The points G and H, 19m apart are on the same side of a tree. The angles of elevation of the top T, of the tree from G and H on the horizontal ground with the foot of the tree are 430 and 38° respectively. (1). Illustrate the information in a diagram. (i). Find, correct to one decimal place, the height of the tree.
Answers
Using relations in a right triangle, we have that the height of the tree is of 91.6 meters.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.The graph for this problem is given at the end of the answer, and using it and the relations, we can build two equations involving x and the height h, and solve the system of equations for h.
From the triangle involving point G(angle of 43º), we can build the following relation:
tan(43º) = h/x
0.9325 = h/x
x = (1/0.9325)h.
x = 1.0724h (because we want to find h, hence we write x as a function of h).
From the larger triangle, that has the angle of 38º, we have the following relation.
tan(38º) = h/(x + 19).
tan(38º) = h/(1.0724h + 19). (considering that x is a function of h, as we found above).
0.7813 = h/(1.0724h + 19).
Hence, we apply cross multiplication to solve for h, as follows:
h = 0.7813(1.0724h + 19).
h = 0.8379h + 14.8447.
0.1621h = 14.8447
h = 14.8447/0.1621
h = 91.6 meters.
Hence:
The height of the tree is of 91.6 meters.
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Related Questions
What is the student error in the multiplication below?
Multiply the ones: 957 times 23 = 2871. Above the 9 in 957 is 1, above the 5 in 957 is 2.
Multiply the tens: 957 times 23 = 2871. 2871 + 1914 = blank. Above the 9 in 957 is 1, above the 5 in 957 is 1.
Answers
Answer:
When multiplying the tens, the student didn't use the 0 place holder for the ones place.
Step-by-step explanation:
When using or doing long multiplication the answer was correct (2871) BUT before multiplying the tens, a zero should be placed in the ones place of the results. So, the tens should be 19140
2871+19140=22011
Answer: 1) When multiplying the ones, the student did not carry over a ten to the next place in the first multiplication.
2) When multiplying the ones, the student should have calculated 3 times 2 plus 5 as 11 and placed a 1 in the tens place.
3) When multiplying the tens, the student did not use the 0 place holder for the ones place.
4) When multiplying the tens, the student should have calculated 2 times 1 plus 9 as 11 and used a 1 should in the hundreds place.
Answer:
The correct option is;
4) When multiplying the tens, the student did not use the 0 place holder for the ones place
Step-by-step explanation:
Here we have when doing long multiplication, the student correctly multiplies the ones as 2871, however, before commencing multiplication of the tens, a 0 should be placed in the ones place of the result as a place holder such that the outcome of the multiplication of the tens should be;
19140
Hence, the correct result should be 2871 + 19140 = 22011
The correct option is therefore, that "When multiplying the tens, the student did not use the 0 place holder for the ones place."
Step-by-step explanation:
The Clear-Bell Cell phone company has a plan that costs
customers $29.99 for a monthly service fee plus 3¢ per minute used.
a. Write a linear equation to model this situation.
b. Identify the slope and the y-intercept. Interpret the slope and y-intercept in the context of this problem.
c. If Polly talks for 136 minutes, how much would her cell phone bill be (excluding taxes)?
Answers
Answer: a. y=0.03x+29.99
b. Slope: 0.03. $0.03 charged every minute Clear-Bell Cell phone is used.
y-int: (0, 29.99). Total cost per month when phone isn't being used.
c. $34.07
Step-by-step explanation:
a. p=Cell phone plan. m=minutes used for phone.
3¢=$0.03
p=29.99+0.03m
y=0.03x+29.99
b. Slope: 0.03. $0.03 charged every minute Clear-Bell Cell phone is used.
y=0.03(0)+29.99
p=29.99 ==> y-int: (0, 29.99). Total cost per month when phone isn't being used.
c. y=0.03(136)+29.99
y=4.08+29.99
y=$34.07
X
. You deposit money in an account that earns Simple interest at an annual rate of 6%. After 8 years.
Y
the account earns $360 in interest. How much money did you deposit in the account?
Answers
Answer:
$750
Step-by-step explanation:
I = interest
p = principle
r = rate
t = time
I = prt Plug in what you know and solve for p
360 = p (.06)(8)
360 =p.48 Divide both sides by .48
750 = p
The principal is deposited in the account is $750.
Given that, rate of interest =6%, time period = 8 years and simple interest = $360.
What is the simple interest?Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.
Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.
Now, 360 = (P×6×8)/100
⇒ 360 = 48P/100
⇒ 48P = 36000
⇒ P = 36000/48
⇒ P = $750
Therefore, the principal is deposited in the account is $750.
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a tripod has three legs each of length 5 feet. when the tripod is set up, the angle between any pair of legs is equal to the angle between any other pair, and the top of the tripod is 4 feet from the ground. in setting up the tripod, the lower 1 foot of one leg breaks off. let $h$ be the height in feet of the top of the tripod from the ground when the broken tripod is set up. then $h$ can be written in the form $\frac{m}{\sqrt{n}}$, where $m$ and $n$ are positive integers and $n$ is not divisible by the square of any prime. find $\lfloor m \sqrt{n} \rfloor$. (the notation $\lfloor x \rfloor$ denotes the greatest integer that is less than or equal to $x$.)
Answers
The value of [m + √n] is 183.
We note that AO=3. From this we can derive that the side length of the equilateral is 3√3. We now use 3D coordinate geometry.A is (0, 0, 0), B is (3√3, 0, 0), C is ((3√3)/2, 9/2, 0), T is ((3√3)/2, 3/2, 4), and S is ((3√3)/10, 3/10, 4/5).We know three points of the SCB plane, so we can write out the equation for the plane. Plane SCB can be expressed as (4√3)x + 4y + 39z - 36 = 0.Applying the distance between a point and a plane formula(ax + by + cz + d)/(√(a² + b² +c²)Put T's coordinates in this in (x, y, z), and replace the values of a, b, c, and d with plane equation coefficients.We get the distance equal to 144/(√1585).A distance of the form m/(√n) is given to us.We have to calculate [m + √n] = [144 + √1585] = 183.To learn more about plane, visit :
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The price of an item has been reduced by $6.18. The new sale price is $30.55. What was the original price?
Answers
Answer:
30.55 + 6.18 = $36.73
Step-by-step explanation:
mark the brainliest
What transformation is represented by the rule
(1, y) → (1, y+3)?
O translation 3 units down
O translation 3 units right
O translation 3 units up
O translation 3 units left
Answers
two third of a number minus 5 gives 11
what is the number?
Answers
Answer: n=24
Step-by-step explanation:
n=number
2/3 * n - 5=11
2n/3=16
2n=48
n=24
2/3n (otherwise written as 2/3 • n) - 5 = 11
Any time there is a fraction of a number, that signifies for multiplication.
Let’s eliminate 5 by adding it to both sides of the equation:
2/3n - 5 + 5 = 11 + 5
2/3n = 16
Now we know that 2/3 of a number gives us 16. Now, let’s divide both of our numbers by 2/3:
• 2/3 divided by 2/3 gives us 1
• 16 divided by 2/3 gives us 24
Hence, 2/3 of 24 gives us 16.
n = 24
Let’s plug 24 into our original equation now:
2/3(24) - 5 = 11
16 - 5 = 11
Because this equation is true, we have solved for n. Our number is 24.
I need help with this one
Answers
Answer:
c) -66%, -0.45, -1/3, 1.8
Step-by-step explanation:
Numbers provided:
-66%-1/3-0.451.8Rewrite them in decimals:
-66% = -0.66-1/3 = -0.33-0.45 = -0.451.8 = 1.8In ascending order (from least to greatest):
-0.66 < -0.45 < -0.33, 1.8-66% < -0.45 < -1/3 < 1.8Solution: -66%, -0.45, -1/3, 1.8
given that $a$ is an odd multiple of $7767$, find the greatest common divisor of $6a^2 49a 108$ and $2a 9$.
Answers
Odd Multiples of 7767 are 1, 3, 9, 863, 2589, 7767.The greatest common divisor of [tex]$6a^2 49a 108$[/tex] = 6×1×49×1×108= 31,752 and
2a9=2×1×9=18
What do you mean by Greatest Common Divisor?The largest positive integer that divides each of two or more non-zero integers is known as the greatest common divisor (GCD) in mathematics. The greatest common divisor of two numbers x and y is shown for x and y. As an illustration, the GCD of 8 and 12 equals 4, or. The words "divisor" and "factor" can be swapped out in the name "largest common divisor" so that alternative names such as "highest common factor" (HCF), etc. can be used instead. In the past, the term biggest common measure has been used to refer to the same idea.
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Find the perimeter and area of the
polygon with the given vertices.
W(5, — 1), X(5, 6), Y(2, — 1), Z(2, 6)
The perimeter is units. The area is
squareunits.
Answers
The perimeter of the polygon will be 20 units and the area will be 21 square units.
From the given vertices a rectangle will be formed. A rectangle is a closed figure in which each interior angle is a right angle. The Perimeter of the rectangle can be given by formula 2(l + b) and the area is given by l×b where l is the length and b is breadth of rectangle. Now from the given points the dimensions of rectangle will follow the order W (5, -1), X (5, 6), Z (2, 6) and Y (2, -1).
The length of the rectangle is given by l = √ (6 + 1) ² + (5 - 5) ²
l = √49
l = 7 units
The breadth of the rectangle is given by b = √ (6 - 6) ² + (2 - 5) ²
b = √9
b = 3 units
Now, the perimeter of rectangle = 2 (l + b)
P = 2(7 + 3)
P = 20 units
Area of the rectangle = l×b
A = 7×3
A = 21 square units.
Thus, the perimeter and area are 20 units and 21 square units respectively.
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How do we find the "rate of change"
Answers
Answer: To find the average rate of change, divide the change in y-values by the change in x-values
Step-by-step explanation:
Identify the rule(s) of algebra illustrated by the statement. (Select all that apply.) 1 · (1 + x) = 1 + x
Answers
The rule(s) of algebra illustrated by the statement is the identity property of algebra
How to identify the rule(s) of algebra illustrated by the statement.?The statement is given as:
1 · (1 + x) = 1 + x
The identity property of algebra states that:
1 * a = a or a * 1 = a
In the above (given) statement, we can see that the expression 1 + x is multiplied by 1 to given 1 + x
This can be illustrated as
1 * a = a
The rule(s) of algebra that illustrates the above equation is the identity property of algebra
Hence, the rule(s) of algebra illustrated by the statement is the identity property of algebra
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|3x + 3|-5> 4
please help me it’s due at 3:30
Answers
Answer:
x > 2 or x < −4
Step-by-step explanation:
Let's solve your inequality step-by-step.
|3x + 3| −5 > 4
Step 1: Add 5 to both sides.
|3x + 3| −5 + 5 > 4 + 5
|3x + 3| > 9
Step 2: Solve Absolute Value.
|3x + 3| > 9
We know either3x + 3 > 9 or 3x + 3 < −9
3x + 3 > 9(Possibility 1)
3x + 3 −3 > 9 −3(Subtract 3 from both sides)
3x > 6
3x > 6 (Divide both sides by 3)
3 3
x > 2
3x + 3 < −9(Possibility 2)
3x + 3 −3 < −9 −3(Subtract 3 from both sides)
3x < −12
3x < -12 (Divide both sides by 3)
3 3
x < −4
Need help rn pleas e
Answers
Answer:
659
Step-by-step explanation: Divishion of practice
Answer:
Area : 63.6 square inches.
Cost: Cost per square inch = 18.60 / 63.6 = $0.29 (rounded to the nearest cent)
Step-by-step explanation:
your bedroom sock drawer contains 4 green socks and 6 yellow socks that are mixed together. the light in your room is broken so you must select your socks in the dark. what is the probability you will select two socks of the same color on your first try?
Answers
The probability of selecting two socks of same color is 0.96.
According to the given question.
Total number of green socks = 4
Total number of yellow socks = 6
So, the total number of socks in a drawer = 4 + 6 = 10
Since as we know that, the probability of an event is computed as: P(E) = Number of favourable outcome /Total number of outcomes. Hence, the probability is the possibility of the occurrence of a random event.
So, the probability of selecting a green scoks = 4/10 = 2/5
And the probability of selecting a yellow socks = 6/10 = 3/5
Therefore, the probability of selecting two socks of same color
= probability of selecting both the green socks or probability of selecting both the yellow socks
= [( 2/5) + (2/5)] × [(3/5)+(3/5)]
= (4/5) × (6/5)
= 24/25
= 0.96
Hence, the probability of selecting two socks of same color is 0.96.
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What are the leading coefficient and degree of the polynomial -u^8+18+10u^3
Answers
Answer:
Step-by-step explanation:
The variable here is u, and the highest power of u is u^8. The first term is thus -u^8, and the coefficient of this is -1. Thus, the leading coefficient of the polynomial is -1. The degree is 8.
A pharmacist mixes 5g of a power with 45cm of water to make a prescription medicine . how much powder should she mix with 81cm of water to make a larger amount of the same medicine.
Answers
The pharmacist should mix 9 g of a power to make a larger amount of the medicine
To solve this problem, we have to state the equation using the information of the problem
Information about the problem:
mass(1) = 5gvolume(1) = 45 cm3volume(2)= 81 cm3mass(2) = ?Calculating the rate of the medicine with the 1st mixed:
rate = mass(1)/ volume(1)
rate = 5g / 45cm3
rate = 0.11 g/cm3
Calculating how much power the pharmacist needs for the volume(2):
mass(2) = rate * volume(2)
mass(2) = 0.11 g/cm3 * 81 cm3
mass(2) = 9 g
What are algebraic operations?We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
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can anyone answer this for me
Answers
Answer:
{-9, 3, 10}
Step-by-step explanation:
Place the elements (the numbers marked by red) within curly brackets.
natalie has a budget of $15,000 dollars to spend on tracking devices to study bison. a radio tracker costs $650 and a gps tracker costs $1400. natalie wants to buy at least 9 radio trackers and more than 3 gps trackers. the following system of inequalities represents this situation, where x is the number of radio trackers and y is the number of gps trackers. x ≥ 9 y > 3 650x 1400y ≤ 15000 which yellow shaded region corresponds to natalie's possible choices?
Answers
Natalie will choose 7 and 8 as the yellow-shaded region corresponds to Natalie's possible choices.
What do you mean by GPS?Even though it appears complex, 3-dimensional trilateration is a straightforward mathematical process that underlies GPS. It's critical to have a fundamental understanding of 2-D Trilateration, which is necessary to completely comprehend 3-D Trilateration. Similar principles apply to three-dimensional trilateration, however, spheres rather than circles are used. Here is how the Global Positioning System uses 3-D trilateration to pinpoint an object's precise location. When the first satellite sends a signal, the GPS receiver measures the distance between the two. Say the distance between the receiver and the satellite is 20 000 miles. This implies that the receiver might be located anywhere on the 20 000 km diameter green sphere's surface and in any direction.
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Which of the following is not a rational number?
Α. 0
B. √2
C. 3/4
D. √4
Answers
Answer: B
Step-by-step explanation: the square root of 2 cannot really be expressed as a fraction where both the numerator and the denominator are integers.
Answer:
B
Step-by-step explanation:
Find the surface area of a cube with side length og 6 1/2 inches.
PLEASE SHOW WORK
Answers
The surface area of a cube with side length of 6 1/2 inches is 253.5 square in
Surface area of cubeThe formula for calculating the surface area of cube is expressed as:
Surface area = 6L^2
where
L is the side length of the cube
Substitute
SA = 6(13/2)^2
SA = 6 * 169/4
SA = 3 * 169/2
SA = 253.5 square in
Hence the surface area of a cube with side length of 6 1/2 inches is 253.5 square in
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Lynden's first two, 100-meter-dash times are 13.075 seconds and 12.55 seconds. what are her mean (average) time? round your answer to the thousandths place.
Answers
The average time of Lynden's first two, 100-meter-dash is 12.813 seconds.
We are given the 100-meter-dash times of Lynden in first two races. So, the average time for first two races will be calculated using the formula -
Average = sum of all observations ÷ total number of observations
Sum of all observations here will be the sum of time of race.
Sum of observations = 13.075 + 12.55
Performing addition
Sum of observations = 25.625 seconds
Number of observations is the number of races whose time is taken in calculation.
Number of observations = 2
Keep the values in formula to find the average time.
Average time = 25.625 ÷ 2
Average time = 12.8125 seconds.
Rounding to nearest thousands place : 12.813 seconds
Hence, the average time of Lynden's first two, 100-meter-dash is 12.813 seconds.
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In ΔUVW, w = 3 inches, ∠W=23° and ∠U=73°. Find the length of u, to the nearest 10th of an inch.
Answers
The length of u by using sine rule is 7.4 to the nearest 10th of an inch.
What is sine rule?In mathematics, sine rule is a trigonometric method which relates the angle and side of a triangle. We can say that by using the sine rule we can find the side of any triangle if we knows the angle and vice versa. This rule is also known as law of sines.
Formulas for sine rule:
If we have three sides a, b, c and angle say A, B and C respectively .Then sine rule is :
[tex]\frac{Sin A}{a} = \frac{Sin B}{ b} = \frac{Sin C}{c}[/tex]
In the given question,
Sine rule will be used to get the unknown side of the triangle.
According to the rule;
[tex]\frac{Sin U}{u} = \frac{Sin V}{ v} = \frac{Sin W}{w}[/tex]
Given w = 3 in, ∠W=23° and ∠U=73°, substitute into the equation above to get u we have;
we can write the eq. as
[tex]\frac{Sin U}{u} = \frac{Sin W}{w}[/tex]
[tex]= > u = \frac{w \ sinu}{sinw} \\\\= > u = \frac{3 sin73}{sin 23} \\\\= > u = \frac{2.87}{0.39}\\ \\= > u = 7.398 = 7.4[/tex]
Hence, length of u is 7.4 inches to the nearest 10th of an inch.
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If M is a midpoint of segment AB and AM=3x+1, if AB=20 cm what is the value of x?
Answers
Answer:
x = 3
Step-by-step explanation:
AB is the line segment and is 20 cm
Since M is the midpoint, AM = MB = 20/2 = 10
3x + 1 = 10
==> 3x = 10- 1 = 9
==> x = 9/3 = 3
Answer:
AB=20 then AM =10
now,
[tex]3x + 1 = 10 \\ 3x = 10 - 1 \\ 3x = 9 \\ x = 3 [/tex]
brainliest to coorrrect answer
Answers
The measures of angles q, r and s are 100°, 135° and 125° and the sum of the three angles equals 360°.
What are the measures of missing angles of a geometric system?
In this problem we find a geometric system generated by three lines no collinear to each other, which generate the triangle DEF. In accordance with the Euclidean geometry, the sum of the measures of internal angles in a triangle equals 180°:
m ∠ FDE + m ∠ DEF + m ∠ DFE = 180° (1)
If m ∠ FDE = 80° and m ∠ DEF = 45°, then the measure of the angle DFE is:
m ∠ DFE = 55°
Finally, we find the values of the angles q, r and s by definition of supplementary angles:
q = 180° - 80°
q = 100°
r = 180° - 45°
r = 135°
s = 180° - 55°
s = 125°
The sum of the measures of angles q, r and s is:
q + r + s = 360°
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I need help solving. Im stuck please help me.
Answers
The expression is
x^0 + (x^9 + x^5)
We know any number to the power of zero (0) is 1, so now we have
1 + (x^9 + x^5)
If we used x=1,
1 + (1^9 + 1^5)
1 + 1 + 1 = 3, ❌ it is not greater than 82
Let’s try x = 2
1 + (2^9 + 2^5)
1 + 512 + 32 = 545
545 is greater than 82
So we know the number has to be more than 1 because 1 did not work
Keitaro walks at a pace of 3 miles per hour and runs at a pace of 6 miles per hour. Each month, he wants to complete at least 36 miles but not more than 90 miles. The system of inequalities represents the number of hours he can walk, w, and the number of hours he can run, r, to reach his goal.
3w + 6r ≥ 36
3w + 6r ≤ 90
A graph shows w on the x-axis, from 0 to 30, and t on the y-axis, from 0 to 24. Two solid lines are shown. The first line has a negative slope and goes through (0, 6) and (12, 0). Everything above and to the right of the line is shaded. The second line has a negative slope and goes through (0, 15) and (30, 0). Everything to the left of the line is shaded.
Which combination of hours can Keitaro walk and run in a month to reach his goal?
2 hours walking; 12 hours running
4 hours walking; 3 hours running
9 hours walking; 12 hours running
12 hours walking; 10 hours running
Answers
The combination of hours that Keitaro can walk and run in a month to reach his goal will be A. 2 hours walking; 12 hours running
How to illustrate the information?From the information, Keitaro walks at a pace of 3 miles per hour and runs at a pace of 6 miles per hour. Each month, he wants to complete at least 36 miles but not more than 90 miles.
The equation is
3w + 6r ≥ 36
3w + 6r ≤ 90
The combination of hours that Keitaro can walk and run in a month to reach his goal will be 2 hours walking; and 12 hours running.
This will be:
3w + 6r ≤ 90
3(2) + 6(12)
6 + 72 = 78
Therefore, 78 is less than 90.
The correct option is A.
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In a week, a man received a paycheck for $826.60. The withholding for taxes was $91.40. If he worked 34 hours in that week, what is his hourly pay rate?
Answers
Answer:
Step-by-step explanation:
Calculus help please
Answers
Step-by-step explanation:
THE POINT WHERE
[tex]f( - 4) = ( { - 4})^{2} + 1 \\ f( - 4) = 16 + 1 \\ f( - 4) = 17[/tex]
Now we have point (-4,17)
the gradient of the tangent line at that point of f(x) is the first derivative f'(x)=2x at that point
f'(x) =m
f'(-4)=2(-4)
f'(-4)=-8
The gradient therefore is -8
the general equation of a straight line is given by
[tex]y = mx + c \\ 17 = ( - 8)( - 4) + c \\ 17 = 32 + c \\ c = 17 - 32 \\ c = - 15 \\ \\ y = - 8x - 15[/tex]
HOPE THIS HELPS!!
write a ratio and sentence comparing the number of jeans bought to the cost
Answers
In words, the ratio of the number of jeans bought to the cost is four to thirty two.
How to write a ratio?
We are told that you just bought 4 pairs of jeans for $32.
Now, since you bought 4 pairs for a cost of $32, then we can say that the ratio to represent the number jeans per dollars is;
4 :32
Thus, writing this in words we can say that the ratio of the number of jeans bought to the cost is four to thirty two.
Alternatively, we can also express it as a fraction with numerator and denominator as 4/32.
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Complete question is;
You just bought 4 pairs of jeans for $32. write a ratio and sentence comparing the number of jeans bought to the cost