4) The instantaneous rate of change of f(x)=x³−5 at (2,3) is:
a) 4
b) 12
c) 48
d) 60

Approximately it will take 2 minutes to pass before they are 3 miles apart.

The time can be defined as the ratio of distance covered by an object to a unit speed. Time refers to the progression of events.

The Formula of Time of a given body can be expressed as,

Time = Distance÷Speed

one group takes a taxi uptown, traveling north at 35 miles per hour

The rest of the friends share another taxi, traveling south at 44 miles per hour

Suppose X as a time before they are 3 miles apart

so forming the equations:

35x+44x=3

79x=3

x=3/79hours.

To convert into minutes multiply x by 60 because 1 hour=60 min

x=3/79*60

x=0.0379*60

x=2.278

x=2 minutes.

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Answer:

See below.

Step-by-step explanation:

Given expression:

[tex]2(7^n) - 2(7^{n-1})+7^{n+1}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}[/tex]

[tex]\implies 2(7^n) - 2(7^{n-1})+7^{n} \cdot 7^1[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}[/tex]

[tex]\implies 2(7^n) - 2\left(\dfrac{7^{n}}{7^{1}}\right)+7^{n}\cdot 7^1[/tex]

Simplify:

[tex]\implies 2(7^n) - \dfrac{2}{7} (7^n)+7(7^{n})[/tex]

Factor out the common term 7ⁿ:

[tex]\implies \left(2- \dfrac{2}{7} +7\right)7^{n}[/tex]

Therefore:

[tex]\dfrac{61}{7}(7^n)[/tex]

A prime number is a whole number greater than 1 that cannot be made by multiplying other whole numbers.  Therefore, the factors of a prime number are 1 and the number itself.

If n is an integer greater than 1, the number will always have at least 4 factors (1, 7, 61 and itself) and therefore cannot be a prime number by definition.

For example:

[tex]n = 2 \implies \dfrac{61}{7}(7^2)=61 \times 7=427[/tex]

[tex]n = 3\implies \dfrac{61}{7}(7^3)=61 \times 7^2=2989[/tex]

Therefore, the largest prime number is when n = 1:

[tex]n = 1 \implies \dfrac{61}{7}(7^1)=61[/tex]

Answer:

Sold:

adults: 375 tickets

student: 324 tickets

Step-by-step explanation:

a + s = 699       Eq. 1

a = s + 51          Eq. 2

a = adult tickets sold

s = student tickets sold

Replacing Eq. 2 im Eq. 1

(s+51) + s = 699

2s + 51 = 699

2s = 699 - 51

2s = 648

s = 648/2

s = 324

From Eq. 2

a = 324 + 51

a = 375

Check:

From Eq. 1:

a + s = 699

375 + 324 = 699

The correct answer is 4. Any x-values that result in the denominator being equal to 0.

When finding the domain of the quotient of two functions, we need to consider the domains of both the numerator and the denominator. The domain of a function is the set of all possible input values for which the function is defined. For the quotient of two functions, this means that the domain is the set of all x-values that are in the domains of both the numerator and denominator.

However, there is one additional restriction on the domain of the quotient of two functions. The denominator of the quotient cannot be equal to 0, because division by 0 is undefined. Therefore, any x-values that result in the denominator being equal to 0 are not included in the domain of the quotient.

In summary, the x-values that are not included in the domain of the quotient of two functions are any x-values that result in the denominator being equal to 0.

One angle in a triangle is 10 degrees larger than the smallest angle, while the third angle is 10 degrees less than twice the smallest angle. As a result, the three angles are 55°, 45°, and 80°.

Three vertices and three sides make up a triangle. The angles of the triangle are formed by the connection of the three sides end to end at a single point. The sum of the triangle's three angles is 180 degrees.

Let's consider the three angles of the triangle as ∠P, ∠Q, and ∠R. Let's consider Q as the smallest angle. The sum of angles P, Q, and R is given as ∠P+∠Q+∠R=180°

Then, ∠P = ∠Q + 10° and ∠R = 2∠Q - 10°. Substituting these two angle values in the above equation,

[tex]\begin{aligned}\angle Q + 10^{\circ}+\angle Q+2\angle Q - 10^{\circ}&=180^{\circ}\\4\angle Q&=180^{\circ}\\\angle Q&=45^{\circ}\end{aligned}[/tex]

Then,

∠P = ∠Q + 10° = 45°+ 10° = 55°

∠R = 2∠Q - 10° = 2(45°) - 10° = 90° - 10° = 80°

The answers are 55°, 45°, and 80°.

The complete question is -

One angle of a triangle measure 10 degrees greater than the smallest angle and the third angle measure 10 degrees less than twice the smallest angle find the measure of the three angles.

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Answer:

r = 6

Step-by-step explanation:

6г - 17r = -66

-(17г - 6r) = -66

-11r = -66

-11r/(-1) = -66/(-1)

11r = 66

11r/11 = 66/11

r = 66/11

r = 6

30ft high above the ground is the lamp.

What is an angle?

An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Here, we have

BC⊥AD and DE⊥AD

∠ABC = ∠ADE(=90°)

Also,∠A=∠A

ΔABC ΔADE (AA similarity)

AB/AD = BC/DE

40/(200 + 40) = 5ft/DE

DE = 5ft×6 = 30ft

Hence, 30ft high above the ground is the lamp.

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The lengths of the segments SH is 16, HM is 8, TH is 8, HR is 12,

TD = 12 and ER = 18.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know a centroid divides a line segment in the ratio of 2 : 1 from vertices

to the other side.

Given, ΔSTR, H is the centroid EH = 6, DH = 4, and SM = 24.

SH = (2/3)×24 = 16.

HM = 8.

As DH = 4 hence TH = 8.

As EH = 6, HR = 12.

TD = (DH + TH) = 12.

ER = 6 + 12 = 18.

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Answer:

[tex]14 \frac{1}{8}[/tex]

Step-by-step explanation:

112 goes into 8 14 times, there is then 1/8 leftover

Product ab has a value of 18 and is shaped like a regular hexagon.

The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The area is the region defined by an object's form. The area of a form is the space covered by a figure or any two-dimensional geometric shape in a plane.

Here,

Let the side of the hexagon be 2.

so the radius of the circle is sqrt(3),

area of hexagon=sqrt(3) * 2 * 3

= 6 sqrt(3)

area of circle is pi (sqrt(3))^2 = 3 pi

3 pi / 6 sqrt(3) = sqrt(3)/ 6

3 * 6 = 18

The value of product ab is 18 which is in the shape of a regular hexagon.

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Based on the provide system of linear equations, the solution is that there is no solution.

A system of linear equations refers to a collection of one or more linear equations involving the same variables. The solution to a system of linear equations refer to the point at which the lines representing the linear equations intersect. If the lines are parallel, they will never intersect hence, the system has no solution.

According to the provided information, the percentage of smokers in Russia is given by the equation 36x+100y=346 and the percentage of smokers in Poland is given by the equation 18x+50y=176. In order to determine the solution of the system of linear equations, multiply the Poland equation by 2 and subtract it from the Russian equation. Hence,

2*(18x+50y=176)

36x + 100y = 352

-(36x+100y=346)

0 = 6

It means the original equations are parallel. As both the variables are eliminated, the system has no solution.

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The match of vector field f for  f(x, y) = y, x is graph II .

We can say that some points for the given function are F(1,2)= (2,1) F(2,1) =(1,2) F(0,1) = (1,0) F(2,3) = (3,2) F(0,2)=(2,0) .

That means arrow heads should start with these points and this is shown accordingly in graph II only.

Therefore ,

option A matches with figure 2

option B matches with figure 1

option C matches with figure 3

option D matches with figure 4

A vector field is a way to visualize them as represented by a number of small arrows each having a magnitude or a direction.

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Answer:

Let the width of the rectangle be w.

Then the length of the rectangle is w+2.

The perimeter of the rectangle is the sum of all its sides, so it is 2(w) + 2(w+2) = 60.

Expanding the parentheses and combining like terms, we get:

2w + 2w + 4 = 60

4w + 4 = 60

4w = 56

w = 14

The width of the rectangle is 14.

The length of the rectangle is 14+2 = 16.

Therefore, the length of the rectangle is 16 and the width is 14.

[tex]x^{2} + y^{2} = t^{2}[/tex] represent the correct graph which is the first figure graph.

Equations with Parameters If x and y are continuous functions of t on an interval I, the equations x = x(t) and y = y(t) are referred to as parametric equations, and t is also known as the parameter. The graph of the parametric equations is the set of points (x, y) obtained as t varies over the interval I.

Since x = tsint

And z= tcost

We have a circle in the x-z plane a

[tex]x^{2} + z^{2} = t^{2}[/tex]

Now, as y = t

The graph will be a helix with movement along the y-axis. Furthermore, the circle made on the x-z plane will have a variable radius since the radius is equal to t which by itself is changing.

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Answer:

 Rs 1400

Step-by-step explanation:

You want the monthly installment payment if the balance of a Rs 34500 purchase after a 6500 deposit earns 10% simple interest and is paid in 24 months.

The outstanding balance is ...

  Rs 34500 -6500 = Rs 28000

The interest on this balance for 24 months is ...

  I = Prt

  I = Rs 28000(0.10)(2) = Rs 5600

The monthly payment will be 1/24 of the total due:

  (28000 +5600)/24 = 1400

Each monthly installment will be Rs 1400.

<95141404393>

The general solution will be:

[tex]$$y(x)=e^{-x / 28}\left(c_1 \cos \left(\frac{\sqrt{55}}{28} x\right)+c_2 \sin \left(\frac{\sqrt{55}}{28} x\right)\right)+x^2-5 x-23$$[/tex]

[tex]$$14 y^{\prime \prime}+y^{\prime}+y=x^2-3 x$$[/tex]

Consider the homogenous equation [tex]$14 y^{\prime \prime}+y^{\prime}+y=0$[/tex]

The auxiliary equation is [tex]$14 m^2+m+1=0$[/tex]

[tex]m=-\frac{1}{28}+i \frac{1}{28} \sqrt{55}[/tex]

The homogenous solution is

[tex]$$y_c(x)=e^{-x / 28}\left(c_1 \cos \left(\frac{\sqrt{55}}{28} x\right)+c_2 \sin \left(\frac{\sqrt{55}}{28} x\right)\right) \text {. }$$[/tex]

Consider the non-homogenous de [tex]$14 y^{\prime \prime}+y^{\prime}+y=x^2-3 x$[/tex] by using the method of undetermined coefficients

consider [tex]$y_p=A x^2+B x+C \Rightarrow y_p^{\prime}=2 A x+B \Rightarrow y_p^{\prime \prime}=2 A$[/tex]

by plugging the values in [tex]$14 y^{\prime \prime}+y^{\prime}+y=x^2-3 x$[/tex]

[tex]$$\begin{aligned}& 28 A+(2 A x+B)+A x^2+B x+C=x^2-3 x \\& \Rightarrow x^2(A)+x(2 A+B)+28 A+B+C=x^2-3 x\end{aligned}$$[/tex]

On comparing both sides we get

A=1.

2A+B =-3

=>B=-3-2A

=>B=-5

28A+B+C=0

=>C=-28A-B

=>C=-23

by plugging the values [tex]y_p=x^2-5 x-23[/tex].

The general solution will be:

[tex]$$y(x)=e^{-x / 28}\left(c_1 \cos \left(\frac{\sqrt{55}}{28} x\right)+c_2 \sin \left(\frac{\sqrt{55}}{28} x\right)\right)+x^2-5 x-23$$[/tex]

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If d is directly proportional to t, then we can say that d = k * t, where k is a constant of proportionality. We can find the value of k by substituting the given values for d and t into this equation:

d = k * t

20 = k * 2

Solving for k, we get k = 10.

Now that we know the value of k, we can calculate the distance the car travels in 3 seconds by substituting 3 for t in the equation d = k * t:

d = 10 * 3

d = 30

Therefore, the car travels 30 meters in a time of 3 seconds.

Answer:

31

Step-by-step explanation:

7, 10, 12, 16, 19, 22, 25, 28, 31

Adding by 3

Hope this works

The inequality that describes the problem is x < 180 × 4, which means that the total amount of money Mr. Dawson wants to spend on groceries in April should be less than $180 multiplied by 4, or $720.

Mr. Dawson is making a grocery budget for the month of April. He plans to split the budget equally among 4 shopping trips and wants to stay under budget. To figure out the maximum amount of money he should spend on groceries in April, he needs to calculate the total amount of money he should spend for all 4 shopping trips. To do this, he multiplies the maximum amount of money he should spend per trip, $180, by the number of trips, 4. This gives us $180 × 4 = $720. Therefore, Mr. Dawson should spend less than $720 on groceries in April. The inequality that describes the problem is x < 180 × 4, which means that the total amount of money Mr. Dawson wants to spend on groceries in April should be less than $720. This inequality ensures that Mr. Dawson will stay under budget and be able to complete his 4 shopping trips for the month of April.

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If the congruence statement ABCA = AFGA is true, then the following must also be true:

B = G, since corresponding angles are congruent

AB = FG, since corresponding sides are congruent

C = F, since corresponding angles are congruent

Thus, the complete congruence statement is ABCA = AFGA, where B = G, AB = FG, and C = F.

The overall price considering the percentages is decreased.

Percentage is defined as "out of 100." Similar to fractions and decimals, percentages are used in mathematics to represent subsets of a whole. When expressing a sum as a percentage, 100 equal components are regarded to make up the whole. A percentage can be shown by the symbol % or, less frequently, by the abbreviation 'pct'.

In stores, online, in commercials, and in the media, you can see percentages practically anywhere. Understanding what percentages signify is a crucial skill that could help you save time and money and raise your employability.

Let us suppose mary bought that antique clock for 100$.

So now in the first year its value is increased by 30% which is 100+30 = 130$ after the 1 st year.

Now the clock price is 130$

So now in the second year its value is decrease by 30% which is 130- 39 = 91 $

So the overall clock price has been decreased by $9 since mary bought it.

The overall price considering the percentages is decreased.

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When a coin is weighted, there is a two-thirds chance that it will land on its head. suppose you toss this coin 15 times. let x represent the number of heads. Mean = 10 and Standard deviation = 2.88

The mean of x, which represents the number of heads when the coin is tossed 15 times, is 10. This is because the probability of getting heads is two-thirds, meaning that two out of every three tosses will result in heads.We apply the following formula to determine the standard deviation:

Standard Deviation = √(p*q*n), where p is the probability of getting heads, q is the probability of getting tails, and n is the number of tosses. In this case, p = 2/3, q = 1/3, and n = 15, so the standard deviation of x is 2.88.

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Answer:Isn't this cheating

Step-by-step explanation:

First, we need to find the total area of the land that is planted with cereals. To do this, we multiply the total area of the land, which is 2 hectares, by the percentage of the land that is planted with cereals, which is 100% - 20% - 10% = 70%. This gives us a total area of 2 hectares * 70% = 1.4 hectares.

Next, we need to divide the total area of 1.4 hectares into three parts, one for each type of cereal. Since 20% of the land is planted with corn, the area of land planted with corn is 1.4 hectares * 20% = 0.28 hectares. Similarly, since 10% of the land is planted with oats, the area of land planted with oats is 1.4 hectares * 10% = 0.14 hectares. Finally, the area of land planted with wheat is 1.4 hectares - 0.28 hectares - 0.14 hectares = 0.98 hectares.

Since 1 hectare is equal to 10,000 square meters, the area of land planted with corn is 0.28 hectares * 10,000 square meters/hectare = 2,800 square meters. The area of land planted with oats is 0.14 hectares * 10,000 square meters/hectare = 1,400 square meters, and the area of land planted with wheat is 0.98 hectares * 10,000 square meters/hectare = 9,800 square meters. So, each surface of land planted with corn is 2,800 square meters, each surface of land planted with oats is 1,400 square meters, and each surface of land planted with wheat is 9,800 square meters.

a and C of the two-member frame=Ax=-300N,Ay=300N, cx=300n, cy=300N.

momentum  of all forces  about A is
=-600x1.5+Cxx3=0

cx=900/3=300n
cx=300n.

momentum of all forces about c is
-600x1.5-AXx3=0                  
Ax=-900/3=-300n
Ax=-300n

forces in Ab components is
600x1.5-Ayx3=0
ay=300n

momentum of all forces about b

600x1.5-ayx3-cyx3+cxx3=0
900-900-900+cxx3=0
cxx3=900
cx=300n

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Answer:

y = 10 cm

Step-by-step explanation:

A = 12 · 5 / 2

A = 6 · 5 = 30 cm²

y = 30 · 2 / 6

y = 5 · 2

y = 10 cm

The cost of the drink after discount is 3.56 dollars.

You don't have enough money to buy the drink.

You are short of 0.89 dollars.

The price of a venti vanilla bean Frappuccino from Starbucks is $4.45, but you have only $3 with you. Your friend is working and gets you a discount of 20%.

The cost of the drink with discount can be calculated as follows:

amount discounted = 20% of 4.45

amount discounted = 20 / 100 × 4.45

amount discounted = 89 / 100

amount discounted =  0.89 dollars

Therefore,

cost of the drink after discount = 4.45 - 0.89

cost of the drink after discount = 3.56 dollars

Therefore, you don not have enough money to buy the drink.

You are short of 4.45 - 3.56 = 0.89 dollars.

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Answer:

Below

Step-by-step explanation:

x = a number

7 / (x+8)

All four measures of the angles are mentioned in the figure.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

If the measure of the angle is more than the right angle that is 90°. Then the angle is known as the obtuse angle.

Move the yellow dabs to make the portions cross. Allow the convergence to be called point V. Cause the lines to cross so that point ∠SVT is a harsh point under 135°.

Let the measure of the angle ∠SVU be 'x' which is greater than 45°. Then the measure of the angle ∠SVT will be '180 - x'.

All four measures of the angles are mentioned in the figure.

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