + 9.4^2-\left(6.5\right)\left(9.4\right)\left(cos\left(131\right)\right)[/tex]

=> simplify

[tex]z=\sqrt{\left(6.5^2+\:9.4^2\right)-\left(6.5\right)\left(9.4\right)\left(-0.65605902899\right)}[/tex]

=> calulcation

[tex]z=\sqrt{-61.1\cos \left(131^{\circ \:}\right)+130.61},\:z=-\sqrt{-61.1\cos \left(131^{\circ \:}\right)+130.61}[/tex]

=> apply rule: Distance must be greater than 0

which is about 14.51828

No, the cone and the cylinder can't have congruent heights and bases.

The volume of a cylinder of radius R and height H is:

V = pi*R^2*H

And for a cone of radius R and height H is:

V = pi*R^2*H/3

So, for the same dimensions R and H, the cone has 1/3 of the volume of the cylinder.

Here, the cylinder has a volume of 120cm³ and the cone a volume of 360cm³, so the cone has 3 times the volume of the cylinder.

This means that the measures must be different, so the cone and the cylinder can't have congruent heights and bases.

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Answer:

Step-by-step explanation:

-4x + 2 = x - 3

-5x + 2 = -3

-5x = -5

x = 1

y = 1 - 3

y = -2

(1, -2)

Answer:

97

Step-by-step explanation:

Number of adult tickets = a.

Number of student tickets = s.

"A total of 388 tickets were sold"

a + s = 388

"the number of student tickets sold was three times the number of adult tickets sold"

s = 3a

a + s = 388

s = 3a

Substitute s in the first equation with 3a.

a + 3a = 388

4a = 388

a = 97

Answer: 97 tickets

The x-intercept of the function [tex]h(x) = 8 * \sqrt[3]{x - 6} + 16[/tex] is -2

The equation of the function is given as:

[tex]h(x) = 8 * \sqrt[3]{x - 6} + 16[/tex]

The x intercept is the x value when h(x) = 0

So, we have:

[tex]8 * \sqrt[3]{x - 6} + 16 = 0[/tex]

Subtract 16 from both sides

[tex]8 * \sqrt[3]{x - 6} = -16[/tex]

Divide both sides by 8

[tex]\sqrt[3]{x - 6} = -2[/tex]

Take the cube of both sides

x - 6 = -8

Add 6 to both sides

x = -2

Hence, the x-intercept of the function [tex]h(x) = 8 * \sqrt[3]{x - 6} + 16[/tex] is -2

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The values of a, b and c from the given exponential function are 7, 9 and 4 respectively

According to the exponential law of indices

[tex]\sqrt[c]{a^b}[/tex]

This can be written as;

[tex]\sqrt[c]{a^b}=a^{\frac{b}{c} }[/tex]

Given the exponential expression

[tex]7^\frac{9}{4}[/tex]

Compare with the original expression

a = 7, b = 9 and c = 4

Hence the values of a, b and c from the given exponential function are 7, 9 and 4 respectively

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The probability to that the student chosen plays football or cricket or both is;

To evaluate the required probability, one must determine the total number of students in the class as follows;

Total number of students = 4 + 8 + (14-8) + (20-8) = 30.

Hence, the required probability is; (30-4)/30 = 26/30 = 13/15.

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The net present value is $305.73. The project should be accepted.

Using this formula

Net present value=Cashflow÷(1+Cost of capital)^ time

Let plug in the formula

Net present value=-$2,400+ ($630÷(1+.09)^1) + ($760÷(1+.09)^2) + ($800÷(1+.09)^3) + ($880 ÷(1+.09)^4) + ($380÷(1+.09)^5)

Net present value=-$2,400+ ( $630÷(1.09)^1) + ($760÷(1.09)^2) + ($800÷(1.09)^3) + ($880 ÷(1.09)^4) + ($380÷(1.09)^5)

Net present value=-$2,400+ ($630÷1.09) + ($760÷1.1881) + ($800÷1.295029) + ($880 ÷1.41158161) + ($380÷1.538639549)

Net present value=-$2,400+ $577.98+$639.68+$617.75+623.41+$246.91

Net present value=$305.73

Based on the above calculation the project should be accepted.

Therefore the NPV is $305.73.

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Answer:

Discount of 25%

Step-by-step explanation:

To find the percent discount, subtract the big number minus small number then divide by the original number.

[tex]\frac{32-24}{32}[/tex]

[tex]\frac{8}{32} \\[/tex]

Reduce

[tex]\frac{1}{4}[/tex]

Change to a decimal by dividing

1/4 = 0.25

Change to a percent by moving the decimal two places right.

0.25 -----> 25%

Answer:  c. Level of Significance

This is the alpha value

alpha is a greek letter with the symbol [tex]\alpha[/tex]

A type 1 error is when the researcher rejects the null, but the null was true (meaning the researcher shouldn't have rejected the null).

Answer:

the fourth option is correct

Step-by-step explanation:

the first equation represents that the cost of 6 bananas is the same as the cost of nine apples. therefore, y is the cost of a single banana and x is the cost of a single apple. the second equation represents the situation of you buying 4 bananas and 2 apples for $8. If x and y represent the cost of each fruit, then the point (x,y) = (1,1.5) means that x, the cost of an apple, is $1.00 and that y, the cost of a banana, is $1.50.

Answer:

he width of the ravin is 47

Answer:

3^5

Step-by-step explanation:

exponents:

1 - ( - 4 ) = 5

Therefore,

3^5

Answer:

[tex]b = \frac{1}{9}[/tex]

Step-by-step explanation:

-9b + b = 2b - (b + 1)

Let's simplify by taking out the parenthesis.

-9b + b = 2b - b - 1

Now, we add like terms.

-8b = b - 1

Now, let's subtract b from both sides of the equal sign in order to isolate b.

-8b - b = b - 1 - b

Simplify!  

-9b = -1

Divide both sides by -9.

-9b ÷ b = -1 ÷ -9

Simplify.

[tex]b = \frac{1}{9}[/tex]

Answer:

[tex]b = \frac{1}{9} [/tex]

Step-by-step explanation:

[tex] - 9b + b = 2b - (b + 1) [/tex]

Solve the brackets.

[tex] - 9b + b = 2b - b - 1[/tex]

Combine like terms.

[tex] - 8b = b - 1[/tex]

Take b to the left side.

[tex] - 8b - b = - 1[/tex]

Combine like terms.

[tex] - 9b = - 1[/tex]

Divide both sides by -9.

[tex] \frac{ - 9b}{ - 9} = \frac{ - 1}{ - 9} \\ b = \frac{1}{9} [/tex]

Answer:

9y

Step-by-step explanation:

Mathematicaly, the product of 9 and a number "y" is:

9y

Answer:

yo can maybe try converting those to every possible answer and you can find the answer that way.

Step-by-step explanation:

Answer:

2×2 mark me brainlist

Answer:

c

Step-by-step explanation:

edge 2023

The probability that event B occurs is 83%. Therefore, option C is the correct answer.

Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or demand that they depend, by some law or rule, on the values of other variables.

Given that, events A and B are independent, and the probability that event A occurs is 83%.

If the outcome of one event has no bearing on the fate of the other, the two events are said to be independent events. Instead, we may say that an event is considered independent if it does not affect the likelihood of another event.

Since, the events A and B are independent, if the probability that event A occurs is 83%.

Then, the probability that event B occurs is 83%.

Therefore, option C is the correct answer.

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