If x = 29°, find the measures of angles 1, 2, and 3.

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:

x = 6

Step-by-step explanation:

Answer:

Step-by-step explanation:

So this shape is made up two geometrical shapes - Triangle and a Rectangle.

So we have to find the area of Rectangle and Triangle

Area of Rectangle =

\(l \times b\)

If we apply this to the given diagram we get,

\(10 \times 6 \\ = 60\)

Now we have to find the area of Triangle

Area of Triangle =

\( \frac{1}{2} \times b \times h\)

If we apply this to the given diagram we get,

\( \frac{1}{2} \times 7 \times 6 \\ = \frac{1}{2} \times 42 \\ = 21\)

So the total area of the given figure is 60 + 21 which is equal to 81 sq.metre

Answer:

\(81m^{2}\)

Step-by-step explanation:

Area of rectangle =Length × Width

so Area of rectangle = 10 × 6=60\(m^{2}\)

The base of triangle equals to the width of rectangle so,

Area of triangle =\(\frac{1}{2}\)×7×6=21\(m^{2}\)

Then add the two areas together so , 60+21=81\(m^{2}\)

Because it's two shapes

In Bermuda, there are a total of 90 telephones for each 100 people. Also there are a total of 3,76,000 telephones in use in Luxembourg according to simple calculations.

Here, they given that a telephone symbol is equal to 5 telephones.

Then according to the given diagram,

1. There are:

= (5 + 5 + 5 + 3) 5 telephones

= ( 18 ) 5 telephones

= 90 telephones.

Therefore, there are a total of 90 telephones for each 100 people.

2. In 2005, the population of Luxembourg was 470,000.

According to the given diagram, there are 80 telephones available for every 100 people.

For 4,70,000:

100 -------------- 80

4,70,000 ------ (x)

After cross multiplication,

x * 100 = 80 * 470000

x = 8 * 47000

x = 3,76,000

Therefore, there are total of 3,76,000 telephones in use in Luxembourg.

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yeaaa free coins

I DONT CARE

Step-by-step explanation:

So, Gina's farm produced approximately 471.8 tons of sweet potatoes this year. Rounded to the nearest whole number, this is 472 tons.

When we talk about an increase, we are referring to a change in quantity or value that is greater than the original amount. In other words, an increase means that something has gotten bigger, larger, or more than it was before.

Given by the question.

To find out how much sweet potatoes Gina's farm produced this year, we need to add 40% of last year's production to the amount produced last year:

40% of 337 tons = 0.4 x 337 = 134.8 tons

Adding this to last year's production gives:

337 + 134.8 = 471.8 tons

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Answer:

Step-by-step explanation:

Product means multiply.

-300

Answer: 4.5

Step-by-step explanation:

30% is equal to 30/100, which is 0.3

If you times 0.3 by 15, you will get 30% of 15

Therefore the answer would be 0.3 x 15 = 4.5

Answer:

Domain is all real numbers

Range is (3, ∞) or y > 3

Step-by-step explanation:

Answer: 19:30 is the current time as per the 24-hour time format

Step-by-step explanation: We know that a day has 24 hours. The time can be shown in two different formats- the 12-hour format and the 24-hour format. 12 hour format ranges only from 1-12 on the hour while 24-hour format varies from 1-24 representing the hour.

      The 24 hour time format is quite simple- marks one number each for one hour. If the Reading says 19:30, it simply means hour 19 of that day. 12-hour time format is different since it makes use of A.M. (Ante Meridiem) and P.M. (Post Meridiem).

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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The the length of each side of the triangle are: 5 units, 8.7 units and 10 units respective

A triangle is a polygon with three sides, three angles, three vertices and sum of angles equal to 180 degrees

From the triangle, Using the trigonometric ratio of sine

Sin C = opposite/Hypothenuse

Sin30 = 5/H

Making h the subject of the relation we have

h= 5/sin30

h=5/0.5

Therefore the value of h=10 units

To find the third side use Pythagoras theorem

10² = 5²+p²

100-25 = p²

75 = p²

Taking the square of both sides

p=√75

p=8.7 units

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Answer:

2/3

Step-by-step explanation:

You can divide a 4 from both 8 and 12, giving you 2 over 3 as your fraction.

Answer:

8/12 in simplest form is 2/3

Step-by-step explanation:

you divide both the denominator and numerator by four

Here using the correct order of operations that is PEMDAS, we get the value to be 13.

PEDMAS can be summed up as a mathematical acronym that lists the various arithmetic operations in order of greatest to least practical use.

The letters stand for:

P stands for parentheses.

Exponents are shown as E.

D stands for division.

The letter M stands for multiplication.

A stand for addition.

S stands for subtraction.

Now in the given question,

15 - (4-3)2

First the parentheses

15 - (1)2

Next is exponents.

15 - 2

At last, after subtracting, we get:

13

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Answer:

Step-by-step explanation:

the degree of a polynomial determines 1:1 the number of solutions.

a quadratic equation (degree 2) has 2 solutions.

the general solution is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = -4

b = -4

c = -1

so,

x = (4 ± sqrt((-4)² - 4×-4×-1))/(2×-4)

when we look at the square root

16 - 16

we see that it is 0.

the square root of 0 is 0, and there is no difference between -0 and +0.

so, we get only one (real) solution : 4/-8 = -1/2

but : formally, there are still 2 solutions (as this is a quadratic equation). they are just identical.

so, I am not sure what your teacher wants to see in this case as answer.

my answer would be 2 real identical solutions. did this help?

There were 8 slices in the whole pizza.

An equation means the formula that expresses the equality of two expressions by connecting them with the equals sign =.  Let us assume the number of slices in the whole pizza is "x".

Since Jim ate two slices which is 25% of the pizza, we will set up the equation:

2 = 0.25x

To solve for "x":

2 / 0.25 = x

x = 8.

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Answer:759

Step-by-step explanation:

The length of EB is approximately 14.6 units when rounded to the nearest tenth.

To find the length of EB, we can use the property of similar triangles in this diagram. By looking at triangle DFE and triangle CFB, we can see that they are similar triangles.

Using the similarity ratio, we can set up the proportion:

DF / CF = DE / EB

Plugging in the given values, we have:

13.1 / 10.9 = 17.5 / EB

To find EB, we can cross-multiply and solve for EB:

13.1 * EB = 10.9 * 17.5

EB = (10.9 * 17.5) / 13.1

EB ≈ 14.6

Therefore, the length of EB is approximately 14.6 units when rounded to the nearest tenth.

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Answer:25.45

Step-by-step explanation:

52936/1 year x 1 year/52 weeks x 1 week/40hours

Answer:

4<x<10

Step-by-step explanation:

-2x<-4

Divide by 2

-x<-4

Divide by -1 (remember if you divide by -1, flip the direction of the sign)

x>4

x-4<6

Add 4 to both sides

x<10

Combine these

4<x<10

The outcomes that are contained in the events are

1 - P(X) = 4/5 and 1 - P(X) is the same as P(Not X)

From the question, we have the following parameters that can be used in our computation:

X = gray colours

Given that

gray colours = 3 and 10

We have

X = 3 and 10

Not X =1, 2, 4, 5, 6, 7, 8

The probability is then calculated as

P(X) = 2/10 = 1/5

For P(Not X), we have

P(Not X) = 1 - 1/5 = 4/5

In (a), we have

P(Not X) = 1 - 1/5 = 4/5

This means that

P(Not X) = 1 - P(X)

So, the solution is

1 - P(X) = 4/5

Using the above (a) and (b) as a guide, we have the following:

1 - P(X) is the same as P(Not X)

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Answer:

I graphed all of the equations on the graph below.

Step-by-step explanation:

At the point (6,4), the equation \(x+y\ge10\) uses 6 + 4 ≥ 10. Also, the equation \(2x+3y\le24\) uses 2(6) + 3(4) ≤ 24.

If this answer is correct, please make me Brainliest!

Answer:

its A !!

Step-by-step explanation:

The functions are evaluated as:

a. (f + g)(x) = 3x² + 2x

b. (f - g)(x) = 3x² - 2x

c. (f * g)(x) = 6x³

d. (f/g)(x) = 2x/3x²

Functions can be evaluated by substituting the expression of each function into the equation given, then simplified algebraically.

Given the functions,

f(x) = 2x

g(x) = 3x²

a. (f + g)(x) = f(x) + (g(x)

Substitute

f(x) + (g(x) = 2x + 3x² = 3x² + 2x

b. (f - g)(x) = f(x) - g(x)

Substitute the functions f(x) and g(x) into the expression f(x) - g(x):

f(x) - g(x) = 2x - 3x² = 3x² - 2x

c. (f * g)(x) = [f(x)][g(x)]

Substitute the functions f(x) and g(x) into the expression [f(x)][g(x)]:

[f(x)][g(x)] = (2x)(3x²) = 6x³

d. (f/g)(x) = f(x)/g(x)

f(x)/g(x) = 2x/3x²

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Answer:

The component of \(\vec u\) orthogonal to \(\vec a\) is \(\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)\).

Step-by-step explanation:

Let \(\vec u\) and \(\vec a\), from Linear Algebra we get that component of \(\vec u\) parallel to \(\vec a\) by using this formula:

\(\vec u_{\parallel \,\vec a} = \frac{\vec u \bullet\vec a}{\|\vec a\|^{2}} \cdot \vec a\) (Eq. 1)

Where \(\|\vec a\|\) is the norm of \(\vec a\), which is equal to \(\|\vec a\| = \sqrt{\vec a\bullet \vec a}\). (Eq. 2)

If we know that \(\vec u =(2,1,1,2)\) and \(\vec a=(4,-4,2,-2)\), then we get that vector component of \(\vec u\) parallel to \(\vec a\) is:

\(\vec u_{\parallel\,\vec a} = \left[\frac{(2)\cdot (4)+(1)\cdot (-4)+(1)\cdot (2)+(2)\cdot (-2)}{4^{2}+(-4)^{2}+2^{2}+(-2)^{2}} \right]\cdot (4,-4,2,-2)\)

\(\vec u_{\parallel\,\vec a} =\frac{1}{20}\cdot (4,-4,2,-2)\)

\(\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)\)

Lastly, we find the vector component of \(\vec u\) orthogonal to \(\vec a\) by applying this vector sum identity:

\(\vec u_{\perp\,\vec a} = \vec u - \vec u_{\parallel\,\vec a}\) (Eq. 3)

If we get that \(\vec u =(2,1,1,2)\) and \(\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)\), the vector component of \(\vec u\) is:

\(\vec u_{\perp\,\vec a} = (2,1,1,2)-\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)\)

\(\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)\)

The component of \(\vec u\) orthogonal to \(\vec a\) is \(\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)\).

Answer:

200

Step-by-step explanation:

pi · radius · height

3.14 · 8 · 25 = 200

extra : i used symbolab.com :)

9514 1404 393

Answer:

  (d) enlargement with scale factor greater than 1

Step-by-step explanation:

The image is obviously larger than the pre-image, so the dilation is an enlargement. The scale factor associated with an enlargement is always greater than 1.

__

Additional comment

In this drawing, the scale factor in the vertical direction is 8/2.5 = 3.2. The scale factor in the horizontal direction is 9/3 = 3.0. The scale factors are different in the different directions.

Answer:

D.

Step-by-step explanation:

Answer:

49

Step-by-step explanation:

x^2-14x+c

Take the coefficient of x

-14

Divide by 2

-14/2 = -7

Square it

(-7)^2

49

This is the number you add

Answer:

8

Step-by-step explanation:

Since the value of j is given we replace the variable with its correct value,

4j

4(2) = 8

To find the value of Az in the geometric sequence, we can use the given information. The geometric sequence is represented as follows: A3, 60, 160, 06 = 9.

From this, we can see that the third term (A3) is 60 and the common ratio (r) is 160/60.

To find Az, we need to determine the value of the nth term in the sequence. In this case, we are looking for the term with the value 9.

We can use the formula for the nth term of a geometric sequence:

An = A1 * r^(n-1)

In this formula, An represents the nth term, A1 is the first term, r is the common ratio, and n is the position of the term we are trying to find.

Since we know A3 and the common ratio, we can substitute these values into the formula:

60 =\(A1 * (160/60)^(3-1)\)

Simplifying this equation, we have:

\(60 = A1 * (8/3)^260 = A1 * (64/9)\)

To isolate A1, we divide both sides of the equation by (64/9):

A1 = 60 / (64/9)

Simplifying further, we have:

A1 = 540/64 = 67.5/8.

Therefore, the first term of the sequence (A1) is 67.5/8.

Now that we know A1 and the common ratio, we can find Az using the formula:

Az = A1 * r^(z-1)

Substituting the values, we have:

Az =\((67.5/8) * (160/60)^(z-1)\)

However, we now have the formula to calculate it once we know the position z in the sequence.

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