For positive acute angles
A
A and
B
,
B, it is known that
cos
A
=
4
5
cosA=
5
4
and
sin
B
=
15
17
.
sinB=
17
15
. Find the value of
cos
(
A
−
B
)
cos(A−B) in simplest form.
Answers
9514 1404 393
Answer:
77/85
Step-by-step explanation:
Given:
cos(A) = 4/5
sin(B) = 15/17
Find:
cos(A-B)
Solution:
From your knowledge of Pythagorean triples, you know that one of them is (3, 4, 5) and another is (8, 15, 17). Using your imagination, or by drawing the triangles, you can determine the needed trig functions to be ...
sin(A) = 3/5
cos(B) = 8/17
__
Alternatively, you can use the Pythagorean identity to find ...
sin(A) = √(1 -cos²(A)) = √(1 -(4/5)²) = √(9/25) = 3/5
cos(B) = √(1 -sin²(B)) = √(1 -(15/17)²) = √(64/289) = 8/17
__
Then application of the angle difference formula is straightforward.
cos(A -B) = cos(A)cos(B) +sin(A)sin(B)
cos(A -B) = (4/5)(8/17) +(3/5)(15/17) = (32 +45)/85
cos(A -B) = 77/85
_____
Some graphing calculators can express the result ...
cos(arccos(4/5) -arcsin(15/17)) ≈ 0.90588235294
... as the fraction 77/85
Related Questions
I have 6 congruent faces and 2 bases.
Answers
Answer:
A cube
Step-by-step explanation:
A cube has 6 of the same faces and there are 2 bases
HELP ME PLZ!!!!! ..................................
Answers
Step-by-step explanation:
the the number on the top corner is adding zeros so 6.3 / 10/3 the answer is for that 6.30
2. 904
3. 9040
4. 90400
5. 904000
PLSSS HELP AND GIVE THE RIGHT ANSWER!!!!!!!!!!!!!!!!!!!
The fourth graders are having lunch in the schoolyard. Two classes of 30 students each, 2 teachers and 2 parents will be there. If 8 people sit at each table, how many tables will be needed for all the people having lunch in the schoolyard?
a) 8
b) 60
c) 64
d) 9
Answers
Answer:
8 tables
Step-by-step explanation:
2 class * 30 students + 2 teachers + 2 parents
= 64 people
64 people * 1 table/8 people = 8 tables
Mark brainliest if this helped
Mark brainliest if this helped
Step-by-step explanation:
8 tables because 30+30 =60
and 2+2=4 which is 64 and 8×8=64
Evaluate f(x)=−5ex+4+3 for x=−6.
Answers
Answer:
f(-6) = 30e+7 or 88.55
Step-by-step explanation:
First you want to plug in the -6 into the function getting you:
-5e(-6)+4+3
You can multiply the -5*-6=30
Then add 4+3 giving you 7
So the final answer is 30e+7
A repair engineer charges a customer £50 for every job and £25
for every hour that he works. Which formula could you use to
find how much he charges, C, for h hours of work?
Answers
Justin and Dan ordered a pizza. Justin ate 1/4 and ate 3/8 of the pizza what fraction of the pizza is left? please show how you got the answer.
Answers
Answer:
3/8 of the pizza is left
Step-by-step explanation:
say the pizza was cut into 8 slices. Justin at 1/4 of the pizza, we can also put that as 2/8. so now 2 slices are gone. that leaves us with 6 slices. Dan ate 3/8 so now 3 more slices are gone. now we only have 3 left. since we started out with 8 we'll use that as a denominator; 3/8. or look at the image attached
Answer:3/8
Step-by-step explanation:
Constance has an apple that weighs 85,000 milligrams and a peach that weighs 0.15 kilograms. Which fruit has the greater mass? Choose the words and numbers to complete the statements. Convert the masses of both fruits to the same unit.
Answers
Answer:
The peach will way more then the apple
Hope this helps you ☜(ﾟヮﾟ☜)
The weight of the peach is greater than the weight of apple
What is unit conversion?In order to translate measurements of a particular amount between different units, a mathematical conversion factor is usually used. This modifies the measurement of the quantity without altering its effects.
The particular circumstances or the intended result control the conversion process. This may be governed by law, a contract, a list of technical specifications, or other publicly available standards.
A precise conversion from one system to another is necessary for some measures in order to maintain the precision of both the original measurement and the conversion.
Based on the connection between a particular pair of original units and a particular pair of target units, each conversion factor is chosen.
Given data ,
Let the weight of apple be = 85,000 milligrams
And , let the weight of the peach be = 0.15 grams
Now , from the unit conversion
1 gram = 1000 milligrams
And , 1 kilogram = 1000 grams
So , the weight of apple A = 85 grams
And , the weight of the peach P = 150 grams
Therefore , P > A
Hence , weight of peach is larger
To learn more about unit conversion click :
https://brainly.com/question/19420601
#SPJ3
girl name are April, may, June, what is the name the mother?
Answers
mary is the 4th childs nam,e
what is 27+27 BumblebeeTuna
Answers
Answer: 54
Step-by-step explanation:
State the domain and range of f(x)=[[x-2]]
Answers
Answer:
domain: -infinity < x <infinity or (-infinity, infinity)
range: -infinity < f(x) < infinity or (-infinity, infinity)
Step-by-step explanation:
PLEASE HELP ME ON THIS!
the height of a rectangular prism is 8 meters, and the volume is 308 cubic meters. what is the area of the prisms base in square meters?
Answers
9514 1404 393
Answer:
38.5 square meters
Step-by-step explanation:
The relevant volume formula is ...
V = Bh . . . . where B is the area of the base, and h is the height
Solving for B, we get ...
B = V/h
B = (308 m³)/(8 m) = 38.5 m²
The area of the prism's base is 38.5 square meters.
find the missing side of each triangle using the pythagorean theorem
Answers
Answer:
x=5
Step-by-step explanation:
The pythagorean theorem stats a^2+b^2=c^2. We are already given the values of the two legs of the triangle so we need to solve for the length of the hypotenuse (the longest part of the triangle). To do so, you put in 3 and 4 as a and b so you get 3^2+4^2=c^2. After squaring both numbers you get 16+9=c^2. Then you add 16 and 9 to get 25=c^2. To get rid of the power of 2, we square root both sides to get rid of the exponent. Since 25 is a perfect square, you get c=5 which means that the x value eqals 5.
5+5(6*7)Easy points cause I love y’all pur
Answers
PLEASE HELP ASAP!!!
A group of students must collect at least $120 to organize a science fair. They have already collected $30. Which graph best represents all remaining amounts of money, in dollars, that the students should still collect to organize the science fair? Number line graph with closed circle on 120 and shading to the right Number line graph with closed circle on 90 and shading to the right. Number line graph with closed circle on 150 and shading to the right Number line graph with closed circle on 30 and shading to the right.
Answers
Answer:
OPITON 2
Step-by-step explanation:
120-30=90 SHE NEED 90 DOLARS MORE
find the 12th term in the sequence: 1/16, -1/8, 1/4
Answers
Answer:
Step-by-step explanation:
hello :
the sequence is geometric because : (1/4)/(-1/8) = (-1/8)/(1/16)=-2 = r
the nth term is : An =A1 × r^(n-1)
a common ratio is : r and A1 the first term
in this exercice : r =2 A1 = 1/16
when : n =12 you have the 12rd term A12
A12 = 1/16 × 2^(12-1) = 1/16 × 2^(11)
Which of the following equations has infinitely many solutions? A. 2x + 5(2x + 6) = 12x + 30 B. 2x + 5 = 2 C. 2(x + 5) + 2 = 6x + 2(x + 2) D. 5x + 2 = 2x + 6
Answers
Answer:
A. 2x + 5(2x + 6) = 12x + 30
Step-by-step explanation:
Infinitely many solutions means the two sides of the equation will be equal to each other, so B and D can be eliminated. Distribute for A and C to check
A. 2x + 5(2x + 6) = 12x + 30
2x + 10x + 30 = 12x + 30
12x + 30 = 12x + 30
C. 2(x + 5) + 2 = 6x + 2(x + 2)
2x + 10 + 2 = 6x +2x + 4
2x + 12 = 8x + 4
You only get the same equation for A, therefore A is the correct answer
Calculate the perimeter of the above triangle.
10 units
30 units
5:
22.9 units
17.1 units
Answers
Step-by-step explanation:
1.
The obvious question to ask in this situation is, “how many miles does Joseph travel on Mondays”? To compute, we each distance: 3 + 6 + 6 = 15.
Joseph travels 15 miles on Mondays.
3.Perimeter means “distance around a closed figure or shape” and to compute we add each length: 3 + 6 + 6 = 15
4.Solution
Just keep adding those side lengths. 6 + 7 + 4 + 4 + 5 + 6 + 2 = 34 units
If you look closely at the shapes in the previous examples, you might notice some ways to write each perimeter as a more explicit formula. See if the results from what we have done so far match the formulas below.
PLEASE HELP thank u very much
Martina designed a painting for art class, as shown in the drawing below. Her design contains 4 circles on a square canvas. Each circle has a radius of 6 inches. The circles touch the edges of the canvas and each other, as show below.
The shaded section of Martina's design will be painted black. Which is closest to the area that will be painted black?
Answers
Answer:
area of shaded region =(6×4)²-4(π6²)=123.61in²
Answer:
area of shaded region (6x4)²-4(6²)=123.61in²
s
Which lines have a y-intercept at (0,4)?
Choose all answers that apply:
А
y=-3x +4
B
y = 4x + 7
y = 5 + 4x
y = 4-2
KHAN ACADEMY
Answers
Answer:
y=-3x+4
Step-by-step explanation:
Using the formula y=mx+b
mx= slope b= y-intercept
hence,
y=-3x+4 has a y-intercept of (0,4)
Answer:
A y=3x +4
Step-by-step explanation:
since when x=0 then y will be at +4
Y=3(0)+
i will give brainliest if you answer this simple question.
if you have 5 candy bars in a bowl and take out 3 how many do you have now?
Answers
Answer:
2
Step-by-step explanation:
5-3=2 you subtract to get the answer
Answer:
2 in the bowl and 3 in the hand
Step-by-step explanation:
The final answer could be anywhere between 2 and 5 depending on what you did with the candy once it was taken out of the bowl. But, the most obvious answer would be 2 left and 3 technicallly gone
Solve the system of equations.
2r+3s=-5
3r+5s=-9
Type an ordered pair
Answers
Answer:
2r + 3s= 9 <=> -6r -9s = -27;
3r + 2s= 12 <=> 6r + 4s = 24;
=> 0*r -5*s = -3 => s = 3/5;
2*r + 3*(3/5) = 9<=> 10*r + 9 = 45 <=> 10*r = 36 => r = 18/5;
The Reeds are moving across the country. Mr. Reed leaves 4.5 hours before Mrs. Reed. If he averages 40mph and she averages 60mph, how many hours will it take Mrs. Reed to catch up to Mr. Reed?
Answers
Mr. Reed DATA:
rate = 40 mph ; time = x 4.5 hrs ; distance = 40x miles
-----
Mrs. Reed DATA:
rate = 60 mph ; time = x hrs ; distance = 60x - 210 miles
------
Equation:
40x = 60x -210
-20x = -210
x = 10.5 hrs
x-3.5 = 7 hrs (Mr. Reed's time)
you need 4/5 of a cup of strawberries for a single pie, how ,many cups are need for 9 pies?
Answers
Answer:
7 2/5 cups
Step-by-step explanation:
4 x 9 = 36
36/5 = 7.2
Elevii au studiat o schiță a corpului uman. Ei au observat că ar putea trasa pe schiță un
cerc pentru care centrul O și punctele A , B și C sunt corespunzătoare unor structuri
anatomice.
Cercul este reprezentat în figura alăturată. Centrul
cercului este punctul O, BC este diametru al cercului, iar
punctul A este situat pe cerc, astfel încât ∢BAO = 60° . Raza
cercului este de 2cm .
6. Calculează lungimea diametrului BC .
7. Determină măsura arcului mic AC .
Answers
Answer:
an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).
Find the mean absolute deviation of the set of data. Round your answer to two
decimal places.
78, 45, 60, 33, 84

Answers
Which of the following verbal sentences represents the algebraic sentence below?
2x – 5 = -15
Answers
If cos 67° is close to 25, which is closest to the length of NO?
Options
2 centimeters
20 centimeters
40 centimeters
60 centimeters
Answers
I really need help I would appreciate it if someone could help me
Answers
Answer:
a) The vertex of the graph is [tex](h,k) = (0, 31)[/tex], b) [tex]a = -16[/tex], c) The equation of the parabola is [tex]f(t) = -16\cdot t^{2}+31[/tex].
Step-by-step explanation:
a) The tennis ball experiments a free fall, that is, an uniform accelerated motion due to gravity and in which effects from Earth's rotation and air viscocity are negligible. The height of the ball in time is represented by a second order polynomial. Hence, the vertex of the parabola is the initial point highlighted in graph.
The vertex of the graph is [tex](h,k) = (0, 31)[/tex].
b) If we know that [tex](h,k) = (0, 31)[/tex], [tex]f(t) = a\cdot (t-h)^{2} + k[/tex] and [tex](t,f(t)) = (1,15)[/tex], then the value of [tex]a[/tex] is:
[tex]f(t) = a\cdot (t-h)^{2} + k[/tex]
[tex]15 = a\cdot (1-0)^{2}+31[/tex]
[tex]15 = a\cdot 1 + 31[/tex]
[tex]a = 15-31[/tex]
[tex]a = -16[/tex]
c) The equation of the parabola is [tex]f(t) = -16\cdot t^{2}+31[/tex].
PLEASE HELP SMART PEOPLE :C
Answers
Answer:
C 290 in^2
Step-by-step explanation:
Please help.
You will get brainliest.
Answers
Answer:
[tex] 18,432\pi \: {in}^{3} [/tex]
Step-by-step explanation:
Base diameter of cylinder = 48 in
So, base radius (r) = 48/2 = 24 in
Height of oil filled in the can (h) = 32 in
Volume of portion of the can that is filled with oil
[tex] = \pi {r}^{2} h \\ \\ = \pi \times (24)^{2} (32) \\ \\ =18,432\pi \: {in}^{3} [/tex]