#8A 90-foot rope from the top of a tree house to the ground forms a 45° angle of elevation from the ground. How high is the topof the tree house? Round your answer to the nearest tenth of a foot.feet
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Given: A 90-foot rope from the top of a tree house to the ground forms a 45° angle of elevation from the ground.
Required: To determine the height of the tree house.
Explanation: The given problem can be represented as follows-
In the figure, AC represents the rope, and AB is the tree house. We need to determine the length of AB.
Recall the trigonometric ratio-
[tex]sin\theta=\frac{OppSide}{Hypotenuse}[/tex]Thus, for triangle ABC we have-
[tex]sinC=\frac{AB}{AC}[/tex]Substituting the values and solving for AB as-
[tex]\begin{gathered} AB=90\cdot sin45\degree \\ =90\times\frac{1}{\sqrt{2}} \\ =63.6396\text{ ft} \\ \end{gathered}[/tex]Thus,
[tex]AB\approx63.6\text{ ft}[/tex]Final Answer: The top of the tree house is 63.6 ft high.
Related Questions
8-23. Cooper Toy Company has designed a new toy that oscillates up and down and its position can be modeled by a sinusoidal curve. At time t = 5 seconds, the toy is at its maximum height, 18 cm above the ground. Four seconds later, the toy is at its minimum height, 6 cm above the ground. Write an equation to model the height, in centimeters of the toy at any time t, in seconds.
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Given data:
The maximum height of the toy at t=5 seconds is M= 18 cm.
The minimum height of the toy at t=9 seconds is m=6 cm.
The expression for the amplitude is,
[tex]\begin{gathered} A=\frac{M-m}{2} \\ =\frac{18-6}{2} \\ =6 \end{gathered}[/tex]The expression for the mean value is,
[tex]\begin{gathered} x=\frac{18+6}{2} \\ =12 \end{gathered}[/tex]The period of the given curve is,
[tex]\begin{gathered} P=\frac{2\pi}{10} \\ =\frac{\pi}{5} \end{gathered}[/tex]The equation for the given curve is,
[tex]y=6\cos (\frac{\pi}{5}(t-4))+12[/tex]Thus, equation of the given curve is y=6 cos(π(t-4)/5)+12.
Rosemary walks each week for exercise. Let d represent the distance walked and h represent the number of hours spent walking. Last week: walked 18 miles in 16 hours This week: d= 2,5h Which statement must be true?
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answer: Last week Rosemary walked at a faster pace.
This because her speed last week was 3 miles per hour and this week was 2.5 miles per hour.
Evaluate the expression 2bc2 for b = 1.5 and c = 5. 0 O 225 O 75 O 30 O O 15
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b= 1.5
c= 5
To evaluate 2bc^2
we substitute b = 1.5 and c = 5 into the equation
[tex]\begin{gathered} 2bc^2 \\ \Rightarrow2x1.5x5^2 \\ \Rightarrow\text{ 2 x 1.5 x 25} \\ \Rightarrow75 \end{gathered}[/tex]The answer = 75
The line plot shows the distance students lived from the school. What is the difference in miles between the students who live closest and furthest away?
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The students who live furthest away, live at 6 3/4 miles
The students who live closest away, live at 5 miles
The difference is:
Which one of the following statements is false?Bias can be reduced by taking a larger sample.O A statistic is used to estimate a parameter.Response errors cannot be completely eliminated, even if a census is taken.O As the sample size increases, the margin of error decreases.O If several high school students are surveyed about their favorite sport, the individuals would be the students.
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Bias can be reduced by taking a larger sample is false because an increase in sample tends to reduce the sampling error but a large sample size cannot correct for the methodological problems (undercover, nonresponse bias, etc.) that produce survey bias.
19/27 what is equivalent to this
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The decimal form of 19/27 is a repeating decimal where the digits 703 keeps repeating indefinitely.
Given that angle 3 equals 3x and angle 6 equals 6x, determine the value for x
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When two lines are crossed by another line (like in this case), the angles matching corners are called corresponding angles:
Now, since angle 3 and angle 6 are consecutive interior angles, we have the following:
[tex]\begin{gathered} 3x+6x=180 \\ \Rightarrow9x=180 \\ \Rightarrow x=\frac{180}{9}=20 \\ x=20 \end{gathered}[/tex]Therefore, x=20
Calculate the constant of proportionality for this table.A. 5/4B. 4/5C. 5 D. 5/2 Write the equation that represents the relationship in the table. Use y and x as variables in your equation.
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The constant of proportionality is the constant value of the ratio of y and x. It is usually denoted as k.
k = y/x
OR
y = kx
From the information given, the value of k is derived as;
[tex]\begin{gathered} k=2\frac{1}{2}\text{ / }\frac{1}{2} \\ k=\frac{5}{2}\times\frac{2}{1} \\ k=5 \end{gathered}[/tex]Where y = kx, then
[tex]y=5x[/tex]That means, the value of y can always be derived by multiplying x by the constant of proportionality
solve each system of the equation by elimination method. -4x+5y=122x+5y=-6
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(-3,0)
1) Let's solve that system, using this method. We need to pick one variable first.
-4x+5y=12
2x+5y=-6
2) Let's eliminate x, multiplying the 2nd equation by 2
-4x+5y=12
4x+10y=-12 Adding both equations simultaneously
---------------------------
15y =0
y= 0
3) Plug y=0 into one of those equations, usually the simplest.
2x+5y=-6
2x+5(0)=-6
2x = -6 Dividing both sides by 2
x= -3
Hence, the answer is (-3,0)
Four times a number increased by five is the same as triple the difference of a number and two . What is the number ?A.x=-11B.x=-7C.x= 2 D.x=-1
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Four times a number: 4*x
Increased by five: 4*x + 5
Triple the difference of a number and two: 3*(x - 2)
Then, the equation is
4*x + 5 = 3*(x - 2)
Applying distributive property:
4*x + 5 = 3*x - 3*2
4*x + 5 = 3*x - 6
3*x is adding on the right, then it will subtract on the left
5 is adding on the left, then it will subtract on the right
4*x - 3*x = - 6 - 5
x = -11
3 8. A toy box is shaped like a cylinder. The diameter is 4 feet and the height of the container is 2 feet. Which measurement is closest to the volume of the toy box in cubic feet? A. 153.5 B. 12.22 C. 10.49 D. 38.37
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Step 1
Write out the formula for volume of cylinder
[tex]\begin{gathered} \text{Volume of cylinder = }\pi r^2h \\ \end{gathered}[/tex]r = radius
h = height
pi = 3.142
Step 2
write out the parameters
diameter = 4 feet
radius = diameter/2 = 4/2 = 2 feet
height = 2 feet
Step 3
input values in the foemula
[tex]\begin{gathered} \text{Volume of a cylinder = }\pi r^2h \\ =\text{ 3.142 }\times2^2\text{ }\times\text{ 2} \\ =\text{ 3.142 x 4 x 2} \\ =\text{ 25.136} \end{gathered}[/tex]racheal recorded the flight of a red bird and a blue bird the red bird flew to 2km less than four times as far as the blue bird and the difference between their flight 298 km how far did the red bird fly
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racheal recorded the flight of a red bird and a blue bird
The red bird flew to 2km less than four times as far as the blue bird
Distance travel by Red Bird - 2 = 4(Distance travel by Blue Bird )
Let the distance travel by blue bird is x
Then distance travel by red bird is :
Distance travel by Red Bird = 4(Distance travel by Blue Bird ) + 2
Distance travel by Red Bird = 4x + 2
The difference between their flight 298
Distance travel by Blue Bird - Distance travel by Red Bird = 298
4x + 2 - x = 298
3x + 2 = 298
3x = 298 - 2
3x = 296
x = 296/3
x = 98.66 km
Since, x express the distance travel by blue bird flight
Distance travel by Blue bird flight is 98.66 km
Distance travel y red bird flight = 4x + 2
Substitute the value of x = 98.66
Distance travel y red bird flight = 4x + 2
Distance travel y red bird flight = 4(98.66) + 2
Distance travel y red bird flight = 396.64 km
So, Red Bird flight cover the distance of 396.64 km
Answer : Red Bird flight cover the distance of 396.64 km
2. Which quadratic function has a graph that passes through the points (-1, 4), (2, -5), and (4, 9)? A O f(x) = 0.522 - 3.5x B f(x) = -2x2 - 2 + 5 CO f(3) = 2? + 7x + 10 D. O f() = 2x2 - 5x - 3
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The given coordinate on the graph is (-1,4), (2,-5) and (4,9).
The general form of the quadratic equation is,
[tex]y=ax^2+bx+c[/tex]Substituting the given coordinates in the general equaion,
[tex]\begin{gathered} 4=a-b+c\ldots.\ldots\text{.}(1) \\ -5=4a+2b+c\ldots\text{.}(2) \\ 9=16a+4b+c\ldots.\text{.}(3) \end{gathered}[/tex]Substracting (1) from (2),
[tex]\begin{gathered} 3a+3b=-9 \\ a+b=-3\ldots(4) \end{gathered}[/tex]Substracting (1) from (3),
[tex]\begin{gathered} 15a+5b=5 \\ 3a+b=1\ldots\text{.}(5) \end{gathered}[/tex]Substracting (4) from (5),
[tex]\begin{gathered} 2a=4 \\ a=2 \end{gathered}[/tex]Substituting in equation (5),
[tex]\begin{gathered} 3(2)+b=1 \\ b=-5 \end{gathered}[/tex]Substititing in equation (1),
[tex]\begin{gathered} 4=2-(-5)+c \\ c=-3 \end{gathered}[/tex]Substituting the value of a,b,c in general equation,
[tex]y=2x^2-5x-3[/tex]Thus, option (D) is the correct solution.
Find the slope-intercept form of the line that passes through the point (3, -6) and is parallel tothe line 4x-2y = -3.
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The slope-intercept form is an equation in the form y = mx + b, where m is the slope and b the intercept with the y-axis.
We have the line 4x-2y = -3, let's arrange it into the slope-intercept form:
[tex]\begin{gathered} 4x-2y=-3 \\ -2y=-4x-3 \\ y=2x+\frac{3}{2} \end{gathered}[/tex]When two lines are parallel, they have the same slope, in the above equation, the slope is 2.
We plug in m=2 in the equation, to have an equation in the form of y = 2x+b, we need to find the value of b (intercept with the y-axis).
To find b, we plug in the point that passes through the line (3,-6)
[tex]\begin{gathered} y=2x+b \\ -6=2\cdot3+b \\ b=-6-6=-12 \end{gathered}[/tex]Now we plug in m = 2 and b = -12, in the slope-intercept form, to get the equation of the line that passes through the point (3,-6) and is parallel to line 4x-2y=-3:
[tex]y=2x-12[/tex]5. Name the following parts of the expression. 6x2 – 2x + 11A. exponentB. coefficientC. constant
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we have
6x^2-2x+11
The constant is 11
In 6x^2 and -2x ------> 6 and -2 are coefficient
in 6x^2 ------> 2 is a exponent
Malorie earned $240 in 6 hours. How much will she earn if she works for 8 hours at the same rateA.246B.280C.320D.380
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Using proportion,
let x be the amount she earn in 8 hours
$240 = 6 hours
x = 8 hours
cross - multiply
6x = 240(8)
6x = 1920
Divide both -side by 6
x = $320
Graph the line with the equation y = (2/5)x – 6.
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ANSWER and EXPLANATION
We are given the equation:
[tex]y\text{ = }\frac{2}{5}x\text{ - 6}[/tex]Since we are not given the domain and range, an easy way to graph it is to find the x and y intercepts and use those points.
To find the x intercept, we have to make y = 0:
=> 0 = (2/5)x - 6
=> (2/5)x = 6
x = (6 * 5) / 2
x = 15
So, the x intercept is (15, 0)
To find the y intercept, we have to make x = 0:
y = (2/5) * 0 - 6
y = -6
So, the y intercept is (0, -6)
Use these points to plot the graph:
find the equation with enfpoints
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the radius is the distance from the centre to either of the 2 given points
Let (x1, y1) = (-4,1) and (x2,y2) = (4,-5) (the given points)
then:
[tex]r\text{ = d = }\sqrt[]{(4-(-4))^2+(-5-1)^2}\text{ = }\sqrt[]{(8)^2+(-6)^2\text{ = }}\text{ 10}[/tex]then, take the equation of the circle is:
[tex](x-0)^2+(y+2)^2\text{ = 10}[/tex]that is:
[tex](x)^2+(y+2)^2\text{ = 10}[/tex]3-2x - 3y = 18у10-10Slope-intercept form:10х-10)
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Answer
The equation in the slope-intercept form is
y = (-2x/3) - 6
Comopa
Explanation
The slope and y-intercept form of the equation of a straight line is given as
y = mx + c
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
c = y-intercept of the line.
So, we just need to simplify the equation given in the form we want
-2x - 3y = 18
-3y = 2x + 18
We can then divide through by -3
(-3y/-3) = (2x/-3) + (18/-3)
y = (-2x/3) - 6
Hope this Helps!!!
A jar contains 2 green marbles, 4 blue marbles, and 3 yellow marbles. A marble is chosen at random from the jar and replaced. Find the possibility that the first marble is green and the second is yellow.
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Answer:
2/27
Explanation:
• Number of green marbles = 2
,• Number of blue marbles = 4
,• Number of yellow marbles = 3
Total = 2+4+3 =9
• Probability of choosing a green marble = 2/9
,• Probability of choosing a yellow marble = 3/9
Therefore, the possibility that the first marble is green and the second is yellow is:
[tex]\begin{gathered} =\frac{2}{9}\times\frac{3}{9} \\ =\frac{2}{27} \end{gathered}[/tex]For which values in the domain is the value of f(x) shown on the graph? select all the apply.A). -1.5B). -2 C). 8D). -21E). 14F). 6
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The graph shows all the values of x from -10 to 10. Then the values that apply are:
-1.5, -2, 8 and 6.
Therefore the answer is A, B, C and F.
p × ____ = 36 , thats what i need help on
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Given data:
The given expression is
the product of two and the difference between eleven and a number
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I need to know the answer to this on a graph
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Graph the linear equation using the slope and y-intercept:
[tex]y=2x+3[/tex]Using a desmos graph to show the equation
price+++++aWhich productis cheaper?+++++ear budshead phones 12 3 4b)price 5 10 15 20
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For the Earbuds:
The price of the earbuds is as shown in the graph below:
Evaluate the slope of the above graph.
The slope of the above graph gives the change in price of earbuds.
Thus,
[tex]\begin{gathered} \text{slope}=\frac{change\text{ in price of earbuds}}{change\text{ in number of earbuds}}=\frac{8-4}{4-2}=\frac{4}{2} \\ =2 \end{gathered}[/tex]Thus, the price of the earbuds is evaluated to be
[tex]\begin{gathered} P\text{ = 2x} \\ \text{where} \\ x\text{ is the number of earbuds to be bought} \end{gathered}[/tex]For headphones:
The price of the headphones is as shown in the table below:
The price change in headphones gives the slope.
The slope is thus evaluated to be
[tex]\begin{gathered} \text{slope}=\frac{change\text{ in price of headphones}}{change\text{ in number of headphones}}=\frac{y_2-y_1}{x_2-_{}x_1}=\frac{10-5}{2-1} \\ =5 \end{gathered}[/tex]Thus, the price of the headphones is evaluated to be
[tex]\begin{gathered} P=5x \\ \text{where} \\ x\text{ is the number of headphones to be bought} \end{gathered}[/tex]A steeper(higher) slope corresponds to a higher price. Since the slope for the headphone is higher than that of the earbud, we can conclude that the Earbud is a cheaper product.
Simplify(x^10)/(x^5)
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the answers to that [tex]y 2 - 1 = 9[/tex]
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You have the following equation:
y/2 - 1 = 9
in order to solve the previous equation, proceed as follow:
y/2 -1 = 9 add 1 both sides
y/2 = 9 + 1 simplify
y/2 = 10 multiply by 2 both sides
y = 20
Hence, the solution for y is y = 20
B. 20
Haseem was given the following enlargement. A triangle has a side with length 22.5 centimeters.What is the perimeter, in centimeters, of the enlarged triangle?
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First, let's calculate the perimeter of the smaller triangle:
[tex]P=3+5+6=14\text{ cm}[/tex]Now, let's calculate the ratio between the corresponding sides of the triangles:
[tex]r=\frac{22.5}{5}=4.5[/tex]Then, to find the perimeter of the bigger triangle, we can multiply the perimeter of the smaller triangle by the ratio:
[tex]\begin{gathered} P=14\cdot4.5\\ \\ P=63\text{ cm} \end{gathered}[/tex]Therefore the correct option is the fourth one.
Is this function f(x)=ײ linear, exponential, or neither?
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We will investigate the three different types of functions.
Linear:-
A linear function expresses a relationship between two variables in a straight line fashion. It develops a relation between two variables linearly. It is also categorized as a polynomial off highest order 1. The general form of a linear function is given below:
[tex]y\text{ = m}\cdot x\text{ + c}[/tex]Where,
[tex]\begin{gathered} m\colon\text{ Slope / Gradient} \\ c\colon\text{ y-intercept} \end{gathered}[/tex]How do you find the area and how much tile he needs ?
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SOLUTION
Let us sketch the composite figure of the floor plan
We are have now divided the floor plan into two sections which consist of two rectangles.
Let us now solve for the area of the floor-plan
The formula for the area of a rectangle is,
[tex]\text{Area}=\text{length}\times width[/tex]Therefore, the area of section A is,
Given
[tex]\begin{gathered} \text{length}=40ft \\ \text{width}=8ft \end{gathered}[/tex]Hence,
[tex]A=40\times8=320ft^2[/tex]Also, the area of section B is
Given
[tex]\begin{gathered} \text{length}=30ft \\ \text{width}=12ft \end{gathered}[/tex]Hence,
[tex]B=30\times12=360ft^2[/tex]Therefore, the amount of the tile needed to cover the floor is the sum of the area of section A and the area section B is
[tex]320ft^2+360ft^2=680ft^2[/tex]Hence, the answer is 680ft² (OPTION A).