Help. Calculus question.

Answer:

168.75, about 169 times

Step-by-step explanation:

1 yd= 36 in

300 yd= 10800 in

10800 in/ 64 in=168.75

Answer:

169

Step-by-step explanation:

We are given that

Circumference of Kiran's bike wheel=64 in

Kiran rides total distance=300 yards

We have to find number of rotations made by wheel.

We know that

1 yard=36 in

300 yards=[tex]36\times 300=10800 in[/tex]

Number of rotation=[tex]\frac{Total\;distance\;covered\;by\; wheel}{Circumference\;of\;wheel}[/tex]

Number of rotations=[tex]\frac{10800}{64}=168.75\approx 169[/tex]

Hence, the wheel rotate=169 times

Answer:

189°

Step-by-step explanation:

∠UPR = ∠UOP + ∠POQ + ∠QOR = 81° + 56° + 52° = 189°

Answer:

B

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 2x + 3y = 4 into this form

Subtract 2x from both sides

3y = - 2x + 4 ( divide all terms by 3 )

y = - [tex]\frac{2}{3}[/tex] x + [tex]\frac{4}{3}[/tex] ← in slope- intercept form

with slope m = - [tex]\frac{2}{3}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{2}{3} }[/tex] = [tex]\frac{3}{2}[/tex], hence

y = [tex]\frac{3}{2}[/tex] x + c ← is the partial equation of the perpendicular line

To find c substitute (- 2, 15) into the partial equation

15 = - 3 + c ⇒ c = 15 + 3 = 18

y = [tex]\frac{3}{2}[/tex] x + 18 → B

The equation of the line that passes through (-2, 15) and is perpendicular to 2x + 3y = 4 is y = 3/2x + 18.

Option B is the correct answer.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

To find the equation of the line that is perpendicular to 2x + 3y = 4, we need to first find its slope.

We can rearrange the equation into slope-intercept form (y = mx + b) by solving for y:

2x + 3y = 4

3y = -2x + 4

y = (-2/3)x + 4/3

So the slope of line 2x + 3y = 4 is -2/3.

Now,

Since we want a line that is perpendicular to this line, we know that its slope will be the negative reciprocal of -2/3, which is 3/2.

Now we have the slope and a point (-2, 15) that the line passes through.

We can use the point-slope form to write the equation:

y - 15 = 3/2(x + 2)

Simplifying:

y - 15 = 3/2x + 3

y = 3/2x + 18

Thus,

The equation of the line that passes through (-2, 15) and is perpendicular to 2x + 3y = 4 is y = 3/2x + 18.

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Answer:

C, 1/2 of the time.

Step-by-step explanation:

all the seconds added together is 90. 45 is half of 90, so half the time the light will be green, the cars will have a 50% chance of coming up to a green light.

Answer:

C.

Step-by-step explanation:

Answer:

  27

Step-by-step explanation:

If the slope of f(x) is no less than 3, then the value of f(9) can be no less than 27.

  f(x) ≈ f(4) +f'(x)·(x-4)

  f(9) = 12 +3(9 -4) = 27 . . . . . for f'(x) = 3.

For larger numbers of f'(x), f(9) will be larger.

We want to find the minimum possible value of f(9) given that:

We will see that the smallest value that f(9) can take is 27.

We know that the derivate of f(x) gives the slope to the tangent line to the graph of f(x) in a given point where it is evaluated.

If this slope is positive, the function is increasing. So if we want to find the minimum value for f(9), then we need to take the smallest slope possible (knowing that it is positive).

Then we must use f'(x) = 3

Now, we can integrate this to get:

f(x) = 3*x + b

Where b is a constant of integration, to find the value of b, we can use the fact that f(4) = 12, then:

12 = f(4) = 3*4 + b

12 = 12 + b

12 - 12 = 0  = b

Thus the equation is just:

f(x) = 3*x

Now we can evaluate this in x = 9 to get:

f(9) = 3*9 = 27

The smallest value that f(9) can take is 27.

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Answer:

C) the difference identity for the cosine function

Step-by-step explanation:

The last line showing shows the cosine of the difference of two angles. The difference identity for the cosine function would seem to be indicated.

Answer:

if she drove away she would have to drive 14 hours, or if it were i the same direction she would have to drive 2 1/2 hours

Step-by-step explanation:

8 1/4 + 5 3/4 = 14

8 1/4 - 5 3/4 = 2 1/2

Lisa has to drive an extra 2 1/2 hours to get to her aunt's house compared to her uncle's house. This is determined by converting the mixed numbers to improper fractions, subtracting the smaller fraction from the larger one, and simplifying the result.

The subject of this question falls under Mathematics, specifically subtraction of fractions. In this question, Lisa takes 8 1/4 hours to get to her aunt's house and 5 3/4 hours to get to her uncle's house. The time difference is the extra distance she must travel to reach her aunt's house compared to her uncle's house.

So, Lisa has to drive for an extra 2 1/2 hours to get to her aunt's house as compared to her uncle's house.

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The Answer is 7.7

Add all the Shoe size From the second Table

7+7+10+6+9+6+8+7.5+8.5+8=77

77 divide by the number of Shoe size

There are 10 shoe size So,

77/10=7.7

Hope this Help:)

Answer:

7.7

Step-by-step explanation:

The mean (or average) is the sum of the data points divided by the number of data points.

μ = (7 + 7 + 10 + 6 + 9 + 6 +8 + 7.5 + 8.5 + 8) / 10

μ = 77/10

μ = 7.7

Answer:

the second one would be more effective because $800*12 will cost a lot more than $650+2 months penalty if u leave

Answer:

4) reflexive property of congruence

5) SAS theorem

6) property of Congruent triangles

Step-by-step explanation:

Given:

In ΔXYZ, line YW ⊥ XZ

Also XW≅ZW

Now

4) by reflexive property of congruence that states that any line,object or figure is congruent to itself

hence YW≅YW

5) By SAS theorem that states that if the two corresponding sides and the angle between those sides of two triangles are congruent then the two triangles are said to be congruent.

Hence ΔWXY≅ΔWZY

6) By property of Congruent triangles that states that if two triangles are congruent then their corresponding sides are also congruent.

Hence XY≅ZY !

Answer:

f(- 2) = 20

Step-by-step explanation:

To evaluate f(- 2) substitute x = - 2 into f(x)

f(- 2) = (- 2)² - 5(- 2) + 6 = 4 + 10 + 6 = 20

The value of the function f(x) = x² - 5x + 6 at x = -2 is 20 after plugging the value of x is -2 in the function.

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:

f(x) = x² - 5x + 6

Plug x = -2

f(-2) = (-2)² - 5(-2) + 6

f(-2) = 4 + 10 + 6

f(-2) = 20

Thus, the value of the function f(x) = x² - 5x + 6 at x = -2 is 20 after plugging the value of x is -2 in the function.

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Answer:

Step-by-step explanation:

If we had a division problem that read "16 divided by 8 equals 2", the 8 would be outside the division sign, the 16 would be under the division sign, and the 2 would be sitting on top of the division sign.  The 8 is called the divisor, the 16 is called the dividend, and the 2 is called the quotient.

The answer you want, then, is "dividend"

The number by which another number is divided is called a divisor. This applies to many mathematical operations, including division, multiplication, and calculations involving exponents, such as in scientific notation.

A number by which another number is to be divided is called a divisor. When we consider a division operation, we usually think of it as a 'dividend' divided by a 'divisor' equals a 'quotient'. If you take an example of 16 ÷ 4 = 4, here, 16 is the dividend (the number being divided), 4 is the divisor (the number that divides the dividend), and the resulting 4 is the quotient (the result of the division).

Similarly, this concept can be applied to complex mathematical operations such as multiplication and division in scientific notation or logarithmic expressions. For example, in scientific notation, when you want to divide two numbers, you divide the numbers out front and subtract the exponents.

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Answer:

y = 178.3 ft

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan27° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{y}{350}[/tex]

Multiply both sides by 350

350 × tan27° = y, hence

y = 178.3

Answer:

Option B.

Step-by-step explanation:  

we know that

If a ordered pair is a solution of the system of inequalities

then

the ordered pair must satisfy both inequalities of the system

Verify each case

Case A) we have

The point (3,-2)

Substitute the value of x and the value of y in both inequalities and then compare the results

Inequality 1

[tex]-2< -3[/tex] ----> is not true

therefore

The ordered pair is not a solution of the system A

Case B) we have

The point (3,-2)

Substitute the value of x and the value of y in both inequalities and then compare the results

Inequality 1

[tex]-2> -3[/tex] ----> is true

Inequality 2

[tex]-2 \geq \frac{2}{3} (3)-4[/tex]

[tex]-2\geq -2[/tex] ----> is true

therefore

The ordered pair is a solution of the system B

Case C) we have

The point (3,-2)

Substitute the value of x and the value of y in both inequalities and then compare the results

Inequality 1

[tex]-2<-3[/tex] ----> is not true

therefore

The ordered pair is not a solution of the system C

Case D) we have

The point (3,-2)

Substitute the value of x and the value of y in both inequalities and then compare the results

Inequality 1

[tex]-2>-2[/tex] ----> is not true

therefore

The ordered pair is not a solution of the system D

Answer:

i think it is b as well! on edg

Step-by-step explanation:

Check the picture below.

Answer:

The answer is 10

Step-by-step explanation:

The value of f(5) will be 10 for the given sequence.

A grouping of two or more items in a logical sequence. the sequential arrangement of two or more items. The sequence is a term used to describe chronological order. You should be familiar with the following four primary categories of sequences: arithmetic sequences, geometric sequences, quadratic sequences, and special sequences. a collection of two or more elements arranged logically. the placement of two or more elements in a particular order. The word "sequence" refers to chronological order. Arithmetic sequences, geometric sequences, quadratic sequences, and special sequences are the four main types of sequences that you should be aware of.

Given, A sequence is defined by the recursive formula f (n + 1) = f(n) – 2. If f(1) = 18.

for n = 1

f(2) = f(1) - 2 = 18 -2 = 16

for n = 2

f(3) = f(2) - 2 = 16 - 2 = 14

for n = 3

f(4) = f(3) - 2 = 14- 2 = 12

for n = 4

f(5) = f(4) - 2 = 12-2 = 10

Therefore, For the above sequence, f(5) will have the value of 10.

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Answer:

I think it is 25.

Step-by-step explanation:

Answer with explanation:

Population Mean = 25

Standard Deviation =2.5

[tex]Z_ {Score} =\frac{5}{100}\\\\Z_ {Score} =0.05\\\\Z_{0.05}=0.5199[/tex]

Let ,Margin of error= m

 And, Sample Population = n  

[tex]m=Z_{0.05} \times \frac{\sigma}{\sqrt{n}}\\\\ m=0.5199 \times \frac{2.5}{\sqrt{25}}\\\\m=0.5199 \times 0.5\\\\m=0.25995[/tex]

m= 0.2599 × 100%

m=25.99%=26%

Option A: 25=Margin of error

Answer:

The center is at 2

Step-by-step explanation:

The spread is only from 0 to 5.

There are two clusters (one at 0-2 and one at 4-5)

The peak is at 5 not at 8

Answer:

oh i did this one the answer is B.

Answer:

A

Step-by-step explanation:

Final answer:

In step 3 of Kai's calculations, he applied the difference law for logarithms.

Explanation:

In step 1, Kai applied the difference law for logarithms by subtracting the logarithms of 3 and 5 from the logarithm of 27.

In step 3, Kai further simplified by using the property that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number. In this case, he applied this property to rewrite 3^3 as (3^2).

Therefore, the correct answer is Step 3.

Answer: 17 in.

Step-by-step explanation:

The sides of an equilateral triangle measure 16 inches. The midpoints of the sides of the triangle are joined to form another equilateral triangle with sides that are half the length of the outer triangle. This process is continued until three triangles are inscribed in the first triangle. The sum of the perimeters of all four triangles is 17 in.

Answer with explanation:

⇒Side of largest equilateral triangle in which three equilateral triangles are inscribed = 16 inches

Perimeter of a triangle = Sum of three sides of triangle

Perimeter of equilateral triangle having side length 16 inches = 16 +16+16=48 inches

⇒→Second equilateral triangle which is inscribed in this equilateral triangle having side length half of that equilateral triangle in which it is inscribed

 [tex]=\frac{16}{2}\\\\=8[/tex] inches

Perimeter of equilateral triangle having side length 8 inches = 8 +8+8=24 inches

⇒→Third equilateral triangle which is inscribed in this equilateral triangle having side length half of that equilateral triangle in which it is inscribed

 [tex]=\frac{8}{2}\\\\=4[/tex] inches

Perimeter of equilateral triangle having side length 4 inches =4+4+4=12 inches

⇒→Fourth equilateral triangle which is inscribed in this equilateral triangle having side length half of that equilateral triangle in which it is inscribed

 [tex]=\frac{4}{2}\\\\=2[/tex] inches

Perimeter of equilateral triangle having side length 2 inches =2+2+2=6 inches

→≡Total Perimeter of all four Equilateral Triangle

  =48 +24+12+6

= 90 inches

Answer:

The answer is C I believe

Answer:

C. You can qualify for opportunities that might otherwise be impossible

Answer:

162π ft²

Step-by-step explanation:

The surface area (SA) of a sphere is

SA = 4πr² ← r is the radius

Calculate r from the volume, that is

V = [tex]\frac{4}{3}[/tex]πr³ = 972π

Multiply both sides by 3

4πr³ = 2916π ( divide both sides by 4π )

r³ = [tex]\frac{2916\pi }{4\pi }[/tex] = 729

Take the cube root of both sides

r = [tex]\sqrt[3]{729}[/tex] = 9, hence

SA = 4π × 9² = 4π × 81 = 324π

[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} V=2,143.57 \end{cases}\implies 2143.57=\cfrac{4\pi r^3}{3}\implies 6430.71=4\pi r^3 \\\\\\ \cfrac{6430.71}{4\pi }=r^3\implies \stackrel{\pi =3.14}{\cfrac{6430.71}{4(3.14) }}=r^3\implies 511.9992\approx r^3 \\\\\\ \sqrt[3]{511.9992}\approx r\implies 7.999996\approx r\implies \stackrel{\textit{rounded up}}{8=r}[/tex]

Answer:

a. [tex]A\geq B[/tex]

Step-by-step explanation:

[tex]sin\frac{\pi }{2} =1[/tex]

and

[tex]cos(-\pi )=-1[/tex]

Answer:

Sin (pi/2) > Cos (-pi)

Step-by-step explanation:

Sin (pi/2) = 1

Cos (-pi)  -1

Step-by-step explanation:

2a. The block of wood has the shape of a rectangular prism.  The log has the shape of a cylinder.

2b. Density is mass divided by volume.  We know the mass, but we need to find the volume.

Volume of a rectangular prism is:

V = whl

where w is the width, h is the height, and l is the length

V = (18)(10)(8)

V = 1440 in³

So the density is:

d = 46.65 lbs / 1440 in³

d = 0.0324 lb/in³

2c.  Volume of a cylinder is:

V = πr²h

where r is radius and h is height.

The circumference is C = 2πr, so r = C / (2π).

r = 25.12 / (2*3.14)

r = 4.00

V = 3.14 (4.00)² (21)

V = 1055.04 in³

So the density is:

d = 39.25 lb / 1055.04 in³

d = 0.0372 lb/in³

2d.  The block is less dense than water; the log is more dense than water.  So he should make the boat out of the block.

Answer:

The side length is multiplied by the scale factor of 3, which makes it 49.5

Step-by-step explanation:

The scale factor goes as follows

length : scale factor

area: scale factor  squared

Volume : scale factor cubed

Since we increased the area by 9, that would be the scale factor squared

Take the square root of 9, which is 3, and that is the scale factor

We want to know what happens to the length

It is multiplied by the scale factor

16.5*3 = 49.5

Final answer:

Option B, a one-time bonus of 10% of a worker’s annual salary, is not an example of exponential growth or decay because it does not involve a percentage change being applied repeatedly over time to a changing base amount.

Explanation:

The question asked is: Which of the following is not an example of exponential growth or decay? The options are: A. a t-shirt shrinks by 2% after each wash, B. a one time bonus of 10% of a worker’s annual salary, C. a yearly pay increase of 3% each year, D. a savings account growing by 3% each year. To answer this, we must recognize that exponential growth or decay refers to processes that grow or decrease at a rate proportional to their current size. This means the amount of increase or decrease changes over time, as it is a percentage of an ever-changing base amount.

Options A, C, and D all describe situations where the quantity changes by a fixed percentage over time, indicative of exponential growth (or decay, in the case of shrinking). Option A discusses a t-shirt shrinking by 2% after each wash, meaning each time it shrinks, it does so based on its current size, which is a characteristic of exponential decay. Option C talks about a yearly pay increase of 3% each year, and Option D describes a savings account growing by 3% each year; both are examples of exponential growth. Therefore, the answer is Option B, a one-time bonus of 10% of a worker’s annual salary, as it does not describe a situation where the growth rate is applied over time to an ever-changing base amount.

ANSWER

[tex]y = 2 \: \sin(x) [/tex]

EXPLANATION

A basic sine curve has equation in the form:

[tex]y = a \: \sin(x) [/tex]

Where 'a' is the amplitude.

In this case a=2 because the amplitude is 2.

[tex]y = 2 \: \sin(x) [/tex]

For a transformed sine function, the general equation is:

[tex]y = a \: \sin(bx + c) + d[/tex]

where a=2 is still the amplitude

[tex]y = 2 \: \sin(3x + \pi) [/tex]

This is also a sine function with an amplitude of 2.

Others include:

[tex]y = 2 \: \sin(x + 1) [/tex]

[tex]y = 2 \: \sin(4x - \pi) [/tex]

e.t.c

[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} V=5275\\ h=23 \end{cases}\implies 5275=\pi r^2(23)\implies \cfrac{5275}{23\pi }=r^2 \\\\\\ \sqrt{\cfrac{5275}{23\pi }}=r\implies 15.144\approx r~\hspace{10em}\stackrel{diameter=2r}{d\approx 30.288}[/tex]