I know the selected answer is correct but I'm not too sure how to get that answer.
Could someone please explain.
Answers
[tex]\tt{ Hey \: there , \: Mr.Panda \: ! } [/tex] ;)
♨[tex] \large{ \tt{ E \: X \: P \: L \: A \: N \: A \: T \: I\: O \: N}}: [/tex]
⤻ Before solving the given question , you should know the answer of these questions :
✺How do you find the hypotenuse , perpendicular and base when the angle ( [tex] \theta \: , \alpha \: ,\beta [/tex] ) is given ?
⇾ The longest side , which is the opposite side of right angle is the hypotenuse ( h ). There are two other sides , the opposite and the adjacent. The naming of these sides depends upon which angle is involved. The opposite is the side opposite the angle involved and it is called the perpendicular ( p ) . The adjacent us the side next to the angle involved ( buy not the hypotenuse ) and it is called the base ( b ).
☄ [tex] \large{ \tt{REMEMBER}} : [/tex]
[tex] \bf{ \sin \theta = \frac{opposite}{hypotenuse} = \frac{perpendicular}{hypotenuse} }[/tex][tex]\bf{ \cos\theta = \frac{adjacent}{hypotenuse} = \frac{base}{hypotenuse} }[/tex][tex] \bf{ \tan \theta = \frac{opposite}{adjacent} = \frac{perpendicular}{base} }[/tex]In the above cases , [tex] \theta[/tex] is taken as the angle of reference.
♪ Our Q/A part ends up here! Let's start solving the question :
❈ [tex] \large{ \tt{GIVEN}} : [/tex]
Perpendicular ( p ) = ? , Hypotenuse ( h ) = 18 & base ( b ) = 16✧ [tex] \large{ \tt{TO \: FIND} : }[/tex]
Value of tan [tex] \theta[/tex]✎ [tex] \large{ \tt{SOLUTION}} : [/tex]
Firstly , Finding the value of perpendicular ( p ) using Pythagoras theorem :
❃ [tex] \boxed{ \sf{ {h}^{2} = {p}^{2} + {b}^{2} }}[/tex] [ Pythagoras theorem ]
[tex] \large{ ⇢ \sf{p}^{2} + {b}^{2} = {h}^{2} }[/tex]
[tex] \large{⇢ \sf{ {p}^{2} = {h}^{2} - {b}^{2} }}[/tex]
[tex] \large{ ⇢\sf{ {p}^{2} = {18}^{2} - {16}^{2} }}[/tex]
[tex] \large{⇢ \sf{ {p}^{2} = 324 - 256}}[/tex]
[tex] \large{⇢ \sf{ {p}^{2} = 68}}[/tex]
[tex] \large{⇢ \sf{p = \sqrt{68}}} [/tex]
[tex] \large{ ⇢\sf{p = \boxed{ \tt{2 \sqrt{17}}} }}[/tex]
Okey, We found out the perpendicular i.e [tex] \tt{2 \sqrt{17}} [/tex] . Now , We know :
❊ [tex] \large{ \sf{ \tan \theta} = \frac{perpendicular}{base} }[/tex]
[tex] \large {\tt{↬ \: tan \theta = \frac{2 \sqrt{17} }{16}}} [/tex]
[tex] \large{ \tt{ ↬ tan \theta = \frac{ \cancel{2} \: \sqrt{17} }{ \cancel{16} \: \: 8} }}[/tex]
[tex] \large{ \tt{ ↬ \boxed{ \tt{tan \theta = \frac{ \sqrt{17} }{8}}}}} [/tex]
⟿ [tex] \boxed{ \boxed{ \tt{OUR\: FINAL \: ANSWER : \boxed{ \underline{ \bf{ \frac{ \sqrt{17} }{8}}}}}}} [/tex]
۵ Yay! We're done!
♕ [tex] \large\tt{RULE \: OF \:SUCCESS }: [/tex]
Never lose hope & keep on working ! ✔ツ Hope I helped!
☃ Have a wonderful day / evening! ☼
# StayInAndExplore ☂
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Answer:
√(17)/8
Step-by-step explanation:
We are given with hypotenuse and base. We can have any ratio related to it, such as secant.
secA = hypotenuse/base
secA = 18/16 = 9/8
sec²A = 81/64
Using sec²A - 1 = tan²A
=> 81/64 - 1 = tan²A
=> 17/64 = tan²A
=> √(17)/8 = tanA
______________________
Using cosine of angle A.
cosA = base/hypotenuse
cos²A = (16/18) = (8/9)² = 64/81
sin²A = 1 - cos²A = 1 - 64/81 = 17/81
Hence,
tanA = √(tan²A) = √(sin²A/cos²A) = √((17/81)/(64/81)) = √(17)/8
This looks complex, either go with the 1st or one Or directly find the value of height using Pythagoras theorem,
18² = 16² + height²
√17 = height
tanA = height/base = √17/8
Related Questions
A school is planning to construct two rectangular play areas in the playground. The length of play area A must be 1 foot longer than four times its width. The width of play area B must be 2 feet longer than the width of play area A, and the length must be 2 feet longer than three times its own width. In addition, the areas of the two play areas must be equal. Write a system of equations to represent this situation, where y is the area of the play areas and x is the width of play area A. Which statement describes the number and viability of the system's solutions?
Answers
Answer:
А.The system has two solutions, but only one is viable because the other results in a negative width.
Step-by-step explanation:
Given
Let:
[tex]L_A \to[/tex] length of play area A
[tex]W_A \to[/tex] width of play area A
[tex]L_B \to[/tex] length of play area B
[tex]W_B \to[/tex] width of play area B
[tex]x \to[/tex] Area of A
[tex]y \to[/tex] Area of B
From the question, we have the following:
[tex]L_A = 1 + 4W_A[/tex]
[tex]W_B = 2 + W_A[/tex]
[tex]L_B = 2 + 3W_B[/tex]
[tex]x = y[/tex]
The area of A is:
[tex]x = L_A * W_A[/tex]
This gives:
[tex]x = (1 + 4W_A) * W_A[/tex]
Open bracket
[tex]x = W_A + 4W_A^2[/tex]
The area of B is:
[tex]y = L_B * W_B[/tex]
[tex]y = (2 + 3W_B) * ( 2 + W_A)[/tex]
Substitute: [tex]W_B = 2 + W_A[/tex]
[tex]y = (2 + 3(2 + W_A)) * ( 2 + W_A)[/tex]
Open brackets
[tex]y = (2 + 6 + 3W_A) * ( 2 + W_A)[/tex]
[tex]y = (8 + 3W_A) * ( 2 + W_A)[/tex]
Expand
[tex]y = 16 + 8W_A + 6W_A + 3W_A^2[/tex]
[tex]y = 16 + 14W_A + 3W_A^2[/tex]
We have that:
[tex]x = y[/tex]
This gives:
[tex]W_A + 4W_A^2 = 16 + 14W_A + 3W_A^2[/tex]
Collect like terms
[tex]4W_A^2 - 3W_A^2 + W_A -14W_A - 16 =0[/tex]
[tex]W_A^2 -13W_A - 16 =0[/tex]
Using quadratic calculator, we have:
[tex]W_A = -14.1[/tex] or [tex]W = 1.13[/tex] --- approximated
But the width can not be negative; So:
[tex]W = 1.19[/tex]
Determine the volume of the CD box shown
7.5 in
6.25 in.
8 in
Answers
Answer:
Step-by-step explanation:
I hope this helps you
Rectangular Prism Volume is
Height. Width. Height
(6.25).(7.5).(8)
375
Length x width x height
Company is testing a robot.The robot is 12 inches tall and weigh 4 pounds.The employees of the company marked a grid on the floor and set the robot at(4,4). They programmed the robot to walk 4 yards east and 6 yards north each minute.What will the robot's location be after 7 minutes? The x coordinate and the y coordinate
Answers
Answer:
[tex]P(2)=(32,46)[/tex]
Step-by-step explanation:
From the question we are told that:
Height of robot [tex]h=12 inches[/tex]
Weight of robot [tex]W=4[/tex]
Start position [tex]P(1)=(4,4)[/tex]
Per minute distance [tex]d=(4,6)[/tex]
Total time [tex]T=7min[/tex]
Generally the distance traveled in 7 minutes [tex]d_T[/tex] is mathematically given by
[tex]d_T=d*T[/tex]
[tex]d_T=(4.6)*7[/tex]
[tex]d_T=(28,42)[/tex]
Generally the position of the robot after 7 minutes is mathematically given by
[tex]P(2)=P(1)+d_T[/tex]
[tex]P(2)=(4,4)+(28,42)[/tex]
[tex]P(2)=(32,46)[/tex]
Therefore the position of the robot after 7 minutes is
[tex]P(2)=(32,46)[/tex]
sean needed to put 7 gallons 3 quarts of gas into his boat on Monday and twice as much on Saturday.if he had a 22 gallon jug of gas available, did he have enough gas for both days?
Answers
Answer:
No
Step-by-step explanation:
7 3/4 x 3 = 22 1/2
Answer please !!!!!!!!!
Answers
Find the measure of the angle indicated.
P
A) 92°
B) 61°
C 86°
D) 34°
Answers
Answer:
92°÷^®√™÷√÷^π^π^^π^π°π°^÷
Ahhhhhh i neeed help
Answers
Answer:
ok hiiiiiiiiiiiiiiiiiiiiiii
Step-by-step explanation:
Answer:
Option C, No real solutions
Hope this helps!
what is the value of x squared + 2 x y / 2 * W + 3 * z for w=2, x=5, y=8 and z=3
Answers
Answer: 114
Step-by-step explanation:
Plug in the numbers. 5*5+2*5*8/2*2+3*3=25+80+9=114
Which expression is equivalent to a^-x?
Answers
Please help! I will give Brainliest!
Who is correct?
Answers
Answer:
Erin
Step-by-step explanation:
I believe Erin is right in this case.
What is an equation of the line that passes through the point (8,-7)(8,−7) and is parallel to the line x+2y=18x+2y=18?
Answers
Answer:
[tex]y=-\frac{1}{2} x-3[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)Parallel lines always have the same slope (m) and different y-intercepts (b)1) Determine the slope (m)
[tex]x+2y=18[/tex]
Rearrange this equation into slope-intercept form (this will make it easier for us to identify the slope)
Subtract x from both sides to isolate 2y
[tex]x+2y-x=-x+18\\2y=-x+18[/tex]
Divide both sides by 2 to isolate y
[tex]y=-\frac{1}{2} x+9[/tex]
Now, we can see clearly that [tex]-\frac{1}{2}[/tex] is in the place of m. Because parallel lines have the same slope, [tex]-\frac{1}{2}[/tex] is therefore the slope of the line we're currently solving for. Plug [tex]-\frac{1}{2}[/tex] into [tex]y=mx+b[/tex]:
[tex]y=-\frac{1}{2} x+b[/tex]
2) Determine the y-intercept
[tex]y=-\frac{1}{2} x+b[/tex]
Plug in the point (8,-7)
[tex]-7=-\frac{1}{2} (8)+b\\-7=-4+b[/tex]
Add 4 to both sides
[tex]-7+4=-4+b+4\\-3=b[/tex]
Therefore, the y-intercept is -3. Plug this back into [tex]y=-\frac{1}{2} x+b[/tex]:
[tex]y=-\frac{1}{2} x-3[/tex]
I hope this helps!
HIII can some one please HELP ME !!!!
Answers
Answer:95
Step-by-step explanation:
how should i solve number 2 ?
Answers
X-1=0
X=1 , ≠-1 , x≠3
Answer X=1
I reallly need help plss -m=5-plssss
Answers
Answer:
[tex]4m ^{2} = 4 \times 5 \times 5 = 100[/tex]
how many terms does 3x + 5y - 17 - 2y + x have?
Answers
Answer:
It has 5 terms
Step-by-step explanation:
Terms are the numbers or values in a equation, so this Equation has 5 terms
x + 5y - 17 - 2y + x.
1. x
2.5y
3.17
4. 2y
5.x
(I listed the terms)
At a surf shop in Malibu, California, a used blue surfboard is on sale for $100. According to the salesperson, the new price represents a 20% discount from the original price. What did it sell for originally?
Answers
Answer:
$125
Step-by-step explanation:
if there was a discount of 20%, the sales price is 100 - 20 = 80% of the original price
let a = original price
this equation can be used to represent the question
a x 0.8 = 100 ]]divide both sides by 0.8
a = 100 / 0.8 = 125
Write the equation of the line passing through the points (0, -4) and (-2, 2).
Answers
Answer:
y=-3x-4
Step-by-step explanation:
i solved it by the two points
PLEASE HELP DUE IN 20 MINUTES!!!
about cylinders
Answers
Answer: Diameter = 4 cm
Step-by-step explanation:
20π = (π)(r^2)(5)
divide by 5 * π
4 = r^2
find the square root of both sides
2 = r
2 * 2 = d
4 = d
Using the image above, describe the error in the statement of the tangent ratio. answer correctly !!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answers
Answer:
the right answer is
tan D=80/18
PLEASE HURRY!!! ACTUALLY ANSWER PLEASE
Answers
Answer:
C
Step-by-step explanation:
Process of elimination
Explain how to add 5.3 + 9.079
Answers
Answer:
14.379
Step-by-step explanation:
1. Line up from left to right
2. Make sure that the decimals are lined up
3. Add the thousandths and hundredths with 0
4. Add 3 in the tenths place
5. Add up 9 and 5 to make 14
*IF YOU DID THE STEPS RIGHT, THEN YOU SHOULD HAVE 14.379 AS YOUR ANSWER*
Answer:
9.079
+5.300
_______
14.379
Step-by-step explanation:
Just line the decimals up and add zeros for 5.3 to 5.300 because you can't do 9.079
+5.3 because your decimal will be in the wrong spot and your answer will come out wrong
Need help with math!! Provided the graph with answers
Answers
I think the first one c and the second one a
5. If position of object x = 3 sinΘ – 7 cosΘ then motion of object is bounded between position.
Answers
9514 1404 393
Answer:
±√58 ≈ ±7.616
Step-by-step explanation:
The linear combination of sine and cosine functions will have an amplitude that is the root of the sum of the squares of the individual amplitudes.
|x| = √(3² +7²) = √58
The motion is bounded between positions ±√58.
_____
Here's a way to get to the relation used above.
The sine of the sum of angles is given by ...
sin(θ+c) = sin(θ)cos(c) +cos(θ)sin(c)
If this is multiplied by some amplitude A, then we have ...
A·sin(θ+c) = A·sin(θ)cos(c) +A·cos(θ)sin(c)
Comparing this to the given expression, we find ...
A·cos(c) = 3 and A·sin(c) = -7
We know that sin²+cos² = 1, so the sum of the squares of these values is ...
(A·cos(c))² +(A·sin(c))² = A²(cos(c)² +sin(c)²) = A²(1) = A²
That is, A² = (3)² +(-7)² = 9+49 = 58. This tells us the position function can be written as ...
x = A·sin(θ +c) . . . . for some angle c
x = (√58)sin(θ +c)
This has the bounds ±√58.
Lines AB and CD are parallel. If mZN is 52" then what is my?
A 128
B. 38
C. 142
D. 52
Answers
Angle A and Angle B are vertical angles. If the measure of Angle A is 30 degrees, what is the measure of Angle B?
Answers
Answer: 30 degrees
Step-by-step explanation: Vertical angles are always congruent. If Angle A and Angle B are vertical then they are equal to each other. They both will way thirty degrees.
How do you find the interquartile range?
Answers
6. In 2002, the bear population in Florida was estimated to be 2,700. In 2019, it was reported to be
4050. What percent does the increase in bears represent? Pls put the steps. Pls help this is due in 15 minutes
Answers
Answer:
50% increase
Step-by-step explanation:
4050-2700 = 1350
1350/2700 = 0.5
Convert to a percentage:
0.5*100 = 50
Which expression is equivalent to 10f−5−5f+2?
15f−3
5f−7
15f−7
−3+5f
Answers
Answer:
[tex]10f - 5-5f +2 =5f -3= -3+5f[/tex]
last option
Answer:
C
Step-by-step explanation:
If we solve 10f-5f+8+69+4, We get 5f+81 (put in comments if you want a step by step explanation on how i solved this).
Let's try to solve each of the options.
A) 15f + 14g + 4
It would not be option A because there isn't a variable such as g in the expression.
B) 15f + 8 + 10g
C) 5f + 69 + 12
5f+ 81
This one is correct because the expression also equals 5f+81
D) 5f + 149 +4
5f+ 153
D would be wrong as well
Hope this helps! <3
solve: 7 (j-5)=-14 what is the value of j?
Answers
Answer:
open bracket
7j - 35 = 14
7j = 14 + 35
7j = 49
divide thru by 7
7j / 7 = 49 / 7
j = 7
Macy took a Math test; her ratio of the correct to incorrect answers was 8:2.
If there were 30 questions on the test, how many did Macy get correct?
FAST RESPONSE PLEASE!!!!
Answers
Answer:
24
Step-by-step explanation:
8 correct for every 2 wrong
multiply both sides by 3
24 correct and 6 wrong
which adds up to 30