From a rock ledge, the angle of elevation to the top of a tree is 22°. The angle of depression to the base of the tree is 12°.
a) Find the height of the rock ledge, to
the nearest metre.
b) Find the height of the tree, to the
nearest metre.
Answers
The height of the rock ledge will be 20.35 meters.
The height of the tree will be 58.75 meters
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The angle of elevation to the top of a tree is 22°.
And, The angle of depression to the base of the tree is 12°.
Now,
Let the height of the rock ledge = x
So, By figure, we get;
⇒ tan 12° = x / 96
⇒ x = 96 × tan 12°
⇒ x = 20.35 meters
And, Let total height of the tree = x + y
= 20.35 + y
Hence, By figure, we get;
⇒ tan 22° = y / 96
⇒ y = 96 × tan 22°
⇒ y = 96 × 0.40
⇒ y = 38.4 meter
Thus, The height of tree = 38.4 meters + 20.35 meters
= 58.75 meters
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To find:-
The height of the rock ledge.Height of the tree .Answer:-
Part A :-
Here we can see that the distance between the rock ledge and the base of the tree is 96m . Also the angle of elevation to the top of the tree from the rock is 22° .
Firstly, we can see that,
[tex]\implies \angle CAD =\angle EDA = 12^o\\[/tex]
This is so because they are alternate interior angles .
Now , in ∆ADE ,
[tex]\implies \tan\theta =\dfrac{p}{b}=\dfrac{AE}{ED}\\[/tex]
[tex]\implies \tan 12^o =\dfrac{AE}{96m} \\[/tex]
[tex]\implies AE = 96\tan12^o m \\[/tex]
[tex]\implies AE = 96 (0.21)m \\[/tex]
[tex]\implies AE = 20.16 \ m \\[/tex]
Hence the height of the rock ledge is 20.16 m.
_______________________________________
Part B :-
Now in ∆ACB , we have;
[tex]\implies \tan\theta =\dfrac{BC}{AC} \\[/tex]
[tex]\implies \tan 22^o =\dfrac{BC}{96m} \\[/tex]
[tex]\implies BC = 96\tan 22^o \ m \\[/tex]
[tex]\implies BC = 96(0.4) m \\[/tex]
[tex]\implies BC = 38.4 \ m \\[/tex]
Now the total height of the tree will be = BC + AE
[tex]\implies h_{tree}= BC + AE \\[/tex]
[tex]\implies h_{tree}=38.4\ m + 20.16 \ m =\boxed{58.56\ m} \\[/tex]
Hence the height of the tree is 58.56m.
and we are done!
Related Questions
say something and i give brainlyest
Answers
Answer:
Its always ily, but never stwywimc
Step-by-step explanation:
A new car loan has a term of loan from 2 - 6 years and the interest rate is between 4% and 8%. what is the longest amount of time you could take to pay off the loan? what is the best interest rate you could get?
Answers
a) The longest time a borrower can take to pay off the new car loan of 2 - 6 years is 6 years.
b) Based on the above, the best interest rate the borrower could get is 8%.
How is the interest rate determined?Many factors are considered in determining the interest rate for a loan.
Some of the factors include:
Loan TermLoan TypeCredit ScoreLoan AmountDown PaymentInterest rate type.We know that the longer the term of a loan, the higher the interest rate charged. This higher rate is meant to compensate the lender for the time value of money, made variable by inflation and credit risks.
Thus, if a loan term varies between two and six years, the longest time to pay off the loan is 6 years while the best interest rate the borrower can be granted is 8%.
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Which cube root function is always decreasing as x increases?
O f(x) = }X-8
O f(x) = 77-5
*(x) = }}-(5-8)
O f(x) = -7/8+5
Help me please don’t send links geez
Answers
Answer:
C
Step-by-step explanation:
Which could NOT be the shape of the graph of a quadratic function?
Answers
Answer:
the bottom right could NOT
the fourth option is the answer (. ^ ᴗ ^.)
Solve: S=2(lw+lw+wh) for w
Answers
Answer:
[tex]w=\frac{s-2lh}{2(h+l)}[/tex]
Step-by-step explanation:
Given the equation, [tex]S=2(lw+lh+wh)[/tex], solve for w.
[tex]S=2(lw+lh+wh)[/tex], distribute the 2.
=> [tex]S=2lw+2lh+2wh[/tex], subtract [tex]2lh[/tex] from both sides.
=> [tex]S-2lh=2lw+2wh[/tex], factor out a [tex]w[/tex] from the right-hand-side.
=> [tex]S-2lh=w(2l+2h)[/tex], now divide [tex](2l+2h)[/tex] from each side.
=>[tex]\frac{S-2lh}{2l+2h}=w[/tex]
Final answer: [tex]w=\frac{s-2lh}{2(h+l)}[/tex]
the point (3, 1) is located on a line with slope of 1/3. which point could also be located on the line?
Answers
The point (5,5/3) also lies on the line.
A point (x, y) is located on a line with slope m if and only if it satisfies the equation:
y = mx + b
where b is the y-intercept of the line. In this case, we know that the point (3, 1) is located on the line, so we can use the information to find the value of b and then write the equation of the line in slope-intercept form.
The y-coordinate of the point (3, 1) is 1, so we can substitute this into the equation and solve for b:
1 = (1/3) * 3 + b
This simplifies to:
1 = 1 + b
so, b = 0
So, the equation of the line is
y = 1/3 * x +0
Now we can use this equation to find the coordinates of any point that lies on the line. So any point (x, y) that satisfies this equation could also be located on the line.
For example, we can pick any x, calculate corresponding y.
x=5, y=5/3
So point (5,5/3) also lies on the line.
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i need help pls i do not get it
Answers
The perimeter and the area of the fountain is calculated to be
94.25 feet and 625.32 square feet respectively
How to find the perimeter and the area of the fountainThe perimeter of the fountain consisting of two semicircles and a quarter circle is
= perimeter of semicircle * 2 + perimeter of circle * 1/4
= π d + 2 π r * 1/4
for semicircle, diameter, d = 20 ft
for circle, radius r, = 20 ft
substituting the values
= 20π + 2 * π * 20 * 1/4
= 20π + 10π
= 30π
= 94.25 feet
Area of the fountain
= area of semicircle * 2 + area of circle * 1/4
area of semicircle * 2 = area of circle of radius 10 ft
for semicircle, radius, r = 10 ft
for circle, radius r, = 20 ft
= π 10² + π 20² * 1/4
= 100π + 100π
= 200π
= 625.32 square feet
The area of the fountain is 625.32 square feet
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Write the augmented matrix for each system of equations.
-2x - 2y + 5z = 1
-5x - 5y + 7z = 4
9x - 2y + 2z = -1
Answers
Answer: it D :)
Step-by-step explanation:
The pairs of polygons below are similar. Give the sale factor of figure A to figure B
Answers
Answer:
Given that Figure A and Figure B are similar polygons, the scale factor of Figure A to Figure B = 5/2.
Recall:
Similar Polygons have corresponding side lengths whose ratio are equal. That is, their pairs of corresponding sides are proportional.
The ratio of any of their corresponding side length = scale factor
Given the two pairs of similar polygons, the scale factor of figure A to figure B will be calculated as follows:
A side length of Figure A = 10
Corresponding side length of Figure B = 4
Scale factor of Figure A to Figure B = 10/4 = 5/2
Step-by-step explanation:
Find the sum of the following series
a 1 + 4 + 7 + 10 + ... to 40 terms.
b. 2+7+12+17+ ... + 102.
Answers
Answer:
They are in A. P so the sum will be 2380
10. The amount of people using a certain product can be modeled by P = 85(1.2) where t is the
number of years since the product was first released. What is the growth rate?
A) 2%
B) 20%
C) 120%
D) 12%
Answers
Answer:
B) 20%
Step-by-step explanation:
Exponential equation:
An exponential equation is given by:
[tex]A(t) = A(0)(1+r)^t[/tex]
In which A(0) is the initial amount and r is the growth rate, as a decimal.
In this question:
[tex]P(t) = 85(1.2)^t[/tex]
Growth rate:
We want to find r, so:
[tex]1 + r = 1.2[/tex]
[tex]r = 1.2 - 1 = 0.2[/tex]
The growth rate is of 0.2 = 2%, and the correct answer is given by option B.
A farmer feeds a cow 9300 milligrams of an antibiotic. Every hour, 50% of the drug breaks down in the cow's body. How much will be left in 6 hours?
Answers
9514 1404 393
Answer:
about 145.3 mg
Step-by-step explanation:
If half breaks down in the hour, then half remains. That is, each hour the amount remaining is multiplied by 1/2. The remainder after 6 hours is ...
(9300 mg)(1/2)^6 = 145.3125 gm
About 145.3 mg will be left after 6 hours.
A high school has found over the years that out of all the students who are offered admission, the proportion who accept is 70%.
After the administration has made some changes to the school, they want to check if the proportion of students accepting
has changed significantly. Suppose they offer admission to 210 students and 156 accept. Is this evidence of a change from
the status quo?
Answers
Answer:
The p-value of the test is 0.1738, which means that for a level of significance above this, there is evidence of a change from the status quo.
Step-by-step explanation:
A high school has found over the years that out of all the students who are offered admission, the proportion who accept is 70%. Test if there is a change from status quo.
At the null hypothesis, we test if the proportion is 70%, that is:
[tex]H_0: p = 0.7[/tex]
At the alternate hypothesis, we test if there is a change from status quo, that is, the proportion is different from 70%. So
[tex]H_a: p \neq 0.7[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
70% is tested at the null hypothesis:
This means that [tex]\mu = 0.7, \sigma = \sqrt{0.7*0.3}[/tex]
Suppose they offer admission to 210 students and 156 accept.
This means that [tex]n = 210, X = \frac{156}{210} = 0.7429[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.7429 - 0.7}{\frac{\sqrt{0.7*0.3}}{\sqrt{210}}}[/tex]
[tex]z = 1.36[/tex]
P-value of the test and decision:
The p-value of the test is the probability that the sample proportion differs from 0.7 by at least 0.7429 - 0.7 = 0.0429, which is P(|z| > 1.36), which is 2 multiplied by the p-value of z = -1.36.
Looking at the z-table, z = -1.36 has a p-value of 0.0869
2*0.0869 = 0.1738
The p-value of the test is 0.1738, which means that for a level of significance above this, there is evidence of a change from the status quo.
When the angle of elevation to the sun is 49°, Naomi's shadow is 5 feet long. The
shadow of a nearby tree is 8 times as long as her shadow. How tall is the tree to the
nearest foot?
Answers
Answer:
46 feet-------------------------------
The height h of the tree is opposite to 49° angle of a right triangle with the other leg:
5*8 = 40 feet longUse tangent to find the value of h:
tangent = opposite/adjacenttan 49° = h/40h = 40*tan 49°h = 46 feet (rounded)The height of the tree is 40 feet to the nearest foot.
How can the height of the tree be found?
It can be found using similar triangles.
Let's call the height of the tree "x".
Since the angle of elevation to the sun is 49°, we have two similar triangles:
Triangle 1: Sun - Naomi - Ground (illustration attached)
Triangle 2: Sun - Tree - Ground
The height of Naomi, 5 feet, is one of the corresponding sides in the two triangles, and the height of the tree, x feet, is the other. We know the ratio of their heights is 8:1, so:
x ÷ 5 = 8
Solving for x, we find that:
x = 40
So the height of the tree is 40 feet to the nearest foot.
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Using the paths shown, how long is the shortest route from Lexington to Somerville?
Answers
Answer:
1 [tex]\frac{1}{4}[/tex] miles
Step-by-step explanation:
the routes from Lexington to Somerville are
Lexington → Brookfield → Somerville with distance
[tex]\frac{3}{8}[/tex] + [tex]\frac{7}{8}[/tex] = [tex]\frac{3+7}{8}[/tex] = [tex]\frac{10}{8}[/tex] = 1 [tex]\frac{2}{8}[/tex] = 1 [tex]\frac{1}{4}[/tex] miles
the other route is
Lexington → Brookfield → Yardley → Somerville with distance
[tex]\frac{3}{8}[/tex] + [tex]\frac{1}{2}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{8}[/tex] + [tex]\frac{4}{8}[/tex] + [tex]\frac{4}{8}[/tex] = [tex]\frac{3+4+4}{8}[/tex] = [tex]\frac{11}{8}[/tex] = 1 [tex]\frac{3}{8}[/tex] miles
the shortest distance is
Lexington → Brookfield → Somerville , a distance of 1 [tex]\frac{1}{4}[/tex] miles
Which property can be used to solve the equation?
10-12
Ο Ο Ο Ο
addition property of equality
O subtraction property of equality
multiplication property of equality
division property of equality
Plz help I’ll give Brainlyest
Answers
Answer:
Subtraction property of equality
Step-by-step explanation:
Without doing any calculations, compare Expression A to Expression B. ( 34 + 25 ) ÷ 1 4 34 + 25 Which statement is true? A. Expression A is 2 times as great as expression B. B. Expression B is 4 times as great as expression A. C. Expression A is 4 times as great as expression B. D. The two expressions are equal to each other.
Answers
Answer:
C. Expression A is 4 times as great as expression B.
Step-by-step explanation:
Without doing any calculations, compare Expression A to Expression B.
A. (34+25) ÷ 1/4
B. 34+25
Which statement is true?
A. Expression A is 2 times as great as expression B.
B.Expression B is 4 times as great as expression A.
C.Expression A is 4 times as great as expression B.
D. The two expressions are equal to each othe
7 long roms of plants
Without doing any calculation,
Expression A = (34+25) ÷ 1/4
= (34 + 25) × 4/1
= 4(34 + 25)
Expression A = 4(34 + 25)
Expression B = 34 + 25
Therefore,
C.Expression A is 4 times as great as expression B.
Tom's toy box is shown below. The toy box is shaped like a rectangular prism. It has 5 wooden faces and is open on the top. What is the risk surface area of the 5 faces of the toy box that are wooden?
Don’t answer if you don’t know, and whoever answers quickly will get Brainliest!
Answers
Answer:
1100 square inches
Step-by-step explanation:
The faces are all rectangles (area = length x width)
Area of bottom: 20 x 10 = 200
Area of front: 20 x 15 = 300
Area of back (same as front) = 300
Area of right side: 10 x 15 = 150
Area of left side (same as right side) = 150
Total of all the sides: 1100
The length of the life an instrument produced by a machine has a normal distribution with mean life of 12 months and standard deviation of 2 months.
What is the probability if X assumes a value greater than 12 months?
Answers
Probability that the length of the life of an instrument is greater than 12 months is 0.5 or 50%
If the length of the life of an instrument produced by the machine has a normal distribution with a mean of 12 months and a standard deviation of 2 months, then the random variable X representing the length of the life of the instrument is also normally distributed.
To find the probability that X assumes a value greater than 12 months, we need to use the cumulative distribution function (CDF) of the normal distribution. The CDF is given by the formula:
F(x) = (1/2) * [1 + erf((x - μ) / (σ * sqrt(2)))]
where μ is the mean, σ is the standard deviation, and erf(z) is the error function.
Plugging in the given values, we get:
F(12) = (1/2) * [1 + erf((12 - 12) / (2 * sqrt(2)))] = (1/2) * [1 + erf(0)] = (1/2) * [1 + 0] = 1/2
Since the CDF gives us the probability that X assumes a value less or equal than x, we need to subtract F(12) from 1:
P(X > 12) = 1 - F(12) = 1 - 1/2 = 0.5
So the probability that the length of the life of an instrument is greater than 12 months is 0.5 or 50%.
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Five people each working eight hours a day can assemble 400 toys in a five day work week. What is the average number of toys assembled per hour per person?
Answers
Answer:
There are 5 people working and each person works 8 hours per day, so there are a total of 58 = <<58=40>>40 hours of work per day.
Over the course of the week, the total number of hours worked is 405 = <<405=200>>200 hours.
The total number of toys assembled is 400 and the total number of hours worked is 200, so the average number of toys assembled per hour per person is 400/200 = <<400/200=2>>2 toys per hour per person. Answer:{2}.
Step-by-step explanation:
A business school wants to compare a new method of teaching reading to slow learners to the current standard method. They decide to base this comparison on the results of a reading teat given at the end of a learning period of six months. Of a random sample of 11 slow learners. 5 are taught by the new method and 6 are taught by the standard method. All 11 children are taught by qualified instructors under similar conditions for a six month period. Assume that the populations are normally distributed and the population variances are equal.
New Method Score: 81 80 79 81 76
Standard Method Score: 69 68 71 68 73 72
Test at 1% level of significance that the new method is worse than the old method, i.e., average score obtained by the new method is less than the average score obtained by the standard method. Compute the mean and standard deviation of each data set.
State the null and the alternative hypotheses.
H0:
H1:
Write down the formula of the test statistics and find its value.
Determine the rejection region and make a decision.
Make a conclusion in the context of the problem.
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
New Method : 81 80 79 81 76
Standard Method Score: 69 68 71 68 73 72
H0 : μn = μa
H0 : μn < μa
New Method :
Using a calculator :
Sample size, n1 = 5
Mean, x1 = 79.40
Standard deviation, s1 = 2.07
Standard Method :
Using a calculator :
Mean, x2 = 70.17
Sample size, n2 = 6
Standard deviation, s2 = 2.14
T = (x1 - x2) / √(s1²/n1 + s2²/n)
(x1 - x1) = (79.40 - 70.17) =79.40 -= 9.23
√(s1²/n1 + s2²/n2) = √(2.07²/5) + 2.14²/6) = 1.2729
T = (x1 - x2) / √(s1²/n1 + s2²/n)
T = 9.23 / 1.2729
Test statistic = 7.25
The Pvalue from Tscore at, smaller n - 1 = 5 - 1 = 4
Pvalue = 0.000961
Decision region :
If Pvalue < α ; Reject H0 ; otherwise fail to reject H0
α = 0.01
Since, Pvalue < α ; We reject H0 ; and conclude that new method is worse rhn the old.
`
Can y’all help me on question 12?!
Answers
Answer:
C)
Step-by-step explanation:
5 x 3 = 15
15 + 6 = 21
Your answear is C
Answer:
C,D, and F should be the correct answers.
Step-by-step explanation:
C. 5(3)= 15+6=21
D. 7(3)= 21-2=19
F. 5(3)=15
The table represents a quadratic function C(t).
t C(t)
−2 1
−1 4
0 5
1 4
2 1
What is the equation of C(t)?
C(t) = −(x − 5)2
C(t) = (x − 5)2
C(t) = −x2 + 5
C(t) = x2 + 5
Answers
The equation that presents the table will be C(t) = - t² + 5. Then the correct option is C.
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The table represents a quadratic function C(t).
t C(t)
−2 1
−1 4
0 5
1 4
2 1
From the table, the coordinate of the vertex will be at (0, 5). Then the equation is given as,
C(t) = a(t - 0)² + 5
C(t) = at² + 5
The equation is passing through the point (1, 4), then we have
4 = a (1²) + 5
4 = a + 5
a = - 1
The equation that presents the table will be C(t) = - t² + 5. Then the correct option is C.
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find the solution to the system of equations y=1/2x +1 y=-x+1
Answers
Answer:
x=0, y=1
Step-by-step explanation:
Pls, solve this equation with the steps u took. 30 POINTS! posted this for the 2nd time
Answers
Answer:
x=2/3
Step-by-step explanation:
when the three turned into a 2 it removed one third, so we need to remove one third from 1, which gives us 2/3.
Basically, if a rectangle side goes from x to y, we figure out the percent decrease, and subtract that percent from the other side to find the variable we need to find on the other rectangle
Tom will create a password for his computer. The password must be a list of three different lowercase letters of the alphabet. How many passwords are possible?
Answers
Find X and Y. can someone please help me with this question, thank you
Answers
3x + 120° + x + 120° = 360°
4x + 240° = 360°
4x = 120°
x = 30°
y = 1/2 (3x - x)
y = 1/2 (90° - 30°)
y = 1/2 × 60°
y = 30°
Find a line that passes through the points (-1,3) and (5,-1)
Answers
y2-y1/x2-x1
= (-1-3)/(5+1)
= -4/6
= -2/3
y = -(2/3)x + c
3 = (2/3) + c
c = -2/3 + 3
c = -2/3 + 9/3
c = -7/3
y = (2/3)x + (7/3)
You pay $5500 for a municipal bond. When it matures after 20 years, you receive 11,900$. What % is your total return?
Answers
Choose Yes or No to tell whether the expression represents a 20% discount off the price of an item that originally cost d dollars.
0.8d (yes or no)
d – 0.2 (yes or no)
d – 0.2d (yes or no)
1 – 0.2d (yes or no)