A blimp provides aerial television views of a tennis game. The television camera sights the stadium at 14° angle of depression. The altitude of the blimp is 300m . What is the line-of sight distance from the television camera to the base of the stadium ? Round to the nearest hundred meters.
Answers
Notice that with the information given, we can make a simple schematics of a right angle triangle for which we know an acute angle, a leg, and are asked to find the other leg of the triangle (or the hypotenuse, since the word "line of sight is not used properly in the text of the problem). The schematics is shown below:
The other leg of the right triangle is pictured in red in the image, if it is what the problem is asking (LINE OF SIGHT DISTANCE, which is always understood as a horizontal reference).
So we can use the tangent function to solve this case, as shown below
[tex]\begin{gathered} \tan (14\circ)=\frac{300}{d} \\ d=\frac{300}{\tan (14)}\approx1203.23 \end{gathered}[/tex]which tells us that the horizontal distance between camera and end of the field is approximately 1203.23 meters.
In the case that the problem is asking for the slant distance between the camera and the end of the field, we need to find the HYPOTENUSE of the right angle triangle (pictured in orange in the image above), and in such case we use the sine function as shown below:
[tex]\begin{gathered} \sin (14)=\frac{300}{\text{hyp}} \\ \text{hyp}=\frac{300}{\sin (14)}\approx1240.07 \end{gathered}[/tex]Which tells us that the slant distance between camera and the end of the field is about 1240.7 meters
From the drawing you sent, it looks more like the teacher may be asking for the slant distance. So please use the second answer : 1240.7 meters.
Please remind you teacher that the standard use of "line of sight" is to represent the horizontal line from which the angle of elevation or angle of depression is measured. So it is not appropriate to use the term in the context it has been used.
Related Questions
Pablo draws Rectangle P. He says that the area is greater than 50 square units. What could the missing side length be? Explain. P. ? units 6 units
Answers
Answer:
Explanation:
Here, we want to get the missing side length
From the question, it was said that the area is greater than 50 square units
What this mean is that the product of the width and length of the rectangle is greater than 50 square units
Therefore, the number in whch we will multiply by 6 must give us a result greater than 50 square units
The highest multiple of 6 closest to 50 is 48 while the closest multiple after 50 is 54
9 multiplied by 6 will give 54 square units
In essence, we can say that the missing side length is 9 square units
the average age of a family of 6 is 30 years. the average of the 3 children in the family is 12 years. if the mother is 4 years younger than the father , calculate the age of the father
Answers
In order to calculate the age of the father, you first consider that the average of the family is 30, then, you have:
(x1 + x2 + x3 + x4 + x5 + x6)/6 = 30
where x3, x4, x5 and x6 are the ages of the children, x1 is the age of the mother and x2 is the age of the father
You cn write the previous expression as:
(x1 + x2)/7 + (x3+x4+x5+x6)/7 = 30
The second term in the second expression is the average age of the children, which is 12. Furthermore, the mother is 4 years younger than the father, that is, x1 = x2 - 4. You replace this values in the expression above and you obtain:
(x1 + x2)/7 + (x3+x4+x5+x6)/7 = 30
(x2 - 4 + x2)/7 + 12 = 30
Next, you solve for x2:
(x2 - 4 + x2)/7 + 12 = 30
(2x2 - 4)/7 + 12 = 30
multiply the previous expression by 7:
2x2 - 4 + 12(7) = 30(7)
2x2 - 4 + 84 = 210
2x2 = 130
x2 = 65
Then, the age of the father is 65
if the spinner was fair and spun 300 times,each outcome would be expected to be observed_____times.
Answers
ANSWER
Each outcome would be expected to be observed 75 times.
EXPLANATION
We have to find the theoretical probability of each outcome. If the spinner is fair, each outcome is equally probable. If we were to spin it 300 times, and the spinner has 4 sections, we would expect that each outcome to be observed:
[tex]\frac{300}{4}=75[/tex]75 times each section.
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Which postulate or theorem could you use to prove AXYZ AABC?
Choose the correct answer below.
O SSS postulate
OSAS postulate
O ASA postulate
O AAS theorem
Answers
ASA theorem
explanation:
angle marked at point a, side marked on line AB, angle marked at point b.
Does the data set display exponential behavior? * {(0, 1), (1, 3), (2, 9), (3, 27)}
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ANSWER
Yes, it does.
EXPLANATION
We want to check if the data set displays an exponential behavior.
An exponential function is one in which the values of the range (y values) increase by a certain factor.
The general form of an exponential function is:
[tex]y=a\cdot b^x[/tex]where a is the starting value
b = factor.
Now, we have to compare the data set with this kind of function.
To do that, we have to find a mock function of the data set using the first two data points to test each x value (domain) for each y value.
Basically, we will replace x in the function with a value and see if we get the correct y.
Therefore, when x = 0:
[tex]\begin{gathered} y=a\cdot b^0 \\ y=a\cdot1 \end{gathered}[/tex]From the data set, we see that, when x = 0, y = 1:
[tex]\begin{gathered} \Rightarrow1=a\cdot1 \\ a=1 \end{gathered}[/tex]That is the value of a.
Now, let us try when x = 1:
[tex]\begin{gathered} \Rightarrow y=1\cdot b^1 \\ y=b \end{gathered}[/tex]From the data set, we see that, when x = 1, y = 3:
[tex]\begin{gathered} \Rightarrow3=b \\ b=3 \end{gathered}[/tex]Now, we can say that we have an exponential function to test with:
[tex]y=3^x[/tex]So, let us test for the remaining values of x and y and see if they match the function.
[tex]\begin{gathered} \text{when x = 2:} \\ y=3^2 \\ y=9 \\ \text{when x = 3:} \\ y=3^3 \\ y=27 \end{gathered}[/tex]As we can see, each x value that goes into the function yields the exact y value as the data set. This means that the exponential function works for it.
Hence, the data set displays an exponential behavior.
Suppose that $6500 is placed in an account that pays 3% interest compounded each year.Assume that no withdrawals are made from the account.Follow the instructions below. Do not do any rounding.
Answers
Given
Part A
[tex]\begin{gathered} P=\text{ \$6,500} \\ r=3\text{ \%} \\ t=1 \end{gathered}[/tex]Formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex][tex]\begin{gathered} A=6,500(1+\frac{0.03}{1})^{1\times1} \\ \\ A=6,500(1.03) \\ A=\text{ \$}6,695 \end{gathered}[/tex]Part B
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \\ P=6500 \\ R=3\text{ \%} \\ t=2 \end{gathered}[/tex][tex]\begin{gathered} A=6500(1+\frac{0.03}{1})^{1\times2} \\ \\ A=6500(1.03)^2 \\ A=6500(1.0609) \\ A=\text{ \$}6895.85 \end{gathered}[/tex]The final answer
in the figure above
Answers
Since AB is tangent to the circle, the angle BAO equals π/2.
The same happens to BC, so the angle BCO also equals π/2.
Now, for any quadrilateral, the sum of the internal angles is 2π. Therefore:
ABC + AOC + BAO + BCO = 2π
ABC + 3π/7 + π/2 + π/2 = 2π
ABC = 2π - 3π/7 - π/2 - π/2 = π - 3π/7 = (7π - 3π)/7
ABC = 4π/7
From 2014-2015 to 2024-2025, the number of students enrolled in an associate degree program is projected to increase by 21.3%. If the enrollment in associatedegree programs in 2014-2015 is 7,800,000, find the increase and the projected number of students in an associate degree program in 2024-2025.The increase is(Round to the nearest whole number as needed.)The projected number of students in an associate degree program in 2024-2025 is(Round to the nearest whole number as needed)
Answers
First, let's convert the percentage into a decimal:
[tex]\frac{21.3}{100}\rightarrow0.213[/tex]And multiply it by the initial amount:
[tex]7800000\cdot0.213=1661400[/tex]This way, the increase would be 1,661,400 , and the proyected number of students would be 9,461,400
1. Ingrid will start college next year. She wasapproved for 10-year unsubsidized Federal Loanfor the amount of $15,000 at 4.29%a) How much interest will Ingrid accrue for 4.5 yearsnonpayment period?b) What will the new principal be when she beginsmaking loan payments?c) How much interest will she pay over the life of theloan?2. Suppose Ingrid only paid the interest during her 4years of school and the six-month grace period.What will she now pay in interest over the term ofthe loan?3. Ingrid made her last monthly interest only paymenton September 1 Her next payment is due onOctober 1. What will be the amount of interestonly payment?4. Suppose Ingrid has decided to apply for a privateloan rather then a federal loan. She has beenapproved for a 10 year loan with APR of 7.8%a) What is her monthly payments?b) What is the total amount she will pay back?c) What is total interest amount?
Answers
Given:
[tex]\begin{gathered} Principal=15,000 \\ rate(r)=4.9\%=0.049 \\ time(t)=10years \end{gathered}[/tex]To Determine: (a) How much interest will Ingrid accrue for 4.5 years non payment period
Solution
Calculate the amount accrued for 4.5years
The formula for finding amount for compound interest is
[tex]A=P(1+r)^{nt}[/tex]Substitute the given into the formula
[tex]\begin{gathered} A=15000(1+0.049)^{4.5} \\ A=15000(1.049)^{4.5} \\ A=18602.91 \end{gathered}[/tex]Step 2: Calculate the interest accrued for 4.5 years
[tex]\begin{gathered} I=A-P \\ I=18602.91-15000 \\ I=3602.91 \end{gathered}[/tex](a) Hence the interest Ingrid will accrued for 4.5 years non-payment period is $3,602.91
(b) The new principal when she begins making loan payments will be the amount accrued for 4.5years nonpayment period. This is as calculated above, which is
$18,602.91
(c) To Determine how much interest will she pay over the life of the loan
Note that the life of the loan is 10 years
[tex]So,t=10[/tex]Substitute the given into the formula for finding the amount as shown below
[tex]\begin{gathered} A=15000(1+0.049)^{10} \\ A=15000(1.049)^{10} \\ A=24201.71 \end{gathered}[/tex]Use the amount to calculate the interest of the life of the loan
[tex]\begin{gathered} I=A-P \\ I=24201.71-15000 \\ I=9201.71 \end{gathered}[/tex]Hence, the interest she would pay over the life of the loan is $9,201.71
i need to know what box i drag each , i tried to attach all them but it didnt allow me .
Answers
Triangle ABC has two angles measuring 59º and 88º. The third angle can be found by using the fact that the three angles of a triangle must sum up to 180º.
So, we have:
[tex]\begin{gathered} \angle A+\angle B+\angle C=180^{\circ} \\ \\ 88^{\circ}+\angle B+59^{\circ}=180^{\circ} \\ \\ 147^{\circ}+\angle B=180^{\circ} \\ \\ \angle B=180^{\circ}-147^{\circ} \\ \\ \angle B=33^{\circ} \end{gathered}[/tex]Now we know the measures of all angles and sides of the given triangle, let's analyze each of the congruence cases.
• For, triangle DEF, we see that:
Side DE is congruent to side AB (because they are represented using the same symbol)
Side EF is congruent to side BC (again, they both are represented by the same symbol)
The angle between sides DE and EF is congruent to the angle between sides AB and BC (they both measure 33º).
Thus, triangle DEF has a pair of sides, and the angle between them congruent two a pair of sides and the angle between them of triangle ABC.
Therefore, those two triangles are congruent by the Side-Angle-Side theorem. Or, for short: SAS.
• For ,triangle GHI ,we see that:
It has a pair of angles, 33º and 59º, that are congruent to a pair of angles of triangle ABC. Also, the side HI between those angles is congruent to side BC.
Thus, triangle GHI and triangle ABC are congruent by the Angle-Side-Angle Theorem. Or, for short: ASA.
For triangle
Diamond form and grouping to factored form a(x-r1)(x-r2) for the first problem on the picture
Answers
Given the expression:
[tex]6x^2-13x-5[/tex]We will factor the expression as follows:
The factors of 6 = 2 x 3 or 1 x 6
The factors of 5 = 1 x 5
The difference must be = -13
So, we will use the factors of 6 = 2 x 3
So, the factoring will be as follows:
[tex]6x^2-13x-5=(3x+1)(2x-5)[/tex]We will write the expression in the form a(x-r1)(x-r2) as follows:
[tex]\frac{1}{6}(x+\frac{1}{3})(x-\frac{5}{2})[/tex]which of the following reflective symmetries apply to the hexagon?
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The line y = -7x/3 is a line of symmetry to the given hexagon while the line y=x is not a line of symmetry to it
This makes the answer to the first statement Yes and the second statement No. That is
Reflective symmetry over the line y=-7x/3 -------------------Yes
Reflective symmetry over the x-axis ------------------------------------No
Algebraic proof write a reason for every step4x = 12x + 32
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The function f(x) is graphed below. 3 2 -5-5-3 -2 3 Using interval notation, the domain is: Using interval notation, the range is: Determine f(2)= Solve f(x) = 0 (enter as list of decimal numbers): The y-intercept is at coordinates: The x-intercepts are (enter as list of decimal coordinates): The zeros are (enter as list of decimal numbers): Over the interval [ - 4, – 2], the function is Select an answer v Over the interval [ - 2, – 1], the function is Select an answer v Over the interval ( - 1,2], the function is Select an answer v Over the interval (2, 4), the function is Select an answer v The minimum value is: The maximum value is:
Answers
Given,
The graph of the curve is shown in the question.
The domain of the function are the input value which are x coordinates values.
The range of the function are the output value which are represent by y coordinates of the graph.
So, from the graph its is clearly seen that the curve taking input from -4 to 4,
Hence, the domain of the function is,
[tex]\lbrack-4,4\rbrack[/tex]So, from the graph its is clearly seen that the curve giving output from 3 to -1,
Hence, the range of the function is,
[tex]\lbrack-1,3\rbrack[/tex]c) from the graph it is seen that when the value of x coordinate is 2 then the value of y coordinate is -1.
[tex]\text{Hence, f(2)=-1}[/tex]The value of x when the coordinates of y is 0 at x=3, -1.5.
[tex]\text{Hence, f(3)=0 and f(-1.5)=0}[/tex]The intercept of the y axis is at (0, -1).
The intercept of the x axis is at (-1.5,0) and (3,0).
The values at which y coordinate is zero is called the zeroes of the graph.
The xeroes of the graph is x=-1.5 and x=3.
In interval [-4,-2], the function is decreasing.
In interval [-2,-1] the function is decreasing.
In interval [-1,2] the function is contant.
ininterval [2,4] the function is increasing.
The maximum value of the graph is 3.
The minimum value of the graph is at -1
in the diagram of JEA below, JEA = 90° and EAJ = 48°. Line segment MS connects points M and S on the triangle, such that EMS = 59°. Find the measure of JSM.
Answers
The value of m∠JSM is 17 degrees.
Given data;
The measure of the ∠JAE = 48 degrees.
The measure of the ∠AEJ = 90 degrees.
The measure of the ∠EMS = 59 degrees.
In triangle JEA;
By angle sum property, we know that;
∠JAE + ∠AEJ + ∠EJA = 180 degree
Substitute the given values in the above expression.
48 degree + 90 degree + ∠EJA = 180 degree
∠EJA = 42 degrees
The angle JMS is,
∠JMS = 180 - ∠EMS (Linear pair)
∠JMS = 180 degrees - 59 degrees = 121 degrees.
In triangle JMS,
By angle sum property, we know that;
∠JMS + ∠JSM + ∠EJA = 180 degree
121 degree + ∠JSM + 42 degree = 180 degree
∠JSM = 17 degree
Thus, the measure of ∠JSM is 17 degrees.
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Determine the area of the figure: 1.5 cm 5 cm 5.5 cm Your answer
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We can add the are of the 3 rectangle, so we get that the area is:
[tex]A=1.5\cdot5+1.5\cdot5+1.5\cdot0.5=15.75\operatorname{cm}[/tex]Hello! I need some assistance with this homework question, pleaseQ13
Answers
we have the new function
[tex]f(x)=\frac{2}{3}\mleft|x\mright|+3[/tex]The vertex of this function is the ordered pair (0,3)
The coordinates of the second point
(2,2) ------------> (2,f(2))
Find the value of f(2)
[tex]\begin{gathered} f(2)=\frac{2}{3}|2|+3 \\ f(2)=\frac{2}{3}\cdot(2)+3 \\ f(2)=\frac{4}{3}+3=\frac{13}{3} \end{gathered}[/tex]the new coordinates of point (2,2) are (2,13/3)
see the attached figure
A. graph quadrilateral KLMN with vertices K(-3,2),L(2,2),M(0,-3)and N(-4,0) on the coordinate grid.B. on the same coordinate grid,graph the image of quadrilateral KLMN after a translation of three units to the right and four units up.C. witch side of the image is congruent to side LM?Name three other pairs of congruent sides.
Answers
The given points are K(-3,2), L(2,2), M(0,-3), and N(-4,0).
If we graph part A, it would be as the image below shows
Notice that these four points for a quadrilateral.
Now, part B is about shifting the quadrilateral three units right and four units up, so its new coordinates would be K'(0,6), L'(5,6), M'(3,1), and N'(-1,4). So, the new parallelogram is shown in the image below, where you would notice the pre-image and the image.
According to the image above, side LM is congruent to L'M', they are corresponding sides of the transformation. The other three congruent sides are NK to N'K', MN to M'N', and KL to K'L'.
Write the equation of a sine or cosine function to describe the graph. Please help I’ve tried but I keep missing something like finding the c/b. Thanks in advance!!!
Answers
Since the function starts at it maximum value, let's use a cosine function to represent it:
[tex]f(x)=A+B\cos(C(x+D))[/tex]Since the midline of the periodic function is y = 2, we have A = 2.
The period of the function is 4pi/3, so we have:
[tex]\begin{gathered} T=\frac{2\pi}{C}\\ \\ \frac{4\pi}{3}=\frac{2\pi}{C}\\ \\ \frac{2}{3}=\frac{1}{C}\\ \\ C=\frac{3}{2} \end{gathered}[/tex]Since the function already starts at its maximum value, there is no horizontal phase shift, so D = 0.
The amplitude is 1 (it goes up and down 1 unit from the midline), so we have B = 1.
Therefore the function is:
[tex]f(x)=2+\cos(\frac{3}{2}x)[/tex]Which number line represents the solution set for the inequality 3(8 - 4x) < 6(x - 5)?-5-4-3-2 -1 01+4123on++at-5-2+ o+1-1234501-5-4-3+o-2-1+1N+W+A+5++-5-4-3-2+o-1NT1345
Answers
To find the solution, lets first simplify the inequality:
[tex]undefined[/tex]Out of 210 racers who started the marathon, 187 completed the race, 16 gave up, and 7 were disqualified. What percentage did not complete the marathon?
Answers
The total number of racers who did not completed the marathon is given by the sum of those who gave up and those who were disqualified.
Then, 16 + 7 = 23 racers did not completed the marathon.
Therefore, is represent a total of 23/210 = 0.11 = 11% (rounded) of the total number of racers.
Two angles are complementary to each other. One angle measures 32°, and the other angle measures (12x − 20)°. Determine the value of x. 64 6.5 32.5 6
Answers
Answer:
B) 6.5
Step-by-step explanation:
Complementary angles are angles that are put together to equal 90 degrees.
Angle one is 32 degrees.
90-32= 58
So we need to get the number 58 for it to be complementary. The reason for this is because 32+58=90. Which would make it complementary.
When we plug in 6.5 we get 58, which is what we want.
12(6.5)- 20= 90
78-20=58
Hope this helps!!!
The value of x is 6.5.
Complimentary angles are known as angles which makes the sum of 90°.
The angles sum up to form a right angle. When two angles complement each other they sum up to be 90°.
According to question one angle - 32° and other angle [12x - 20].
⇒ 32 + [12x - 20] = 90
⇒ 12x - 20 = 58
⇒ 12x = 78
⇒ x = 6.5
Hence, the value of x is 6.5.
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Find the product: (2×^2+3)^2
Answers
(2x + 3)²
We will simply expand
(2x + 3)(2x + 3)
2x(2x+3) + 3(2x+ 3)
open the parentheses
4x² + 6x + 6x + 9
4x² + 12x + 9
Hello! I'm having a hard time solving and graphing this
Answers
Answer:
A = 25π units² = 78.5 units²
Explanation:
The circle with a center at (-1, 2) that passes through (-6, 2) has a radius equal to 5 because the distance between the center and the point is calculated as
-1 - (-6) = -1 + 6 = 5
Then, the area of the circle is equal to
A = πr²
A = π(5)²
A = 25π
Replacing π = 3.14, we get
A = 25(3.14)
A = 78.5
Therefore, the answer is
A = 25π units² = 78.5 units²
there are 550 students how many teachers were there be in ratio form
Answers
The ratio of teacher to student is equivalent so teacher to the student ratio is same for all the school A, B, C and D.
Equate the teacher to school ratio for school A and school C to obtain the number of teachers in school C.
[tex]\begin{gathered} \frac{15}{330}=\frac{x}{550} \\ x=\frac{15\cdot550}{330} \\ =25 \end{gathered}[/tex]The number of teacher is school C is 25.
Equate the teachers to students ratio for the school A and school D to obtain the number of students in school D.
[tex]\begin{gathered} \frac{15}{330}=\frac{36}{y} \\ y=\frac{36\cdot330}{15} \\ =792 \end{gathered}[/tex]
The number of students in school D is 792.
Which of the following is equivalent to the radical expression below when x is greater than or equal to 7
Answers
SOLUTION
The radical expression given is
[tex]\sqrt[]{x-7}.\sqrt[]{x+1}[/tex]Applying the rule
[tex]\sqrt[]{a}\times\sqrt[]{b}=\sqrt[]{ab}[/tex]We obtain
[tex]\sqrt[]{x-7}\times\sqrt[]{x+1}=\sqrt[]{(x-7)(x+1)}[/tex]Expanding the parenthesis, we have
[tex]\begin{gathered} \sqrt[]{(x(x+1)-7(x+1)} \\ =\sqrt[]{x^2+x-7x-7} \\ =\sqrt[]{x^2-6x-7} \end{gathered}[/tex]The radical expression is equivalent to
[tex]\sqrt[]{x^2-6x-7}[/tex]The right option is A
use the display of data to find the mean, median, mode, and midrange 10,3, 11,3, 12,4, 13,5, 14,2, 15,3
Answers
The mean, median, mode and midrange of the given data is 7.92, 7.5, 3 and 8.2 respectively.
What is median and midrange?The mid-way between the least value and the greatest value of the data set is called the midrange, and the median is the middle number in a sorted list of numbers.
Given a data 10,3, 11,3, 12,4, 13,5, 14,2, 15,3
Mean = (2+3+3+3+4+5+10+11+12+13+14+15)/12 = 7.92
Median = 15/2 = 7.5
Mode = 3
Midrange = (2+15)/2 = 8.2
Hence, The mean, median, mode and midrange of the given data is 7.92, 7.5, 3 and 8.2 respectively.
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describe the transformations that occur from the parent function f(x) = x2 to the function g(x) =2(x+1)^2-7
Answers
we have
f(x)=x^2
this is a vertical parabola with vertex at (0,0)
and
we have
g(x)=2(x+1)^2-7
this is a vertical parabola with vertex at (-1,-7)
so
the transformation of f(x) to g(x) is equal to
(0,0) ------> (-1,-7)
the rule of the translation is equal to
(x,y) --------> (x-1, y-7)
that means ------> the translation is 1 unit at left and 7 units down
and we have a second transformation
(x,y) -------> (ax, y)
the factor a is 2
therefore
First transformation
x^2 --------> 2x^2
second transformation
2x^2---------> 2(x+1)^2-7
1.2.12 m18 inC3.4.35 km5.6.15.6 cm7 mm
Answers
The required solution is the circumference of the circle for the given radius or diameter
The formula for the circumference of a circle with radius r is :
[tex]C\text{ = 2 }\pi\text{ r}[/tex]The formula for the circumference of a circle with diameter d is:
[tex]C\text{ = }\pi\text{ d}[/tex]For the first circle with a radius of 12m:
[tex]\text{Circumference = 2}\times\text{ }\pi\text{ }\times\text{ 12 = 24}\pi[/tex]For the second circle with a diameter of 18in :
[tex]C\text{ = }\pi\text{ }\times\text{ 18 = 18}\pi[/tex]For the third circle with a radius of 2.8ft:
[tex]\begin{gathered} C\text{ = 2 }\times\text{ }\pi\times\text{ 2.8 } \\ =\text{ 5.6}\pi \end{gathered}[/tex]For the fourth circle with a diameter of 35km:
[tex]\begin{gathered} C\text{ = }\pi\text{ d} \\ =\text{ }\pi\text{ }\times\text{ 35 = 35}\pi \end{gathered}[/tex]For the fifth circle with a radius of 7mm:
[tex]\begin{gathered} C\text{ = 2 }\times\pi\times\text{ r} \\ =\text{ 2 }\times\text{ }\pi\text{ }\times\text{ 7} \\ =\text{ 14}\pi \end{gathered}[/tex]For the sixth circle with a radius of 15.6 cm:
[tex]\begin{gathered} C\text{ = 2}\pi r \\ =\text{ 2 }\times\text{ }\pi\text{ }\times\text{ 15.6 } \\ =\text{ 31.2 }\pi \end{gathered}[/tex]Note: Circumference has a unit. It's unit depends on the unit of the radius/ diameter
a ladder is leaning against the side of a brick wall the base of the ladder is 6 feet away from the brick wall the top of the ladder touches the brick wall at 8 feet from the ground how long is the ladder 4ft 10 feet or 14 feet or 7 feet
Answers
The base of ladder is at distance of b = 6 feet from the wall.
The height of top of ladder from ground is h = 8 feet.
Let the length of ladder be l.
Determine the length of ladder by using the pythagoras theorem.
[tex]\begin{gathered} l^2=(6)^2+(8)^2 \\ =36+64 \\ =100 \\ l=\sqrt[]{100} \\ =10 \end{gathered}[/tex]So length of the ladder is 10 feet.