Answer:
See below ↓
Step-by-step explanation:
We need to prove :
⇒ cos⁻¹ [tex]\frac{12}{13}[/tex] + sin⁻¹ [tex]\frac{3}{5}[/tex] = tan⁻¹ [tex]\frac{56}{65}[/tex]
Let's simplify the LHS.
cos⁻¹ [tex]\frac{12}{13}[/tex] + sin⁻¹ [tex]\frac{3}{5}[/tex]Convert the inverse cos and sin functions into inverse tan functions
tan⁻¹ [tex]\frac{5}{12}[/tex] + tan⁻¹ [tex]\frac{3}{4}[/tex][∴This can be found taking a right triangle and labeling the sides, and then using Pythagorean Theorem, we can find the missing side and take the ratio of tan]Identity
tan⁻¹ x + tan⁻¹ y = tan⁻¹ [tex]\frac{x+y}{1-xy}[/tex]Using this identity, we can simplify our earlier equation!
⇒ tan⁻¹ [(5/12 + 3/4)/(1 - (5/12 x 3/4))]
⇒ tan⁻¹ [(20 + 36) / (48 - 15)
⇒ tan⁻¹ (56/65)
⇒ RHS
⇒ Proved ∴√
[tex]\text{L.H.S}\\\\=\cos^{-1} \dfrac{12}{13} + \sin^{-1} \dfrac 35\\\\=\sin^{-1} \dfrac 5{13} + \sin^{-1} \dfrac 35\\\\[/tex]
[tex]=\sin^{-1}\left[\dfrac 5{13}\sqrt{1- \left(\dfrac 35 \right)^2} + \dfrac 35\sqrt{1-\left(\dfrac 5{13} \right)^2} \right]\\\\=\sin^{-1} \left(\dfrac 5{13} \sqrt{1-\dfrac 9{25} }+\dfrac 35 \sqrt{1-\dfrac{25}{169}} \right)\\\\=\sin^{-1} \left(\dfrac 5{13} \sqrt{\dfrac{16}{25}}+\dfrac 35 \sqrt{\dfrac{144}{169}} \right)\\\\=\sin^{-1} \left(\dfrac{5}{13} \cdot \dfrac 45 + \dfrac 35 \cdot \dfrac{12}{13} \right)\\[/tex]
[tex]=\sin^{-1} \left(\dfrac 4{13} +\dfrac{36}{65}\right)\\\\=\sin^{-1} \left(\dfrac{20}{65} + \dfrac{36}{65} \right)\\\\=\sin^{-1} \left(\dfrac{20+36}{65} \right)\\\\=\sin^{-1} \left(\dfrac{56}{65} \right)\\\\=\text{R.H.S}[/tex]
The diagram shows a track composed of a rectangle with a semicircle on each end. The area of the rectangle is 7,200 square meters. What is the perimeter of the track? Use 3.14 for Pi
Answer:
The perimeter of the track is the two circumferences of the semicircles (when combined, they form one circle, so we can just find the circumference of the circle) added to the lengths of the rectangle (160 meters).
To find the circumference of the circle, we need to know the diameter.
Circumference of a circle: dπ or 2rπ, where d represents diameter and r represents radius
The diameter of the circle happens to be the same as the width of the rectangle. We know that the area of a rectangle is found by multiplying its length by its width. We know that the area is 14400 and that its length is 160.
Width: area divided by length
14400160=90
The diameter of the circle and the width of the rectangle is 90 meters.
Circumference:
90⋅π=90π→ If you are using an approximation such as 3.14 for π, multiply that by 90
Add 160⋅2 to the circumference since the lengths of the rectangle are also part of the perimeter.
160⋅2=320
The perimeter of the track is 548.4 meters.
What is the perimeter?The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.
Given that, the area of the rectangle is 7,200 square meters.
From the figure, length of a rectangle = 120 meter
Here, area of rectangle = Length×Width
120×Width=7200
Width = 60 meter
So, diameter of semicircle is 60 meter.
Radius = 30 meter
Perimeter of track = Perimeter of rectangle + Circumference of two semicircle
= 2(120+60)+2πr
= 360+2×3.14×30
= 360+188.4
= 548.4 meters
Therefore, the perimeter of the track is 548.4 meters.
To learn more about the perimeter visit:
https://brainly.com/question/6465134.
#SPJ3
Suppose that the objective function coefficient for product C increases by $8. What impact will this have on the current values of the optimal solution
When the objective function coefficient for the product increases by $8, the impact on the current values of the optimal solution is that the current solution will change.
What is an objective function?An objective function simply means the function whose value is to be either maximized or minimized over the alternatives.
In this case, when the objective function coefficient for the product increases by $8, the impact on the current values of the optimal solution is that the current solution will change. The change is due to the varied objectives.
Learn more about objective function on:
https://brainly.com/question/26100401
Karen's mom is filling 12 birthday hats with candy for her birthday party. Each hat is shaped like a cone with a height of 6 inches and a radius of 3 inches.
Which statements are true? Choose all that are correct.
The volume of each birthday hat is 56.55 in³ and the 12 hats has a total volume of 678.58 in³
What is volume?
Volume is the amount of space occupied by a three dimensional shape or object.
The volume of a cone is given by:
volume = (1/3) * π * radius² * height
The cone that has a height of 6 inches and a radius of 3 inches. Hence:
Volume = (1/3) * π * 3² * 6 = 56.55 in³
For 12 hats:
Volume = 12 * 56.55 in³ = 678.58 in³
The volume of each birthday hat is 56.55 in³ and the 12 hats has a total volume of 678.58 in³
Find out more on volume at: https://brainly.com/question/12410983
Abigail had a fish tank that was in the shape of a box. The dimensions were 12 inches deep by 24 inches wide by 18 inches tall. How many cubic inches of water will it take to completely fill the tank?
Show your work
Two sides of an isosceles triangle have lengths 12 and 18. What
is the greatest possible value of the perimeter of the triangle?
Please help me.
The greatest possible value of the perimeter of the triangle is 48
What is the perimeter of a triangle?The perimeter of a triangle is the sum of the lengths of the three sides of the triangle.
An isosceles triangle has 2 equal sides and the length of the 2 sides must be greater than the length of one.
Perimeter A= 12×2+18=42
Perimeter B= 12+18×2=48
Therefore the greatest possible perimeter of the triangle is Perimeter B (48) since the sum of lengths of the two equal sides(18) is greater than the third side (12) and 48 is greater than 42.
Please read more about perimeter of triangle here:
https://brainly.com/question/15211769
6
x
+
8
<
3
x
+
4
give your answer as an improper fraction in its simplest
6x + 8 < 3x + 4
6x - 3x < 4 - 8
3x < -4
x < - 4/3
Answer:
-4/3
Step-by-step explanation:
6. Didi took out a loan of S12,600 to buy a car. After one month, an interest fee of 0.5% on this
loan is added to what she owes. After the fee is added, she then makes a payment of $200 to
start paying off her loan.
Given that the interest fee will increase what she owes while the payment will decrease what
she owes, how much money does Didi owe after one month
Answer:
$12,463
Step-by-step explanation:
The amount owed after one month is the sum of the original amount and the interest fee, less the amount paid.
__
The interest fee is 0.5% of $12,600, so is ...
0.005 × $12,600 = $63
After her $200 payment, the amount Didi owes is ...
$12,600 +63 -200 = $12,463 . . . owed after 1 month
The diagnols of a rhombus are 21 and 16 centimeters long find the area of the rhombus
Answer:
168 cm²
Step-by-step explanation:
The area of a quadrilateral with diagonals that intersect at right angles is half the product of the lengths of the diagonals. A rhombus is one such quadrilateral, so the area of this one is ...
A = 1/2(d1)(d2)
A = (1/2)(21 cm)(16 cm) = 168 cm²
The area of the rhombus is 168 cm².
help me please. lesson 9.3 converse if the pythagorean theorem
Answer:
acute
Step-by-step explanation:
Here are some helpful rules that will help you out in the future with these questions.
If...
a^2 + b^2 = c^2 its a right triangle
a^2 + b^2 < c^2 its obtuse
a^2 + b^2 > c^2 its acute
so...
Since 6+8>10
its acute
The function f(x) equals the number of feet above sea level a rock climber is at x
minutes. After 45 minutes the climber reaches his maximum height of 800ft. above
sea level. He stays on the mountain for 2 hours.
What is the practical domain of f(x)?
For the function f(x), the practical domain will be [0 min, 165 min]
What is the practical domain?
We define the practical domain as the section of the domain that has practical meaning.
In this case, the part of the domain that we care about is only when the rock climber is on the mountain.
In this case, we assume that the climb starts at x = 0 minutes.After 45 minutes, the climber reaches the top, at x = 45 minutes.And the climber stays on the mountain for 2 hours more, until x = 120 min + 45 min = 165 minutes.After that, the function does not work anymore, then the practical domain will be [0 min, 165 min]
If you want to learn more about domains, you can read:
https://brainly.com/question/1770447
A six-faced die is rolled .
a)Find the probability of it landin on a value more than 4
b)find the probability of it landing on an even number
Answer:
[A] 2/6
[B] 1/2
Step-by-step explanation:
Given:
A six-faced die is rolled .
To Find:
Find the probability of it landing on a value more than 4
Find the probability of it landing on an even number
Part A:
Knowing that a six-faced die has six number on it (1,2,3,4,5,6)
Thus, the probability of it landing on an value more than 4 is 2/6.
Because 5 and 6 is more than 4
Part B:
1,3,5 = Odd
2,4,6 = Even
Thus, the probability of it landing on an even number is 3/6 Simplify 1/2 . Which also is 50%.
~Lenvy~
Mathh question helppp
Answer:
60% test score
Step-by-step explanation:
When x is 6, y is 60
Please help with an explanation of how you found the answer because I am really confused. I will mark brainliest for best answer!
Answer:
The answer is A
Step-by-step explanation:
The minimum is 52 and the maximum is 65 therefore B and C are false.
Data set total number is 13 D medium is 56
so A is the correct answer
Write x=2 in slope intercept form
When x=a the slope is undefined . And when y is b the slope is zero
A middle school took all of its 6th grade students on a field trip to see a ballet. The
students filled 702 seats, leaving 35% vacant. How many total seats were in the
theater?
By working with percentages, we will see that there are 1,080 seats in the theater.
How many total seats were in the theater?
We know that the students filled 702 seats, leaving 35% vacant.
Then 702 seats represents the (100% - 35% = 65%) of the total number of seats.
So, if the total number of seats is S, we can write:
(65%/100%)*S as the 65% of S.
Then we solve:
(65%/100%)*S = 702
0.65*S = 702
S = 702/0.65 = 1,080
There are 1,080 seats in the theater.
If you want to learn more about percentages, you can read:
https://brainly.com/question/843074
per
Write your answer as a fraction or as a whole or mixed num
1
6
km
13
1
km
1
13
6
km
13
6
1 18 km
13
Answer:
5 11/13km
Step-by-step explanation:
4 ( 1 6/13)
4× 19/13
= 5 11/13
Chin-Mae has a fishtank that measures 75 cm by 45 cm by 35 cm. He also has a jug that holds 1.75 litres. He uses the jug to fill the fishtank with water. How many full jugs of water does it take to fill the fishtank? Show how to check your answer.
To find the volume of a rectangular prism, we can use the following formula:
[tex]V=lwh[/tex]
l = lengthw = widthh = heightConverting between mL and L1000 mL = 1 L
Solving the QuestionWe're given:
Fish tank measurements: 75 cm by 45 cm by 35 cmJug capacity = 1.75 LTo solve this question, we could follow these steps:
Find the volume of the tankDivide the volume of the tank by the jug capacityFind the volume of the tank
[tex]V=lwh[/tex]
⇒ Plug in the measurements: 75 cm by 45 cm by 35 cm
[tex]V=75*45*35\\V=118125[/tex]
Divide the volume of the tank by the capacity of the jug
There is a relationship between cm³ and mL, not cm³ and L. Convert the 1.75 L for the jug capacity to mL:
1.75 × 1000
= 1750
118125 ÷ 1750
= 67.5
AnswerIt takes 68 full jugs of water to fill the tank.
How can 8.34… be written in the form a/b where a and b are integers?
The decimal value 8.34 written as a ratio of a/b is 417/50
Conversion of decimal to fractionFractions are values written as a ratio of two integers
Given the decimal value 8.34, we are to convert it to a decimal value as shown:
8.34 = 834/100
Write in a simplified form834/100 = 417/50
Hence the decimal value 8.34 written as a ratio of a/b is 417/50
Learn more on fractions here: https://brainly.com/question/78672
Rachel has a coupon for 15% off any
two pairs of earrings at one of her
favorite stores. If each pair of
earrings that she purchased cost
$12.99, and the sales tax in her state
is 6.5%, then what is the total
amount she spent after using her
coupon?
Answer:
Total Payment: $23.52
Savings: $4.15
Tax: $1.44
Find the sum of the following polynomials
(3x^3+ 8x^2– 3) + (7x^3- 4x + 4)
Answer:
10x^3+8x^2-4x+1 is answer
need help :((((((((((((((((((((((
At a clover city council meeting, a plan to fund more sign language programs was presented. the reasoning behind the request was that less than 25% of parents with hearing-impaired children have the ability to pass a sign-language exam. if this is true, the council will agree to fund more programs for these parents. the council decides to take a 175-person volunteer sample of parents in clover city that have children with auditory issues and conduct a significance test for h0: p = 0.25 and ha: p < 0.25, where p is the proportion of these parents that can pass the sign language exam. they will perform the significance test at a significance level of ? = 0.05 for the hypotheses.
part a: describe a type ii error that could occur. what impact could this error have on the situation?
part b: out of the 175 volunteer parents of children with hearing problems, 54 passed, resulting in a p-value of 0.96. what can you conclude from this p-value given the data of the 175 parents is sufficient to perform a significance test for the hypotheses?
part c: what possible defect in the study can you find in part b? explain
The type II error is the probability of accepting the null hypothesis when it's false.
How to explain the probability?a. From the information, the proportion of parents who passes the sign language test is not less than 25%.
b. Since the p value is greater than 0.05, the null hypothesis is rejected. Therefore, the proportion of parents who passes the sign language test is not less than 25%.
c. The possible defect in the study is that the parents if the children with hearing problem should be selected randomly.
Learn more about probability on:
https://brainly.com/question/24756209
I need the assistance of smarter beings than I..... I'm so lost.....
Answer:
[tex]\sf \bold{ 1 * (-3)^{n-1}}[/tex]
Explanation:
first term, a₁ = 1
difference between the terms: -3
used geometric formula : [tex]\bold{\sf a_1 * (r)^{n-1}}[/tex]where "a₁ is first term" and "r refers to common difference"
formula for this nth term: [tex]\sf \bold{ 1 * (-3)^{n-1}}[/tex]What are the x-intercepts of ? f(x)=x3+4x2-9x-36? A. (1,0),(2,0),(3,0) B. (-1,0),(2,0),(18,0) C. (-6,0)(2,0)(3,0) D.(-4,0),(-3,0)(3,0)
Answer:
D. (-4,0),(-3,0)(3,0)
Step-by-step explanation:
Simplify 3xy(5x +3 - 7y)
[tex]3xy(5x+3-7y)=15x^2y+9xy-21xy^2[/tex]
solve for the x in the triangle .
Help is number 2 correct and help for number one
Number 2 is incorrect :
[tex]\frac{-25x^{3}+15x }{5x} = \frac{-25x^{3}}{5x} + \frac{15x}{5x} = -5x^{2} + 3[/tex]
Number 1 :
[tex](-5)^{3} . 13^{-2} . (-5) .13^{9} = -125 . \frac{1}{13^{2}} .(-5).13^{9} = 625 . \frac{13^{9}}{13^{2}} = 625 . 13^{7}[/tex] (i dont think we can bare calculate this cause it;s too big ;-;)
What is the volume of the square pyramid?
Answer:
you can solve by using the formula
volume = length x width x height
(I'm also bad at math so sorry if this isn't very helpful)
Step-by-step explanation:
1 all the bases are the same which means your length and width should be 5m
2 just multiply 5 x 5 x 14.2 and that should give you the awnser
Please help!
Find the value of x. Round to the nearest tenth for numbers #19.
Find the value of x. Round to the nearest degree # 23 & #27.
-Answer the last question :)
LAST QUESTION: The lengths of the diagonals of a rhombus are 2in. and 5in. Find the measures of the angles of the rhombus to the nearest degree.
The values of x in the triangles and the angles in the rhombus are illustrations of tangent ratios
The values of x in the triangles are 21.4 units, 58 degrees and 66 degreesThe angles in the rhombus are 44 and 46 degrees, respectivelyHow to determine the values of x?Triangle 1
The value of x is calculated using the following tangent ratio
tan(25) = 10/x
Make x the subject
x = 10/tan(25)
Evaluate
x = 21.4
Triangle 2
The value of x is calculated using the following tangent ratio
tan(x) = 8/5
Evaluate the quotient
tan(x) = 1.6
Take the arc tan of both sides
x = arctan(1.6)
Evaluate
x = 58
Triangle 3
The value of x is calculated using the following tangent ratio
tan(x) = 0.34/0.15
Evaluate the quotient
tan(x) = 2.27
Take the arc tan of both sides
x = arctan(2.27)
Evaluate
x = 66
How to calculate the angles of the rhombus?The lengths of the diagonals are:
L1 = 2 in
L2 = 5 in
Represent the angles with x and y.
The measures of the angles are calculated using the following tangent ratios
tan(0.5x) = 2/5 and y = 90 - x
Evaluate the quotient
tan(0.5x) = 0.4
Take the arc tan of both sides
0.5x = arctan(0.4)
Evaluate
0.5x = 22
Divide by 0.5
x = 44
Recall that:
y = 90 - x
This gives
y = 90 - 44
Evaluate
y = 46
Hence, the angles in the rhombus are 44 and 46 degrees, respectively
Read more about tangent ratio at:
https://brainly.com/question/13347349
The population of Atlanta Georgia in the year 2000 was 417,000 people. If the population increases at a rate of 1.2% each year, find the approximate population of Atlanta in
2020.
Step-by-step explanation:
geometric sequence :
a0 = 417,000
a1 = a0 × 1.012 (that is adding 1.2% for 2001)
a2 = a1 × 1.012 = a0 × 1.012²
an = a0 × 1.012^n
a20 (for the year 2020 after starting in 2000) =
= a0 × 1.012²⁰ = 417,000 × 1.012²⁰ = 529,354.1291...
if we need to round that to a full number, we get
≈ 529,534
our round it to full thousands
≈ 530,000
i don't know what result format you need. please pick the required one.