one fifth of sum of two angles is 24 and their diffetence is 14 find the two angles​

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):

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

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

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

Answer:

17.32 meters

Step-by-step explanation:

Let’s call the height of the tower H. The distance from the point to the base of the tower is 10 m. The angle of elevation from the point to the top of the tower is 60 degrees.

Using trigonometry, we can calculate that:

tan (60) = H / 10

H = 10 * tan (60)

H = 10 * √3

H = 17.32 m

Therefore, the height of the tower is 17.32 meters.

Let me know if I helped :)

The limit of the difference quotients for f(x) = x^2 + 2x + 1 as x approaches -1 is indeterminate.

To find the limit of the difference quotients for the function f(x) = x^2 + 2x + 1 as x approaches -1, we need to evaluate the following expression:

lim(x→-1) [f(x) - f(-1)] / (x - (-1))

First, let's substitute the values into the expression:

lim(x→-1) \([(x^2 + 2x + 1) - (-1^2 + 2(-1) + 1)] / (x + 1)\)

Simplifying further:

lim(x→-1) \([(x^2 + 2x + 1) - (1 - 2 + 1)] / (x + 1)\)

lim(x→-1)\([x^2 + 2x + 1 - 0] / (x + 1)\)

lim(x→-1) \((x^2 + 2x + 1) / (x + 1)\)

Now, we can directly substitute x = -1 into the expression:

\((-1^2 + 2(-1) + 1) / (-1 + 1)\)

(1 - 2 + 1) / (0)

0 / 0

We have obtained an indeterminate form of 0/0. This indicates that we need to further simplify the expression or use other techniques, such as L'Hôpital's rule, to evaluate the limit. However, without additional information or simplification, we cannot determine the precise value of the limit at x = -1.

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The value of x in the lines is 126 degree

We are given that;

Three parallel line and one intersecting line

Angles= (x-6) and 60

Now,

By supplementary angles property

Angle 1 + Angle 2 = 180 degree

Substituting the values of angles

x-6 + 60 = 180

x + 54 = 180

x = 180-54

x = 126

Therefore by supplementary angles answer will be 126 degree.

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Answer:

S=sin −1 (1.8266968)=ERROR

No possible triangles

Step-by-step explanation:

Using the unitary method, we found out that the cost of 6.5 ounces of a medium soft serve is $3.64.

What is meant by the unitary method?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, and then multiplying that value to determine the required value. This method allows us to calculate both the value of many units from the value of one unit and the value of one unit from the value of many units. In the unitary technique, the value of a unit or one quantity is always counted first, and the values of additional or fewer quantities are then determined. This method is known as the unitary method for this reason.

Given,

The cost of an ounce of medium soft serve = $0.56

The amount of soft serve in a medium size  = 6.5 ounces

We are asked to find the cost of the total amount of soft serve in a medium size.

This can be done using the unitary method.

If 1 ounce = $0.56

Then for 6.5 ounces, the cost is = 6.5 * 0.56 = $3.64

Therefore using the unitary method, we found out that the cost of 6.5 ounces of a medium soft serve is $3.64.

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Answer:100

Step-by-step explanation:

Answer:

The last one. The table with 12 sections and 2 letters in each one.

Explanation: For every flip (12 total flips) there were 2 coins. So there are 12 sections in the table (the amount of times the coins were flipped) and 2 letters for each one (representing that 2 coins were flipped at the same time).

Hope this helps <3333

y = x²-5

f(x) = x² - 5

f(-4) = (-4)² - 5

f(-4) = 16 - 5

f(-4) = 11

give me brainliest pls hehe

Answer:i need brainy answered sorry

Step-by-step explanation:sorry

Answer:

first google docs second google sheets

Step-by-step explanation:

first google docs second google sheets third google forms forth google drawing 5th google maps 6th google slides

The sum of the internal angles of the polygons are

a) The sum is A = 540°

b) The sum is A = 360°

c) The sum is A = 1800°

The sum of the interior angles of a polygon is given by the formula

Sum of Interior angles of a polygon with n sides is

nθ = 180° ( n - 2 )

where n is the number of sides

θ = angle in degrees

Given data ,

Let the sum of the internal angles of a polygon be represented as A

Now , the value of A is

The sum of exterior angle of n polygon is = 360°

Now ,

a)

The number of sides of the polygon = 5 sides

So , Sum of Interior angles of a polygon with n sides is

nθ = 180° ( n - 2 )

Substituting the value of n = 5 in the equation , we get

nθ = 180° ( 5 - 2 )

nθ = 180° x 3

nθ = 540°

b)

The number of sides of the polygon = 4 sides

So , Sum of Interior angles of a polygon with n sides is

nθ = 180° ( n - 2 )

Substituting the value of n = 4 in the equation , we get

nθ = 180° ( 4 - 2 )

nθ = 180° x 2

nθ = 360°

c)

The number of sides of the polygon = 12 sides

So , Sum of Interior angles of a polygon with n sides is

nθ = 180° ( n - 2 )

Substituting the value of n = 12 in the equation , we get

nθ = 180° ( 12 - 2 )

nθ = 180° x 10

nθ = 1800°

Hence , the sum of the internal angles of the polygon is solved

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Each ticket costs $37.5 according to the calculation t = ($175 - $25)/4.

Equation is a mathematical statement that expresses two expressions as equal. It consists of two expressions separated by an equal sign (=). An equation is used to solve for a unknown value by using known values and following the rules of algebra and arithmetic. Equations can be used to solve for a single unknown, multiple unknowns, and even non-numeric values.

Given that the total cost for parking and four tickets to a baseball game is $175.00.

$25 is the parking fee.

4 tickets cost $175 - $25.

Suppose that each ticket costs t.

t =($175 - $25)/4

Each ticket costs $37.5.

The equation follows.Each ticket costs $37.5 according to the calculation t = ($175 - $25)/4.

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Answer:

30 and 10

Step-by-step explanation:

Main concepts:

Concept 1.  Geometric Sequence

Concept 2. Common ratio

Concept 3. Finding the next terms

Concept 1.  Geometric Sequence

Geometric sequences are a specific type of sequence with a pattern where a specific number is multiplied to each term to get the next term.

For instance, a completely different geometric sequence 1,2,4,8,16,... is geometric because you multiply any term by 2 to get the next term.

Concept 2. Common ratio

In a geometric sequence, this number that you can multiply by to get the next term (in the "1,2,4,8,16,..." example, the number 2) is called the common ratio because taking the ratio of two sequential terms of the sequence (dividing two terms in a row) always gives the same answer:

This process of finding ratios will yield a common ratio only if the sequence is a Geometric Sequence.

Concept 3. Finding the next terms

Since we're told that the sequence we're given in the question is a Geometric sequence, it must have a common ratio (otherwise, it wouldn't be a geometric sequence).

Find the common ratio by dividing sequential terms:

270/810 = 1/3

90/270 = 1/3

So, for the sequence in the question, the common ratio is 1/3.  Each term is multiplied by 1/3 to get the next term in the sequence.  (This is equivalent to dividing each term by 3 to get the next term in the sequence, if you prefer division and/or to avoid fractions)

So, to get the next two terms in the sequence, multiply by the common ratio:

90 * 1/3 = 30

30 * 1/3 = 10

So, the next two terms of the sequence are 30 and 10

Answer:

15=teach 10=tutor

Step-by-step explanation:

5/75 = 15

3/30=10

Answer:

it would be 3 tutors and 15 students for each teacher

Step-by-step explanation:

3×30=90 so 30 can go into 110 3 times witch will be 90. next 75÷5=15

Answer:

To find the absolute value of an negative number, just take away the negative sign

The absolute value of a number can NEVER be negative

Step-by-step explanation:

For example, to find the absolute value of -22, it would be 22, since it is 22 points away from zero. To find the absolute value of -99.9, it would be 99.9.

A negative number is NOT always the absolute value of a number.

For example, the absolute value of 34 is, 34. If you plot it on a number line, it is 34 points away from zero, therefore proving a negative number is NOT always the absolute value of a number.

The absolute value of a number can NEVER be negative.

Answer:

The absolute value of a number is always POSITIVE! To find the absolute value, all you need to do is take away the negative sign!

Have a great day!

Answer:

The height is 1.25m.

Step-by-step explanation:

Volume = 1/3 πr²h

Given:

V = 13.4 m³

r = 3.2 m

Asked: height (h)

Substitute the formula with the given values then solve

13.4m³ = 1/3π(3.2m)²h

13.4(3) = 10.24πh

40.2 = 10.24πh

h = 40.2/10.24π

h = 1.25m

The height of the cone is 1.25 meters.

We know that the volume of the cone is given by

V = (1 / 3) * π * r ^2 * h................equation 1

where,

V is the volume of the cone.

r is the radius of the cone's base

h is the height

The volume and radius of the cone are given,

V = 13.4 m

r = 3.2m

substituting these values in equation 1 we get,

13.4 = (1 / 3) * 3.14 * 3.2 ^ 2 * h

on simplifying further

13.4 = 10.717  * h

h = 1.25m

The height of the cone is 1.25 meters.

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Answer:

What is that

Step-by-step explanation:

I have no idea

Answer:

5.5

7.5 =

h

23.5

7.5h = 129.25

h = 17.2

3

The flagpole is 17.2 feet long.

The measure of height of flagpole is 40.25 feet.

Given that, a flagpole casts a shadow that is 23 feet long.

Heights and Distances is a study about the applications of Trigonometry. It has many real-life applications, such as measuring the object’s height, depth of the object, the distance between two celestial objects etc. The formulas and the ratios of trigonometry are helpful in the study of heights and distances.

Jorge is 5.25 feet tall, and while standing near the flagpole he casts a shadow that is 3 feet long.

Let the height of the flagpole be x.

Now, tan θ=5.25/3 -------(I)

and tan θ=x/23 -------(II)

Equation (I)=(II), we get

5.25/3 = x/23

⇒ 3x=5.25×23

⇒ 3x=120.75

⇒ x=120.75/3

⇒ x=40.25 feet

Therefore, the measure of height of flagpole is 40.25 feet.

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The largest area would be a square shape.

A square has 4 equal sides:

1800/4 = 450

Now because the street side doesn't have fencing, add that side length to one side of the fencing:

450 +450 = 900

Now the fence would have two widths of 450 feet and one length of 900 feet.

Area = length x width = 450 x 900 = 405,000 square feet.

The lines L1 and L2 are not parallel and intersect at a single point. We have also found the point of intersection.

If the direction vectors are parallel, then the lines are parallel. If the direction vectors are not parallel but do not intersect, then the lines are skew. If the direction vectors are not parallel and do intersect, then the lines intersect at a single point.

To determine whether the given lines are parallel, skew, or intersecting, we need to compare their direction vectors. The direction vectors of the lines are the coefficients of the parameters t and s in the respective equations. Thus, the direction vector of L1 is <2,-1,3> and the direction vector of L2 is <4,-2,5>.

To check whether the direction vectors are parallel, we can compute their cross product. If the cross product is the zero vector, then the direction vectors are parallel.

<2,-1,3> × <4,-2,5> = (7,2,-10)

Since the cross product is not zero, the direction vectors are not parallel. Thus, the lines are either skew or intersecting.

To determine whether the lines are intersecting, we can set the parametric equations of the lines equal to each other and solve for t and s. This will give us the point of intersection.

3 + 2t = 1 + 4s

4 - t = 3 - 2s

1 + 3t = 4 + 5s

Rearranging the equations, we get:

2t - 4s = -2

t + 2s = 1

3t - 5s = 3

Using Gaussian elimination or other methods, we can solve for t and s:

t = 11/13

s = 2/13

Substituting these values back into either equation gives us the point of intersection:

x = 3 + 2(11/13) = 37/13

y = 4 - (11/13) = 41/13

z = 1 + 3(11/13) = 40/13

Thus, the lines intersect at the point (37/13, 41/13, 40/13).

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Complete Question:

Determine whether the lines L1 and L2 are parallel, skew, or intersecting. If they intersect, find the point of intersection.

L1: x = 3 + 2t, y = 4 – t, z = 1 + 3t

L2: x = 1 + 4s, y = 3 – 2s, z = 4 + 5s

Answer:

2 3/4

Step-by-step explanation:

So area is just base X height

3 X 11/12

2 3/4

Answer: The distance would be sqrt181

Step-by-step explanation: Use the distance formula to find the distance between two points.

6 kiloliters are approximately equal to 202,884.14 fluid ounces.

We have,

To convert 6 kiloliters (kL) to fluid ounces (fl oz), we need to use the conversion factor between these two units.

The conversion factor states that 1 kiloliter is equal to 33814.0227 fluid ounces.

This means that for every kiloliter, there are 33814.0227 fluid ounces.

To convert 6 kiloliters to fluid ounces, we multiply the given value (6 kL) by the conversion factor (33814.0227 fl oz/kL).

= 6 kL x 33814.0227 fl oz/kL

= 202884.1362 fl oz

Therefore,

6 kiloliters are approximately equal to 202,884.14 fluid ounces.

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Answer:

42

Step-by-step explanation:

Rectangle: A = 6 x 5 = 30

Triangle: A = 1/2(6 x 4) = 12

Area of figure: 30 + 12 = 42

Answer:

area of rectangle+area of triangle= area of figure

6×5 + 1/2×4×6=30+24= 42

or

given figure is a trapezium

so we know are of trapezium= 1/2×sum of parallel sides×height

= 1/2×( 5+9)×6

=42

Answer:

New volume on this is 480 cubic inches

Step-by-step explanation:

The volume of a rectangular prism is area of base * height

That would be;

l * b * h = lbh

we have all this as 60

Doubling all, we have

2l * 2b * 2h = 8lbh

Recall lbh = 60

So 8lbh = 8 * 60 = 480 cubic inches

The slope of a line parallel to 2y= 6x+8 is 3.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

In Mathematics and Geometry, parallel lines are two (2) lines that are always the same (equal) distance apart and never meet. Therefore, two (2) lines are parallel under the following conditions:

m₁ = m₂

By making y the subject of formula, we have:

2y = 6x + 8

y = 3x + 4

Therefore, the slope is 3.

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