Answers
Answer:
15) The length of the line segment DE is 14.908.
16) The measure of the angle W is approximately 31.792°.
17) The length of the ladder is approximately 23.182 feet.
Step-by-step explanation:
15) We present the procedure to determine the length of segment DE:
(i) Determine the length of the line segment DF by trigonometric relations:
[tex]\tan C = \frac{DF}{CF}[/tex] (1)
([tex]C = 61^{\circ}[/tex], [tex]CF = 24[/tex])
[tex]DF = CF\cdot \tan C[/tex]
[tex]DF = 24\cdot \tan 61^{\circ}[/tex]
[tex]DF \approx 43.297[/tex]
(ii) Determine the length of the line segment DE by trigonometric relations:
[tex]\tan F = \frac{DE}{DF}[/tex] (2)
([tex]DF \approx 43.297[/tex], [tex]F = 19^{\circ}[/tex])
[tex]DE = DF\cdot \tan F[/tex]
[tex]DE = 43.297\cdot \tan 19^{\circ}[/tex]
[tex]DE \approx 14.908[/tex]
The length of the line segment DE is 14.908.
16) We present the procedure to determine the measure of the angle W:
(i) Determine the length of the line segment XZ by trigonometric relations:
[tex]\sin Z = \frac{XY}{XZ}[/tex] (3)
([tex]XY = 15[/tex], [tex]Z = 25^{\circ}[/tex])
[tex]XZ = \frac{XY}{\sin Z}[/tex]
[tex]XZ = \frac{15}{\sin 25^{\circ}}[/tex]
[tex]XZ \approx 35.493[/tex]
(ii) Calculate the measure of the angle W by trigonometric relations:
[tex]\tan W = \frac{XZ}{WZ}[/tex] (4)
([tex]XZ \approx 35.493[/tex], [tex]WZ = 22[/tex])
[tex]W \approx \tan^{-1} \left(\frac{22}{35.493}\right)[/tex]
[tex]W \approx 31.792^{\circ}[/tex]
The measure of the angle W is approximately 31.792°.
17) The system form by the ladder, the ground and the wall represents a right triangle, whose hypotenuse is the ladder, which is now found by the following trigonometric relation:
[tex]\cos \theta = \frac{x}{l}[/tex] (5)
Where:
[tex]\theta[/tex] - Angle of the ladder above ground, in sexagesimal degrees.
[tex]x[/tex] - Distance between the foot of the ladder and the base of the wall, in feet.
[tex]l[/tex] - Length of the ladder, in feet.
If we know that [tex]x = 6\,ft[/tex] and [tex]\theta = 75^{\circ}[/tex], then the length of the ladder is:
[tex]l = \frac{x}{\cos \theta}[/tex]
[tex]l = \frac{6\,ft}{\cos 75^{\circ}}[/tex]
[tex]l \approx 23.182\,ft[/tex]
The length of the ladder is approximately 23.182 feet.
Related Questions
PLEASE I NEED HELP!!!!
Answers
Q. Determine if the rates are equilvalent. Explain your reasoning. 25 hours in 5 days; 8 hours in 2 days. . .
[tex] \dashrightarrow [/tex] No!, as, we have 25 hours in 5 dyas is the equals to 5. While, 8 hours in 2 days is equals to 4.
Here, is a difference of 1 in 5 and 4.
I really, REALLY need help. I will give brainliest to whoever figures it out.
Answers
Answer:
79.5 + 5.5x = Y
Step-by-step explanation:
Sumo wrestler gained 5.5 kg per month
After 11 month, he weighed 140 kg.
Let x be his current weight.
Then x + 11(5.5) = 140
x = 140 - 60.5
x = 79.5
If Y is the weight of the wrestler after t months, then the linear equation would be:
79.5 + 5.5t = Y
Triangle ABC is an equilateral triangle with vertices at A(-2,2), B(1,5), and C(-3,6) (Round your answers to the nearest hundredth, 2 decimal places) . a) (2 pts) Determine the length of a side of the triangle. b) (2 pts) Calculate the perimeter of the triangle. c) (2 pts) Now increase the triangle by a scale factor of 4. How long is each side now? d) (2 pts) What is the perimeter of the new triangle? e) (2 pts) What is the area of the original triangle?
Answers
Answer:
The answer is below
Step-by-step explanation:
The distance between two points A(x₁, y₁) and B(x₂, y₂) on the coordinate is:
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\[/tex]
An equilateral triangle is a triangle with three equal sides (all sides are equal).
a) Given vertices at A(-2,2), B(1,5), and C(-3,6):
[tex]AC=\sqrt{(-3-(-2))^2+(6-2)^2}=\sqrt{1+16}=\sqrt{17}=4.12\ unit\\\\AB=BC=AC=4.12\ unit[/tex]
b) Perimeter = AB + BC + AC = 3 * AC = 3 * 4.12 = 12.36 unit
c) If the scale factor is increased by 4, all the sides would also increase by 4. Hence the new length would be:
A'B' = B'C' = A'C' = 4 * AC = 4 * 4.12 = 16.48 unit
d) Perimeter = A'B' + B'C' + A'C' = 3 * A'C' = 3 * 16.48 = 49.44 unit
e) Area = [tex]\frac{\sqrt{3} }{4}*AC^2=\frac{\sqrt{3} }{4} *4.12^2=7.35\ unit^2[/tex]
What is the probability of living another year for a woman who is 73 years old ?
a) 0.951716
b) 0.968048
c) 0.980413
d) 0.991871
Answers
Answer:
0.980413
Step-by-step explanation:
The table for the deaths and death rate per 100,000 population is attached below ;
73 years fall in the 65 - 74 years category ; with 1958.7 deaths (Female)
Hence, the probability of living another year is :
Number of deaths per 100,000 population ;
P(death) = 1958.7 / 100,000 = 0.019587
Probability of living another year = 1 - P(death)
1 - 0.019587 = 0.980413
Answer:
C. 0.980413
FHKEDIbEDSAJFWBHES
There are 20 chocolates in a box.
Some of the chocolates contain nuts and the rest do not.
The probability that a chocolate containing nuts is picked at random from the
box is 0.6
How many of the chocolates in the box contain nuts?
Answers
Answer:
12 nutted chocolates
Step-by-step explanation:
0.6 is equal to 60% and 60% 0f 20 is 12.
HELP!!! I'm struggling in this class could you please help a person out?
Answers
Answer:
Options (2) and (3)
Step-by-step explanation:
Rigid transformation like translation, rotation or reflection form the image with no change in the area or shape.
By applying dilation, area of the image shape gets dilated by the scale factor 'k'.
If k > 1, area of the image will be greater than the original shape.
If 0 < k < 1, are of the image will be smaller than the original.
Option (1),
There is a dilation by a scale factor of [tex]\frac{2}{3}[/tex] and [tex]0<\frac{2}{3}<1[/tex],
Therefore, image will be smaller than the original.
Option (2)
There are two dilations.
First dilation is by a scale factor of 2 and the second is by a scale factor of [tex]\frac{2}{3}[/tex].
By first dilation area of the image will get doubled.
Followed by the dilation by a scale factor of [tex]\frac{2}{3}[/tex], area of the image will be dilated by the scale factor = [tex]2\times \frac{2}{3}[/tex]
= [tex]\frac{4}{3}[/tex]
Since, [tex]\frac{4}{3}>1[/tex], image will be greater than the original.
Option (3)
In this option polygon is dilated by a scale factor [tex]\frac{3}{2}[/tex].
Since, [tex]\frac{3}{2}>1[/tex]
Image will have the greater area than the original.
Option (4)
In this option polygon is dilated by a scale factor [tex]\frac{1}{2}[/tex].
Therefore, area of the image will be less than the area of the original.
Options (2) and (3) will be the correct options.
what is the measure of each exterior angle of a regular dodecagon?
Answers
Answer:
30°
Hope this answer is right!
Step-by-step explanation:
to go around the shape, you make a complete circle: 360°. So, divide 360° by the dodecagon's twelve exterior angles. Each exterior angle is 30°.
look at the image for the question
Answers
Answer:
Answer is y = 6
Step-by-step explanation:
Solve for y.
Answer:
Y=6 I think but I’m not positive.
sorry if I’m wrong.
haha
get it? POSITIVE?
What is the slope of the line shown below?
10
O A-4
5
B. -2
ရှိ မရှိ ။
(2,4)
C. 2
10
15
45
O D. 4
10
Answers
Answer:
C) 2
Step-by-step explanation:
PLEASE HELP MEE!! 50 POINTS
URGENT
The function y= x^2-10x+31 has a _____ (minimum, maximum) value of __ (5, 10, 31, 6)
Answers
Answer:
minimum value of 6
Step-by-step explanation:
Given
y = x² - 10x + 31
with a = 1, b = - 10
Since a > 0 then the function has a minimum value
The minimum value is the y- coordinate of the vertex.
The x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex] = - [tex]\frac{-10}{2}[/tex] = 5
Substitute x = 5 into the function for y- coordinate of vertex
y = 5² - 10(5) + 31 = 25 - 50 + 31 = 6
The function has a minimum value of 6
1. Given that (27 ^ (n + 3))/(81 ^ (p - 1)) = 3 , express p in terms of h.
Answers
9514 1404 393
Answer:
p = 3/4n +3
Step-by-step explanation:
Expressing the given equation in terms of powers of 3, we have ...
(27^(n+3))/(81^(p-1)) = 3
(3^3)^(n+3)/(3^4)^(p-1) = 3^1 . . . . as powers of 3
3(n +3) -4(p -1) = 1 . . . . . . . . . . . . log base 3 (or, equate exponents)
3n +9 -4p +4 = 1 . . . . . . . . . . . . . eliminate parentheses
3n +12 = 4p . . . . . . . . . . . . . . . . add 4p -1
p = 3/4n +3 . . . . . . . . . . divide by 4
Write an equation that represent the value of an 8700 investment that has 9.1% interest rate compounded yearly y=a(b)^x
Answers
Answer:
future value = $8700(1.091)^x
Step-by-step explanation:
The formula for calculating future value:
FV = P (1 + r) n
FV = Future value
P = Present value = 8700
R = interest rate = 9.1%
N = number of years = x
future value = $8700(1.091)^x
Given the formula below, solve for x.
Answers
Answer:
find X in X with x if you find X with x in with x you got a formula
Age of car = 8 years. Original cost = $18,000. The cost of maintenance and repairs is $
Answers
From the graph it seems to be around the area of 10%.
So,
18,000 * 0.10 = $1,800
What is the recursive formula for this geometric sequence?
-3, -21, -147, -1029, ...
Answers
The common multiplier is 7 but the actual formula you take the first term then multiply it by the multiplier raised to the n-1
Question 27(Multiple Choice Worth 1 points)
(07.03 LC)
How many solutions does the equation 4y - 4y - 12 = 14-2 have?
One
None
Two
Infinite
Answers
Answer:
none
Step-by-step explanation:
any value on y cancel 4y and then we will have -12=12 which is not true.
In parallelogram EFGH if m∡GHE=160 find ∡m∡EFG
Answers
Answer:
160°
Step-by-step explanation:
since it is a parallelogram it's opposite angles must be equal . So,
angle GHE = angle EFG
160 degree = angle EFG
A cubical reservoir has capacity of 480000 l itters of liquid. If ifs length and breadth are 10m and 8m respectively, find the hight of the reservoir.
Answers
Answer:
Height = 6000 m
Step-by-step explanation:
[tex]Volume = length \times breadth \times height \\\\480000 = 10 \times 8 \times height\\\\480000 = 80 \times height\\\\height = \frac{480000}{80} = 6000 \ m[/tex]
The diameter of a circle is 19 inches. If the diameter is extended 5 inches beyond the circle to point C, how long is the tangent segment from point C to the circle? Use the figure below to help guide your response. Explain your answer and show all work.
Answers
Answer:
Exact Length = 2*sqrt(30)
Approximate Length = 10.95445
======================================================
Work Shown:
(tangent)^2 = (external secant)*(whole secant)
(CD)^2 = (CB)*(CA)
(CD)^2 = (CB)*(CB+BA)
x^2 = 5*(5+19)
x^2 = 120
x = sqrt(120)
x = sqrt(4*30)
x = sqrt(4)*sqrt(30)
x = 2*sqrt(30) .......... exact length
x = 10.95445 ............. approximate length
The length of the tangent segment is; x = 10.95
Length of TangentFrom secant theorem, we know that;
Tangent ² = length of external secant × total length of secant.
From the image, we see that;
Length of tangent is x.
External secant = 5
Total length of secant = 19 + 5 = 24
Thus;
x² = 5 × 24
x² = 120
x = √120
x ≈ 10.95
Read more about length of tangent at;https://brainly.com/question/9132922
A. write the ratio of girls to boys in the class with 12 girls and 15 boys. reduce to the lowest terms.
B. use the information from part A to estimate the number of girls in the school if there are a total of 1350 students in the whole school and in part A is representative of all classes in the school
WILL GIVE BRAINLIEST
Answers
Answer:
A. 4:5
B. 600 girls
Step-by-step explanation:
A. g : b = 12 : 15 = 4 : 5
B. the numbers of girls = 4/(4+5) × 1350
= 4/9 × 1350 = 600
The function a(b) relates the area of a trapezoid with a given height of 14 and one base length of 5 with the length of its other base. It takes as input the other base value, and returns as output the area of the trapezoid a(b) = 14 * (b + 5)/2 Which equation below represents the inverse function b(a) , which takes the trapezoid's area as input and returns as output the length of the other base? N(c) = (c + 15)/20; n(c) = (c + 20)/15; n(c) = (c - 20)/15; n(G) = (Q - 15)/20
Answers
Answer:
[tex]b(a) = \frac{a}{7} -5[/tex]
Step-by-step explanation:
Given
[tex]a(b) = 14 * \frac{b + 5}{2}[/tex]
Required
The inverse function
We have:
[tex]a(b) = 14 * \frac{b + 5}{2}[/tex]
[tex]a(b) = 7(b + 5)[/tex]
Rewrite as:
[tex]a = 7(b + 5)[/tex]
Divide by 7
[tex]\frac{a}{7} =b + 5[/tex]
Subtract 5
[tex]b = \frac{a}{7} -5[/tex]
Express as:
[tex]b(a) = \frac{a}{7} -5[/tex] --- the inverse function
Help me now now now now now
Answers
Answer:
-2 = -6
Step-by-step explanation:
first, you type -2 in the left box and -6 in the middle box
how do i do this, please explain....
Answers
Answer:
this is from a angle I think you want to write perimeter and area of this ×+1= and you want see that
Can somebody help plz help me with this?
Answers
Answer:
N-8
Step-by-step explanation:
if a number is divided by three and then two is added,the answer is twenty-nine.what is the number
Answers
Answer:
81
Step-by-step explanation:
the answer is 81, just out this in the solution
Answer:
81
Step-by-step explanation:
29-2=27
27*3=81
if we divide 81 by 3 we get 27 and 27 plus 2 is 29 so it is 81
A larger number is double the sum of 3 and a smaller number. The larger number is 2 less than 3 times the smaller number. If y represents the larger number and x represents the smaller number, which equations model the situation? Check all that apply.
y=3x-2
3x-y=2
3x-y=-2
y=2-3x
y=2(x+3)
Answers
Answer:
1,2, and 5
Step-by-step explanation:
y=2*(3+x)
y=3x-2
3x-y=2
can someone please help me in this question
Answers
Answer:
a. 26 cm²
b. 55 cm²
c. 78 cm²
d. 89.27 cm²
Step-by-step explanation:
a. The shape can be decomposed into two rectangles
Area of the larger rectangle = L*W
L = 7 cm
W = 2 cm
Area of the larger rectangle = 7*2 = 14 cm²
Area of the smaller rectangle = L*W
L = 4 cm
W = 5 - 2 = 3 cm
Area of the larger rectangle = 4*3 = 12 cm²
Area of the compound shape = 14 + 12 = 26 cm²
b. The shape can be decomposed into a rectangle and a triangle.
Area of the compound shape = area of rectangle + area of triangle
= L*W + ½*b*h
L = 8 cm
W = 5 cm
b = 5 cm
h = 14 - 8 = 6 cm
Plug in the values
Area = 8*5 + ½*5*6
Area = 40 + 15
= 55 cm²
c. The shape can be decomposed into a rectangle and a trapezoid
Area of the compound shape = area of the rectangle + area of the trapezoid
= L*W + ½(a + b)h
L = 12 cm
W = 3 cm
a = 12 cm
b = 9 cm
h = 4 cm
Plug in the values
Area = 12*3 + ½(12 + 9)4
Area = 36 + 42
Area = 78 cm²
d. The shape can be decomposed into a rectangle and a semicircle
Area of the compound shape = area of the rectangle + area of the semicircle
= L*W + ½(πr²)
L = 10 cm
W = 5 cm
r = ½(10) = 5 cm
Plug in the values
Area = 10*5 + ½(π*5²)
Area = 50 + 39.27
Area = 89.27 cm²
Congruent angle pairs : find value of x and the value of y
Answers
Simplify (3x2 + 2x - 3) (x + 5)
Answers
Answer:
3(x)^3 + 2(x)^2 + 22x - 15
Step-by-step explanation:
(3(x)^2 + 2x - 3) (x + 5)
=>(3(x)^2 + 2x - 3) (x) + (3(x)^2 + 2x - 3) (5)
=>3(x)^3 + 2(x)^2 - 3x + 15x + 10x - 15
=>3(x)^3 + 2(x)^2 + 22x - 15
In 2014, a town's population was 795 people. By 2020, the population had grown to 1262 people. a. Create an exponential equation for the town's population "n" years from 2014. Round your multiplier to the nearest hundredth (2 decimal places).
Answers
Answer: [tex]P=795(1.84)^n[/tex]
Step-by-step explanation:
Given
Initial population was [tex]795[/tex] people
By 2020, it becomes [tex]1262[/tex] people
Suppose the population follows the trend [tex]P=P_oa^{n}[/tex]
where, [tex]n[/tex] is the number of years after 2014
For year 2020 it is 6. Insert the values
[tex]\Rightarrow 1262=795a^{6}\\\\\Rightarrow 1.587=a^{6}\\\\\text{Taking log both sides}\\\\\Rightarrow \log (1.587)=6\log (a)\\\Rightarrow \log (a)=0.2645\\\\\Rightarrow a=10^{0.2645}\\\Rightarrow a=1.84[/tex]
Thus, the exponential population trend is [tex]P=795(1.84)^n[/tex]