Need help finding the area..

The values of θ for different conditions were calculated with the help of trigonometric functions.

Given that;

The difference in length of a spring on a pogo stick from its non-compressed length when a teenager is jumping on it after θ seconds can be described by the function,

f (θ) = 2 sin θ + √ 2

Hence, We can simplify as;

A) Function is,

f (θ) = 2 sin θ + √ 2

f (θ) = 2 sin θ + √ 2 = 0

2 sin θ + √ 2 = 0

2 sin θ = -  √ 2

sin θ = - 1/√2

θ = nπ ± π/4

Where, n = 1, 3, 5, 7, ...

So, At θ = nπ ± π/4 pogo stick's spring will be equal to its non compressed length.

2) If the angle was doubled, the function will look like this,

f (θ) = 2 sin 2θ + √ 2

f (θ) = 2 sin 2θ + √ 2 = 0

2 sin 2θ + √ 2 = 0

2 sin 2θ = -  √ 2

sin 2θ = - 1/√2

θ = nπ/2 + π/8

Where, n = 1, 3, 5, 7, ...

n = 1;

θ = π/2 + π/8

θ = 5π/8

n = 2;

θ = π + π//8

θ = 9π/8

Hence, Solutions are, 5π/8, 9π/8, ...

3) g (θ) = 1 - cos²θ + √2

g (θ) = sin²θ + √2

sin²θ + √2 = 2 sinθ + √2

sin²θ - 2 sinθ= 0

sinθ (sinθ - 2) = 0

sinθ = 0

θ = nπ

Where, n = 1, 3, 5, 7, ..

So, θ = nπ , the lengths of springs from the original pogo stick and the toddler's pogo stick are equal.

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ1

Answer:

124

Step-by-step explanation:

To find the number that should be added to the data so that the range of the data is 63, we first need to find the current range of the data.

The range of a set of data is the difference between the largest and smallest values in the set.

So, to find the current range of the data, we need to subtract the smallest value from the largest value:

Range = largest value - smallest value

Range = 97 - 61

Range = 36

This means that the current range of the data is 36.

To increase the range to 63, we need to add a number that is 63 - 36 = 27 larger than the current range.

To do this, we can add 27 to the largest value in the data set, which is 97:

97 + 27 = 124

So, we should add 27 to the data set to increase the range to 63.

Therefore, the complete set of data would be:

78, 61, 95, 77, 85, 97, 124

Check:

To find the range of the data set 78, 61, 95, 77, 85, 97, 124, we need to subtract the smallest value from the largest value:

Range = largest value - smallest value

Range = 124 - 61

Range = 63

Therefore, the range of the data set 78, 61, 95, 77, 85, 97, 124 is 63.

A) Maxine calculated the total mass of pH powder sold on day 1 by evaluating the algebraic expressions for small and large container sales.

B) If the variable s represents the number of containers sold, the value of the algebraic expression 0.75s represents the total mass of pH powder sold each day.

C) The algebraic expression to represent the mass (in kilograms) of powder sold in large containers daily is 1.25l.

D) The algebraic expression to show how Maxine calculated the total mass of pH powder sold on day 1 is 0.75s + 1.25l, which is evaluated to be 49.25 kg.

E). Using the algebraic expression, the total mass of powder sold on Day 2 and 3 is as follows:

An algebraic expression is a combination of of variables and constants, together with mathematical operands (addition, subtraction, division, and multiplication, etc.).

pH Plus Power Sales

Day       # of small containers    # of large containers    Total Mass

                    (0.75 kg)                            (1.25 kg)              (Kilograms)

Day 1               14                                       31                        49.25 kg

Day 2              19                                      42                        66.75 kg

Day 3             24                                      28                        53.00 kg

Let the number of small containers sold = s

Let the number of large containers sold = l

The mass of a small container = 0.75 kg

The mass of a large container = 1.25 kg

Total mass of small containers sold daily  = 0.75s

Total mass of large containers sold daily = 1.25l

Total mass of small and large containers sold daily = 0.75s + 1.25l

Day 1 = 0.75(14) + 1.25(31) = 49.25 kg

Day 2 = 0.75(19) + 1.25(42) = 66.75 kg

Day 3 = 0.75(24) + 1.25(28) = 53.00 kg

pH Plus Power Sales

Day       # of small containers    # of large containers    Total Mass

                    (0.75 kg)                            (1.25 kg)              (Kilograms)

Day 1               14                                       31                        49.25 kg

Day 2              19                                      42

Day 3             24                                      28

Learn more about algebraic expressions at https://brainly.com/question/4344214.

#SPJ1

The steps to graph the absolute value functions are given below.

We have,

Absolute value functions of form f(x) = |ax + b| have a characteristic shape, which depends on the values of a and b.

Here are some general guidelines for graphing these functions:

Find the y-intercept:

To find the y-intercept of the graph, set x=0 and solve for y.

This gives f(0) = |b|, so the y-intercept is at the point (0,|b|).

Find the x-intercept(s):

To find the x-intercepts of the graph, set y = 0 and solve for x.

If b > 0, there are two x-intercepts: x = -b/a and x = b/a.

If b = 0, there is one x-intercept at x=0.

If b < 0, there are no x-intercepts.

Determine the direction of the graph:

If a > 0, the graph opens upwards, like a "V".

If a < 0, the graph opens downwards, like an upside-down "V".

Determine the vertex:

The vertex is the point where the graph changes direction.

If a > 0, the vertex is at (-b/a, 0).

If a < 0, the vertex is at (b/a, 0).

Sketch the graph:

Use the information above to sketch the graph of the absolute value function.

Plot the y-intercept, the x-intercept(s), and the vertex, and then draw a smooth curve connecting these points.

Thus,

The graph of the absolute value functions is given above.

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ1

Answer: -20

Step-by-step explanation: I got negative twenty because if f(x) equals negative thirteen the we add negative seven because we need to flip the sign since it is negative and when you add you get negative twenty

To check, simply solve the eqation the way it first was, for example, f(x)=-20+7 which would be correct, equaling -13

Hopefully this helped, I' sorry if i am wrong

The crate of bananas is heavier than the bag of apples by 53 1/4 pounds.

An apple and a banana are both kinds of fruits. They both weigh differently.

Weight of a bag of apple = 8 7/8 pounds

Weight of a crate of bananas = 6 times as heavy as the apples

= 6 × 8 7/8

= 6 × 71 /8

= 426 / 8

= 53 1/4 pounds

Therefore, the weight of a crate of bananas is 53 1/4 pounds

Read more on fraction:

https://brainly.com/question/17220365

#SPJ1

The probability that a randomly selected bag contains fewer than 1050 chocolate​ chips is 0.84.

(a) The probability of a randomly selected bag containing between 1000 and 1400 chips is 0.75.

This is calculated using the standard normal distribution formula:

P(1000 < X < 1400)

= P(z < (1400-1252)/129) - P(z < (1000-1252)/129)

= 0.75

(b) The probability of a randomly selected bag containing fewer than 1050 chips is 0.26.

This is calculated using the standard normal distribution formula:

P(X < 1050) = P(z < (1050-1252)/129)

= 0.26

(c) The proportion of bags containing more than 1175 chips is 0.84.

This is calculated using the standard normal distribution formula:

P(X > 1175) = P(z > (1175-1252)/129)

= 0.84

(d) The percentile rank of a bag containing 1050 chips is 26%.

This is calculated using the standard normal distribution formula:

P(X < 1050) = P(z < (1050-1252)/129)

= 0.26

Therefore, the probability that a randomly selected bag contains fewer than 1050 chocolate​ chips is 0.84.

Learn more about the standard deviation visit:

brainly.com/question/13905583.

#SPJ1

Answer:

(-2, -6)

Step-by-step explanation:

Midpoint = (x1 + x2)/2, (y1 + y2)/2

= (-3 + -1)/2, (-5 + -7)/2

= (-4/2), (-12/2)

= (-2, -6)

The solution is, the value of the angle & x is:

x = 43

43°, 51°, 86°

We have,

The sum of the angles is ...

 x° + (x +8)° + 2x° = 180°

 4x +8 = 180 . . . . . . . . . . . collect terms, divide by °

 x +2 = 45 . . . . . . . . . . divide by 4

 x = 43 . . . . . . . . . . subtract 2

 x +8 = 51

 2x = 86

The angles are 43°, 51°, 86°.

To learn more on angle click:

brainly.com/question/28451077

#SPJ1

complete question:

The sum of the angle measures of a triangle is 180°. Find the value of x. Then find the angle measures of the triangle.

[tex]\textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left( ~~ \cfrac{\pi \theta }{180}-\sin(\theta ) ~~ \right) ~~ \begin{cases} r=radius\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=5\\ \theta =80 \end{cases} \\\\\\ A=\cfrac{5^2}{2}\left( ~~ \cfrac{\pi (80) }{180}-\sin(80^o ) ~~ \right)\implies A=\cfrac{25}{2}\left(\cfrac{4\pi }{9}- \sin(80^o) \right) \\\\\\ A=\cfrac{50\pi }{9}-\cfrac{25\sin(80^o)}{2}\implies A\approx 5.1~cm^2[/tex]

The number of triangle that can be formed is one, with angles m∠S and m∠T derived to be 127° and 33° using the sine rule.

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

Using the sine rule;

29/sin20° = 32°/sinT

T = (33 × sin20°)/29° {cross multiplication}

m∠T = 23 {to the nearest degree}

m∠S = 180 - (20 + 23)° {sum of interior angles of a triangle}

S = 127°

Therefore, the number of triangle that can be formed is one, with angles m∠S and m∠T derived to be 127° and 33° using the sine rule.

Read more about sine rule here: https://brainly.com/question/4372174

#SPJ1

The amounts needed to make 6 servings are given as follows:

Sauce: 12 servings.

Oregano: 3/4 teaspoons.

Here, we have,

The needed amounts to make 6 servings of the recipe are obtained applying the proportions in the context of the problem.

From the first line of the table, we get the amounts of sauce and oregano per serving are follows:

Sauce: 8/4 = 2 cups.

Oregano: 0.5/4 = 1/8 teaspoons per serving.

Hence the amounts for six servings are given as follows:

Sauce: 6 x 2 = 12 servings.

Oregano: 6 x 1/8 = 6/8 = 3/4 teaspoons.

More can be learned about proportions at brainly.com/question/24372153

#SPJ1

The requried measure of the side QT in triangle SQT is 59 units.

A figure is shown with two triangles, SQT and SQR.

Since in the question we are given to RS = ST 81, QR = v + 33, and QT = 3v 19,

As RS = St and SQ is a common side both the triangle are congruent, QT = QR

v + 33 = 3v - 19
52 = 2v
v = 26

Now,
QT = 3(26) - 19
QT = 59

Thus, the requried measure of the side QT in triangle SQT is 59 units.

Learn more about triangles here:

https://brainly.com/question/22062407

#SPJ1

Answer: 15 square units

Step-by-step explanation:

Area of a triangle is 1/2bh

x = b = 6

H=5

1/2(6)(5)

1/2(30)

Area = 15 square units

x = -5±-55i/5 is the solution and the best method to solve is by using the general formula.

Given the quadratic equation below;

2x^2+5x+10=0

The best method to solve the equation is by using the completing the square method as shown below:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

From the equation;

a = 2

b = 5

c = 10

Substitute into the formula to have:
x = -5±√5²-4(2)(10)/2(2)
x = -5±√25-80/4

x = -5±√-55/5

x = -5±-55i/5

Hence the solution to the given system of equation is x = -5±-55i/5

Learn more on quadratic equation formula here: https://brainly.com/question/1214333

#SPJ1

$48.07 would be the monthly payments on the loan.

We must first determine the total amount of interest charged over the course of the 4-year term in order to determine the monthly payments on a basic interest add-on loan.

The formula for simple interest is:

I = P * r * t

where I is the interest charged, P is the principal (the amount borrowed), r is the annual interest rate as a decimal, and t is the time period in years.

In this case, P = $1,426.25, r = 0.1545 (15.45% expressed as a decimal), and t = 4 years. So, the total amount of interest charged is:

I = $1,426.25 * 0.1545 * 4

I = $881.25

Adding the interest to the principal, we get the total amount paid over the 4-year term:

Total amount = $1,426.25 + $881.25

Total amount = $2,307.50

We must divide the sum by the number of months left in the loan term in order to get the monthly installments. As the loan period is 4 years long, there are 48 months:

Monthly payment = Total amount / Number of months

Monthly payment = $2,307.50 / 48

Monthly payment = $48.07

Therefore, the monthly payments on the loan would be $48.07.

Learn more about percentages here:

https://brainly.com/question/29306119

#SPJ1

The calculated area of the figure is 59/2 square units

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

A (1, 2) B (1, 7) C (9, 7) D (9, 3) E (6, 5)

The area is then calculated as

Area = 1/2 * | (x1y2 + x2y3 + ... + xny1) - (y1x2 + y2x3 + ... + ynx1) |

So, we have

Area = 1/2 * | (1 * 7 + 1 * 7 + 9 * 3 + 9 * 5 + 6 * 1) - (2 * 1 + 7 * 9 + 7 * 9 + 3 * 6 + 5 * 1) |

Evaluate

Area = 1/2 * 59

So, we have

Area = 59/2

Hence, the area is 59/2 square units

Read more about area at

https://brainly.com/question/24487155

#SPJ1

The value of the x as shown in the graph will be 16.61 ft.

From the sine rule in the triangle,

In a triangle ABC, where a, b, and c are the side lengths opposite to the angles A, B, and C respectively, and where the opposite angles A, B, and C are opposite to sides a, b, and c respectively, the Sine Rule states:

[tex]\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}[/tex]

Use the Law Of Sines to solve this:

(Sin 7)/9 = (Sin 13)/x

Cross multiply...

x(Sin 7) = 9(Sin 13)

Divide both sides by Sin 7

x = [9(Sin 13)]/(Sin 7)

x = 16.61254121

therefore, for the ramp, the value of the x will be 16.612 ft.

Learn more about the sine rule here:

https://brainly.com/question/30339234

#SPJ1

Edouard Manet's Luncheon on the Grass was shown in the Salon des Refuses after it was rejected for the annual salon.

Option D is the correct answer.

We have,

Edouard Manet's painting "Luncheon on the Grass" was first rejected by the Paris Salon in 1863, as it was considered scandalous due to the nudity of the female figure in the painting.

In response to this rejection,

Emperor Napoleon III ordered an exhibition to be held for all the rejected paintings, which was known as the Salon des Refusés (Salon of the Refused).

Thus,

Edouard Manet's Luncheon on the Grass was shown in the Salon des Refuses after it was rejected for the annual salon.

Learn more about Edouard Manet's painting here:

https://brainly.com/question/26188885

#SPJ1

Answer:

B)  6

Step-by-step explanation:

Calculate the value of c by substituting point (0, 15) into the quadratic equation formula:

[tex]f(x)=ax^2+bx+c[/tex]

[tex]\begin{aligned}f(0)=a(0)^2+b(0)+c&=15\\0+0+c&=15\\c&=15\end{aligned}[/tex]

Therefore:

[tex]f(x)=ax^2+bx+15[/tex]

Substitute the point (1, 22) into the formula and create an equation for a in terms of b:

[tex]\begin{aligned}f(1)=a(1)^2+b(1)+15&=22\\a+b+15&=22\\a+b&=7\\a&=7-b\end{aligned}[/tex]

Therefore:

[tex]f(x)=(7-b)x^2+bx+15[/tex]

Finally, substitute another point from the table (-3, 6) and solve for b:

[tex]\begin{aligned}f(-3)=(7-b)(-3)^2+b(-3)+15&=6\\(7-b)9-3b+15&=6\\63-9b-3b+15&=6\\78-12b&=6\\-12b&=-72\\b&=6\end{aligned}[/tex]

Therefore, the value of b is 6.

Answer:

6

Step-by-step explanation:

Answer:

[tex]y = \frac{ - 1}{2} *\sqrt{x-1} - 5[/tex]

Step-by-step explanation:

The standard equation of a square root function with vertex at point (h,k) is given by:

[tex]y = a \times \sqrt{x - h} + k[/tex]

where (h,k) is the vertex and "a" is a coefficient that determines the vertical stretch and direction of the square root function.

We know that the vertex of our square root function is (1, -5), so we can substitute those values into the equation to get:

y = [tex] a*\sqrt{x-1} - 5[/tex]

Now, we need to find the value of "a". To do that, we will use the fact that the square root function passes through point (5, -7). Substituting these coordinates into the equation, we get:

[tex]-7 = a*\sqrt(5-1) - 5[/tex]

-2 = 4a

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

Now that we know the value of "a", we can substitute it into our equation to get the final equation of the square root function:

[tex]y = \frac{ - 1}{2} *\sqrt{x-1} - 5[/tex]

Therefore, the equation of the square root function with a vertex at (1, -5) and passing through (5, -7) is

[tex]y = \frac{ - 1}{2} *\sqrt{x-1} - 5[/tex]

Answer:

[tex]f(x) = -\sqrt{x-1} - 5[/tex]

Step-by-step explanation:

The standard form of a square root function is:

[tex]f(x)=a\sqrt{x-h}+k[/tex]

where "a" is a scaling factor determining the vertical stretch or compression of the function, and (h, k) is the vertex.

Given the vertex is (1, -5), substitute h = 1 and k = -5 into the equation:

[tex]f(x) = a\sqrt{x - 1} - 5[/tex]

Substitute the point (5, -7) that the function passes through to find the stretch factor "a":

[tex]\begin{aligned}-7 &= a \sqrt{5 - 1} - 5\\-7 &= a \sqrt{4} - 5\\-7 &= 2a - 5\\-7 +5&= 2a - 5+5\\-2&= 2a\\\dfrac{-2}{2}&=\dfrac{2a}{2}\\-1&=a\\a &= -1\end{aligned}[/tex]

Substitute the value of "a" back into the equation:

[tex]f(x) = -\sqrt{x-1} - 5[/tex]

Therefore, the equation of the square root function with a vertex at (1, -5) and passes through the point (5, -7) is:

[tex]\boxed{f(x) = -\sqrt{x-1} - 5}[/tex]

We can use Newton's law of cooling to solve this problem:

T(t) = T_a + (T_0 - T_a) * e^(-kt)

where T(t) is the temperature of the object at time t, T_a is the ambient temperature, T_0 is the initial temperature of the object, and k is a constant. We can solve for k by using the information that the object cools from 200 degrees to 131 degrees in 5 minutes:

131 = 20 + (200 - 20) * e^(-5k)

Simplifying this equation, we get:

e^(-5k) = 0.625

Taking the natural logarithm of both sides, we get:

-5k = ln(0.625)

k = -ln(0.625) / 5

k ≈ 0.1078

Now we can use this value of k to find the temperature of the object after 9 minutes:

T(9) = 20 + (200 - 20) * e^(-0.1078 * 9)

T(9) ≈ 94.9 degrees Celsius

Therefore, the temperature of the object at the end of 9 minutes will be approximately 94.9 degrees Celsius.

We can see here that filling up the remaining spaces:

AB ≅ CD: Opposite sides are congruent.

∠ABC and ∠BCD are supplementary: Consecutive angles are supplementary.

An angle is actually known to be a geometric figure that is formed by the joining together of two rays or endpoints which are known as vertex.

The sides or legs of the angle are known to be make up the rays.

Angles are actually known to be measured in degrees, with a full circle containing 360 degrees.

Learn more about angle on https://brainly.com/question/25716982

#SPJ1

The approximate population after 3 years is 1526.

Given that, principal=820, rate of interest=23% and time period=3 years.

If a constant rate of growth be R% per annum, then population after n years = P(1+R/100)ⁿ.

Here, population after 3 years is 820(1+23/100)³

= 820×1.23³

= 820×1.860867

= 1525.91094

≈ 1526

Therefore, the approximate population after 3 years is 1526.

To learn more about the population increase and decrease visit:

https://brainly.com/question/27779235.

#SPJ1

All the four ordered pairs that relate the side length of a pentagon to the perimeter of the pentagon are,

⇒ (1, 5) (2, 10) (3, 15) (4, 20)

Given that;

Fernando also learns in math class that the rule Add 1 to the side length of a pentagon with equal sides length results the rule Add 5 to the perimeter.

Now,

Here are four ordered pairs that relate the side length of a pentagon to the perimeter of the pentagon:

⇒ (1, 5) (2, 10) (3, 15) (4, 20)

Hence, In each pair, the first number represents the side length of the pentagon, and the second number represents the perimeter of the pentagon.

And,  If you add 1 to the side length in each pair, you'll see that the perimeter increases by 5, just as Fernando learned in math class.

Learn more about the coordinate visit:

https://brainly.com/question/24394007

#SPJ1

The distance between the points G and H is D = 8 units

Given data ,

Let the distance between 2 points be represented as D

Now , let the first point be G ( 0 , 8 )

Let the second point be H ( 8 , 8 )

Now , let the distance between G and H be D , where

D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)

D = √ ( 0 - 8 )² + ( 8 - 8 )²

D = √64 units

D = 8 units

Hence , the distance is 8 units

To learn more about distance between two points click :

https://brainly.com/question/12661159

#SPJ1

Answer:

World's Fair. Is the correct answer

The equation that best represents the population of the town, which increases exponentially at the rate of 6% every year, after x years is C. y = 158,260(1.06)ˣ.

Exponential growth refers to a constant percentage or rate of growth per period.

The opposite of exponential growth is exponential decay and refers to the constant rate of decay in value per period.

The town's initial population = 158,260

Growth rate per year = 6%

Let x = the number of years of growth

Let y = the population after x years

y = 158,260(1 + 0.06)^x

Thus, the correct equation representing population growth after x years is Option C.

Learn more about exponential growth equations at https://brainly.com/question/2456547.

#SPJ1