100 points
1942 divded by 2^4

The intervals that satisfy the given trigonometric Inequality are; 0 ≤ x < 3π/2 and 3π/2 < x ≤ 2π

We are given the trigonometric Inequality;

2 sin(x) + 3 > sin²(x)

Rearranging gives us;

sin²(x) - 2 sin(x) - 3 < 0

Factorizing this gives us;

(sin(x) - 3)(sin(x) + 1) < 0

Thus;

sin(x) - 3 = 0 or sin(x) + 1 = 0

sin(x) = 3 or sin(x) = -1

sin(x) = 3 is not possible because sin(x) ≤ 1.

Thus, we will work with;

sin(x) = -1 for the interval 0 ≤ x ≤ 2π radians.

Then, x = sin⁻¹(-1)

x = 3π/2.

Now, if we split up the solution domain into two intervals, we have;

from 0 ≤ x < 3π/2, at x = 0. Then;

sin²(0) - 2 sin(0) - 3

= 0² - 0 - 3

= -3 < 0

Thus, the interval 0 ≤ x < 3π/2 is true.

From 3π/2 < x ≤ 2π, take x = 2π. Then;

sin²(2π) - 2 sin(2π) - 3

= 0² - 0 - 3

= -3 < 0

Thus, the interval 3π/2 < x ≤ 2π is also true.

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Answer:

[tex]f'(x)=-8\sin2x+\frac{1}{x} +1[/tex]

Step-by-step explanation:

I assume by [tex]\log(x)[/tex], the base is [tex]e[/tex], so let [tex]\log_e(x)=\ln(x)[/tex]:

[tex]\displaystyle f(x)=4\cos2x+\ln x+x\\\\f'(x)=\frac{d}{dx}(4\cos2x+\ln x + x)\\\\f'(x)=\frac{d}{dx}(4\cos2x)+\frac{d}{dx}(\ln x)+\frac{d}{dx}(x)\\\\f'(x)=-8\sin2x+\frac{1}{x}+1[/tex]

Remember that by the chain rule, to find the derivative of [tex]4\cos2x[/tex], you must find the derivative of the inside, which is [tex]\displaystyle \frac{d}{dx}(2x)=2[/tex], and multiply it by the outside derivative. Recall that [tex]\displaystyle \frac{d}{dx}\cos(x)=-\sin(x)[/tex], so replace [tex]-\sin(x)[/tex] with [tex]-4\sin(2x)[/tex], and multiply by 2 to get [tex]-8\sin(2x)[/tex] as your derivative.

Also remember that [tex]\displaystyle \frac{d}{dx}\ln(x)=\frac{1}{x}[/tex], one of the more basic derivatives.

The derivative of the function f(x)= 4cos2x + logx + x is f'(x)=-8sin2x+1/x+1.

A differential equation is an equation that contains one or more functions with its derivatives.

The given function is four times of cos2x plus logx plus x.

f(x)= 4cos2x + logx + x

We need to find the derivative of it f'(x)

d/dxf(x)=d/dx(4cos2x)+d/dx(logx)+d/dx(x)

f'(x)=4d/dx(cos2x)+d/dx(logx)+d/dx(x)

We know that

d/dx(cosx)=-sinx

d/dx(logx)=1/x

d/dx(x)=1

Apply in above equation

f'(x)=4d/dx(cos2x)+d/dx(logx)+d/dx(x)

f'(x)=4.2(-sin2x)+1/x+1

f'(x)=-8sin2x+1/x+1

Hence the derivative of function f(x)= 4cos2x + logx + x is f'(x)=-8sin2x+1/x+1.

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Answer:

  (d)  32

Step-by-step explanation:

An estimate is a value that is intended to approximate the result of a detailed calculation. Often, the target is an estimate that is within about 10% of the actual value. A "rough order of magnitude" (ROM) estimate is intended to be within about a factor of 3 of the actual value.

__

An estimate is generally made by using a reduced number of significant figures in the calculations. Often, the numbers used will be rounded to 1 or 2 significant figures. The math is often accomplished mentally, so methods of mental arithmetic are often used to simplify the calculations.

We are asked for an estimate of the product (-24.98)(-1.29). We notice there are an even number of minus signs, so the result will be positive. The values are (25)(1.3) when rounded to 2 significant figures.

Along with the rounded values, it is often useful to make note of the direction and magnitude of the errors due to rounding. Here, we have rounded both numbers up. The number 25 is high by 0.02, and the number 1.3 is also high by 0.01. These can be used to estimate the error in the estimated value.

The desired product can be computed several different ways. Either or both of the numbers 25 and 1.3 can be represented in a fashion that facilitates the (mental) arithmetic. Here are three (3) methods that could be used.

Ryder's estimate was 32.

_____

Additional comment

The actual product is ...

  (25 -0.02)(1.3 -0.01) = (25)(1.3) -0.02(1.3) -0.01(25) +(0.02)(0.01).

As a first approximation of the error in the product 32.5, we can sum the middle two terms:

  -0.02(1.3) and -0.01(25) = -0.026-0.25 = -0.276.

Then the first refinement of the estimate will give us ...

  32.500 -0.276 = 32.224

The actual value is obtained by adding the final error term:

  32.224 +0.0002 = 32.2242 . . . . the actual product with estimate errors resolved.

Answer:

yo

Step-by-step explanation:

its C, or 20

edge

ur welcome

The slope and y-intercept of the equation are - 3 / 2 and 7 respectively.

The slope and y-intercept of an equation can be easily found using slope intercept equation.

y = mx + b

where

Therefore,

3x + 2y = 14

2y = -3x + 14

y = -3 / 2 x + 7

Therefore,

slope = - 3 / 2

y-intercept = 7

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Answer:

Circumference: 25.12m

Area: 50.24 [tex]m^{2}[/tex]

Step-by-step explanation:

Formula for circumference of a circle: C=[tex]\pi d[/tex] or C=[tex]2\pi r[/tex] since the diameter is double the radius

C=3.14*2*4=3.14*8=25.12

Formula for area of a circle: A=[tex]\pi r^{2}[/tex]

A=3.14*[tex]4^{2}[/tex]=3.14*4*4=3.14*16=50.24

Answer:

1L container as the capacity of the sink is obviously at least 1L and most probably much more than 1L

Step-by-step explanation:

letter C

Answer:

8th graders i think is the answer

Step-by-step explanation:

Answer:

The 9th grades had given a higher percentage because even without converting to a percent, you can tell just by seeing that there is a 1 number difference if you would try to add.

Answer:

-2

-1

-2

-3

Step-by-step explanation:

For an odd function, f(-x) = -f(x).

f(2) = 2; f(-2) = -2

f(3) = 1; f(-3) = -1

f(4) = 2; f(-4) = -2

f(6) = 3; f(-6) = -3

Answer:

2 out of seven or 2/7 or 28.5%

Step-by-step explanation:

there are two "yeses" out of 7 total choices

Answer:

Paul and Krystal spent 13 hours at the pool

Step-by-step explanation:

I Thank

The time taken to cover a distance of 814 miles for Caynon's home will be 22 hours.

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.

Given that:-

The time will be calculated as:-

First, we will calculate the speed to cover the distance of Brother's house:-

Speed = Distance / Time

Speed = 481 / 13 = 37 miles per hour.

Now the time to cover a distance of 814 miles will be calculated as:-

Time = Distance / Speed

Time = 814 / 37

Time = 22 hours

Therefore the time taken to cover a distance of 814 miles for Caynon's home will be 22 hours.

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Answer:

B

Step-by-step explanation:

Divide y by x for each ordered pair:

2/4 = 1/2

3/6 = 1/2

5/10 = 1/2

7/14 = 1/2

All ratios are equal, so it is proportional.

Answer: B

Answer:

b

Step-by-step explanation:

mark brainliest

Answer:

[tex]\displaystyle x=-\frac{9}{2},\:x=-4[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{2}{x+6}-\frac{1}{x+3}=2\\\\\frac{2(x+3)}{(x+6)(x+3)}-\frac{(x+6)}{(x+6)(x+3)}=2\\ \\\frac{(2x+6)-(x+6)}{(x+6)(x+3)}=2\\ \\\frac{x}{(x+6)(x+3)}=2\\ \\x=2(x+6)(x+3)\\\\x=2(x^2+9x+18)\\\\x=2x^2+18x+36\\\\0=2x^2+17x+36[/tex]

[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\frac{-17\pm\sqrt{(17)^2-4(2)(36)}}{2(2)}\\\\x=\frac{-17\pm\sqrt{289-288}}{4}\\\\x=\frac{-17\pm\sqrt{1}}{4}\\\\x=\frac{-17\pm1}{4}\\ \\x_1=\frac{-18}{4}=-\frac{9}{2},\: x_2=\frac{-16}{4}=-4[/tex]

Answer:

what happened to you brooooooooo

Answer:

57

Step-by-step explanation:

9+6(2^2+4)

Calculate 2 to the power of 2 and get 4.

9+6(4+4)

Add 4 and 4 to get 8.

9+6×8

Multiply 6 and 8 to get 48.

9+48

Add 9 and 48 to get 57.

57

Answer: A

Step-by-step explanation:

[tex]$$Given $m \angle A=9 x-7, \quad m \angle B=7 x-9, m \angle C=28-2 x$ \\For the triangle $m \angle A+m \angle B+m \angle c=180$$$\begin{aligned}&\Rightarrow(9 x-7)+(7 x-9)+(28-2 x)=180 \\&\Rightarrow 9 x+7 x-2 x-7-9+28=180 \\&\Rightarrow 14 x=180-28+16 \\&\Rightarrow 14 x=168 \\&\Rightarrow \quad x=12\end{aligned}[/tex]

[tex]$$Therefore,\\&m \angle A=9 x-7=9 \times 12-7=101^{\circ}\\&m \angle B=7 x-9=7 \times 12-9=75^{\circ} \\&m \angle C=28-2 x=28-2 \times 12=28-24=4^{\circ}\\[/tex]

[tex]$$Since $m \angle A=101^{\circ}$ so $B C$ is the longest side of a triangle $\triangle A B C$ \\\\Since $m \angle C=4^{\circ} S 0$ SB is the shortest side of a triangle $\triangle A B C$\\\\So listing the sides in $\triangle A B C$ from shortest to longest is: (a) $\overline{A B}, \overline{A C}, \overline{B C}$[/tex]

Answer:

c. (x+7)^2+(y-6)^2=50

Step-by-step explanation:

The equation of a circle is; (x+7)²+(y-6)² = 50

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

The points on the circle are L(-2, 11) and centre is N(-7, 6)

Find the radius,

D = √(-7+2)²+(6-11))²

D = √25+25

D = √50

We know that, the equation of a circle is given by,

( x − a )² + ( y − b )² = r² , where ( a , b ) represents the centre of the circle,

Here, centre is N(-7, 6)

Therefore, the equation of a circle is;

(x+7)²+(y-6)² = 50

Hence, the required equation is (x+7)²+(y-6)² = 50

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Using exponential function concepts, it is found that the first graph to the similar problem represents an exponential decay.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

As x goes to positive infinity, a exponential function approaches a constant, hence a graph similar to the first one of the similar problem linked below represents exponential decay.

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Answer:

downwards

Step-by-step explanation:

the equation of a parabola in vertex form is

f(x) = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

• if a > 0 then parabola opens upwards

• if a < 0 then parabola opens downwards

for

f(x) = - 4(x - 3)² + 9 with a = - 4 < 0 , then

the parabola opens downwards

Answer: andres is 5 years old pls banned him he called e a mean word like the N word

Step-by-step explanation:

Answer:

B) h=63

Step-by-step explanation:

Multiply both sides by 9.

h/*9=9*7

Simplify

h=63

[tex]\bf{\dfrac{h}{9}=7 \ \ \to \ \ \ Exercise \ to \ solve }[/tex]

Multiply both sides by 9.

Multiply 7 and 9 to get 63.

Therefore, the correct option is "B".

[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

Answer:

Step-by-step explanation:

From the information,we get:

Two stacks of books together are = 7 1/2 inches tall.

One stack is given,that is = 4 3/4 inches.

To Find:

Solution:

Let us assume that the other height of the book be x.

Then the equation will be:

[tex] 4\cfrac{3}{4} + x = 7\cfrac{1}{2} [/tex]

Convert the mixed fractions to fractions:

[tex] \implies \: \cfrac{19}{4 } + x = \cfrac{15}{2} [/tex]

Subtract 19/4 from both sides:

[tex] \implies \: x + \cfrac{19}{4} - \cfrac{19}{4} = \cfrac{15}{2} - \cfrac{19}{4} [/tex]

[tex] \implies \: x = \cfrac{11}{4} =\boxed{ 2 \cfrac{3}{4} \rm \: inches}[/tex]

Hence, we can conclude that:

The height of the other book is 2 3/4 inches.

Answer:

let say the number is x, then 30x÷100=78, x=260...from this we can calculate 95 percent of 260 which is equal to 247

The 95 percentage of the number is A = 247

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage change is the difference between the measured value and the true value , as a percentage of the true value

Percentage change =( (| Measured Value - True Value |) / True Value ) x 100

Given data ,

Let the number be represented as n

Now , We can set up two equations based on the given information

30 percentage of the number is 78 ,

So , 0.3 ( n ) = 78

0.65 ( n ) = 169

Solving for n in the first equation, we get:

n = 260

Substituting n = 260 into the second equation, we can check that it is true:

0.65(260) = 169

Now, we can find 95% of the number by multiplying it by 0.95

0.95 x 260 = 247

Hence , 95% of the number is 247

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Answer:

a) they are corresponding angles

b) B=55° (proven)

C=55 (Angles opposite equal sides)

B+C+X=180° ( sum of angles of a triangle)

55°+55°X=180

110°+X=180°

X=180°-110°

X=70°

The match of the expressions are:

The numbers are products of 10.

This means that the numbers can be represented as exponents, where the base is 10 and the exponent is the number of zeros.

Using the above highlight, we have:

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