Let F(x) = E^(3x Sin (x)). Find F'(x) (2024)

Given

Arc AB = 80 degree

Find

Measure of angle AOB

Explanation

By properties of circle,

[tex]\angle AOB=2\times\angle AOC[/tex]

so,

[tex]\angle AOB=2\times80\degree=160\degree[/tex]

Final Answer

correct option is C

We can write the numbers as a sum of other number, so:

[tex]\begin{gathered} 16\cdot15=(10+6)\cdot(10+5) \\ 16\cdot15=(10\cdot10)+(10\cdot5)+(6\cdot10)+(6\cdot5) \\ 16\cdot15=100+50+60+30 \\ 16\cdot15=150+90 \\ 16.15=240 \end{gathered}[/tex]

we have the functions

[tex]\begin{gathered} f(x)=5logx \\ g(x)=logx^5 \end{gathered}[/tex]

Find out (g/f)(x)

[tex]\left(g/f\right)\left(x\right)=\frac{g(x)}{f(x)}=\frac{logx^5}{5logx}[/tex]

Apply property of logarithms

[tex]\begin{gathered} (\frac{g}{f})(x)=\frac{logx^{5}}{5logx}=\frac{5logx}{5logx}=1 \\ \\ therefore \\ \\ (\frac{g}{f})(x)=1 \end{gathered}[/tex]The answer is 1

The factors of p(x) = [tex]x^{4} -16[/tex] are [tex](x^{2} -4) (x^{2} +4)[/tex].

According to the question,

We have the following information:

p(x) = [tex]x^{4} -16[/tex]

Now, we can solve this expression by using the identity. Now, the identity to be used here is [tex]a^{2} - b^{2} = (a-b) (a+b)[/tex].

(More to know: there are many identities which can be used to find the factors of an expression. There ae different ways to find the factors of an expression.)

In this case, the value of a is [tex]x^{2}[/tex] and the value of b is 4.

We can convert this fraction into this identity:

[tex](x^{2})^{2} -4^{2}[/tex]

So, we have the following expression:

[tex](x^{2} -4) (x^{2} +4)[/tex]

Hence, the factors of the given expression are [tex](x^{2} -4) (x^{2} +4)[/tex].

To know more about factors here

https://brainly.com/question/24182713

#SPJ1

To answer this question, we have to multiply the volume that each student needs times the number of students:

[tex]40\cdot120mL=4800mL[/tex]

Convert this volume to liters (1L=1000mL):

[tex]4800mL\cdot\frac{1L}{1000mL}=4.8L\approx5L[/tex]

It means that the assistant must order 5L of acid.

Apply the compound interest formula:

A = P (1+r/n)^nt

where:

A = future vale

P = Principal investment = $2000

r= interest rate (decimal form) = 3.5 /100= 0.035

t= years

n= number of compounding periods per year (4)

Replacing:

A = 2000 (1 + 0.035/4)^4(5)

A = 2000 ( 1.00875)^20

A= $2,380.68

Answer

Elena must have substracted 1/2x from both sides of the equation.

Lin must have multiplied both sides of the equation by 2

Explanation

The equation given is

[tex]\frac{1}{2}x+3=\frac{7}{2}x+5[/tex]

For Elena to have arrived at

[tex]3=\frac{7}{2}x-\frac{1}{2}x+5[/tex]

Then Elena must have substracted 1/2x from both sides of the equation.

That is;

[tex]\begin{gathered} \frac{1}{2}x+3=\frac{7}{2}x+5 \\ \text{Substracting }\frac{1}{2}x\text{ from both sides of the equation will give Elena first step} \\ \frac{1}{2}x+3-\frac{1}{2}x=\frac{7}{2}x+5-\frac{1}{2}x \\ 3=\frac{7}{2}x-\frac{1}{2}x+5 \end{gathered}[/tex]

For Lin to have arrived at

[tex]x+6=7x+10[/tex]

It shows Lin must have multiplied both sides of the equation by 2

That is;

[tex]\begin{gathered} \frac{1}{2}x+3=\frac{7}{2}x+5 \\ \text{Multiply both sides of the equation by the lowest common mutiple } \\ \text{of the denominator which is 2.} \\ \frac{1}{2}x(2)+3(2)=\frac{7}{2}x(2)+5(2) \\ x+6=7x+10 \end{gathered}[/tex]

The probability that a randomly selected sushi roll contains salmon and is labeled not spicy is given by

[tex]P(salmon\: and\: not\: spicy)=\frac{n(salmon\: and\: not\: spicy)}{n(\text{total)}}[/tex]

Where n(salmon and not spicy) is 4 (intersection of salmon and not spicy)

n(total) is the total number of sushi rolls

[tex]n(total)=3+3+4+5=15[/tex]

So, the probability that a randomly selected sushi roll contains salmon and is labeled not spicy is

[tex]P(salmon\: and\: not\: spicy)=\frac{n(salmon\: and\: not\: spicy)}{n(\text{total)}}=\frac{4}{15}[/tex]

Therefore, the probability that a randomly selected sushi roll contains salmon and is labeled not spicy is 4/15

First, we need to note the given properties:

Side TS is equal to side RS:

[tex]TS=RS[/tex]

Also, side WS is equal to side XS:

[tex]WS=XS[/tex]

And our third given information is that angle ∠WSX is equal to ∠TSR, becuase they are vertical angles.

From this, we can also find the if the proportions are equal, in this case they are, because:

[tex]\begin{gathered} \frac{WS}{TS}=\frac{XS}{RS}=\frac{4}{2} \\ \frac{WS}{TS}=\frac{XS}{RS}=2 \end{gathered}[/tex]

Thus, we have two similar sides and 1 equal angle in the middle of them.

The triangle is SAS (Side angle side).

The flow chart is:

Given: The function below

[tex]y=-x^2+6[/tex]

To Determine: The graph of the parabola and the vertex

Solution

Determine the vertex

The vertex form of a parabola is

[tex]\begin{gathered} y=a(x-h)^2+k \\ vertex=(h,k) \end{gathered}[/tex][tex]\begin{gathered} h=-\frac{b}{2a} \\ k=f(-\frac{b}{2a}) \end{gathered}[/tex]

Note:

[tex]\begin{gathered} If \\ ax^2+bx+c=0 \\ y=-x^2+6 \\ a=-1,b=0,c=6 \end{gathered}[/tex][tex]\begin{gathered} Therefore \\ h=\frac{-(0)}{2\times-1}=0 \\ y=-x^2+6 \\ when,x=0 \\ y=-0^2+6 \\ y=0+6 \\ y=6 \end{gathered}[/tex]

The coordinate of the vertex is (0, 6)

Let us take two points on the left

[tex]\begin{gathered} x=-2 \\ y=-(-2)^2+6 \\ y=-4+6 \\ y=2,(-2,2) \\ x=-1 \\ y=-(-1)^2+6 \\ y=-1+6 \\ y=5(-1,5) \end{gathered}[/tex]

Let us take two points on the right

[tex]\begin{gathered} x=1 \\ y=-(1)^2+6 \\ y=-1+6 \\ y=5,(1,5) \\ x=2 \\ y=-(2)^2+6 \\ y=-4+6 \\ y=2,(2,2) \end{gathered}[/tex]

Let us plot the 5 points as a graph as shown below

Hence, the vertex is (0, 6) and two points on the left of the vertex are (-1,5) and (-2, 2), and two points to the right of the vertex are (1, 5) and (2, 2)

31.

The domain of a function is the set of all values that its variable can take.

To find the domain of a function, search for restrictions over its variable in its rule of correspondence. Remember that common restrictions are:

1. The denominator must be different to 0.

2. The argument of square roots cannot be negative.

For the given function:

[tex]f(x)=4-x[/tex]

In this rule of correspondence, the variable x does not appear in a denominator or inside a square root. Then, there are no restrictions over the variable x and the domain is the set of all real numbers, which can be represented using interval notation as:

[tex](-\infty,\infty)[/tex]

To sketch the graph of the function, notice that it is the equation of a line with slope -1 and y-intercept 4:

One unit on the x axis equals: 4 units

One unit on the y axis equals: 4 units

Explanation:

To determine the scales for x and y axes, we will consider the highest and lowest values for x and y respectivey.

(3,20), (-14, 11), (0, 13), (19, 2), (1, -17)

For x axes:

The lowest number is -14

The highest number is 19

We can say the units on the x axes will be from -20 to 20

For y axes:

The lowest number is -17

The highest number is 20

We can say the units on the y axes will be from -20 to 20

Since there are 5 boxes or lines before the arrow, each line can represent 20/5

Each line will represent 4 unit

If 1 unit represents 1 line:

One unit on the x axis equals: 4 units

One unit on the y axis equals: 4 units

we have

2x^5-x^4+3x^2-x+5 ÷ (x-1)

2x^4+x^3+x^2+4x+3

-2x^5​+2x^4

----------------------------

x^4+3x^2-x+5

-x^4+x^3

--------------------

x^3+3x^2-x+5

-x^3+x^2

--------------------

4x^2-x+5

-4x^2+4x

---------------------

3x+5

-3x+3

------------

8 --------> remander

therefore

2x^5-x^4+3x^2-x+5 =(x-1)(2x^4+x^3+x^2+4x+3)+8

The expression to simplify is:

[tex]9\sqrt[]{2}(4\sqrt[]{6})[/tex]

When we are multiplying two racial expressions, we multiply the constants together and the square roots together. So, the next step is:

[tex]\begin{gathered} 9\sqrt[]{2}(4\sqrt[]{6}) \\ =(9\times4)(\sqrt[]{2}\times\sqrt[]{6}) \\ =36(\sqrt[]{2}\times\sqrt[]{6}) \end{gathered}[/tex]

Now, we an use the property

[tex]\sqrt[]{a}\times\sqrt[]{b}=\sqrt[]{a\times b}[/tex]

to simplify it further:

[tex]\begin{gathered} 36(\sqrt[]{2}\times\sqrt[]{6}) \\ =36(\sqrt[]{2\times6}) \\ =36\sqrt[]{12} \end{gathered}[/tex]

We can break apart the square root using the property:

[tex]\sqrt[]{ab}=\sqrt[]{a}\sqrt[]{b}[/tex]

So, we have:

[tex]\begin{gathered} 36\sqrt[]{12} \\ =36\sqrt[]{2}\sqrt[]{2}\sqrt[]{3} \end{gathered}[/tex]

For the final simplification, we use the property,

[tex]\sqrt[]{a}\sqrt[]{a}=a[/tex]

The final answer is:

[tex]\begin{gathered} 36\sqrt[]{2}\sqrt[]{2}\sqrt[]{3} \\ =36(2)\sqrt[]{3} \\ =72\sqrt[]{3} \end{gathered}[/tex]Answer[tex]72\sqrt[]{3}[/tex]

Answer: We have to find the average value of the function:

[tex]f(x)=4x^3[/tex]

The average value of a function is defined as follows:

[tex]f_{avg}=\frac{1}{b-a}\int_a^bf(x)dx\Rightarrow(a,b)\text{ is interval }[/tex]

By using the definition of the average value of the function, the average is determined as follows:

[tex]\begin{gathered} \begin{equation*} f_{avg}=\frac{1}{b-a}\int_a^bf(x)dx \end{equation*} \\ \\ b=3,a=1 \\ -------------------------- \\ \therefore\rightarrow \\ \\ f_{avg}=\frac{1}{3-1}\int_1^34x^3dx=\frac{1}{2}\int_1^34x^3dx \\ \\ \\ f_{avg}=\frac{4}{2}\int_1^3x^3dx=2\int_1^3x^3dx \\ \\ \\ f_{avg}=2\int_1^3x^3dx=2[\frac{x^4}{4}\Rightarrow(1,3)] \\ \\ \\ f_{avg}=2[\frac{(3)^4}{4}-\frac{(1)^4}{4}]=2[\frac{81}{4}-\frac{4}{4}]=2[\frac{77}{4}] \\ \\ --------------------- \\ f_{avg}=38.5 \end{gathered}[/tex]

Therefore the answer is 38.5.

The centre of the first circle (small) is (3,7)

The centre of the second circle (big) is (3,2)

Since the x co-ordinate is same no translation occured horizontally

The y co-ordinate reduced by 5 so the translation was 5 unit down along y-axis.

Hence the translation that occured is:

[tex](x,y)=(0,-5)[/tex]

Hence (0,-5) is the translation value.

We have a polynomial with factors (x+2) and (x+6), thats mean that the polynomial has the form:

[tex]P(x)\approx(x+2)\cdot(x+6)[/tex]

Q) The question ask us about the values of x that make that polynomial equal to 0. i.e we want to find the values of x such that we have:

[tex]P(x)\approx(x+2)\cdot(x+6)=0[/tex]

A) Looking the last equation we see that if we replace x by -2 or x by -6 we get the polynomial equal to 0!

So the correct answer is letter A.

[tex]A\text{.-}2\text{ and -6}[/tex]

The volume of the figure will be the volume of the sphere minus the volume of the cylinder. The volume of the sphere will be:

[tex]\begin{gathered} Vs=\frac{4}{3}\pi r^3 \\ where \\ r=10units \\ Vs\approx4186.67units^3 \end{gathered}[/tex]

The volume of the cylinder is:

[tex]\begin{gathered} Vc=\pi r^2h \\ where\colon \\ r=4units \\ h=\frac{3}{4}(2\cdot10)=15units \\ so\colon \\ Vc=\pi(4^2)(15) \\ Vc\approx753.6units^3 \end{gathered}[/tex]

Therefore, the volume of the figure is:

[tex]\begin{gathered} V=Vs-Vc \\ V=4186.67-753.6 \\ V=3433.07units^3 \end{gathered}[/tex]

Answer:

V = 3433.07 units³

The equivalent expression 2 / 7 d¹¹ for given exponential expression

6d⁻⁴ / 21 d⁷ which is determined by dividing by the GCF of 3.

Given,

An equivalent expression for 6 times d raised to the negative fourth power all over quantity 21 times d raised to the seventh power end quantity.

What is an exponential function?

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

It is a relation of the form y = aˣ in mathematics, where x is the independent variable

We have been the given expression below as:

⇒ 6d⁻⁴ / 21 d⁷

To begin, divide the numerator and denominator by the GCF of 3.

If the negative exponent is relocated to the denominator, it will turn positive.

So you will have

⇒ 2 / 7 d⁷d⁴

Add the exponents because their base is the same,

⇒ 2 / 7 d⁷⁺⁴

⇒ 2 / 7 d¹¹

Therefore, the equivalent expression 2 / 7 d¹¹ for given exponential expression 6d⁻⁴ / 21 d⁷.

Learn more about the exponential function at:

https://brainly.com/question/14355665

#SPJ1

Answer:

its A i took the flvs test

Step-by-step explanation:

we have that

volume of the cylinder is

V=pi(r^2)h

Volume of the cone is

V=(1/3)pi(r^2)h

that means

the volume of the cylinder is three times the volume of the cone

therefore

the volume of the cone is

78/3=26 cm3

answer is the option A

Given:

A party supply store sells cups in packages of 6 and plates in packages of 8.

We need the same number for each item.

so, we will find the least common multiple of 6 and 8

6 = 1 x 2 x x 3

8 = 1 x 2 x 2 x 2

========================

LCM = 1 x 2 x 2 x 2 x 3 = 24

So, we need 24 plates and 24 cups

so, the answer will be:

The number of packages of cups = 24/6 = 4 packages

The number of packages of plates = 24/8 = 3 packages

The given information is:

- The gas tank has the shape of a cylinder, 4 ft long, and a diameter of 1.8 ft.

- The gas is poured at a rate of 1.7 ft^3 per minute.

The total volume of the empty tank is:

[tex]\begin{gathered} V=\pi *(\frac{d}{2})^2*h \\ V=3.14*(\frac{1.8ft}{2})^2*4ft \\ V=3.14*(0.9ft)^2*4ft \\ V=3.14*0.81ft^2*4ft \\ V=10.1736ft^3 \end{gathered}[/tex]

The rate is 1.7ft^3 per minute, then the time needed to fill the empty tank is:

[tex]\frac{10.1736ft^2}{1.7ft^3\text{ / min}}=5.98\text{ min}[/tex]

The answer is 6 minutes.

The cosecant is given by the inverse of the sine function, and the cotangent function is given by the cosine over the sine.

So, first let's calculate the sine function, then the cosine, and finally the cotangent.

(since the angle is in Quadrant IV, the sine is negative, the cosine is positive and the cotangent is negative)

[tex]\begin{gathered} \csc (\theta)=\frac{1}{\sin (\theta)} \\ -\frac{\sqrt[]{638}}{22}=\frac{1}{\sin (\theta)} \\ \sin (\theta)=\frac{-22}{\sqrt[]{638}} \\ \\ \sin ^2(\theta)+\cos ^2(\theta)=1 \\ (-\frac{22}{\sqrt[]{638}})^2+\cos ^2(\theta)=1 \\ \frac{484}{638}+\cos ^2(\theta)=1 \\ \cos ^2(\theta)=\frac{638}{638}-\frac{484}{638} \\ \cos ^2(\theta)=\frac{154}{638} \\ \cos (\theta)=\frac{\sqrt[]{154}}{\sqrt[]{638}} \\ \\ \cot (\theta)=\frac{\cos (\theta)}{\sin (\theta)} \\ \cot (\theta)=\frac{\frac{\sqrt[]{154}}{\sqrt[]{638}}}{\frac{-22}{\sqrt[]{638}}} \\ \cot (\theta)=-\frac{\sqrt[]{154}}{22} \end{gathered}[/tex]

Therefore the value of cot(theta) is equal to -(√154)/22.

Three points must be noncollinear to determine a plane. (Option D)

Explanation:

A straight line doesn't define a plane because a plane must be 2-dimensional

Three collinear points are three points on the same line. This also is insufficient in determining a plane.

A-line and a point on the line. This is similar to having a straight line.

If the roots of the quadratic equation are -2 and -5, then the factors of the quadratic equation must be:

[tex](x+2)(x+5)=0[/tex]

The quadratic equation in standard form goes by this pattern:

[tex]ax^2+bx+c=0[/tex]

So, to be able to find the standard form of the quadratic equation, let's multiply the two factors:

[tex]\begin{gathered} (x)(x+5)+2(x+5)=0 \\ x^2+5x+2x+10=0 \\ x^2+7x+10=0 \end{gathered}[/tex]

Therefore, the quadratic equation in standard form of the given roots is x² + 7x + 10 = 0.

Given the expression:

[tex]\frac{j^3k^{}}{h^0}[/tex]

Where,

h = 8

j = -1

k = -12

Let's plug in the values to the expression:

[tex]\frac{j^3k^{}}{h^0}[/tex][tex]\frac{(-1)^3(-12)^{}}{8^0}[/tex]

Recall: Any number that is raised to the power of zero is always equal to 1.

We get,

[tex]\frac{(-1)^3(-12)^{}}{8^0}\text{ = }\frac{(-1)(-12)}{1}\text{ = (-1)(-12)}[/tex]

Recall: When multiplying integers of the same sign, the product is always a positive integer.

We get,

[tex](-1)(-12)\text{ = 12}[/tex]

Therefore, the answer is 12, letter A.

Firstly, let us represent the bearings on a diagram;

From the diagram, we can find the value of d using pythagoras theorem. since it forms a right angled triangle.

[tex]\begin{gathered} d^2=4.3^2+1.8^2 \\ d=\sqrt[]{(4.3^2+1.8^2)} \\ d=\sqrt[]{(18.49+3.24)} \\ d=4.66\text{ miles} \end{gathered}[/tex]

Therefore, the distance of the final destination from the trailhead is;

[tex]4.66\text{ miles}[/tex]

Explanation:

If we get 12 slices from 2 cakes, this means that the sum of the slices of each cake is 12. Therefore, each cake has 6 slices:

In the unit rate, the denominator is always 1, so we want to know the amount of slices per cake

Answer:

The unit rate is 6 slices per cake

We are given the function

[tex]|x\text{ -3\mid+1}[/tex]

and asked to check from which function this came from. We solve this by comparison

THe square root function looks like this

[tex]\sqrt{x}[/tex]

the quadratic function looks like this

[tex]x^2[/tex]

a linear function looks like this

[tex]ax+b[/tex]

and the absolute value function looks like this

[tex]|x|[/tex]

the only function that looks alike is the absolute value function. So the correct answer is the absolute value function