(Q1) Which is the graph of the catenary y=e^x+e^-x/2

Answer:

Step-by-step explanation:

[tex]a_1=5,\ a_2=6,\ a_n=a_{n-1}+a_{n-2}\\\\a_3=a_2+a_1\\a_4=a_3+a_2\\a_5=a_4+a_3\\\\\text{first term:}\ 5\\\text{second term:}\ 6\\\text{third term:}\ 6+5=11\\\text{fourth term:}\ 11+6=17\\\text{fifth term:}\ 17+11=28[/tex]

Answer:

6/7

Step-by-step explanation:

8/14 simplified is 4/7.

So 2/7+4/7=6/7.

Answer:

V=64

Step-by-step explanation:

What you do is go based off the volume formula of a cube which is V=a^3.

You have a side length of 4.

V=4^3.

V=64.

I think 145 but I’m not quite sure

Answer:

116. add all and subtract respective to the date.

Step-by-step explanation:

Answer:

The distance  from the plane to SCCA is 34,203.0 feet approximately,  and the horizontal distance is 32,708.5 feet approximately.

Step-by-step explanation:

You can draw a right triangle like the one shown in the figure attached, where:

x: horizontal distance.

y: distance from the plane to SCCA.

You can calculate x as following:

[tex]tan\alpha=\frac{opposit}{adjacent}[/tex]

Where:

[tex]\alpha=17\°\\opposite=10,000\\adjacent=x[/tex]

Substitute and solve for x:

[tex]tan(17\°)=\frac{10,000}{x}\\\\x=\frac{10,000}{tan(17\°)}\\\\x=32,708.5ft[/tex]

You can calculate y as following:

[tex]sin\alpha=\frac{opposit}{hypotenuse}[/tex]

Where:

[tex]\alpha=17\°\\opposite=10,000\\hypotenuse=y[/tex]

Substitute and solve for y:

[tex]sin(17\°)=\frac{10,000}{y}\\\\y=\frac{10,000}{sin(17\°)}\\\\y=34,203.0ft[/tex]

Answer:

Remainder is 691.

Step-by-step explanation:

Given function is [tex]10x^4-6x^3+5x^2-x+1[/tex].

Now we need to find remainder if we divide given function [tex]10x^4-6x^3+5x^2-x+1[/tex] by (x-3)

(x-3) means plug x=3 into [tex]10x^4-6x^3+5x^2-x+1[/tex] to find remainder.

[tex]10x^4-6x^3+5x^2-x+1[/tex]

[tex]=10(3)^4-6(3)^3+5(3)^2-(3)+1[/tex]

[tex]=10(81)-6(27)+5(9)-(3)+1[/tex]

[tex]=810-162+45-3+1[/tex]

[tex]=856-162-3[/tex]

[tex]=856-165[/tex]

[tex]=691[/tex]

Hence remainder is 691.

Answer:

The remainder = 691

Step-by-step explanation:

Let p(x) = 10x⁴ - 6x³ + 5x² - x + 1

We have to divide p(x) by (x - 3)

To find the remainder we  have to find p(3)

To find the remainder

p(x) = 10x⁴ - 6x³ + 5x² - x + 1

p(3) = 10 * (3)⁴ - 6*(3)³ + 5* (3)² - 3 + 1

 = (10 * 81 ) - ( 6 * 27 ) + (5 * 9) - 3 + 1

 = 810 - 162 + 45 - 3 + 1 = 691

Therefore the remainder is 691

Answer:

lol

Step-by-step explanation:

Answer: option d.

Step-by-step explanation:

Based on the information given in the problem, you know that:

[tex]tan^2x=\frac{1}{2}[/tex]

You also know that:

[tex]sec^2(x)=tan^2(x)+1[/tex]

Substitute values. Then, you obtain:

[tex]sec^2(x)=\frac{1}{2}+1\\\\sec^2(x)=\frac{3}{2}[/tex]

Apply square root to both sides. Therefore, you obtain:

[tex]\sqrt{sec^2(x)}=\±\sqrt{\frac{3}{2}}\\\\sec(x)=\±\frac{\sqrt{3}}{\sqrt{2}}\\\\sec(x)=\±\frac{\sqrt{3}}{\sqrt{2}}\frac{\sqrt{2}}{\sqrt{2}}\\\\sec(x)=\±\frac{\sqrt{3(2)}}{2}\\\\sec(x)=\±\frac{\sqrt{6}}{2}[/tex]

Answer:

D

Step-by-step explanation:

Answer:

Option a. 1C, 2A, 3B, 4D.

Step-by-step explanation:

1) We know that tan(x)=sin(x)/cos(x). If x=0, sin(x)=0 and cos(x)=1 then tan(x)=0. For that reason, we know that the graph passes through the point (0,0).

If x=45, then sin(45)= [tex]\frac{\sqrt{2}}{2}[/tex] and cos(45)=[tex]\frac{\sqrt{2}}{2}[/tex]. Thus tan(45)=1. The only graph that passes through the point (0,0) and is possitive when x=45 is the graph C.

2) We know that cot(x)=cos(x)/sin(x). If x=0, sin(x)=0 and cos(x)=1 then tan(x)=+∞. For that reason, we know that the graph has an asymptote in y=0, in other words, it never crosses the y-axis.

If x=45, then sin(45)= [tex]\frac{\sqrt{2}}{2}[/tex] and cos(45)=[tex]\frac{\sqrt{2}}{2}[/tex]. Thus cot(45)=1. The only graph that has an asymptote in y=0 and is possitive when x=45 is the graph A.

3) We know that -tan(x)=-sin(x)/cos(x). If x=0, sin(x)=0 and cos(x)=1 then -tan(x)=0. For that reason, we know that the graph passes through the point (0,0).

If x=45, then sin(45)= [tex]\frac{\sqrt{2}}{2}[/tex] and cos(45)=[tex]\frac{\sqrt{2}}{2}[/tex]. Thus -tan(45)=-1. The only graph that passes through the point (0,0) and is negative when x=45 is the graph B.

) We know that -cot(x)=-cos(x)/sin(x). If x=0, sin(x)=0 and cos(x)=1 then tan(x)=-∞. For that reason, we know that the graph has an asymptote in y=0, in other words, it never crosses the y-axis.

If x=45, then sin(45)= [tex]\frac{\sqrt{2}}{2}[/tex] and cos(45)=[tex]\frac{\sqrt{2}}{2}[/tex]. Thus -cot(45)=-1. The only graph that has an asymptote in y=0 and is negative when x=45 is the graph D.

The correct matches of the functions with their graphs are as follows: 1) y = tan(x) matches with graph C, 2) y = cot(x) matches with graph A, 3) y = -tan(x) matches with graph B, and 4) y = -cot(x) matches with graph D.

1) y = tan(x) matches with graph C:

  - The tangent function has a period of π (180 degrees) and is undefined at odd multiples of π/2 (90 degrees). This is why it has vertical asymptotes at x = π/2, 3π/2, etc.

  - The graph of y = tan(x) passes through (0, 0) because tan(0) = 0.

  - It has a repeating pattern where it increases to positive infinity as it approaches the vertical asymptotes and decreases to negative infinity as it approaches the odd multiples of π/2.

2) y = cot(x) matches with graph A:

  - The cotangent function is the reciprocal of the tangent function: cot(x) = 1/tan(x). It is undefined at even multiples of π/2 (0, π, 2π, etc.), which is why it has vertical asymptotes at x = 0, π, 2π, etc.

  - The graph of y = cot(x) never crosses the y-axis, and it has an asymptote at y = 0.

  - It has a repeating pattern where it approaches 0 as it approaches the vertical asymptotes.

3) y = -tan(x) matches with graph B:

  - The negative tangent function, -tan(x), is the reflection of the positive tangent function y = tan(x) about the x-axis.

  - The graph of y = -tan(x) passes through (0, 0) because -tan(0) = 0.

  - It has a repeating pattern similar to the positive tangent but is reflected about the x-axis.

4) y = -cot(x) matches with graph D:

  - The negative cotangent function, -cot(x), is the reflection of the positive cotangent function y = cot(x) about the x-axis.

  - The graph of y = -cot(x) never crosses the y-axis, similar to the positive cotangent, and it has an asymptote at y = 0.

  - It has a repeating pattern similar to the positive cotangent but is reflected about the x-axis.

To know more about functions, refer here:

https://brainly.com/question/21939592

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The approximate probability that there will not be enough vegan meals is 94.88%.

To calculate the approximate probability that there will not be enough vegan meals, we need to find the probability that 18 or more vegans will come to the restaurant. Since the survey showed that approximately 4% of people in the city are vegans, we can use this information to estimate the probability.

First, we find the number of vegans in the city and surrounding area by multiplying the total population by the percentage of vegans: 600,000 * 0.04 = 24,000.

Next, we calculate the probability of 18 or more vegans showing up out of 24,000 by using a binomial distribution with n = 350 (the number of people expected on opening night) and p = 0.04 (the probability of a person being vegan). We then sum the probabilities for 18, 19, 20, ..., 350 vegans.

Using a calculator or statistical software, we find that the approximate probability is 0.9488, or 94.88%.

Answer: The answers are 2.54x and 30.48 cm.

Step-by-step explanation: The formula to determine the number of centimeters in x inches is 2.54x. To solve for the number of centimeters in 12 inches the formula is 2.54 x 12 = 30.48 cm.

Answer:

B is the answer because the other equations have real numbers

Step-by-step explanation:

Answer:

B is the correct answer

Step-by-step explanation:

Answer:

  8

Step-by-step explanation:

If each portion is 1/8 of the cake, there are 8 equal-size portions. That is what the denominator of the fraction means.

Sadie can cut the rectangular cake into 8 portions if each portion is 1/8 of the whole cake.

To determine how many portions Sadie can cut the rectangular cake into if each portion is 1/8, we need to understand that she is essentially dividing the cake into 8 equal parts.

Here's a step-by-step explanation:

Whole Cake: The entire rectangular cake represents one whole (1).

→ Portion Size: Each portion is 1/8 of the whole cake.

→ Calculation: We divide 1 by 1/8. Mathematically, this is the same as multiplying by the reciprocal,

so 1 ÷ (1/8) = 1 × 8

                 = 8.

Therefore, Sadie can cut the rectangular cake into 8 portions of size 1/8 each.

Area = 1/2(diagonal) * √4*side^2 - diagonal^2

Area = 1/2(16)*√(4*17^2 - 16^2)

Area = 8 * √(4*289-256)

Area = 8 *√900

Area = 8 * 30

Area = 240 m^2

Answer:

4√34

Step-by-step explanation:

the question asks for the value of the hypotenuse

Applying the Pythagorean equation

a²+b²=c² where a=12cm, b=20cm and c?

substituting values to equation

12²+20²=c²

144+400=c²

544=c²

√544=c

√16 × √34 =c

4×√34

4√34

ANSWER

[tex] 4 \sqrt{34} cm[/tex]

EXPLANATION

The missing side is the hypotenuse of the right triangle.

According to the Pythagoras Theorem, the length of the square of the hypotenuse is equal to the sum of the length of the squares of the two shorter legs.

Let the hypotenuse be x.

Then,

[tex] {x}^{2} = {20}^{2} + {12}^{2} [/tex]

[tex]{x}^{2} = 400 + 144[/tex]

[tex] {x}^{2} = 544[/tex]

Take positive square root of both sides.

[tex]x = \sqrt{544} [/tex]

[tex]x = 4 \sqrt{34} [/tex]

343 is the answer because 14 tens is 1 hundred and 4 tens

The number that represents 2 hundreds, 14 tens, and 3 ones is 343, by adding each place value: 200 + 140 + 3.

The student asks how to represent the quantity consisting of 2 hundreds, 14 tens, and 3 ones in a single number.

To solve this, we can convert each quantity to its respective place value in the decimal system and sum them.

Two hundreds is equal to 200 (2 x 100), 14 tens equals 140 (14 x 10), and 3 ones equals 3 (3 x 1).

Adding them together gives us 200 + 140 + 3 = 343.

Answer:

The ratio for sin(X) is [tex]\frac{\sqrt{119} }{12}[/tex]

The ratio for cos(X) is [tex]\frac{5}{12}[/tex]

Step-by-step explanation:

- The ratio of the sine of a right triangle is:

[tex]sin(\alpha)=\frac{opposite-side}{hypotenuse}[/tex]

Since we need the ratio for angle X, [tex]\alpha =X[/tex]. From the picture we can infer that the opposite side of X is [tex]\sqrt{119}[/tex]. The hypotenuse (the side opposite to the right angle) is 12, so replacing the values:

[tex]sin(X)=\frac{\sqrt{119} }{12}[/tex]

- The ratio of the cosine is:

[tex]cos(\alpha)=\frac{adjacent-side}{hypotenuse}[/tex]

Similarly, [tex]\alpha =X[/tex], adjacent side = 5, and hypotenuse = 12, so

[tex]cos(X)=\frac{5}{12}[/tex]

Answer:

Sin X =√119/12

Cs X = 5/12

Step-by-step explanation:

It is given a right angled triangle.

Points to remember

Sin θ = Opposite side/Hypotenuse

Cos θ = Adjacent side/Hypotenuse

To find the value of Sin X  

Here X is an angle

Opposite side = √119

Hypotenuse = 12

Sin X = Opposite side/Hypotenuse = ZY/XY = √119/12

To find the value of Cos X

Adjacent side of X = 5

Cos X = Adjacent side/Hypotenuse = XZ/XY = 5/12

Answer:

Step-by-step explanation:

(x - 4)

What you are being asked to do is find the exact same binomial in the top as is in the bottom.

But there's a small catch. You must stipulate that x cannot equal 4. If it does, then you will get 0/0 which is undefined. You can't have that happening -- not at this level.

Any other value for x is fine.

Sure.  To make an equilateral triangle we make any segment AB, which is already done, then we draw one circle (or an arc from the circle) with center A and radius AB, and one circle with center B and radius AB.  The two circles intersect at two points; we call either one of them C and ABC is equilateral.

Answer: C

Answer:

Each base is 40

Step-by-step explanation:

An isosceles triangle has a total of 180. An isosceles has two sides that are the same and one different. Think of “sos” in the word isosceles to help. If one is 100, then you have 80 left. 80 divided by 2 is 40.

ANSWER

The number is 18.

EXPLANATION

Let the number be x.

When this number is divided by 3, we obtain the quotient,

[tex] \frac{x}{3} [/tex]

When 5 is subtracted from this quotient, we get,

[tex] \frac{x}{3} - 5[/tex]

If the result is 1, then we have;

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

We group similar terms to get,

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

This gives us,

[tex] \frac{x}{3} = 6[/tex]

Multiply both sides by 3.

[tex]x = 6 \times 3[/tex]

[tex]x = 18[/tex]

Therefore the number is 18.

Answer:

C 294

Step-by-step explanation:

We can use proportions to solve.  Put number of miles over gallons

202 miles          x miles

--------------- = ----------------

11 gallons           16 gallons

Using cross products

202*16 = 11 x

Divide by 11 on each side

202*16/11 = 11x/11

293.81818181818 =x

To the nearest whole number

294 miles =x

Answer:

Step-by-step explanation:

f(x) + n - shift the graph of f(x) n units up

f(x) - n - shift the graph of f(x) n units down

f(x - n) - shift the graph of f(x) n units to the right

f(x + n) - shift the graph of f(x) n units to the left

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

f(x) = x² - 4x + 4 shifted 3 units to the right. Therefore g(x) = f(x - 3):

g(x) = (x - 3)² - (x - 3) + 4           use (a - b)² = a² - 2ab + b²

g(x) = x² - 2(x)(3) + 3² - x - (-3) + 4

g(x) = x² - 6x + 9 - x + 3 + 4           combine like terms

g(x) = x² + (-6x - x) + (9 + 3 + 4)

g(x) = x² - 7x + 16

Answer:

1/4

-64

Step-by-step explanation:

Answer:

The correct option is D) [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Consider the provided figure.  

We need to find the probability that a random leaf that lands on the rectangle lands within the section shaped like a trapezoid.

For this first find the total area as shown:

The given figure is a rectangle.

The area of rectangle is [tex]l\times b[/tex]

Where, l = 6 cm + 3 cm = 9 cm and b = 5cm

Therefore the area of the rectangle is;

Area of rectangle = [tex]9cm\times 5cm=45cm[/tex]

Now find the area of trapezoid.

The area of trapezoid is: [tex]\frac{a+b}{2}h[/tex]

Where h is the height and a and b are the parallel sides.

Area of trapezoid = [tex]\frac{9+3}{2}\times 5=30[/tex]

Thus, the area of trapezoid is 30 cm.

Therefore, the probability that a random leaf that lands on the rectangle lands within the section shaped like a trapezoid is:

[tex]Probability=\frac{\text{Area of trapezoid}}{\text{Area of rectangle}}[/tex]

[tex]Probability=\frac{30}{45}=\frac{2}{3}[/tex]

Hence, the correct option is D) [tex]\frac{2}{3}[/tex]

Answer:

2/3

Step-by-step explanation:

I got it right

Answer:

C

Step-by-step explanation:

The formula we use here is:

Length of arc = [tex]\frac{\theta}{360}*2\pi r[/tex]

Where

[tex]\theta[/tex]  is the central angle

r is the radius

Putting the given information into the formula we can solve for the central angle:

[tex]LengthOfArc=\frac{\theta}{360}*2\pi r\\4=\frac{\theta}{360}*2\pi(5)\\4=\frac{\theta}{360}*10\pi\\\frac{4}{10\pi}=\frac{\theta}{360}\\\theta=\frac{4*360}{10\pi}\\\theta=45.84[/tex]

rounded to nearest degree, we have 46 degree

C is the right answer.

Answer: OPTION C

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

- Use the following formula for calculate the measure fo the central angle:

[tex]\theta=\frac{s}{r}[/tex]

Where s is the arc length and r is the radius.

- Know the lenght of the arc and the radius, you can substitute values.

Therefore, you obtain;

[tex]\theta=\frac{4}{5}=0.8\ radians[/tex]

Convert to degrees:

[tex]\frac{(0.8)(180\°)}{\pi}=45.83\°[/tex]≈46°

Answer:

[tex]x\ge3[/tex]

Step-by-step explanation:

The given function is [tex]f(x)=\sqrt{x-3}[/tex].

The domain of this function refers to all values of x, for which the function is defined.

This square root function is defined when the expression under the radical sign is greater or equal to zero.

That is; the domain of the function is [tex]x-3\ge0[/tex]

This implies that [tex]x\ge3[/tex]

Answer:

Step-by-step explanation:

You need to multiply .75 and 9 you'll get 6.75 .. then you need to take 20 and subtract 6.75 and you'll get 13.25

Answer:

C is the correct choice.