The length of minor arc AC is calculated by finding the proportion of the total circumference that the arc's angle represents. In this case, the length of minor arc AC is 3π units.
Explanation:In circle geometry, the length of an arc (minor arc AC in this case) is proportional to the measure of its central angle. By knowing the central angle and the circumference of the circle, we can calculate the length of the arc. The formula for the circumference of a circle is 2πr, where r is the radius. In this case, AB is the radius, which equals to 15 units. So the circumference of the circle would be 2π * 15 = 30π units.
Now, the measure of the entire circle in terms of degrees is 360º. The measure of AC is given as 36º. Hence, minor arc AC is 36º out of the total 360º, which is (36/360) = 1/10. Therefore, the length of minor arc AC would be 1/10 of the total circumference.
Calculating the length of minor arc AC would be = 1/10 * 30π = 3π units.
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An open-top bin is to be made from a 15-centimeter by 40-centimeter piece of plastic by removing a square from each corner of the plastic and folding up the flaps on each side. What size square should be cut out of each corner to get a bin with the maximum volume?
No squares should be cut. Maximum volume is zero. Dimensions remain 15cm by 40cm by 0cm.
To find the size of the square that should be cut out from each corner to maximize the volume of the bin, we need to follow these steps:
1. Understand the problem : We have a rectangular piece of plastic with dimensions 15 cm by 40 cm. By removing squares from each corner and folding up the flaps, we can form an open-top bin. We want to find the size of the squares to be cut out to maximize the volume of the bin.
2. Define variables : Let's denote the side length of the square to be cut out from each corner as [tex]\( x \)[/tex] cm.
3. Express the volume of the bin : After cutting out squares and folding up the flaps, the dimensions of the resulting bin will be [tex]\( (15 - 2x) \)[/tex] cm by [tex]\( (40 - 2x) \)[/tex] cm by [tex]\( x \)[/tex] cm. So, the volume of the bin can be expressed as: [tex]\[ V = x(15 - 2x)(40 - 2x) \][/tex]
4. Maximize the volume: To find the maximum volume, we need to find the critical points of the function [tex]\( V \)[/tex]. We'll take the derivative of [tex]\( V \)[/tex] with respect to [tex]\( x \)[/tex], set it equal to zero, and solve for [tex]\( x \)[/tex].
[tex]\[ \frac{dV}{dx} = (15 - 2x)(40 - 2x) + x(-4)(40 - 2x) + x(15 - 2x)(-4) \][/tex]
[tex]\[ 0 = (15 - 2x)(40 - 2x) - 8x(40 - 2x) - 4x(15 - 2x) \][/tex]
5. Solve for [tex]\( x \)[/tex] : Solve the equation for [tex]\( x \)[/tex] to find the critical points.
[tex]\[ 0 = 600 - 70x + 4x^2 \][/tex]
[tex]\[ 0 = 4x^2 - 70x + 600 \][/tex]
Solve for [tex]\( x \)[/tex] using the quadratic formula:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
where [tex]\( a = 4 \)[/tex], [tex]\( b = -70 \)[/tex], and [tex]\( c = 600 \)[/tex].
[tex]\[ x = \frac{-(-70) \pm \sqrt{(-70)^2 - 4(4)(600)}}{2(4)} \][/tex]
[tex]\[ x = \frac{70 \pm \sqrt{4900 - 9600}}{8} \][/tex]
[tex]\[ x = \frac{70 \pm \sqrt{-4700}}{8} \][/tex]
Since the discriminant is negative, there are no real solutions for [tex]\( x \)[/tex] in this case. Therefore, we need to check the endpoints of our interval.
6. Check endpoints : Since [tex]\( x \)[/tex] must be non-negative and [tex]\( (15 - 2x) \)[/tex] and [tex]\( (40 - 2x) \)[/tex] must also be positive, the possible range for [tex]\( x \)[/tex] is [tex]\( 0 \leq x \leq 7.5 \)[/tex] cm.
When [tex]\( x = 0 \), \( V = 0 \)[/tex] (no bin is formed).
When [tex]\( x = 7.5 \), \( V = 7.5(15 - 2(7.5))(40 - 2(7.5)) = 7.5(0)(25) = 0 \)[/tex] (no bin is formed).
7. Conclusion : The maximum volume of the bin is achieved when no squares are cut out from the corners. Therefore, to maximize the volume, no squares should be cut out from the corners of the plastic, resulting in a rectangular prism with dimensions [tex]\( 15 \times 40 \times 0 \)[/tex] cm³, which does not form a bin.
So, the maximum volume of the bin is [tex]1000cm^3[/tex]
To maximize the volume of the bin, we need to determine the dimensions of the squares that should be cut out from each corner to form the bin. Let's denote the side length of the square to be cut out as
x centimeters.
When the squares are cut out and the flaps are folded up, the dimensions of the resulting bin can be expressed as follows:
Length of the bin: 40−2x centimeters
Width of the bin: 15−2x centimeters
Height of the bin (equal to the side length of the square cut out): x centimeters
The volume V of the bin is given by the product of its length, width, and height:
V=(40−2x)(15−2x)x
To find the maximum volume, we need to find the value of
x that maximizes this function. We can do this by taking the derivative of
V with respect to x, setting it equal to zero, and solving for x.
Let's find the derivative of V with respect to x:
[tex]$\frac{d V}{d x}=15(40-2 x)-2(15-2 x)(40-2 x)$[/tex]
Now, let's set the derivative equal to zero and solve for x:
[tex]$15(40-2 x)-2(15-2 x)(40-2 x)=0$[/tex]
After solving for x, we can substitute the value of
x back into the expression for the volume
V to find the maximum volume of the bin. Let's do these calculations.
First, let's simplify the derivative[tex]\frac{dv}{dx}[/tex]
[tex]$\begin{aligned} & \frac{d V}{d x}=15(40-2 x)-2(15-2 x)(40-2 x) \\ & =600-30 x-\left(30 x-4 x^2\right) \\ & =600-30 x-30 x+4 x^2 \\ & =600-60 x+4 x^2\end{aligned}$[/tex]
Now, we set the derivative equal to zero and solve for x:
[tex]$600-60 x+4 x^2=0$[/tex]
Dividing both sides by 4:
[tex]$150-15 x+x^2=0$[/tex]
Rearranging and factoring:
[tex]$$\begin{aligned}& x^2-15 x+150=0 \\& (x-10)(x-15)=0\end{aligned}$$So, $x=10$ or $x=15$.[/tex]
Since x=15 would result in a negative side length for the bin, we discard it.
Thus, the optimal size square to be cut out from each corner is 10 centimeters.We can then find the maximum volume
V by substituting x=10 into the volume formula:
[tex]$V=(40-2 \times 10)(15-2 \times 10) \times 10=(20)(-5) \times 10=1000 \mathrm{~cm}^3$[/tex]
So, the maximum volume of the bin is [tex]1000cm^3[/tex]
What are the coordinates of point C of the directed segment from A(-8,4) to B(10,-2) that partitions the segment such that AC:CB is 2:1?
Final answer:
To find the coordinates of point C that partitions the segment from A(-8,4) to B(10,-2) in the ratio 2:1, we use the formula for internal division of a line segment, resulting in the coordinates (4, 0).
Explanation:
The coordinates of point C that partitions the segment from A(-8,4) to B(10,-2) in the ratio 2:1 can be found using the formula for internal division of a line segment. Since AC:CB is 2:1, we consider the section ratio to be 2/3 and multiply it by the difference in the corresponding x and y coordinates of A and B, then add to the coordinates of point A.
The x-coordinate of point C is calculated as follows:
Cx = Ax + (Bx - Ax) * m/(m+n)
Where Ax is the x-coordinate of point A, Bx is the x-coordinate of point B, and m/n is the ratio (2/1 in this case), so m=2 and n=1.
Cx = (-8) + (10 - (-8)) * 2/(2+1) = -8 + 18 * 2/3 = -8 + 12 = 4
The y-coordinate of point C is calculated similarly:
Cy = Ay + (By - Ay) * m/(m+n)
Cy = 4 + ((-2) - 4) * 2/(2+1) = 4 + (-6) * 2/3 = 4 - 4 = 0
Thus, the coordinates of point C are (4, 0).
The radius of the water bottle is about _______cm.
Answer:
45.216
Step-by-step explanation:
2 x 3.14 x7.2
Answer:
Step-by-step explanation:
Volume of water bottle = 143 cubic cm
πr²h = 143
3.14*r²*7.2 = 143
[tex]r^{2}=\frac{143}{3.14*7.2}\\\\r^{2}=6.325\\[/tex]
r = 2.51
r = 2.5 cm
The top of the chimney needed to be replaced. The new top for the chimney will cost $800 plus $40 per hour for labor. If it took the chimney guy 75 minutes to complete the work, how much will Mrs. Bredice pay?
Answer:
Step-by-step explanation:
A rectangular page is to contain 24 sq. in. of print. The margins at the top and bottom of the page are each 1.5 inches. The margins on each side are 1 inch. What should the dimensions of the page be so that the least amount of paper is used
Answer:
Dimensions of page should be width of 6 inches and height of 9 inches
Step-by-step explanation:
Let x be the width of the printed part in inches
Let y be height of the printed part in inches.
Thus, Area of printed part; A = xy
And area of printed part is given as 24.
Thus, xy = 24
Making y the subject, we have;
y = 24/x
Now, the question says the top and bottom margins are 1.5 inches.
Thus, width of page = x + 1 + 1 = x + 2
And also the margins on each side are both 1m in length, thus the height of page will be:
y + 1.5 + 1.5 = y + 3
So area of page will now be;
A = (x + 2)•(y+3)
From earlier, we got y = 24/x
Thus,plugging this into area of page, we have;
A = (x + 2)•((24/x)+3)
A = 24 + 3x + 48/x + 6
A = 30 + 3x + 48/x
For us to find the minimum dimensions, we have to find the derivative of A and equate to zero
Thus,
dA/dx = 3 - 48/x²
Thus, dA/dx = 0 will be
3 - 48/x² = 0
Multiply through by x²:
3x² - 48 = 0
Thus,
3x² = 48
x² = 48/3
x = √16
x = 4 inches
Plugging this into y = 24/x,we have;
y = 24/4 = 6 inches
We want dimensions of page at x = 4 and y = 6.
From earlier, width of page = x + 2.
Thus,width = 4 + 2 = 6 inches
Height = y + 3 = 6 + 3 = 9 inches
So dimensions of page should be width of 6 inches and height of 9 inches
To minimize paper usage, we need to find the dimensions of the rectangular page. By setting up an equation and solving it, we can find the width and length of the page that result in the least amount of paper used.
Explanation:To minimize the amount of paper used, we need to find the dimensions of the page that will result in the smallest possible area. Let's assume the length of the page is 'L' inches and the width is 'W' inches. We can set up the equation:
Next, we can use the quadratic formula to solve for L:
To find the minimum value of L, we can consider the factors contributing to the uncertainty:
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Maria is making a candle in the shape of a cylinder. She wants the candle to have a height of 3 cm and a radius of 2 cm. How much wax does Maria need?
12 cm3
12 cm2
18 cm3
20 cm2
Answer:
V(cylinder) = πr²h
h=3 cm
r=2 cm
V(cylinder) = πr²h = π*2²*3 =12π cm³
Answer : 12π cm³.
Answer:
A
Step-by-step explanation:
12π cm³
A fertiliser is produced by mixing water and pesticide in the ratio of 9:3. The final quantity of fertiliser is 48 litres. What is the quantity of water and pesticide that is needed?
Answer:
Step-by-step explanation:
9 + 3 = 12
[tex]Water=\frac{9}{12}*48\\\\=9*4[/tex]
Water = 36 liters
Pesticide = 48 - 36 = 12 liters
Simplify the trigonometric function
Answer:
a. csc²θ
Step-by-step explanation:
You can use the identities ...
1 +tan² = sec²
cot = cos/sin
sec = 1/cos
csc = 1/sin
___
Then the expression becomes ...
[tex]\cot^2{\theta}(1+\tan^2{\theta})=\cot^2{\theta}\sec^2{\theta}=\dfrac{\cos^2{\theta}}{\sin^2{\theta}\cos^2{\theta}}=\dfrac{1}{\sin^2{\theta}}\\\\=\boxed{\csc^2{\theta}}[/tex]
A group of hikers climbed to the top of a mountain. They climbed 2000 feet each day for five days to get to the top. Approximately how many miles tall was the mountain?
Answer:
The mountain is 1.89 miles tall
Step-by-step explanation:
Firstly, we need to compute the value in feet of the total distance traveled by the group.
We were told they traveled 2000 feet per day for 5 days, the total distance they have hiked would be 2000 * 5 = 10,000 feet
Now, we need to convert this to miles
Mathematically ;
1 foot = 0.000189 mile
Hence, 10,000 feet = 10,000 * 0.000189 = 1.89 miles
This means the mountain is 1.89 miles tall
The radius of a circle is (7x+3)cm. Write an expression to represent the area of the circle in simplified form
Answer:
A = π(7x + 3)² cm²
Step-by-step explanation:
A = πr² is the appropriate equation. If r = 7x + 3 cm, then the area of this particular circle is:
A = π(7x + 3)² cm²
Final answer:
The area of a circle with radius (7x+3)cm is represented by the simplified expression 49x²π + 42xπ + 9π square centimeters.
Explanation:
To find the area of a circle with radius (7x+3)cm, we use the formula for the area of a circle, which is A = πr². So, substituting the given radius into this formula, we get:
A = π(7x+3)²
To simplify the expression, we square the binomial:
A = π(49[tex]x^2[/tex] + 42x + 9)
Therefore, the area of the circle in simplified form is 49[tex]x^2[/tex]π + 42xπ + 9π square centimeters.
an elevator at a construction site has a maximum capacity of 2500 pounds. if the elevator operator weights 160 pounds and each cement bag weighs 60 pounds, how many bags of cement can be safely lifted on the elevator in one trip?
Answer:
39 bags (at max)
Step-by-step explanation:
160 + 60x《2500
60x《2340
x《39
Answer: the answer would be 39 bags of cement
Step-by-step explanation: 2500- 160= 2340
2340/60 (each bag of cement) it equals 39
What is the volume of the prism shown below?
A rectangular prism with length of 6 inches, height of 7 inches, and width of 3 inches.
16 cubic inches
21 cubic inches
90 cubic inches
126 cubic inches
Answer:
The answer is 126!!! Hope I helped!!!
Step-by-step explanation:
1. 6 x 3 = 18
2. 18 x 7 = 126
Answer:
126
Step-by-step explanation:
Multiply 7 x 6 x 3 which is equal to 126.
Have a great day! Your amazing. I do a lot of answers on edg 6th grade.
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Each month. Diana donates the same amount of money to a charity. If she donates 1,500 in one year, how much does she donate each month?
Answer: $125
Step-by-step explanation:
1500/12=125
Micah recorded the amount of time his mom and dad spend reading bedtime stories. He plotted the data in the box plot below.
A box plot titled Minutes mom spends reading. The number line goes from 10 to 25. The whiskers range from 13 to 25, and the box ranges from 15 to 19. A line divides the box at 16.
Minutes Mom Spends Reading
A box plot titled Minutes dad spends reading. The number line goes from 10 to 25. The whiskers range from 11 to 19, and the box ranges from 12 to 15. A line divides the box at 13.
Minutes Dad Spends Reading
Which is an accurate comparison of the two data sets?
The lengths of time that his mom reads are typically longer and have less variability than the lengths of time that his dad reads.
The lengths of time that his mom reads are typically longer and have more variability than the lengths of time that his dad reads.
The lengths of time that his mom reads are typically shorter and have less variability than the lengths of time that his dad reads.
The lengths of time that his mom reads are typically shorter and have more variability than the lengths of time that his dad reads.
Answer:
The lengths of time that his mom reads are typically longer and have more variability than the lengths of time that his dad reads.
Step-by-step explanation:
The Mom's plot is longer in ranges, therefore, she would have more variability than the dad.
Answer:
B
Step-by-step explanation:
f the angle of elevation from the point on the ground to the top of the tree is 34° and the point is 25 feet from the base of the tree, what is the height of the tree (to the nearest tenth of a foot)?
A) 14.0 feet
B) 16.9 feet
C) 19.3 feet
D) 20.7 feet
Given:
The angle of elevation from the point on the ground to the top of the tree is 34° and the point is 25 feet from the base of the tree.
We need to determine the height of the tree.
Height of the tree:
Let the height of the tree be h.
The height of the tree can be determined using the trigonometric ratio.
Thus, we have;
[tex]tan \ \theta=\frac{opp}{adj}[/tex]
Substituting the values, we get;
[tex]tan \ 34^{\circ}=\frac{h}{25}[/tex]
Multiplying both sides by 25, we have;
[tex]tan \ 34^{\circ} \times 25=h[/tex]
[tex]0.6745 \times 25=h[/tex]
[tex]16.8625=h[/tex]
Rounding off to the nearest tenth of a foot, we get;
[tex]16.9=h[/tex]
Thus, the height of the tree is 16.9 feet.
Hence, Option B is the correct answer.
Correct option is B. The height of the tree can be found using the tangent of the angle of elevation, which is the ratio of the tree's height to the distance from the base. Applying the formula, the height is approximately 16.9 feet, matching option B.
To calculate the height of the tree given the angle of elevation and the distance from the point on the ground to the base of the tree, we can use trigonometric functions, specifically the tangent function in a right triangle. The tangent of an angle in a right triangle is the ratio of the opposite side (height of the tree) to the adjacent side (distance from the point on the ground to the tree).
Using the formula:
tangent(angle) = opposite / adjacent
Substitute the given values:
tangent(34°) = height of the tree / 25 ft
Now solve for the height:
height = 25 ft * tangent(34°)
Use a calculator to find:
height = 25 ft * 0.6745
height = 16.9 ft
Therefore, the height of the tree is approximately 16.9 feet (to the nearest tenth of a foot), making option B the correct answer.
Add 3 to x, double what you have, then subtract 1 from the result
Answer:
-6
Step-by-step explanation:
3x * 2 = 6x - 1 = -6
The required result of the given expression is 2x - 5.
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
Now the given expression is,
Add 3 to x, double what you have, then subtract 1
So, we can write,
Add 3 to x = 3 + x
Double = 2(3 + x)
Subtract from = 1 - 2(3 + x)
Simplifying we get,
1 - 6 + 2x
solving we get,
1 - 6 + 2x = 2x - 5
this is the required result.
Thus, the required result of the given expression is 2x - 5.
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What is the area of a rectangle 15 feet by 2 feet's rectangle. The shape of a flag is a rectangle. The length is 15 ft. And the width is 2 feet. What is the total area of the rectangle?
Answer:
30 ft^2
Step-by-step explanation:
Area of rectangle is length x width
= 15ft x 2ft = 30 ft^2
Two of the steps in the derivation of the quadratic
formula are shown below.
Which operation is performed in the derivation of the
quadratic formula moving from Step 6 to Step 7?
subtracting bi from both sides of the equation
Step 6: barangan = (x +
Step 7: tvb22400 = x +
squaring both sides of the equation
taking the square root of both sides of the equation
taking the square root of the discriminant
Please help quick
Answer:
a
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
taking the square root of both sides of the equation
The Roosevelt’s and the jaspers live in the same city and pay the same sales tax rate, and both families made 16,000 in taxable purchase last year if the Roosevelt’s made 91,000 and the jaspers made 37,000 last year is the sales tax in their city an example of a regressive tax
Answer:
Yes, the sales tax in their city is an example of regressive tax
Step-by-step explanation:
Firstly, we need to understand what is meant by the term regressive tax.
What is meant by a regressive tax system is a system of taxation in which there is a decrease in tax rate as there is an increase in amount subjected to tax.
Now, the key to knowing if what we have in the question is a regressive taxation is by calculating the percentage of the tax that was paid.
For the Roosevelt’s , the percentage of tax paid would be 16,000/91,000 * 100% = 17.6%
For the Jasper’s, the percentage of tax paid would be 16,000/37,000 * 100% = 43.24%
We can see that at a lower amount subjected to tax, the Jasper’s paid more and thus we can conclude irrevocably that sales tax in their city is an example of a regressive tax
what is the probability of tossing at least 1 tail of you toss 3 coins at once
Explanation: Probability of NOT getting a tail in 3 coin toss is (12)3=18 . Probability of getting at least 1 tail in 3 coin toss is 1−18=78
The sum of three consecutive numbers is one hundred thirty - eight.
What is the smallest of the three numbers
Answer:
45
Step-by-step explanation:
The average of the three numbers is the middle one: 138/3 = 46. Then the smallest of the three consecutive numbers is 45.
Final answer:
The smallest of the three consecutive numbers that add up to 138 is 45.
Explanation:
To find the smallest of the three consecutive numbers that add up to one hundred thirty-eight, we first need to represent the numbers algebraically.
Let x be the smallest number, x+1 is the next number, and x+2 is the largest number.
The equation that represents their sum is:
x + (x + 1) + (x + 2) = 138
To solve for x, we combine like terms:
3x + 3 = 138
Then we subtract 3 from both sides:
3x = 135
And divide both sides by 3 to find x:
x = 135 / 3
x = 45
Therefore, the smallest number is 45.
Ahmed was studying the shapes of quartz crystals, one of which he outlined below.
A figure can be broken into a parallelogram and triangle. The parallelogram has a base of 3 feet and height of 5 feet. The triangle has a base of 3 feet and height of 2 feet.
What is the area of the quartz crystal he was studying, in square feet?
Feet squared
Answer:
The answer is 18 feet squared
Step-by-step explanation:
Answer:
The answer is 18 ft squared
Step-by-step explanation:
i just got 100% i know all the right answers
Ethan and Chloe shared £50 in the ratio 1:4
Ethan's share is £10, and Chloe's share is £40, resulting in a total of £50.
To determine the amounts Ethan and Chloe received when sharing £50 in the ratio 1:4, follow these steps:
1. Calculate the Total Parts in the Ratio:
Add the parts of the ratio: 1 + 4 = 5.
2. Determine the Share for Each Part:
Divide the total amount by the total parts: £50/5 = £10.
3. Multiply the Share per Part by Respective Parts:
- Ethan's share: £10 * 1 = £10
- Chloe's share: £10 * 4 = £40
Therefore, Ethan received £10, and Chloe received £40.
In summary, when the ratio is 1:4, the total ratio parts are 5, and each part represents £10. Ethan's share is £10, and Chloe's share is £40, resulting in a total of £50.
Complete question:
Ethan and Chloe shared £50 in the ratio 1:4. What is the amount received by each of them.
Ethan received £10 and Chloe received £40.
Ethan and Chloe shared £50 in the ratio 1:4. To determine the amount received by each of them, we can follow these steps:
1. Calculate the total parts in the ratio:
o The ratio is 1:4, which means there are a total of 1 + 4 = 5 parts.
2. Divide the total amount (£50) into these parts:
o Each part is worth £50 ÷ 5 = £10.
3. Allocate the shares based on the ratio:
o Ethan receives 1 part, which is £10.
o Chloe receives 4 parts, which is 4 × £10 = £40.
Therefore, Ethan received £10 and Chloe received £40.
Complete question:
Ethan and Chloe shared £50 in the ratio 1:4. What is the amount received by each of them?
A racecar can go round the track 48 times in 8 minutes how many times can it go around the track per minute
Answer:
6 times
Step-by-step explanation:
48/8=6
Answer: 10 seconds for one time around the track.
Step-by-step explanation:
48 times=8 minutes
1 time= 8/48
8/48=4/24
4/24=2/12
1/6. 1/6 of a minute equals 10 seconds.
The answer is 10 seconds
A theme park ride has a ride that is located in a sphere. The ride goes around the widest circle of the sphere which has a circumference of 521.24 yd. What is the surface area of the sphere? Use 3.14
Answer:
The surface area of the sphere is 86525.84 square yards
Step-by-step explanation:
The widest circle of the sphere has the same radius of the sphere
Use the circumference of the circle to find its radius, then use it to find the surface area of the sphere
The formula of the circumference of the circle is C = 2π r
The formula of the surface area of the sphere is SA = 4π r²
∵ The circumference of the widest circle is 521.24 yards
∴ C = 521.24
- Equate the formula of the circumference by it
∴ 2π r = 521.24
∵ π ≈ 3.14
∴ 2(3.14) r = 521.24
∴ 6.28 r = 521.24
- Divide both sides by 6.28
∴ r = 83 yards
Now use the formula of the surface area of the sphere to find it
∵ The radius of the sphere = the radius of the widest circle
∴ The radius of the sphere is 83 yards
∵ SA = 4π r²
- Substitute r by 83 and π by 3.14
∴ SA = 4(3.14)(83)²
∴ SA = 86525.84
The surface area of the sphere is 86525.84 square yards
NGC is a hot air balloon in the sky from her spot on the ground. The angle of elevation from Angie to the balloon is 40°. If she steps back 200 feet, the new angle of elevation is 10°. If Angie is 5.5 feet tall, how far off the ground is a hot air balloon?
Answer:
The distance from hot air balloon to the ground [tex]AC=50.1457 ft[/tex].
Step-by-step explanation:
Labelled diagram of given scenario is shown below.
Given that,
An angle of elevation of Hot air balloon by Angie is [tex]40[/tex]°.
When she stepped back [tex]200 ft[/tex] then angle of elevation was [tex]10[/tex]°.
Height of Angie is [tex]5.5 ft[/tex].
To find: How far off the ground is a hot air balloon.
So, from figure
Height of Angie [tex](BC) = 5.5ft[/tex]
In triangle Δ[tex]ABD[/tex],
⇒ [tex]tan {40\si {\degree}} = \frac{AB}{BD}[/tex]
⇒ [tex]AB = tan (40) \times BD[/tex] ....................(1)
Now, In triangle Δ[tex]ABE[/tex]
⇒ [tex]tan (10)= \frac{AB}{200+BD}[/tex]
⇒ [tex]AB = tan(10)\times (200+BD)[/tex]
Here, substituting the value [tex]AB[/tex] from Equation (1) we get,
[tex]tan(10)\times (200+BD)= tan(40)\times BD[/tex]
[tex]tan(10)\times 200+tan(10)\times BD= tan(40)\times BD[/tex]
⇒ [tex]BD\times (tan(40)-tan(10))=tan(10)\times 20[/tex]
⇒ [tex]BD\times 0.6628 = 35.2654[/tex]
⇒ [tex]BD = \frac{35.2654}{0.6628} =53.2067 ft[/tex]
Now, finding the value of [tex]AB[/tex] from equation (1)
[tex]AB= tan(40)\times 53.2067=0.8391\times 53.2067[/tex]
[tex]AB=44.6457 ft[/tex]
Therefore Length of [tex]AC= AB+BC[/tex] = [tex](44.6457 + 5.5) ft[/tex]
[tex]AC=50.1457 ft[/tex].
Hence,
The distance from hot air balloon to the ground [tex]AC=50.1457 ft[/tex].
Are the following two matrices inverses of one
another? (Urgent please help)
A=[ 4 2] B= [ -4 -2]
[-11 -6] [ 11 7]
a)Yes, because they are opposites.
b)Yes, because their product is equal to the
identity matrix
c)No, because they are not opposites.
d)No because their product is not equal to the matrix
Answer: D
Step-by-step explanation:
The correct answer is d) No because their product is not equal to the identity matrix.
The matrices are given in the question as follows:
[tex]A= \left[\begin{array}{ccc}4&2\\-11&-6\end{array}\right] \\B= \left[\begin{array}{ccc}-4&-2\\11&6\end{array}\right][/tex]
To determine if two matrices are inverses of each other, we need to check if their product is equal to the identity matrix.
Let's calculate the product of matrices A and B:
[tex]A{\times}B = \left[\begin{array}{ccc}4\times-42+2\times11&4\times-2+2\times6\\-11\times-4+(-6\times11)&-11\times-2-6\times6\end{array}\right][/tex]
Simplifying the calculations to get:
[tex]A{\times}B = \left[\begin{array}{ccc}6&4\\-22&-14\end{array}\right][/tex]
The resulting matrix is not equal to the identity matrix:
[tex]A{\times}B = \left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]
Therefore, matrices A and B are not inverses of each other.
The correct answer is d) No because their product is not equal to the identity matrix.
To learn more about the matrix click here:
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Y=6x-14
y=-8x what is the equation
Step-by-step explanation:
Putting value of y
-8x = 6x - 14
-8x - 6x = - 14
-14x = - 14
x = - 14/-14
x = 1
Cross sections are formed by slicing through figure parallel to its base. in which figure will the cross section and the base NOT be the same size?
Answer:
B
Step-by-step explanation:
The second one gets smaller as it gets taller.
Answer:
the answer is BStep-by-step explanation:
What is the image point of (6,-
1) after a translation left 4 units and down 5 units?
Answer:
(2, -6)
Step-by-step explanation:
Answer:
The Right Answer Is (2,-6)
Step-by-step explanation:
I hope this help you!