let f be the function given by f(x)=sin x + e^-x +3x. which of the following statements is true for y=f(x).

[tex]\stackrel{\textit{one added to the }\sqrt{\qquad }}{1+\sqrt{\quad }}~~,~~ \stackrel{\sqrt{~~}\textit{ of a number and one}}{\sqrt{x+1}}\implies 1+\sqrt{x+1}\stackrel{\textit{equals}}{=}4 \\\\\\ \sqrt{x+1}=3\implies \left( \sqrt{x+1} \right)^2=3^2\implies x+1=9\implies \boxed{x=8}[/tex]

the answer is 4160$

     After 6 years of investment of $3200 compounded continuously, final amount in the account will be $4319.55.

Moneysaver's Bank offers a saving account with the features as,

Expression to calculate the final amount when compounded continuously,

Final amount = [tex]P.e^{rt}[/tex]

Here, P = Principal amount

r = Rate of interest

t = Duration of investment

By substituting the values in the expression,

Final amount = [tex]3200.e^{0.05\times 6}[/tex]

                      = 3200(1.3498588)

                      = 4319.548

                      ≈ $4319.55

  Therefore, after 6 years of investment of $3200, final amount in the account will be $4319.55.

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Answer:

y=1

Step-by-step explanation:

the y values r 1 n even using the calculation it will give 1 as y

Linear equations can represent parallel lines, perpendicular lines and lines with no relationship at all.

The equation of the line in form of y =mx + b is [tex]\mathbf{y = 2x + 17}[/tex]

The equation is given as:

[tex]\mathbf{y =-\frac x2 - 6}[/tex]

For a linear equation y = mx + b, the slope of the equation is m

So, by comparison:

[tex]\mathbf{m =-\frac 12}[/tex]

The relationship between the slopes of perpendicular lines is:

[tex]\mathbf{m_2 =-\frac 1{m_1}}[/tex]

So, we have:

[tex]\mathbf{m_2 =-\frac 1{-1/2}}[/tex]

[tex]\mathbf{m_2 =2 }[/tex]

This means that, the slope of the line that passes through point (-8,1) is 2

The line equation is then calculated as:

[tex]\mathbf{y = m(x - x_1) + y_1}[/tex]

This gives

[tex]\mathbf{y = 2(x + 8) + 1}[/tex]

Open brackets

[tex]\mathbf{y = 2x + 16 + 1}[/tex]

Simplify

[tex]\mathbf{y = 2x + 17}[/tex]

Hence, the equation of the line in form of y =mx + b is [tex]\mathbf{y = 2x + 17}[/tex]

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Answer:

Step-by-step explanation:

The volume of the tank= (50x30X20) cm^3

                                       = 30000cm^3

                                       = 30 l

1 l costs 300 tk

therefore 30 l costs= 30X300 taka

                                = 90000 taka

Answer:

since negative and negative are plus we add it but not

change the sign

Step-by-step explanation:

so the answer is -21

hope I helped

Step-by-step explanation:

the radius is diameter divided by 2

7/2/2 =1 .75

circumference of a circle is 2πr

2*22/7*1.75=11

3.14*11 =34.54

Answer:

the function is odd.

Step-by-step explanation:

f(x) is even if f(−x)=f(x) . f(x) is odd if f(−x)=−f(x) . Since −1x=−f(x).

Answer:

Odd

Step-by-step explanation:

There are two ways a function can be determined even or odd.

1. Graph

If the line of symmetry is the y=axis, the function is even.

If it can be rotated 180˚ about the origin and lines up with the original equation, it is odd.

If none of the cases above are satisfied, the function is neither.

2. f(-x)

If you substitute -x for x and you get the equation to be the same as before, the function is even.

If you substitute -x for x and you get the previous equation * -1, the function is odd.

If none of the cases above are satisfied, the function is neither.

Answer: b

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

Answer:

x=17.7

Step-by-step explanation:

Pythagorean theory

a²+b²=c²

16²+7.5²=c²

256+56.25=c²

√312.25=√c²

c=17.7

Answer:

X=4

Step-by-step explanation:

1. Simplify the expression

2. Multiply the fractions:

3. Break up the fraction:

4. Find the greatest common factor of the numerator and denominator:

5. Factor out and cancel the greatest common factor:

6. Simplify the fraction:

7. Multiply the fractions:

8.Solve by distributing:

9. Simplify the arithmetic:

10.Break up the fraction:

11. Find the greatest common factor of the numerator and denominator:

12. Factor out and cancel the greatest common factor:

13.Combine the fractions:

14. Combine the numerators

15. Find the greatest common factor of the numerator and denominator:

16. Factor out and cancel the greatest common factor:

17. Simplify the right side:

Answer:

There would be $5,372.99 in Camilla's account after 4 years.

Step-by-step explanation:

Total Principal $5,000.00

Total Interest $372.99

* interest rate of 1.8% compound monthly is equivalent to annual rate of 1.815%

Camilla will have approximately $5,454.41 in her account after 4 years.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Camilla invests $5,000 into an account with a 1.8% interest rate that is compounded monthly.

Now, After 4 years, the investment will grow to:

= $5,000 (1 + (1.8%/12))¹²ˣ⁴

= $5,000 (1 + (1.8%/12))⁴⁸

= $5,454.41

Hence, Rounding this to the nearest cent gives us a final answer of $5,454.41.

So, Camilla will have approximately $5,454.41 in her account after 4 years.

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Answer:

∠ A = 43°

Step-by-step explanation:

Since the triangles are similar then corresponding angles are congruent, so

∠ B = ∠ T  = 55°

The sum of the 3 angles in a triangle = 180°

sum the 3 angles in Δ ABC and equate to 180

2x - 9 + 3x + 4 + 55 = 180 , that is

5x + 50 = 180 ( subtract 50 from both sides )

5x = 130 ( divide both sides by 5 )

x = 26

Then

∠ A = 2x - 9 = 2(26) - 9 = 52 - 9 = 43°

Answer:

D  [tex]\sqrt{x+4}[/tex]

Step-by-step explanation:

Answer:

Percentage is the answer

ATQ

[tex]\\ \tt\longmapsto 2(x+6x)=1190[/tex]

[tex]\\ \tt\longmapsto 2(7x)=1190[/tex]

[tex]\\ \tt\longmapsto 7x=595[/tex]

[tex]\\ \tt\longmapsto x=595/7[/tex]

[tex]\\ \tt\longmapsto x=85[/tex]

19, 15.5

20, 25

21, 1/16

22, 4

23, 11

24, 8

25, 19.5

26, 30

27, 4

28, 56

29, 6.5

30, 4

31, 21

32, 112

33, 3,200

here are they

a. By the chain rule,

[tex]\dfrac{dy}{dx} = \dfrac{dy}{dt}\cdot\dfrac{dt}{dx} = \dfrac{dy}{dt}\cdot\dfrac{1}{\frac{dx}{dt}}[/tex]

Given that [tex]y=e^t+e^{-t}[/tex] and [tex]x=e^{-t}[/tex], we have the derivatives

[tex]\dfrac{dy}{dt} = e^t -e^{-t}[/tex]

[tex]\dfrac{dx}{dt} = -e^{-t}[/tex]

and so

[tex]\dfrac{dy}{dx} = \dfrac{e^t - e^{-t}}{-e^{-t}} = 1-e^{2t}[/tex]

Set this equal to zero and solve for t :

[tex]1-e^{2t} = 0[/tex]

[tex]1 = e^{2t}[/tex]

[tex]\ln(1) = \ln\left(e^{2t}\right)[/tex]

[tex]0 = 2t \ln(e)[/tex]

[tex]0 = 2t[/tex]

[tex]t=0[/tex]

This value of t corresponds to x = e⁰ = 1 and y = e⁰ - 1/e⁰ = 1 - 1 = 0. So the only point on the curve where the derivative dy/dx is zero is (1, 0).

b. Compute the second derivative. Since dy/dx is a function of t, we'll momentarily replace it with f(t). By the chain rule,

[tex]\dfrac{d^2}{dx^2} = \dfrac d{dx} \dfrac{dy}{dx} = \dfrac{df}{dx} = \dfrac{df}{dt}\cdot\dfrac{dt}{dx} = \dfrac{df}{dt}\cdot\dfrac{1}{\frac{dx}{dt}}[/tex]

We have

[tex]\dfrac{df}{dt} = -2e^{2t}[/tex]

and we've already committed dx/dt. So

[tex]\dfrac{d^2}{dx^2} = \dfrac{-2e^{2t}}{-e^{-t}} = 2e^{3t} [/tex]

Substitute the first and second derivative into the differential equation:

[tex]\left(\dfrac{d^2y}{dx^2}\right)^2 + \dfrac{dy}{dx} - 1 = 0[/tex]

[tex]\left(2e^{3t}\right)^2 + (1-e^{2t}) - 1 = 0[/tex]

[tex]4e^{6t} -e^{2t}= 0[/tex]

[tex]e^{2t} (4e^{4t} - 1) = 0[/tex]

[tex]4e^{4t} - 1 = 0[/tex]

[tex]4e^{4t} = 1[/tex]

[tex]e^{4t} = \dfrac14[/tex]

[tex]\ln\left(e^{4t}\right) = \ln\left( \dfrac14\right)[/tex]

[tex]4t \ln(e) = -\ln(4)[/tex]

[tex]4t = -\ln(4)[/tex]

[tex]t = -\dfrac{\ln(4)}4[/tex]

Answer:

{-2}

Step-by-step explanation:

Answer:

B)-2

Step-by-step explanation:

In functions, X is your input. Y is the output unless specifically stated otherwise :P

Brainliest? <3

Given polynomial:

(4x²-3x+7) - (x²+8x-5)

⇛ 4x²-3x+7-x²-8x+5

⇛ (4x²-x²) +(-3x-8x)+(7+5)

⇛ (4-1)x²+(-3-8)x+12

⇛ 3x²+(-11)x+12

⇛ 3x²-11x+12

Note:-

When subtracting two polynomials,change the symbols of the each term in the second polynomial which is subtracted from the first polynomial.

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Answer:

[tex]3x^2-11x+12[/tex]

Step-by-step explanation:

First, distribute the negative:

[tex]4x^2-3x+7-x^2-8x+5[/tex]

Then combine like terms:

[tex]3x^2-11x+12[/tex]

Answer:

false

Step-by-step explanation:

3(2×−4)=8+2×+6

Multiply 3 and 2 to get 6.

6(−4)=8+2×6

Multiply 6 and −4 to get −24.

−24=8+2×6

Multiply 2 and 6 to get 12.

−24=8+12

Add 8 and 12 to get 20.

−24=20

Compare −24 and 20.

Willie needs to keep same force acting by him on the cart inorder to balance the force.

Let's check how?

[tex]\\ \sf\longmapsto F_{net}=100-100=0N[/tex]

.Hence verified