In traveling across flat land, you see a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5°. After you drive 15 miles closer to the mountain, the angle of elevation is 9° (see figure). Approximate the height of the mountain. (Round your answer to one decimal place.)
Answers
[tex]\bf tan(3.5^o)=\cfrac{y}{15+x}\implies 15+x=\cfrac{y}{tan(3.5^o)}\\\\\\ \boxed{x=\cfrac{y}{tan(3.5^o)}-15} \\\\\\ tan(9^o)=\cfrac{y}{x}\implies x\cdot tan(9^o)=y\\\\\\ \left[ \cfrac{y}{tan(3.5^o)}-15 \right]tan(9^o)=y \\\\\\ \left[ \cfrac{y-15tan(3.5^o)}{tan(3.5^o)} \right]tan(9^o)=y \\\\\\[/tex]
[tex]\bf \cfrac{y\cdot tan(9^o)-15tan(3.5^o)tan(9^o)}{tan(3.5^o)}=y \\\\\\ y\cdot tan(9^o)-15tan(3.5^o)tan(9^o)=y\cdot tan(3.5^o) \\\\\\ ytan(9^o)-ytan(3.5^o)=15tan(3.5^o)tan(9^o) \\\\\\ \stackrel{common~factor}{y}[tan(9^o)-tan(3.5^o)]=15tan(3.5^o)tan(9^o) \\\\\\ y=\cfrac{15tan(3.5^o)tan(9^o)}{tan(9^o)-tan(3.5^o)}[/tex]
make sure your calculator is in Degree mode.
the amount is small, but bear in mind that is mile units.
To solve such problems we must know about Tangent (Tanθ).
What is Tangent (Tanθ) ?The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm{Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
The height of the mountain is 1.495 miles.
Given to us
AB = 15 miles∠CAD = 3.5°∠CBD = 9°In ΔCAD,[tex]\rm{ tan(\angle A) = \dfrac{Perpendicular}{Base}[/tex]
[tex]tan(\angle A) = \dfrac{CD}{AD}[/tex]
[tex]tan(3.5^o) = \dfrac{CD}{15+x}[/tex]
[tex]CD=tan(3.5^o) \times(x+15)[/tex]
In ΔCBD,[tex]\rm{ tan(\angle B) = \dfrac{Perpendicular}{Base}[/tex]
[tex]tan(\angle B) = \dfrac{CD}{BD}[/tex]
[tex]tan(9^o) = \dfrac{CD}{x}[/tex]
[tex]CD=tan(9^o) \times(x)[/tex]
Equating CD,
[tex]tan(3.5^o) \times (x+15) = tan(9^o) \times x\\\\(x+15)= \dfrac{tan(9^o) }{tan(3.5^o) }\times x\\\\x+15=2.59\ x\\15 = 2.59x-x\\15= 1.59x\\x = 9.44[/tex]
Substituting the value of x
[tex]CD=tan(9^o) \times(x)[/tex]
[tex]CD=tan(9^o) \times(9.44)\\CD= 1.495[/tex]
Hence, the height of the mountain is 1.495 miles.
Learn more about Tangent (Tanθ) function:
https://brainly.com/question/10623976
Related Questions
Find the percent change. Tell whether it is a percent increase or decrease. from 50 to 42
Answers
If the percent change is positive, it is an increase.
If the percent change is negative, it is a decrease.
percent change = (42 - 50)/(50) * 100 = -8/50 * 100 = -16%
It is a 16% decrease.
What happens when you multiply a fraction by 1?
Answers
You push the ball with a force of 22.8N which includes a- 2.3N frictional force. So, what is the net force while you push the ball?
Answers
They are opposing forces. you subtract the frictional force.
22.8 N - 2.3 N = 20.5 N
The perimeter of a rectangle is 16 inches. The equation that represents the perimeter of the rectangle is 2l + 2w = 16, where lrepresents the length of the rectangle and w represents the width of the rectangle. Which value is possible for the length of the rectangle?
Answers
It is basically a trick question. Firstly we have to ficus on the given formula to get to the answer for this question.
2l + 2w = 16
2(l + w) = 16
l + w = 8
l = 8 - w
Mow w cannot be less than 1. So the length of the rectangle cannot be more than 7. So we can conclude that 7 inches is the correct option or the first option is the correct option among the given options.
Hope this helped!!!!!
name each polynomial by degree and number of terms calculator.
1. -8
2. -4 + 10n
3. 5a^4 - 2a^3 + 7a
4.-3+8v^2
5. -9^5 + 6x^3 - 7x^2 -
9x^4
Answers
1. X=0
2. N=1, linear equation
3. A=4 (looking at the biggest exponent remember), quartic function
4. V=2, quadratic equation
5. X=3, cubic equation
6. X=4, quartic equation
Hope I helped :)
A candle is 17 in. tall after burning for 3 hours. After 5 hours, it is 15 in. tall. Write a linear equation to model the relationship between height h of the candle and time t. Predict how tall the candle will be after burning 8 hours.
Answers
x = 3 , y = 17
x = 5 , y = 15
m = (15 - 17)/(5 - 3) = -2/2 = -1
y - 17 = -1(x - 3)
y = -x + 20
at x = 8 => y = 12 in Hope it Helps :)
BRAINLIEST TO BEST ANSWER!!!
What are the domain and range of the function???
Answers
the curved line starts at (6,0) so the domain is x≥6
the range is the Y value, since the curved line continues off the graph and does not cross over the x axis the range would be y≥0
Please write the function
Answers
Given an int variable n that has been initialized to a positive value and, in addition, int variables k and total that have already been declared, use a do...while loop to compute the sum of the cubes of the first n whole numbers, and store this value in total. thus if n equals 4, your code should put 1*1*1 + 2*2*2 + 3*3*3 + 4*4*4 into total. use no variables other than n, k, and total.
Answers
Suppose a triangle has sides 3, 4, and 5. Which of the following must be true?
A.The triangle in question is not a right triangle.
B.The triangle in question is a right triangle.
C.The triangle in question may or may not be a right triangle.
Answers
Answer: B.The triangle in question is a right triangle.
Step-by-step explanation:
The Converse of Pythagoras theorem says that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides then the triangle is a right triangle.
The given sides of triangle : 3, 4, and 5.
Here, Measurement of largest side = 5
Then , [tex]5^2=25[/tex]
Also, [tex]4^2+3^2=16+9=25[/tex]
[tex]\Rightarrow\ 5^2=4^2+3^2[/tex]
Hence, by the converse of Pythagoras theorem, the triangle in question is a right triangle.
Answer:
HAS TO BE A RIGHT ANGLE
Step-by-step explanation:
…..
Which has the smaller scale: a map on which 1 inch equals 200 miles a map on which 1 inch equals 100 miles?
Answers
BRAINLIEST!! THANKS!! STARS!!
Find ONLY the areas of the polygons
Answers
11.
area for lower left = 52*62 = 3224
area for upper right = 68*54 = 3672
total area = 3224 + 3672 = 6896 square yards
12.
area of upper left = 57-69 = 3933
area of lower right = 24*37 = 888
total area = 3933 +888 = 4821 square feet
Convert the mixed number to a decimal. 4 6/25 A. 4.12 B. 4.24 C. 4.25 D. 4.625
Answers
4 6/25 = 106/25 = 4.24
Are number 2,3,5,7 and 8 correct?
Answers
Reason 2: Same Side Interior Angle Theorem
Reason 3: Definition of Supplementary
Reason 5: Definition of Congruence
Reason 7: Definition of Supplementary
------------------------------------
Explanation:
Reason 2: The "Same Side Interior Angle Theorem" is the idea that if we know two lines are parallel, then the interior angles on the same side of the transversal line will be supplementary (add to 180 degrees). In other words, the two angles can be combined to form a straight angle
Reason 3: If we're told two angles are supplementary, then by definition it means they add to 180 degrees.
Reason 5: If two angles are congruent, then they have the same measure (eg: both are 60 degrees)
Reason 7: This is the reverse of reason 3, more or less. If we know two angles add to 180 degrees then we can say they are supplementary. When it comes to definitions we can reverse it (i.e, if P, then Q reverses to if Q then P)
The graph of y=-4x+7 is:
A. a line that shows the set of all solutions to the equation.
B. a point that shows one solution to the equation.
C. a point that shows the y-intercept.
D. a line that shows only one solution to the equation.
Answers
Answer:
A. A line that shows the set of all solutions to the equation
Step-by-step explanation:
The density of water is 1.0 g/cm3 how many deciliters of water will fill
a.5-l bottle
Answers
Question 12 information reference tables look at each expression. is it a factor of 8x4 + 2x2 – 45 when this expression is fully factored? select yes or no for expressions a –
d.
a. 2x2 + 3 yes no
b. 2x2 + 5 yes no
c. 2x – 3 yes no
d. 4x2 – 9 yes no
Answers
(a) 2x^2 + 3....no
(b) 2x^2 + 5...yes
(c) 2x - 3....yes
(d) 4x^2 - 9)...no...not when it is fully factored
divide -2x^3-5x^2+4x+2 by x+2
Answers
Final answer:
The detailed answer explains how to divide a polynomial by another using long division method.
Explanation:
To divide -2x³-5x²+4x+2 by x+2, we will perform polynomial long division:
-2x³-5x²+4x+2 / x+2
Start by dividing the leading terms: -2x³ / x = -2x². Multiply x+2 by -2x² to get -2x³-4x². Subtract this from -2x³-5x² to get x². Bring down the 4x next. Continue the process and you will get a quotient of -2x²+x-2 with a remainder of 6.
the weight of a rectangular block of metal varies jointly as its length, width and thickness. If the weight of a 13dm by 8dm by 6dm block of aluminum is 18.2kg, find the weight of a 16dm by 10dm by 4dm block of aluminum??
Answers
Factor the expression. 21x2 + 55x + 14
Answers
Is the 2 an exponent or variable?
Answer:
(3x + 7)(7x + 2)
Step-by-step explanation:
Alvin’s age is two times Elga’s age. The sum of their age is 60. What is Elga’s age?
Answers
x = Elgas age
2x = Alvins age
x +2x = 60
3x =60
x = 60/3 = 20
Elga is 20 years old
Final answer:
By setting Elga's age as x and establishing an equation based on the given relationship and sum of their ages, we calculated Elga's age to be 20 years old.
Explanation:
To determine Elga's age, we will use the information given:
1. Alvin's age is two times Elga's age.
2. The sum of their ages is 60.
Let's define Elga's age as x. Then, Alvin's age would be 2x since it is two times Elga's age. The sum of their ages can be written as the following equation:
x + 2x = 60
This simplifies to 3x = 60. To find Elga's age, we divide both sides by 3:
3x / 3 = 60 / 3
x = 20
Therefore, Elga's age is 20 years old.
Which conjunction or disjunction is equivalent to the following inequality?
|a - 9| ≤ 4
a - 9 ≤ 4 AND a - 9 ≤ - 4
a - 9 ≤ 4 AND a - 9 ≥ - 4
a - 9 ≤ 4 OR a - 9 ≤ - 4
a - 9 ≤ 4 OR a - 9 ≥ - 4
Answers
|x - a| ≤ k => - k ≤ x - a ≤ k
So, |a - 9| ≤ 4 => - 4 ≤ a - 9 ≤ 4
Which is a - 9 ≥ - 4 and a - 9 ≤ 4.
That is the second option.
Answer: a - 9 ≤ 4 and a - 9 ≥ - 4
Answer:
a - 9 ≤ 4 and a - 9 ≥ - 4
Step-by-step explanation:
At the beginning of the week, Naveen has 87 trading cards. On Monday, he gets 9 more. On Tuesday, he gives 16 away. On Wednesday, he is given 3 by a friend. On Thursday, he sells all of his cards to a collector. The collector pays him a rate of c for every card that Naveen has. If Naveen earns $124.50 from the sale, what is c, the rate that the collector pays for each card?
$1.08
$1.50
$41.50
$83.00
Answers
is
$1.50
87+9= 96
96-16=80
80+3= 83
$124.50/ 80= $1.56 per card,
$1.50 is the closest option to the exact answer
Complete the inequality statement with the symbol that makes it true.
1.67 ___ 16.7
>
<
=
Answers
Answer:
The symbol in the blank space would be '<'
Step-by-step explanation:
Since, in inequality,
'>' = greater than,
'<' = less than,
'≥' = greater than equal to,
'≤' = less than equal to,
Now, 1.67 × 10 = 16.7
⇒ 16.7 is 10 times of 1.67,
That is,
1.67 is less than 16.7
⇒ 1.67 < 16.7
Hence, THIRD option is correct.
Calculate the value of the area between the function f(x)=x^2-4f(x)=x2−4 and the x-axis on the interval from x = 0 to x = 2. round your answer to one decimal place.
Answers
f(x) = x² - 4
Differentiating,
f'(x) = 2x
Then, we officially have 2.
f'(2) = 2(2) = 4
f'(0) = 2(0) = 0
To determine the area, subtract the given answer to get 4 units squared.
Answer: 4 units/guarrantee
[tex] A = \int\limits^2_0 {(x^{2}-4) } \, dx [/tex]
A = [x³/3 - 4x]lim 0->2
A = (2³/3 - 4(2)] - (0³/3 - 4(0)]
A = 16/3 - 0
A = 16/3 ≈ 5.3 sq. units
Which of these is the statement of the zero product rule?
A. If a • b = 0, then either a = 0 or b = 0, but not both.
B. If a • b = 0, then a = 0 and b = 0.
C. If a • b = 0, then a = 0.
D. If a • b = 0, then either a = 0 or b = 0, or both.
Answers
Answer: Hello mate!
If you have any real number A; you always have that:
A*0 = 0
this means that the product between a number A and zero, is equal to zero, and this is for every number. (note that A can be equal to 0, and 0*0 = 0)
Then if a*b = 0, you know that, at least one of the numbers is equal to zero, and there is possible that both numbers are equal to zero.
And with this information, you can see that the right answer is D.
"if If a • b = 0, then either a = 0 or b = 0, or both."
because:
0*b = 0
a*0 = 0
0*0 = 0
Final answer:
The zero product rule states that if the product of two multiplicands equals zero, then at least one of the multiplicands must be zero, which is correctly represented by option D.
Explanation:
The correct statement of the zero product rule is: If a • b = 0, then either a = 0 or b = 0, or both. This is accurately represented by option D. The zero product rule is a foundational concept in algebra that asserts when the product of two or more numbers or variables equals zero, at least one of the multiplicands must be zero. It's crucial for solving equations where a product is set equal to zero, as it allows for each factor to be set equal to zero and solved individually. This rule is pivotal in finding solutions to polynomial equations, among others. For example, in the equation (x + 2)(x - 3) = 0, applying the zero product rule we set each factor equal to zero: x + 2 = 0 or x - 3 = 0, leading to the solutions x = -2 or x = 3, respectively.
What does it mean for a set of financial records to be comprehensive?
a. Comprehensive records are protected against theft and fire.
b. The records must contain sufficient information to cover all of your financial plan. c. At least two people must be able to view and assess the records.
d. The records must contain every one of your financial files, such as pay stubs and receipts.
Answers
Answer:
B. The records must contain sufficient information to cover all of your financial plan.
Step-by-step explanation:
For a set of financial records to be comprehensive, means - The records must contain sufficient information to cover all of your financial plan.
One should prepare all the strategies before hand and all the details of ones financial plans should be thoroughly examined , before implementing any plan.
confused on this question
Answers
since WZ is a bisector of the quadrilateral, that means, it makes two equal halves at the vertex Z and W, that means each triangle gets of those twin angles, so those two angles are the same for both triangles.
now, notice, the segment WZ is shared by both triangles, and thus the tickmark, is the same length for both.
so, you have on Angle and then a Side and then another Angle, two angles and the side between them equal in each triangle, thus congruents by ASA.
Taylor made 5 1⁄4 cups of iced tea. How many 10 ounce glasses can he fill to the brim with iced tea?
Answers
4
Explanation:
Word problems like this are always a bit tricky to get to the bottom to.
But to put it simply, this question is asking how many times can 10 oz be taken out of 5 1/4 cups. This is also shown as:
5 1/4 cups ÷ 10 ounces
First, make both numbers the same units. Since ounces are smaller, convert 5 1/4 cups into ounces.
5 1/4 cups
5 cups = 40 ounces
1/4 cup = 2 ounces
40 + 2 = 42 ounces.
so now do this:
42 ÷ 10 = 4.2
So Taylor can fill 4 full glasses with iced tea.
The Witches coven are making a potion and Ethel, Glinda, Locasta and Circe each add a different ingredient. When the potion is finished, there is 1/4 of the bat blood left, 1/3 of the knotgrass, 1/2 of the moonstone and 5/8 of the unicorn hair. Ethel used the most. Glinda used the least. Locasta used more than Circe. Who used the moonstone?
Answers
The moonstone was used by [tex]\fbox{\begin\\\ \bf Circe\\\end{minispace}}[/tex].
Further explanation:
It is given that a potion is prepared by a group of witches. The members in the group are Ethel, Glinda, Locasata and Circe.
The ingredients used in the preparation of the potion are bat blood, knotgrass, moonstone and unicorn hair.
Each member of the group add a different ingredient which means that no two member of the group add the same ingredient.
As the preparation of the potion is finished it is observed that the [tex]\dfrac{1}{4}th[/tex] of the bat blood is left, [tex]\dfrac{1}{3}rd[/tex] of the knotgrass is left, [tex]\dfrac{1}{2}nd[/tex] of the moonstone is left and [tex]\dfrac{5}{8}th[/tex] of the unicorn hair is left.
From the above statement it is concluded that [tex]25\%[/tex] of the bat blood is left, [tex]33.33\%[/tex] of the knotgrass is left, [tex]50\%[/tex]of the moonstone is left and [tex]62.5\%[/tex] of unicorn hair is left.
Therefore, the percentage of ingredients used in the preparation of the potion are as follows:
Bat blood: [tex]75\%[/tex] is used
Knotgrass: [tex]66.67\%[/tex] is used
Moonstone: [tex]50\%[/tex] is used
Unicorn hair: [tex]37.5\%[/tex] is used
As per the question Ethel used the most so, the ingredient bat blood was used by Ethel.
As per the question Glinda used the least so, the ingredient unicorn hair was used by Glinda.
It is given that Locasta used more than Circe so, the ingredient knotgrass was used by Locasta and moonstone was used by Circe.
Therefore, the ingredient moonstone was used by [tex]\fbos{\begin\\\ \bf Circe\\\end{minispace}}[/tex].
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Percentages and Fraction
Keywords: Percentages, fraction, Ethel, Glinda, Locasata, Circe, potion, bat blood, knotgrass, moonstone, unicorn hair, numbers, witches, coven, simplification.