A circle has a radius of 6 inches and a central angle of 60°. What is the measure of the arc length associated with this angle?

Answer:

2 reflection across the y axis

Answer:

28 degrees

Step-by-step explanation:

We know that (4x + 7) + (2x + 5) add up to a straight angle = 180 degrees, so we have the equation 4x + 7 + 2x + 5 = 180.

By combining like terms, we get 6x + 12 = 180.

Subtract 12 from both sides of the equation to get 6x = 168. Divide both sides by 6 and you get x = 28.

\(6, 8, 9\) is NOT a right one because \(6^2+8^2\neq9^2\).

Hope this helps.

Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

16.7, 6.7 and 22 degrees respectively are the measures of a, c and m<C

The given diagram is a triangle with the following sides

Hypotenuse = AC = 18

m<A = 68 Degrees

We need to determine the measure of a, b and m<C

Using the trigonometry identity

sin 68 = a/18

a = 18sin68

a = 16.7

Similarly;

cos68 = c/18

c = 18cos68

c = 6.7

Since the sum of angles in a triangle is 180 degrees, hence:

m<C = 90 - m<A

m<C = 90 - 68

m<C = 22 degrees

Hence the measure of a, c and m<C is 16.7, 6.7 and 22 degrees respectively.

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Answer/Step-by-step explanation:

The given park of sugar cubes has has 24 cubes of sugar.

The cube of sugar has equal side length of ½ in.

Volume of the park of sugar cubes = 24 * volume of 1 cube of sugar

Volume of 1 cube of sugar = \( \frac{1}{2} * \frac{1}{2} * \frac{1}{2} \)

= \( \frac{1}{8} in^3 \)

Volume of the park of sugar cubes = \( 24 * \frac{1}{8} = \frac{24}{8} = 3 in^3 \)

Given the word problem, we can deduce the following information:

1. The two planes are 3950 miles apart.

2. Their speeds differ by 40 mph.

3. Time =5 hours

To determine the speed of each plane, we first let:

x= speed of the fist plane

x+40 =speed of the second plane

Based on the above information, the combined speed is 2x+40. Our equation would be:

Next, we find the value of x:

Hence,

x= speed of the fist plane=375 mph

x+40 =speed of the second plane=375+40= 415 mph

Answer:

150

Step-by-step explanation:

because 30 x 5 =150

Answer:

150°

Step-by-step explanation:

Here,

In linear pair we get the rest of its side angle we get is,

30° + x(unknown value) = 180°

=> x = 150°

Now,

Angle 1 = x. [As corresponding Angles]

So , value of 1 is 150° (Ans)

Answer:

4

3

0

Step-by-step explanation:

f(x) = y = -1/2 × sqrt(x+3)

2y = -sqrt(x+3)

4y² = x + 3

x = 4y² - 3

now renaming this, so that the normal symbols and names are used for this function definition, so that the input variable is called "x" :

f-1(x) = 4x² - 3

basically, just by itself, this function would be defined for all possible real values of x.

but because it is the inverse of the original function, which generates only values of y<=0, then for the inverse function that same range applies for its input variable x

x<=0

The number of strides the runner will make during 1 hour run will be =

10,800.

To calculate the distance or number of strides made by the runner in an

hour, the graph given above is considered as follows;

The y-axis which represents the number of strides is plotted against the x-axis which is the number of hours.

From the graph

20 minutes= 3600 strides

60 minutes = X strides

make X the subject of formula;

x= 3600×60/20

= 216000/20

= 10,800

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Answer:

See attachment for cube

Step-by-step explanation:

Given

\(Length = 6cm\)

\(Width = 3cm\)

\(Height = 2cm\)

Required

The net of the cuboid

A cuboid has 6 faces.

The dimension of these faces are:

Length and Width; Length and Height;

Length and Width; Length and Height;

Width and Height; Width and Height;

This means that the faces will have the following dimensions:

6cm by 3cm; 6cm by 2cm

6cm by 3cm; 6cm by 2cm

3cm by 2cm; 3cm by 2 cm

Taking into account the above measurements and dimensions, you draw 6 faces, then join similar sides lengths.

See attachment for net of the cuboid

The solution of the system of equation is given by the point where the

ordered pair of each equation are equal.

The solution of the equation system is x = -6

Reasons:

y₁ = 2·x + 7

y₂ = 1.5·x + 4

The values of y₁ for x < -7  are;

y₁₍₋₈₎ = 2 × (-8) + 7 = -9

y₁₍₋₉₎ = 2 × (-9) + 7 = -11

y₁₍₋₁₀₎ = 2 × (-10) + 7 = -13

Therefore, we get;

The values of y₁ for x < -7 = -9, -11, -13,...

The values of y₂ for x < -7  are;

y₂₍₋₈₎ = 1.5 × (-8) + 4 = -8

y₂₍₋₉₎ = 1.5 × (-9) + 4 = -9.5

y₂₍₋₁₀₎ = 1.5 × (-10) + 4 = -11

The values of y₂ for x < -7  are; -8, -9.5, -11

The values of y₁ for x > -5  are;

y₁₍₋₄₎ = 2 × (-4) + 7 = -1

y₁₍₋₃₎ = 2 × (-3) + 7 = 1

y₁₍₋₂₎ = 2 × (-2) + 7 = 3

Therefore, we get;

The values of y₁ for x > -5 = -1, 1, 3

The values of y₂ for x > -5  are;

y₂₍₋₄₎ = 1.5 × (-4) + 4 = -2

y₂₍₋₃₎ = 1.5 × (-3) + 4 = -0.5

y₂₍₋₂₎ = 1.5 × (-2) + 4 = 1

The values of y₂ for x > -5  are; -2, -0.5, 1, ...

The table is presented as follows;

\(\begin{tabular}{|c|r|r|}x&y_1&y_2\\-2&3&1\\-3&1&-0.5\\-4&-1&-2\\-5&-3&-3.5\\-6&-5&-5\\-7&-7&-6.5\\-8&-9&-8\end{array}\right]\)

From the above table the solution to the system of equation (the value of x

at which y₁ = y₂) is x = -6.

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The equilibrium point for James T-shirt business is (P, Q) = (7, 24).

To find the equilibrium point (P, Q) for James T-shirt business

we need to set the demand function equal to the supply function and solve for the values of P and Q.

Demand function: P = -Q + 31

Supply function: P = Q - 17

Setting them equal:

-Q + 31 = Q - 17

Adding Q to both sides and subtracting 31 from both sides:

2Q = 48

Dividing both sides by 2:

Q = 24

Now, we can substitute this value of Q into either the demand or supply function to find the corresponding value of P.

P = Q - 17

P = 24 - 17

P = 7

Therefore, the equilibrium point for James T-shirt business is (P, Q) = (7, 24).

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Answer:

272 is the test score for Brandi.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 250 and standard deviation of 25:

This means that \(\mu = 250, \sigma = 25\)

Brandi scored at the 81st percentile on this test. What was her test score?

The z-score of her score of X has a p-value of 0.81. This means that her score is given by X when Z = 0.88.

\(Z = \frac{X - \mu}{\sigma}\)

\(0.88 = \frac{X - 250}{25}\)

\(X - 250 = 0.88*25\)

\(X = 272\)

272 is the test score for Brandi.

Answer:

288 donuts

Step-by-step explanation:

Answer:

288 donuts

Step-by-step explanation:

72 divided by 2 is 36 so that means you will make 36 donuts in 1 hour so now we have our unit rate which is 36. so then you multiply 36 by 8 and you get 288. that is your answer

Answer:

5500 is correct Answer.

Please mark me as brainlist answer.

Answer:

\(30m + 15 = 3(10m + 5)\\\)

\(30m + 15 = 5(6m+3)\)

Step-by-step explanation:

Given

\(30m + 15\)

Required

Equivalent expressions

We have:

\(30m + 15\)

Factor out 3

\(30m + 15 = 3(10m + 5)\)

Also:

\(30m + 15\)

Factor out 3

\(30m + 15 = 5(6m+3)\)

What is the question of it ?

The limit lim(x approaches 0) (cosec(2x) - x*cosec³(x)) is undefined.

We have,

To evaluate the limit of the expression as x approaches 0, we can simplify the expression first.

The expression is given as lim(x approaches 0) (cosec(2x) - x cosec³(x)).

Using trigonometric identities, we can rewrite cosec(2x) as 1/sin(2x) and cosec³(x) as 1/(sin(x))³.

Substituting these into the expression,

We get lim(x approaches 0) (1/sin(2x) - x (1/(sin(x))³)).

Now, let's evaluate the limit term by term:

lim(x approaches 0) (1/sin(2x)) = 1/sin(0) = 1/0 (which is undefined).

lim(x approaches 0) (x (1/(sin(x))³))

= 0 (1/(sin(0))³)

= 0 x 1/0 (which is also undefined).

Since both terms of the expression are undefined as x approaches 0, we cannot determine the limit of the expression.

Therefore,

The limit lim(x approaches 0) (cosec(2x) - x*cosec³(x)) is undefined.

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The equation of tangent to the curve y = 8√x  at the point (4,16) is  y = 2x + 8 .

We have to find equation of tangent line to the curve y = 8√x at the point (4, 16), we first find the slope ;

So , slope of the tangent line is  derivative of function y = 8√x at point (4, 16).

which means :  y' = 4\(x^{-\frac{1}{2} }\)  ;

At the point (4, 16), the value of x is 4.

So , y' = 4 × \(4^{-\frac{1}{2} }\) = 2 .

By Using the point slope form, the equation of the tangent line is ;

⇒ y - 16 = (2)(x - 4)  ;

Simplifying this equation, we get:

⇒ y - 16 = 2x - 8

⇒ y = 2x + (16 - 8)

⇒ y = 2x + 8 .

Therefore, the equation of the tangent line to the curve is y = 2x + 8 .

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The given question is incomplete , the complete question is

Find an equation for the tangent to the curve y = 8√x  at the point (4,16) .

The angular speed of the wheels in radians per minute is 0.033 and the number of revolutions per minute do the wheels make is 0.0052

In this case, we are dealing with a truck with wheels that have a diameter of 34 inches. The circumference of the wheels is equal to the diameter multiplied by pi, or 34 x pi, which is approximately 106.81 inches. To convert this to miles per hour, we need to divide it by the number of inches in a mile, which is 63,360. Thus, the linear speed of the truck is:

v = (106.81/63360) x 55 = 0.09375 miles per minute

Next, we need to calculate the angular speed of the wheels in radians per minute. The angular speed is defined as the number of radians covered by the wheel in one minute, and it can be calculated using the formula:

ω = v/r

where ω is the angular speed, v is the linear speed, and r is the radius of the wheel. Since we are given the diameter of the wheel, we need to divide it by 2 to get the radius, which is:

r = 34/2 = 17 inches

Substituting the values for v and r into the formula for angular speed, we get:

ω = (0.09375)/(17 x pi/60) ≈ 0.033 radians per minute

Finally, we need to calculate the number of revolutions per minute that the wheels make.

This can be done by dividing the angular speed by 2pi, which is the number of radians in one revolution. Thus, the number of revolutions per minute is:

n = ω/(2pi) ≈ 0.0052 revolutions per minute

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Complete Question:

A truck with 34 inch diameter wheels is traveling at 55mi/h. Find the angular speed of the wheels in radians per minute? And how many revolutions per minute do the wheels make?

Answer:

y = -2/7(x) + 3

Step-by-step explanation:

The equation of a line can be stated as y = mx + b, where m is the slope and b is the y-intercept (the value of the function when x = 0).  To find the equation of the line, we'll start by finding the slope.

The slope can be expressed as \(\frac{y_{2} - y_{1}}{x_{2}-{x_1}}\)

Substituting in our coordinates, we have:

\(m = \frac{1 - 5}{7 - (-7)} = \frac{-4}{7 + 7} = \frac{-4}{14}\), which can be simplified to \(-\frac{2}{7}\)

Plugging that back into our equation, we have y = \(-\frac{2}{7}\)x + b

Now, to find b, we substitute in one of our sets of coordinates.  Let's use (-7, 5)

x = -7 and y = 5, which gives us:

\(5 = -\frac{2}{7} (-7) + b\)

\(-\frac{2}{7} (-7) = 2\), which gives us:

5 = 2 + b

Subtracting 2 from both sides, we get:

3 = b

Plugging that back into our equation, we have \(y = -\frac{2}{7} x + 3\)

Step-by-step explanation:

x-a