The Local maxima and minima will be at X = 0 , 4 , -5 and point of inflation will be at [tex]\frac{(-1 + \sqrt{61})}{3},[/tex] [tex]\frac{(-1 - \sqrt{61})}{3}[/tex].
What is Maxima and Minima ?The curve of a function has peaks and troughs called maxima and minima. A function may have any number of peaks and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph. Maxima will be the curve's highest point within the specified range, while minima will be its lowest.
Extrema is the result of maxima and minima combined. The graph in the graphic below shows several peaks and falls. We obtain the function's maximum and lowest values at x = a and 0 respectively, and at x = b and c respectively. The valleys are the minima and all the peaks are the maximum.
The peaks and minima of the function that appear in a certain interval are known as local maxima and minima. The value of a function at a place in a certain interval for which the values of the function near that point are always smaller than the value of the function at that point would be considered a local maximum. Local minima, on the other hand, would be the value of the function at a location where the values of the function nearby are higher than the value of the function at that location.
When the concavity of a function's graph (or picture) changes, a point of inflection is identified. We need to determine where the second derivative of the function switches from negative to positive, or vice versa, in order to determine this in algebra. So, we calculate the provided function's second derivative.
The fuction is :
[tex]3x^{4} + 4x^{3} -120x^{2} + 120[/tex]
So for local Maxima and minima first derivatives should be zero
Therefore,
[tex]\frac{d}{dx}\\[/tex] ([tex]3x^{4} + 4x^{3} -120x^{2} + 120[/tex] ) = 0
⇒ [tex]12x^{3} + 12x^{2} - 240x = 0[/tex]
⇒ [tex]x^{3} + x^{2} - 20x = 0[/tex]
⇒[tex]x(x^{2} + x - 20) = 0 \\[/tex]
⇒x(x-4)(x+5) = 0
For x = 0, 4 , -5 there is a local maxima or minima.
Now for Point of Inflation second derivative is zero
Therefore,
[tex]\frac{d^{2} }{dx^{2} }[/tex] ( [tex]3x^{4} + 4x^{3} -120x^{2} + 120[/tex]) = 0
⇒ [tex]\frac{d}{dx}[/tex][tex]12x^{3} + 12x^{2} - 240x = 0[/tex]
⇒ [tex]36x^{2} + 24x - 240 = 0[/tex]
⇒[tex]3x^{2} + 2x - 20 = 0[/tex]
⇒ x = [tex]\frac{(-1 + \sqrt{61})}{3},[/tex] [tex]\frac{(-1 - \sqrt{61})}{3}[/tex]
So the point of inflations are [tex]\frac{(-1 + \sqrt{61})}{3},[/tex] [tex]\frac{(-1 - \sqrt{61})}{3}[/tex].
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Write the expression \[\frac{4+6a}{5}-\frac{1+3a}{4}\] as a single fraction.
The expression [tex]\[\frac{4+6a}{5}-\frac{1+3a}{4}\][/tex] as a single fraction is [tex]\frac{9a-11}{20}[/tex]
What is algebraic expression ?
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
According to question
⇒ [tex]\[\frac{4+6a}{5}-\frac{1+3a}{4}\][/tex]
⇒ taking LCM of 4, 5 = 20
now [tex]\[\frac{4(4+6a)-5(1+3a)}{20}[/tex]
⇒ (16 +24a - 5 - 15a)/20
⇒ ((24a - 15a) - (16-5))/20
⇒ (9a - 11)/20
hence, the expression [tex]\[\frac{4+6a}{5}-\frac{1+3a}{4}\][/tex] as a single fraction is [tex]\frac{9a-11}{20}[/tex]
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Leon Starr purchased 55 shares of stock at
$41.09 per share. His online stockbroker charged him
a $15.99 commission. What is the total amount that he
paid for the stock?
Total amount paid for the stock:
Answer: $2,275.94
Step-by-step explanation: First, we need to find how much he pays for the stocks alone. So, we would use this equation:
41.09(55)
41.09 x 55
That would get us to $2,259.95. Now, we have to add the $15.99, bc he had to pay a fee. So $2,259.95 + 15.99 = $2,275.94. I hope this helped!
If a loading ramp is placed next to a truck, at a height of 8 feet, and the inclined portion of the ramp is 23 feet long, what angle (in degrees) does the ramp make with the ground?
Answer:
≈20.35°
Step-by-step explanation:
height = 8
hypotenuse =23
angle is x
sin(x) =8/23
[tex]sin^{-1} (\frac{8}{23} )[/tex] ≈20.35°
x is about ≈20.35°
The ramp makes an angle of approximately 20.86 degrees with the ground.
Given that there is a truck with a ramp at a height of 8 feet the size of the ramp is 23 feet,
we need to find the angle ramp make with the ground.
To find the angle that the ramp makes with the ground, we can use the sine function.
The sine of an angle is equal to the opposite side divided by the hypotenuse in a right triangle.
In this case, the opposite side is the height of the ramp (8 feet), and the hypotenuse is the length of the inclined portion of the ramp (23 feet).
Let's calculate the angle:
sin(angle) = opposite/hypotenuse
sin(angle) = 8/23
To find the angle, we need to take the inverse sine (or arcsine) of both sides of the equation:
angle = arcsin(8/23)
We can find the approximate value of the angle:
angle ≈ 20.86 degrees
Therefore, the ramp makes an angle of approximately 20.86 degrees with the ground.
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11. A triangle has a base length of 3.9 cm and a height of 9 cm. Which dimensions could
be the measurements of a similar triangle?
The dimensions that could be the measurements of a similar triangle are; base = 7.8 cm and height = 18 cm
How to Identify a similar triangle?Two triangles are said to be similar provided that they have the same ratio of corresponding sides and an equal pair of corresponding angles.
Now, we are given the side lengths of the triangle as a base length of 3.9 cm and a height of 9 cm.
Thus, this means that a similar triangle will have same ratio of side lengths. Thus;
If new height is h and new base is b, then we have;
9/h = 3.9/b
Thus,
h/b = 9/3.9
If we multiply the right side top and bottom by 2, then we have;
h/b = 18/7.8
18 and 7.8 cm could be similar dimensions.
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Given the points (1, -4) and (4, 5), construct two equations in point slope form using each of the points. Construct and upload the graph of the line. Show your work and upload your graph for your teacher to review.
The equation of line passes through the points (1, -4) and (4, 5) will be;
⇒ y = 3x - 7
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (1, -4) and (4, 5).
Now,
Since, The equation of line passes through the points (1, -4) and (4, 5)
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (5 - (-4)) / (4 - 1)
m = 9 / 3
m = 3
Thus, The equation of line with slope 3 is,
⇒ y - (-4)= 3 (x - 1)
⇒ y + 4 = 3x - 3
⇒ y = 3x - 3 - 4
⇒ y = 3x - 7
Therefore, The equation of line passes through the points (1, -4) and (4, 5) is given as;
⇒ y = 3x - 7
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Can anyone help me ASAP?
Answer:
Equation 1 - x + 4y = 12
Equation 2 - 2x + 4x = 16
Cost of 1 Cheeseburger - $4
Cost of 1 Taco - $2
Step-by-step explanation:
Cheeseburger(x) and Taco(y)
x + 4y = 12 and 2x + 4y = 16
x = - 4y + 12
2(- 4y + 12) + 4y = 16
- 8y + 24 + 4y = 16
- 4y = - 8
y = 2
x + 4(2) = 12
x + 8 = 12
x = 4
A company has computed a seasonal index for its quarterly sales. Which of the following statements is not correct?
Multiple Choice
The sum of the four quarterly seasonal index numbers is 4.
The index for any quarter must be between 0 and 2.
The average index is 1.
An index of 0.75 for quarter-one sales indicates that sales were 25 percent lower than average sales.
An index of 1.10 indicates sales 10% above the norm.
The option b "The index for any quarter must be between 0 and 2" is correct.
In the given question, we have to find the incorrect statement about a company has computed a seasonal index for its quarterly sales.
For its quarterly sales, the corporation has created a seasonal indicator.
Consequently, it is correct that the four quarterly seasonal index figures add up to 4.
True, the average index is 1.
In this situation, an index of 0.75 for the first quarter's sales implies that they were 25% below average, while an index of 1.10 shows that they were 10% over average.
Hence, the incorrect statement of the option b "The index for any quarter must be between 0 and 2" is correct.
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Evaluate the expression for the given value of the variable 4c - 3. C= -2
Answer:
-11
Step-by-step explanation:
4c - 3 Substitute -2 for c
4(-2) - 3
-8 - 3
-11
Answer:
-11
Step-by-step explanation:
We are given the value of c, so we just need to plug it in. We can do this by replacing "c" with "-2" in our given expression.
4c - 3 ⇒ 4(-2) - 3
Now, we can simplify this.
-8 - 3 = -11
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find two polynomials whose difference is 2x^2 + x + 4
The two polynomials whose difference is 2x^2 + x + 4 are
6x² + 3x + 5 and 4x² + 2x + 1.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
The difference between the two polynomials is 2x² + x + 4.
The two polynomials are:
6x² + 3x + 5 _____(1)
4x² + 2x + 1 ______(2)
The difference between (1) and (2)
6x² + 3x + 5 - 4x² - 2x - 1
2x² + x + 4
Thus,
The two polynomials are 6x² + 3x + 5 and 4x² + 2x + 1.
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I could really use some help I got 10 mins left on quiz please help
The value of x in the problem is 0
Given that PQR is a straight line
In this problem PQ+QR=PR
The value of PQ is 9
The value of QR is not given but given an equation 2x+3
And QR is x+12
So PQ+QR=PR
9+2x+3=x+12
12+2x=x+12
2x-x=12-12
x=0
Therefore, the value of x in the problem is 0
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The Picture and Sound electronics store has hired Brennan to work in the warehouse. He uses a pulley with a hand crank to lift heavy boxes. He turns the crank 15 times to lift a box 15 feet. He turns the crank 45 times to lift a box 45 feet.
In this relationship, x represents the number of times Brennan turns the crank to lift a box, and y represents the height the box has been lifted (in feet).
Graph two points for this relationship and the line passing through them.
The graph (created with MS Excel) of the height the box is lifted to the number of times Brennan turns the crank to lift the box which is the graph of the proportional relationship, y = x, is attached.
What is a proportional relationship?A proportional relationship is one in which one variable (the output variable) is a constant multiple of the another variable known as an input variable.
The number of times Brennan turns the crank = x
The height to which the box is lifted = y
The points on the graph are; (15, 15), and (45, 45)
The ratio of the y-values to the x-values is 15/15 = 45/45 = 1, which indicates that the relationship is a proportional relationship
A point on the graph of a proportional relationship is the point (0, 0), therefore, the points on the graph are; (0, 0), (15, 15), and (45, 45)
Please find attached the graph of the proportional relationship between the number of times Brennan turns the crank to the height to which the box is lifted created with MS Excel
The relationship between the variables x and y is; y = x
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what is 309x317/9-4+7/8x3
[tex]340.11[/tex] or [tex]\frac{32651}{96}[/tex].
Step-by-step explanation:1. Write the expression.[tex]\frac{(\frac{309*317}{9-4+7})}{8x3}[/tex]
3. Solve the main denomonator.[tex]\frac{(\frac{309*317}{9-4+7})}{24}[/tex]
4. Solve the secondary denominator.[tex]\frac{(\frac{309*317}{12})}{24}[/tex]
5. Solve the secondary numerator.[tex]\frac{(\frac{97953}{12})}{24}[/tex]
6. Solve the main numerator.[tex]\frac{(8162.75)}{24}[/tex]
7. Simplify the fraction.[tex]340.11[/tex] or [tex]\frac{32651}{96}[/tex].
evaluate the six trigonometric functions at 11pi/3. (give an exact answer, not a decimal approximation.)
The six trigonometric functions at 11π/3 are as follows-
sin (11π/3) = -[tex]\sqrt{3}[/tex]/2
cos (11π/3) = 1/2
tan (11π/3) = -[tex]\sqrt{3}[/tex]
cot (11π/3) = -1/[tex]\sqrt{3}[/tex]
sec (11π/3) = 2
cosec (11π/3) = -2/ [tex]\sqrt{3}[/tex]
Let us evaluate the six trigonometric functions at 11π/3 as follows -
11π/3 can be written as (6π+5π)/3 = 2π + 5π/3.
a. sin (11π/3) = sin (2π + 5π/3)
this angle is greater than or equal to 0 and less than 2π.
= sin (5π/3)
Finding the angle with equivalent trigonometric values in the first quadrant. Also, sin is negative in the 4th quadrant.
= -sin (π/3)
= -[tex]\sqrt{3}[/tex]/2
Hence, sin (11π/3) = -[tex]\sqrt{3}[/tex]/2
b. cos (11π/3) = cos (2π + 5π/3)
this angle is greater than or equal to 0 and less than 2π.
= cos (5π/3)
Finding the angle with equivalent trigonometric values in the first quadrant. Also, cos is positive in the 4th quadrant.
= cos (π/3)
= 1/2
Hence, cos (11π/3) = 1/2
c. tan (11π/3) = tan (2π + 5π/3)
this angle is greater than or equal to 0 and less than 2π.
= tan (5π/3)
Finding the angle with equivalent trigonometric values in the first quadrant. Also, tan is negative in the 4th quadrant.
= -tan (π/3)
= -[tex]\sqrt{3}[/tex]
Hence, tan (11π/3) = -[tex]\sqrt{3}[/tex]
d. cot (11π/3) = 1/ tan (11π/3)
Hence, cot (11π/3) = - 1/ [tex]\sqrt{3}[/tex]
e. sec (11π/3) = 1/ cos (11π/3)
Hence, sec (11π/3) = 2
f. cosec (11π/3) = 1/ sin (11π/3)
Hence, cosec (11π/3) = -2/ [tex]\sqrt{3}[/tex]
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a line passes through the point (-6,3) and has a slope of 3/2
The equation of slope intercept form is y = 3/2x + 12 if a line passes through the point (-6,3) and has a slope of 3/2.
Define slope intercept form.The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation. The slope, m, is a measure of how steep a line is. The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables.
Given
A line passes through the point (-6,3)
and has a slope of 3/2
Slope intercept form
y = mx + b
Equation,
y - 3 = 3/2(x - (-6))
y - 3 = 3/2(x+6)
2y - 6 = 3x + 18
2y = 3x + 24
y = 3/2x + 12
The equation of slope intercept form is y = 3/2x + 12 if a line passes through the point (-6,3) and has a slope of 3/2.
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What is the area of this triangle?
Enter your answer in the box.
units?
Answer:
Below
Step-by-step explanation:
If you turn it sideways and use the y-axis portion as the base (4) , you can see height = 5
Area = 1/2 * b * h = 1/2 * 4 *5 = 10 units^2
A reactor coolant tank is being filled with coolant at the rate of 400 gallons per hour with t>0 measure in hours. If the tank originally contained 200 gallons of coolant, approximately how many gallons are in the tank after 8 hours?
The gallons after 8 hours will be 3400 gallons.
How to illustrate the expression?Expression refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
Numbers, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations.
In this case, the reactor coolant tank is being filled with coolant at the rate of 400 gallons per hour with t>0 measure in hours.
Therefore, the gallons after 8 hours will be:
= 200 + 400(8)
= 200 + 3200
= 3400 gallons.
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HELP ASAP
3. If the aspect ratio of a tire is 50%, width 10 inches, and the rim diameter is 19 inches, what is the tire diameter?
a. 59in b. 35.8in
d. 49in
4. The standard print paper is 11" by 8.5 in. What is the aspect ratio of a standard print paper?
a. 11:8
c. 8.5
c. 29 in
b. 22:17
d. 11
3) The tire diameter using the aspect ratio is; 29 inches
4) The aspect ratio of a standard print paper is; 22:17
How to solve aspect ratio problems?The aspect ratio is defined as the relationship between the width and height.
Now, in this case, the aspect ratio must be in whole numbers and not decimals and as such we can solve as follows;
3) We are told that the aspect ratio of a tire is 50%.
Thus, the aspect ratio is; 50/100 = 1/2 or 1:2.
Now, we are told that width 10 inches, and the rim diameter is 19 inches, then it means that the tire diameter = 10/2 + 19 + 10/2 = 29 inches
4) The standard print paper is 11" by 8.5. This can also be written as;
11 by 17/2 or 11 * 2 : 17
= 22:17
This then gives us the aspect ratio.
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NO LINKS!! Please help me with this problem. Part 1gg
Answer:
Graph A
Step-by-step explanation:
Given piecewise function:
[tex]f(x)=\begin{cases}9+x, \;\;\:\:x\leq3\\x^2+3,\;\;x > 3\end{cases}[/tex]
To graph the given piecewise function:
Draw the line y = 9 + x for the domain (-∞, 3].Draw the curve y = x² + 3 for the domain (3, ∞).The line y = 9 + x is a straight line with a positive gradient.
It crosses the x-axis at (-9, 0) and crosses the y-axis at (0, 9).
Therefore, the only graph that shows the line y = 9 + x is the first graph.
Knowledge Check
Find x
x=
Answer:
x is 44 Hope that helps.
Solve the system if we x-3y=0 and 3x-6y=9 by combining the equations.
Step-by-step explanation:
Hope u get it x=3×3
x=9
It didn't include in the photo
exercise 28 a sample of 20 joint specimens of a particular type gave a sample mean proportional limit stress of 8.52 mpa and a sample standard deviation of 0.78 mpa.
A 95% % lower confidence bound for the true average proportional limit stress of all such joints is 8.01.
In the given question, a sample of 20 joint specimens of a particular type gave a sample mean proportional limit stress of 8.52 mpa and a sample standard deviation of 0.78 mpa.
We have to calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints.
Sample size: n = 13
Sample mean: x’ = 8.52 mps
Sample standard deviation: s = 0.78 mps
95% lower confidence bound for the true average proportional limit stress of all such joints
Level of Significance (α) = 1-95% = 5% = 0.05
α/2 = 0.025
So the value of t(α/2) = 1.8
The confidence interval = x’± t(α/2)*s/√n
Now putting the value:
The confidence interval = 8.41± (1.8)*(0.78)/√12
The confidence interval = 8.41± (1.8)*(0.226)
The confidence interval = 8.41± 0.4068
The confidence interval = (8.41- 0.4068, 8.41+ 0.4068)
The confidence interval = (8.01, 8.82)
A 95% % lower confidence bound for the true average proportional limit stress of all such joints is 8.01.
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The right question is:
A sample of 12 joint specimens of a particular type gave a sample mean proportional limit stress of 8.41 mpa and a sample standard deviation of 0.78 mpa.
Calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints. (Round your answer to two decimal places.)
Period:
9) Maria walked 20 miles yesterday. Today she walked 30 miles. What was the percent of increase Maria walked?
10) Pedro goes to 70 % of the basketball teams games. If the basketball team plays 20 games, how many did he go to?
11) Your bill at a restaurant comes to $ 24.00. You want to leave a 15% tip. What is your final bill?
12) Monica wants to buy a bag of Taxis for $13.50. If the store is having a discount of 20% off, how much is she spending?
13) How much interest is earned on $ 100 at 70 % for 9 years?
14) How much interest is earned on a $42 investment at 5 % for three years?
The percent of increase Maria walked if found as the 50%.
Explain the term percent increase?The amount that a percentage has increased over time is expressed as a percent increase.One would need to figure out the difference between the initial value and the final value, subtract to determine the precise sum of the drop, in order to arrive at this amount.The formula for the percentage increase is given as;
Percent increase = Increase / original number x 100
original number = 20 miles
Increase = 30 miles - 20 miles
Increase = 10 miles
So,
Percent increase = 10 / 20 x 100
Percent increase = 50%
Thus, the percent of increase Maria walked if found as the 50%.
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The correct question is-
9) Maria walked 20 miles yesterday. Today she walked 30 miles. What was the percent of increase Maria walked?
Graph the rational function Start by drawing the vertical and horizontal asymptotes. Then plot two points on each piece of the graph. Finally, click on the graph-a-function button X ?
The horizontal and vertical asymptotes for the function f(x) =6/(-2x +1) is equal to y = 0 and x = 1/2 respectively.
Graph is attached.
As given in the question,
Given function is :
f(x) =6 /(- 2x +1)
f(x) = y
Degree of the numerator is zero
Degree of the denominator is 1.
Degree of denominator is greater than the degree of numerator.
Function represent the horizontal asymptotes for y =0
To get the vertical asymptotes equate denominator equals to zero
(- 2x +1) = 0
⇒2x = 1
⇒x = 1/2
Vertical asymptotes is given by x =1/2.
Graph is attached.
Therefore , the horizontal and vertical asymptotes for the given function is equal to y=0 and x =1/2 respectively.
The above question is incomplete, the complete question is:
Graph the rational function. f(x) =6 /(- 2x +1) Start by drawing the vertical and horizontal asymptotes. Then plot two points on each piece of the graph. Finally, click on the graph-a-function button X.
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for the independent-measures t test, which of the following describes the estimated standard error of the difference in sample means (whose symbol is
For an independent-measures t test, the option that describes the estimated standard error of the difference in sample means is D. an estimate of standard distance between the difference in the sample mean and the difference in the corresponding population mean.
What is a T test?A statistical test called a t test is employed to compare the means of two groups. It is frequently employed in hypothesis testing to establish whether a procedure or treatment actually affects the population of interest or whether two groups differ from one another.
The Independent Samples t Test compares the means of two separate groups to see if there is statistical support that the population mean values are statistically significantly different. A parametric test is called the Independent Samples t Test. For instance, you could determine whether first-year graduate salaries varied by gender using an independent t-test.
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Complete question
for the independent-measures t test, which of the following describes the estimated standard error of the difference in sample means (whose symbol is
a. a weighted average of the two sample
b. the difference between the standard deviationa
c. The variance
d. an estimate of standard distance between the difference in the sample mean and the difference in the corresponding population mean.
an application is using a two-dimensional list defined as follows: write a statement that creates an empty two-dimensional list named values with 4 rows and 3 columns. write nested loops that get an integer value from the user for each element in the list, example: values
Complete Question :
An application is using a two-dimensional list defined as follows: 1. Write a statement that creates an empty two-dimensional list named values with 4 rows and 3 columns. 2. Write nested loops that get an integer value from the user for each element in the list, for example: values= [[1, 2, 3], [10, 20, 30], [100, 200, 300],[1000, 2000, 3000]] 3. Write a function named row_values that accepts values as argument and returns the sums of each row and displays the result as a list named row 4. Write a function named column_values that accepts values as arguments and returns the sums of each column and displays the result as a list named column 5. Write a function called sum_values that sums all the elements of the array and displays the result.
Sum of rows : [ 6, 60, 600, 6000 ]
Sum of columns : [ 1111, 2222, 3333]
Sum of all elements : 6666
The nested loops are :
Enter a number at row 0, and column 0 : 1
Enter a number at row 0, and column 1 : 2
Enter a number at row 0, and column 2 : 3
Enter a number at row 1, and column 0 : 10
Enter a number at row 1, and column 1 : 20
Enter a number at row 1, and column 2 : 30
Enter a number at row 2, and column 0 : 100
Enter a number at row 2, and column 1 : 200
Enter a number at row 2, and column 2: 300
Enter a number at row 3, and column 0 : 1000
Enter a number at row 3, and column 1 : 2000
Enter a number at row 3, and column 2 : 3000
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From a hot-air balloon, Violet measures a 24° angle of depression to a landmark
that's 806 feet away, measuring horizontally. What's the balloon's vertical distance
above the ground? Round your answer to the nearest tenth of a foot if necessary.
The balloon's vertical distance above the ground is 358.9 feet.
An angle is said to be that of depression when it is measured downwards with respect to the horizontal plane.
So that applying the appropriate trigonometric function to solve the question, we have;
Tan θ = Opposite side/ Adjacent side
But,
θ = 90 - 24
= 66
θ = [tex]66^{o}[/tex]
Let the vertical distance of the balloon be represented by x.
Tan 66 = 806/ x
x = 806/ Tan 66
= 806/ 2.246
= 358.86
x = 358.9 feet
The balloon's vertical distance above the ground is 358.9 feet.
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PLEASE ANSWERE ASAP
If BC = 16.7 ft, what is AY?
The length of segment AY is 16.7 ft if the length of segment BC is 16.7 ft
How to determine the length of the side length AYFrom the question, we have the following parameters that can be used in our computation:
BC = 16.7 ft
The measures of the angles are not given
However, the marks on the side lengths imply that:
The points A, B and C divides the line segments XY, XZ and YZ into equal segmentsThe parallel segments are equal segmentsUsing the above as a guide, we have the following:
AY = BC
This is because these segments are parallel segments
Recall that parallel segments are equal segments
Substitute the known values in the above equation, so, we have the following representation
AY = 16.7
Hence, the length of AY is 16.7 ft
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A laser rangefinder is locked on a comet approaching Earth. The distance g(x) , in kilometers, of the comet after x days, for x in the interval 0 to 42 days, is given by g(x)=300,000csc(π42x) .
a. The blue line represents g(x) = 250,000csc(π30x).
b. g(5) = 25,000 km. This is the distance of the comet from Earth after 5 days.
c. The minimum distance between the comet and Earth is 250,000 km, which occurs when x = 0. This corresponds to the constant csc(π30x).
d. The equation has a vertical asymptote at x = 30/π.
Write the solution to following questions:a. Graph the value of x on the range [0,35].b. Analyze g(5) and explain the results.c. What is the shortest path the comet must take to reach Earth? When does this take place? What equation constant does this match up to?d. Find any vertical asymptotes and explain their significance.a. Graph g(x):
To graph g(x), we can plot several points on the interval [0,35] and then connect them to form a graph of the function. For example, we can plot the points (0,250,000), (5,50,000), (10,25,000), (15,16,667), (20,12,500), (25,10,000), (30,8,333) and (35,7,143). Connecting these points will give us a graph of the function g(x).
b. Evaluate g(5):
The value of g(5) can be found by plugging in x = 5 into the equation: g(5) = 250,000 csc(π30*5) = 50,000 km. This means that after 5 days, the comet will be 50,000 km away from Earth.
c. Minimum distance between the comet and Earth:
The minimum distance between the comet and Earth can be found by taking the derivative of the equation and setting it to 0.
d. Vertical Asymptotes:
The vertical asymptotes of g(x) occur at x = 0 and x = 30. This means that the comet approaches an infinitely large distance from Earth at x = 0 and x = 30.
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In a storage locker, there are 15 large boxes and 26 small boxes. The large boxes each weigh 24 pounds. The small boxes each weigh 16 pounds. How much do all of the boxes weigh altogether?
Answer:
864
Step-by-step explanation:
Graph the solution of the inequality on a number line.
2(x − 3) – 5x < x-2
Ο
Α.
OB.
OC
OD.
℗
-5 -4 -3 -2 -1 0 1 2
←
+1
-5 -4 -3 -2 -1 0 1
#2
0111
1
-5 -4 -3 -2 -1 0
2
3 4 5
3 4 5
3 4
+
5
4
110111
-5 -4 -3 -2 -1 0 1 2 3 4 5
Answer:
Choice D : x > - 1
Step-by-step explanation:
Left hand side (LHS) of the inequality can be siimplified
[tex]2\left(x-3\right)-5x = 2x - 6 - 5x = -3x -6\\\\[/tex]
Inequality becomes
[tex]-3x-6 < x-2[/tex]
Move x to the left side and -6 to the right side:
[tex]-3x - x < -2 + 6\\\\-4x < 4\\\\[/tex]
Multiply both sides by -1(the inequality sign changes to >)
[tex]4x > -4\\\\[/tex]
Divide both sides by 4:
[tex]x > -1[/tex]
The number line corresponding to this is the fourth choice
