A surveying instrument aimed at a location can “shoot” the distance to the location, giving the surveyor a measurement. A surveyor used such an instrument to record the distance to a point on a tree 60 m from his position. After rotating his surveying instrument 57° to the left, he measured the distance from his same position to a fence post 35 m away.
a.) Draw the diagram and label the tree as point T, the surveyor as point S, and the fence post as point F.
b.) Determine the distance between the point on the tree and the fence post. (Show
the appropriate formula, substitutions, and work. Give the distance to the nearest tenth of
a meter.)
c.) Use the Law of Sines to find the measure of T. (Show the appropriate formula, substitutions, and work. Give the measure of T to the nearest degree.)
d.) Find mF
Please Help Me :(
Answers
b. Here we are looking for the distance between the tree (T) and the fence post (F). So we want the length of FT. We have the lengths of two sides and an angle and want the other side. The side we seek is opposite the angle whose measure we know. In this case we can use the law of cosines.
The law of cosines is: [tex] c^{2} = a^{2} + b^{2} -2abcosC[/tex]
I have labeled the side we want FT this c in the diagram. It is opposite the 57 degree angle which we will call C. (Little c is the side and big C is the angle). We call the other two sides of the triangle a and b. It doesn't matter which is which. So we have the following:
a= FS = 35
b= ST = 60
c = FT
angle C = angle S = 57 degrees
We plug the above values into the law of cosines and solve for c as follows:
[tex]c^{2} = a^{2} + b^{2} -2abcosC[/tex]
[tex]c^{2} = 35^{2} + 60^{2} -2(35)(60)cos57[/tex]
[tex]c^{2} = 1225+ 3600-(4200)(.544639)[/tex]
[tex] c^{2} =2537.51606[/tex]
[tex]c=50.3737[/tex]
You are asked to round to the nearest tenth (one decimal place) which gives the answer 50.4 meters
c. You are asked to find the measure of angle T. Further you are asked to do so using the Law of Sines. The law of sines is: [tex] \frac{a}{sinA} = \frac{B}{sinB} = \frac{c}{sinC} [/tex]. Even though there are three fractions set equal to eahc other, when we use the Law of Sines to find an angle (or a side) we need only use two fractions in most cases. Using the labels we used in part B we have the following:
A = T = the angle we are looking for
a = FS = 35 meters
C = S = 57 degrees
c = FT = 50.4 meters
We substitute these into the Law of Sines and solve for A as follows:
[tex] \frac{a}{sinA} = \frac{c}{sinC} [/tex]
[tex] \frac{35}{sinA} = \frac{50.4}{sin57} [/tex]
[tex] \frac{35}{sinA} = \frac{50.4}{.8386705} [/tex]
[tex]50.4sinA=29.353469[/tex]
[tex]sinA=.58241011662[/tex]
Here we use the arc sin (on a calculator it looks like sin to the negative 1 but it's called arcsin)
[tex] sin^{-1}(.58241011662)=A [/tex]
[tex]A=35.62023656[/tex]
You are asked to round this to the nearest degree which means to the nearest whole number. The answer is 36 degrees.
d. You are asked for the measure of angle F. Recall that the sum of the measures of the angles in a triangle is 180 degrees. We know that S = 57 degrees and T = 36 degrees (from part c). So to find the missing angle we add these and subtract their sum from 180.
[tex]F = 180-(36+57)[/tex]
F=180-93
F=87
The measure of angle F is 87 degrees
NOTE: Angles can be measure in degrees and in radians. This problem uses degrees so it is important that your calculator is set to degrees when doing this problem.
Related Questions
James pays $120.00 for golf clubs that are on sale fo 20% off at golf pros. At nine iron ,the same clubs cost $8.00'less than they cost at golf pros. They are on sale for 13% off
Answers
Help please !!!!!!!!!!!
Answers
An antifreeze solution freezes at -100 °c. what is the freezing point on the fahrenheit scale? -82 °f -212 °f -88 °f -73 °f -148 °f
Answers
Your answer is the last option, -148°F
The formula to convert temperatures from Celcius to Farenheit is:
(C° x 9/5) + 32 or (C° x 1.8) + 32
So to solve, plug in -100°C and follow the order of operations (PEMDAS).
(-100 x 1.8) + 32
(-180) + 32
-148
-100°C is equal to -148°F
The freezing point of the antifreeze solution in Fahrenheit is -148 °F, calculated using the formula for converting Celsius to Fahrenheit.
To convert a temperature from the Celsius scale to the Fahrenheit scale, you can use the following formula: F = (C imes 9/5) + 32, where F represents the Fahrenheit temperature, and C represents the Celsius temperature.
In this case, we are given the freezing point of an antifreeze solution, which is -100 °C. Applying the formula, we get F = (-100 x 9/5) + 32. This calculation gives us F = (-180) + 32, which simplifies to F = -148 °F.
So, the freezing point of the antifreeze solution on the Fahrenheit scale is -148 °F.
In the diagram, the radius of the outer circle is 5cm and the area of the shaded region is 16π cm^2. What is the radius or the inner circle?
Answers
By using the area of the ring we will see that the radius of the inner circle is 3cm.
What is the radius of the inner circle?
I assume that we have some kind of ring. To get the area of the ring, we need to take the area of the circle defined by the outer radius of the ring, and subtract the area defined by the circle with the inner radius of the ring.
Remember that the area of a circle of radius R is:
A = pi*R^2
We know that:
The radius of the outer circle is 5cm, so its area is:
A = pi*(5cm)^2 = pi*25cm^2
And the area of the ring is pi*16 cm^2
Then the area of the inner circle should be such that:
pi*25cm^2 - A' = pi*16cm^2
Then, solving for A'
A' = pi*25cm^2 - pi*16cm^2 = pi*9cm^2 = pi*(3cm)^2
So the radius of the inner circle is 3cm.
If you want to learn more about circles, you can read:
https://brainly.com/question/1559324
Air is escaping from a spherical balloon at the rate of 4cc/min. how fast is the surface area of the balloon shrinking when the radius is 24 cm? (a sphere of radius r has volume 4 3 πr3 and surface area 4πr2 .)
Answers
V = (4/3) πr ^ 3
Deriving we have:
V '= (3) (4/3) (π) (r ^ 2) (r')
Clearing r 'we have:
r '= V' / ((3) (4/3) (π) (r ^ 2))
Substituting values:
r '= 4 / ((3) (4/3) (π) ((24) ^ 2))
r '= 0.000552621 c / min
Then, the surface area is:
A = 4πr2
Deriving we have:
A '= 8πrr'
Substituting values:
A '= 8π (24) (0.000552621)
A '= 0.33 cm ^ 2 / min
Answer:
The surface area of the balloon is shrinking at:
A '= 0.33 cm ^ 2 / min
-9 > -2 -3/4v solve.
Answers
The population of a city has increased by 26 % since it was last measured. If the current population is 44,100 , what was the previous population?
Answers
The previous population of the city was 35000.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Assume the previous population to be [x].
Then, we can write -
x + 26% of x = 44100
x + 26x/100 = 44100
x + 13x/50 = 44100
(50x + 13x)/50 = 44100
63x = 44100 x 50
63x = 2205000
x = 35000
Therefore, the previous population of the city was 35000.
To solve more questions on percentage increase, visit the link below-
https://brainly.com/question/17135126
#SPJ5
The previous population of the city was 35,000 before experiencing a 26% increase to the current population of 44,100.
Explanation:To calculate the previous population of a city that has experienced a 26% increase to its current population of 44,100, we need to reverse the percentage increase. The formula for this is:
Previous population = Current population / (1 + Percentage increase)
In this case, the percentage increase is 26%, or 0.26 in decimal form. The calculation is:
Previous population = 44,100 / (1 + 0.26) = 44,100 / 1.26
This gives us:
Previous population = 35,000 (rounded to the nearest whole number)
Hence, the previous population of the city was approximately 35,000 before the 26% increase to the current 44,100.
Choose the best answer.
The most expensive type of life insurance is:
term insurance
whole-life insurance
endowment life insurance
limited-payment life insurance
Answers
Answer:
Endowment life insurance
Step-by-step explanation:
got it right on odyssey
Factor the trinomial below.
9x2 + 6x + 1
A. (9x + 1)(x – 1)
B. (9x + 1)(x + 1)
C. (3x + 1)(3x + 1)
D. (3x + 1)(3x – 1)
Answers
9x² + 6x + 1
9x² + 3x + 3x + 1
3x(3x + 1) + 1(3x + 1)
(3x + 1)(3x + 1)
A color called “shocking pink” is made by mixing red paint with white paint. The ratio of red to white is 2 to 7. How much red paint should be mixed with 16 fl. oz of white paint?
Answers
Answer:
4.5 oz
Step-by-step explanation:
YO!!!!!!WILL GIVE 100 POINTS!!!!!!!!!!!BRAIN!!!!!!!!!!!!
Answers
f (x) = ((x + 2) ^ 2) * (x-4) * (x + 1) ^ 3
The roots are given by:
((x + 2) ^ 2) * (x-4) * (x + 1) ^ 3 = 0
x + 2 = 0
x = -2 (multiplicity 2)
x-4 = 0
x = 4 (multiplicity 1)
x + 1 = 0
x = -1 (multiplicity 3)
Answer:
option A
Answer:
Following function:
f (x) = {(x + 2)²} × (x-4) × (x + 1)³
The roots are given by:
{(x + 2)²} × (x-4) × (x + 1)³ = 0
x + 2 = 0
x = -2
x-4 = 0
x = 4
x + 1 = 0
x = -1
Answer:
option A
Step-by-step explanation:
Vivian's insurance company pays for 80% of her foot surgery, after she pays a $500 deductible. How much will Vivian pay for her surgery if it costs $9600?
2320
2420
2820
after doing the math and writing it out. it has to be one of these three answers but i do beleive that its the second answer but i need reassurance
Answers
We have been given that Vivian's insurance company pays for 80% of her foot surgery, after she pays a $500 deductible. We have been given that her surgery costs $9600 and we need to find how much will Vivian have to pay for her surgery.
Since we know that the insurance company will pay any amount after Vivian has paid $500. Therefore, the remaining amount after Vivian pays $500 as deductibles will be $9600 - $500 = $9100.
Now we know that Vivian's insurance company will pay 80% of this amount, therefore, Vivian will have to pay the 20% of $9100 in addition to the $500 she already paid.
20% of $9100 is [tex]9100\cdot \frac{20}{100} = \$1820[/tex]
Therefore, the total amount that Vivian pays for surgery is $500 + $1820 = $2320.
Therefore, the first choice given is the right answer.
The probability that a dessert sold at a certain café contains strawberries is 26%. The probability that a dessert contains both strawberries and whipped topping is 18%. Find the probability that a randomly chosen strawberry dessert contains whipped topping. Round to the nearest tenth of a percent.
Answers
P(Whipped) = x
P(Strawberry and Whipped) = P(Strawberry).P(Whipped) = 18% = 0.18
∴ P(Whipped) = P(Strawberry and Whipped)/P(Strawberry) = 0.18/0.26 = 0.6923 = 69.23%
To nearest tenth,
P(whipped topping) = 69.2%
∴ Probability that a randomly selected desert contains whipped topping is 69.2%.
The probability that a strawberry dessert contains whipped topping is approximately 69.2%
We are given that the probability a dessert contains strawberries (P(S)) is 26%, or 0.26, and the probability that a dessert contains both strawberries and whipped topping (P(S and W)) is 18%, or 0.18.
To find the probability that a randomly chosen strawberry dessert contains whipped topping (P(W|S)), we use the conditional probability formula:
[tex]P(W|S) = \frac{P(S and W)}{P(S)}[/tex]
Substituting the given values, we get:
[tex]P(W|S) = \frac{0.18}{0.26} \approx 0.6923[/tex]
Rounding to the nearest tenth of a percent we get the probability that a randomly chosen strawberry dessert contains whipped topping to be 69.2%.
In a standard deck of cards there are 13 spades, 13 clubs, 13 hearts, and 13 diamonds. The spades and the clubs are black and the hearts and the diamonds are red.
If two cards are chosen at random from a deck, one at a time, and replaced after each pick, what is the probability that a black card is chosen first and a heart is chosen second?
-1/8
-1/2
-2/3
-3/4
Answers
The shortest side of a right triangle measures 88 m. the lengths of the other two sides are consecutive odd integersodd integers. find the lengths of the other two sides.
Answers
x+2 - the side, that has value of consecutive odd integer of x
x+2 is the longest side, so it is a hypotenuse
(x+2)² = x²+88²
x²+4x+4 = x² + 7744
4x=7740
x= 1935
x+2=1935+2=1937
Check
1937²=1935²+88²
3751969=3751969
A right triangle has sides if length 4,12 and 13 what is its perimeter
Answers
Answer:
29
Step-by-step explanation:
The perimeter is the sum of the side lengths:
4 + 12 + 13 = 29
The perimeter of the triangle is 29. (It is not a right triangle.)
___
A right triangle with side lengths 12 and 13 will have a short side of 5. Its perimeter is 30.
solve the equation 4(-x+4)=12
Answers
-4x-16=12 add 16 to both sides
-4x=28 divide by -4
x=-7
The answer is x=-7
Write the quadratic function in vertex form: f(x) = 4x2 + 2x -5
A)f(x) = 4(x + 14)2 - 214B)f(x) = 4(x + 116)2 - 214C)f(x) = 4(x + 14)2 - 194D)f(x) = 4(x + 116)2 - 194
Answers
f(x) = 4x^2 + 2x - 5
= 4(x^2 + (2/4)x) - 5
= 4(x^2 + (1/2)x ) -5
= 4(x^2 + (1/2)x + 1/16 ) - 4/16 - 5
= 4(x+1/4) - 21/4 <= in vertex form
Here h= -1/4 and k = -21/4. The vertex is at (-1/4, -21/4)
Answer:its B
Step-by-step explanation:
f(x) = -4 (x + 1/4)² - 15/4
When darcy's school bus travels at 30 miles per hour, it gets from her home to school in 12 minutes. what is the speed of darcy's bus if it makes the same trip in 18 minutes?
Answers
speed=distance/time------> distance=speed*time
step 1
find the distance with
speed=30 miles/hour-----> 30 miles/60 minutes-----> 0.5 miles/minute
time=12 minutes
distance=speed*time------> distance=0.5/12----> distance=6 miles
the distance from home to school is 6 miles
step 2
find the speed with
distance=6 miles
time=18 minutes
speed=6/18----> 0.33 miles/minute-----> *60----> 20 miles/hour
the answer is
20 miles/hour or 0.33 miles/minutes
which of the following parametric equations are equivalent to the polar equation r=3 cos theta
Answers
x = rcos (θ)
Where "r" is the radius
Likewise y = rsin (θ)
Therefore, in the expression r = 3cos (θ) one can write r as:
r = x / cos (θ)
So:
x / cos (θ) = 3cos (θ)
x = 3cos ^ 2 (θ)
The same for y ...
y = rsin (θ)
y = 3cos (θ) sin (θ).
Finally the correct answer is option 2.
x = 3cos ^ 2 (θ) y = 3cos (θ) sin (θ).
Answer:
B
Step-by-step explanation:
It takes 8 minutes for Byron to fill the kiddie pool in the backyard using only a handheld hose. When his younger sister is impatient, Byron also uses the lawn sprinkler to add water to the pool so it is filled more quickly. If the hose and sprinkler are used together, it takes 5 minutes to fill the pool. Which equation can be used to determine r, the rate in parts per minute, at which the lawn sprinkler would fill the pool if used alone?
A. 5/8 + 5r = 8
B. 5/8 + 5r = 1
C. 5(5/8) = r
D. 5/8 = 5r
Answers
rate of lawn sprinklerand hose would be 5 minutes /r ( rate per minute)
we would then want to add that to the ratio of the lawn sprinkler and hose together together which would be 5 minutes for both / 8 minutes for hose
we want to add those together to equal 100 percent, which can also be written as 1
so the correct equation would be B) 5/8 + 5/r = 1
Answer:
B,5/8+5r=8
Step-by-step explanation:
3. The roof of a castle tower is shaped like a cone. The base of the cone is 24 m across and the height is 16 m. The slant height of the roof, which is unknown, is the hypotenuse of the right triangle formed with the radius and the height of the cone. (a) Sketch the roof of the castle tower. Label the known lengths as described AND label the unknown length as x. (b) What is the slant height of the roof? SHOW YOUR WORK!
Answers
Next, you must use the Pythagorean theorem.
The theorem state a^2 + b^2 = c^2
When calculated, we get 12^2 + 16^2 = 20^2
Your answer is 20
Compare your prediction with the total number of pennies on Row 1. How would you change your estimate? Is the result surprising?
Answers
Answer:
a statement that your prediction was less than or greater than the actual count
a statement about how you would change your estimation process
Step-by-step explanation:
Choose any of these two.. There both correct btw
The statements that is true about your prediction of the total pennies on rows 1-4 are statement (b) and (d).
A predictive function is one of mathematical function that helps us to know about future events based on past events. There are many types of functions that can be classified as predictive functions.
The prediction was off by greater than 1,000,000 of the actual total. After seeing the result for rows 1-4, you would indeed change your prediction for the total because it indicates a significant deviation.
Complete question
Check every statement that is true about your prediction of the total pennies on rows 1-4.
a) Your prediction was off by less than or equal to 1,000,000 of the actual total.
b) Your prediction was off by greater than 1,000,000 of the actual total.
c) After seeing the result for rows 1-4, you would change your prediction for the total.
d After seeing the results for rows 1-4, you would not change your prediction for the total.
Brainly a garden has width 13−−√ and length 713−−√. what is the perimeter of the garden in simplest radical form?
Answers
The correct answer is:
16√13.
Explanation:
The perimeter of a figure is found by adding together the lengths of all of the sides. The side lengths of this garden are: √13, √13, 7√13 and 7√13. This is because opposite sides in a rectangle are congruent.
Adding these together we have:
√13+√13+7√13+7√13 = (1+1+7+7)√13 = 16√13
solve 3√5c*7√15c^2 please show your work
Answers
21√(75c³)
21√(25 c² 3c)
21√(5² c² 3c)
21× 5c√(3c)
105c√(3c)
Find the sum of the series
Answers
(3*2+1)+(3*3+1)+(3*4+1)
=(6+1)+(9+1)+(12+1)
=7+10+13
=30
Thus the sum of the series is:
30
Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?
A) 17 miles
B) 32 miles
C) 37 miles
D) 40 miles
Answers
Answer:
D) 40 miles
Step-by-step explanation:
First we must find the distance between the mall and the house. The figure formed is a right triangle. The length of the side from the mall to the house forms the hypotenuse of the triangle. We can use the Pythagorean theorem to find the length:
a² + b² = c²
The two legs of the triangle, a and b, are 15 and 8:
15² + 8² = c²
225 + 64 = c²
289 = c²
Take the square root of each side:
√289 = √(c²)
17 = c
This makes the total distance
15+8+17= 40 miles
Hey! Pretty easy once you get the hang of these problems.
So you start off with the Pythagorean Theorem. Which is : a^2 + b^2 = c^2
Then just fill it in :
15^2 + 8^2 = c^2
225 + 64 = c2
289 = c^2
17 = c
And last :
15 + 8 + 17 = 40 MILES
hoped this helped!! :))
Geo: Topic 3- Parallelograms 1pt A rhombus is a parallelogram with all four sides of equal length. One way to determine if a given parallelogram is a rhombus is to test whether its diagonals are perpendicular. The vertices of a parallelogram are M(−1,2), N(9,2), P(3,−6), and Q(−7,−6). Determine whether the parallelogram is a rhombus by checking to see if the diagonals are perpendicular. What is the slope of MP¯¯¯¯¯¯? What is the slope of NQ¯¯¯¯¯¯? Are diagonals MP¯¯¯¯¯¯ and NQ¯¯¯¯¯¯ perpendicular? Is the parallelogram a rhombus?
Answers
A clown is juggling at a circus. The path of the ball is given by the parametric equations x=2cos t+2 and y=3sin t+3. In what direction is the ball moving?
-up and to the right
-counterclockwise
-down and to the right
-clockwise
Answers
[tex] \left \{ {{x=2cost+2} \atop {y=3sint+3}} \right. [/tex]
Note that this parametric equation is an ellipse. The graph of this equation is given in figure below. So, we well substitute some values of t in the equation:
If t = 0
x = 4 and y = 3
P0(4, 3)
if t = 1
x = 3.08 and y = 5.52
P1(3.08, 5.52)
if t = 2
x = 1.16 and y = 5.72
P2(1.16, 5.72)
Finally, as shown in the figure, the answer is B. counterclockwise. Notice the trajectory that follows P0, P1 and P2.
1. B. Counterclockwise
2. C. (30,401)
3. A. t=2(x-3)
4. C. She should have taken both the positive and negative square root
5. C. y=x^2+8x-25/8
6. D. Hyperbola
7. A. Graph A
Find the average value have of the function h on the given interval. h(u) = (15 − 10u)−1, [−1, 1]
Answers
The average value have of the function h(u) = (15 − 10u)−1 on the given interval [−1, 1] is -5.
What is average value of the function?The average value of a function is given by the formula:
[tex]fav = \frac{1}{b - a} \int\limits^b_a f({x}) \, dx[/tex]
Now the given function is,
h(u) = (15 − 10u) − 1
or, h(u) = 15 − 10u − 1
or, h(u) = 14 − 10u
So, the average value on the given interval [−1, 1] is given as:
[tex]fav = \frac{1}{1 - (-1)} \int\limits^1_{-1} h({u}) \, du[/tex]
Thus, putting the value of h(u) we get,
[tex]fav = \frac{1}{(1 + 1)} \int\limits^1_{-1} (14 - 10u) \, du[/tex]
Thus integrating we get,
fav = (1/2) { [14u] - [10u²/2]
⇒ fav = (1/2) { [14u] - [5u²]
Applying the limits we get, -1 to 1,
⇒ fav = (1/2) { 14[-1 + 1] - [5{-1² + 1²}]
Solving we get,
⇒ fav = (1/2) { 14[0] - [5{1 + 1}]
⇒ fav = (1/2) {- [5{2}]
⇒ fav = -5
Thus, the average value have of the function h(u) = (15 − 10u)−1 on the given interval [−1, 1] is -5.
To learn more about functions :
brainly.com/question/17068704
#SPJ2