Answer:
[tex]\cos(A + B) = \frac{23}{265}[/tex]
Step-by-step explanation:
Given
[tex]\tan A=\frac{28}{45}[/tex]
[tex]\cos B=\frac{3}{5}[/tex]
Required
[tex]\cos(A+B)[/tex]
In trigonometry:
[tex]\cos(A+B) = \cos\ A\ cosB - sinA\ sinB[/tex]
We need to solve for cosA, sinA and sinB
Given that:
[tex]\tan A=\frac{28}{45}[/tex] and the tangent of an angle is a ratio of the opposite side (x) to the adjacent side (y),
So, we have:
[tex]x =28[/tex] and [tex]y = 45[/tex]
For this angle A, we need t calculate its hypotenuse (z).
Using Pythagoras,
[tex]z^2 = x^2 + y^2[/tex]
[tex]z = \sqrt{x^2 + y^2[/tex]
[tex]z = \sqrt{28^2 + 45^2[/tex]
[tex]z = \sqrt{2809[/tex]
[tex]z = 53[/tex]
From here, we can calculate sin and cos A
[tex]\sin A= \frac{opposite}{hypotenuse}[/tex] and [tex]\cos A= \frac{adjacent}{hypotenuse}[/tex]
[tex]\sin A= \frac{x}{z}[/tex]
[tex]\sin A= \frac{28}{53}[/tex]
[tex]\cos A= \frac{y}{z}[/tex]
[tex]\cos A= \frac{45}{53}[/tex]
To angle B.
Give that
[tex]\cos B=\frac{3}{5}[/tex] and the cosine of an angle is a ratio of the adjacent side (a) to the hypotenuse side (c),
So, we have:
[tex]a = 3[/tex] and [tex]b = 5[/tex]
For this angle B, we need to calculate its opposite (b).
Using Pythagoras,
[tex]c^2 = a^2 + b^2[/tex]
[tex]5^2 = 3^2 + b^2[/tex]
[tex]25 = 9 + b^2[/tex]
Collect like terms
[tex]b^2 = 25 - 9[/tex]
[tex]b^2 = 16[/tex]
[tex]b = \sqrt{16[/tex]
[tex]b = 4[/tex]
From here, we can calculate sin B
[tex]\sin B= \frac{opposite}{hypotenuse}[/tex]
[tex]\sin B = \frac{b}{c}[/tex]
[tex]\sin B = \frac{4}{5}[/tex]
Recall that:
[tex]\cos(A+B) = \cos\ A\ cosB - sinA\ sinB[/tex]
and
[tex]\cos B=\frac{3}{5}[/tex] [tex]\sin B = \frac{4}{5}[/tex] [tex]\sin A= \frac{28}{53}[/tex] [tex]\cos A= \frac{45}{53}[/tex]
[tex]\cos(A + B) = \frac{45}{53} * \frac{3}{5} - \frac{28}{53} * \frac{4}{5}[/tex]
[tex]\cos(A + B) = \frac{135}{265} - \frac{112}{265}[/tex]
[tex]\cos(A + B) = \frac{135-112}{265}[/tex]
[tex]\cos(A + B) = \frac{23}{265}[/tex]
The value of [tex]\cos (A+B)[/tex] is [tex]-\frac{96}{265}[/tex].
Trigonometrically speaking, the sine, cosine and tangent of an angle are described by the following formulas:
[tex]\sin \theta = \frac{y}{\sqrt{x^{2}+y^{2}}}[/tex] (1)
[tex]\cos \theta = \frac{x}{\sqrt{x^{2}+y^{2}}}[/tex] (2)
[tex]\tan \theta = \frac{y}{x}[/tex] (3)
Where:
[tex]\theta[/tex] - Angle, in sexagesimal degrees.[tex]x[/tex] - Adjacent leg.[tex]y[/tex] - Opposite leg.And we have the following trigonometric identity for the cosine of the sum of angles:
[tex]\cos (A+B) = \cos A\cdot \cos B - \sin A \cdot \sin B[/tex] (4)
By (1) and (2), we rewrite (4):
[tex]\cos (A+B) = \frac{x_{A}\cdot x_{B}}{\sqrt{x_{A}^{2}+y_{A}^{2}}\cdot \sqrt{x_{B}^{2}+y_{B}^{2}}} - \frac{y_{A}\cdot y_{B}}{\sqrt{x_{A}^{2}+y_{A}^{2}}\cdot \sqrt{x_{B}^{2}+y_{B}^{2}}}[/tex]
If we know that [tex]x_{A} = 28[/tex], [tex]y_{A} = 45[/tex], [tex]x_{B} = 3[/tex] and [tex]y_{B} = 4[/tex], then the cosine for the sum of angles is:
[tex]\cos (A+B) = \frac{28\cdot 3}{\sqrt{28^{2}+45^{2}}\cdot \sqrt{3^{2}+4^{2}}}-\frac{45\cdot 4}{\sqrt{28^{2}+45^{2}}\cdot \sqrt{3^{2}+4^{2}}}[/tex]
[tex]\cos (A+B) = -\frac{96}{265}[/tex]
The value of [tex]\cos (A+B)[/tex] is [tex]-\frac{96}{265}[/tex].
We kindly invite to check this question on trigonometric identities: https://brainly.com/question/24836845
A law firm is going to designate associates and partners to a big new case. The daily rate charged to the client for each associate is $800 and the daily rate for each partner is $1500. How much would the law firm charge the client daily if 9 associates and 4 partners were assigned to the case? How much would the law firm charge the client daily if aa associates and pp partners were assigned to the case?
Answer:
$8700
Step-by-step explanation:
Associates cost $800 each, you have 9 associates, so multiply 800 by 9 which gives you: $800x 9= $7200.
Partners cost $1500 each, you have 4 partners, so multiply 1500 by 4 which gives you: $1500x 4=$6000.
Then add the two together like this: $7200+$1500= $8700.
Answer:
The system 800x+1300y=12300 and y = x+3 can be used to determine the number of associate assigned to the case and the number of partners assigned to the case where x represent the number of associates and y represent the number of partners.
Step-by-step explanation:
Given,
Per day charge of each associate = $800
Per day charge of each partner = $1300
Total charged per day = $12300
Let,
x be the number of associates
y be the number of partners
According to given statement;
800x+1300y=12300 Eqn 1
y = x+3 Eqn 2
The system 800x+1300y=12300 and y = x+3 can be used to determine the number of associate assigned to the case and the number of partners assigned to the case where x represent the number of associates and y represent the number of partners.
Keywords: linear equation, addition
Step-by-step explanation:
What is the solution to m/-7<_ 14
Answer:
-98
Step-by-step explanation:
simplify both sides
Juan paid $42 in taxi fare from the hotel to the airport. The cab charged a $7 initial fee plus $2.50 for each additional mile. How many miles was it from the hotel to the airport?
Answer:
It was 14 miles from the hotel to the airport.
Step-by-step explanation:
From the information given, the taxi fair is equal to the initial fee plus the result of multiplying the price per mile for the number of miles, which is:
t=7+2.50x, where:
t is the taxi fair
x is the number of miles
Now, you can replace t with 42 and solve for x to find the miles:
42=7+2.50x
42-7=2.50x
35=2.50x
x=35/2.50
x=14
According to this, the answer is that it was 14 miles from the hotel to the airport.
suppose a+b=10 and the value of a increases by 1. If the sum remains the same, what must happen to the value of b?
Answer:
[tex]b[/tex] decreases by [tex]1[/tex]
Step-by-step explanation:
If the value of [tex]a[/tex] increases by [tex]1[/tex] and the sum remains the same, then the value of [tex]b[/tex] decreases by [tex]1[/tex].
Example:
Suppose [tex]a=7[/tex] and [tex]b=3[/tex].
[tex]a+b = 10[/tex]
[tex]b = 10-a[/tex] (minus [tex]a[/tex] on both sides)
Now, let [tex]a = 8[/tex] ([tex]a[/tex] has increased by [tex]1[/tex]):
[tex]b = 10-8[/tex]
[tex]=2[/tex]
From the comparison of the previous value of [tex]b[/tex] to the current value of [tex]b[/tex], the value of [tex]b[/tex] has decreased by [tex]1[/tex].
Hope this helps :)
Mike can run a mile in 12 minutes. He starts at 11:30 AM. and runs 4 miles. What time does Mike finish his run at?
Answer: Mike stops running at 12:18 PM
Step-by-step explanation: We know he runs 1 mile each 12 minutes and we also knows he ran 4 miles so the equation is 12*4 or (12 times 4) which is equal to 48. We then add 38 minutes to 11:30 AM and end up at 12:18 PM.
Answer:
12:18 P.M
Step-by-step explanation:
So the first thing I did was find out the amount of time it takes Mike to run 4 miles by multiplying 12 x 4 = 48
So Mike spends 48 minutes running the 4 miles.
Now we add 48 minutes to 11:30. So since there is no such thing as 11:78 I first subtracted the 30 minutes from the 48 minutes and added that to 11:30 which gave me 12:00 pm and then I just added the reamaining18 minutes.
which in conclusion means,
Mike will finish his 4 miles at 12:18 P.M
Heyy I need help with these two questions for math before he emails my mom saying i didnt do my work bc my brain isnt working properly rn
Answer:
4 pieces and B
Step-by-step explanation:
Answer: The answer to the first one is probably 8.
Step-by-step explanation:
I just read the problem and saw it as a division problem. I then divided 4/6 by 1/12. I ended up with 8, if this is wrong i'm incredibly sorry.
find x intercept if y=-5x+60
Answer:
-12 bla bla bla bla bla bla bla
Can someone help pls?
Answer:
Step-by-step explanation:
Let the original width be x
Then the original length = x + 11
Area = x * (x + 11)
If you decrease each side by 7 you get
Area 1 = (x - 7)(x + 4)
So area - area1 =
x (x + 11) -98 = (x - 7)(x + 4) Remove the brackets
x^2 + 11x - 98 = x^2 - 7x + 4x - 28 Combine the like terms
x^2 + 11x - 98 = x^2 - 3x - 28 Add 98 to both sides
x^2 + 11x = x^2 - 3x + 70 Cancel the x^2
11x = -3x + 70 Add 3x to both sides
14x = 70 Divide by 14
x = 70 / 14
x = 5
=====================
Original conditions
Answer width = 5
Length = 16
If you check this, you will get totally bizarre answers. Don't check it. It gives negative results. You can do this in math, but not in the real world.
If f(x)=−5x−8 and g(x)=2x+1, then what is (f∘g)(5.7)?
Answer:
(f*g)(5.7)= -452.6, hopefully that answers your question
The value of a new car decreases by about 15% in the first year. How much will a car be worth after one year if its initial value was $1,500? If you get stuck, consider using diagrams or a table to organize your work.
Answer:
After one year, the car will be worth $1,275.
Step-by-step explanation:
We know that a new car value decreases by 15% every year. So, we first need to find 15% of $1,500.
1,500 x 0.15 = $225.
Now, me must subtract $225 from the initial value, or $1,500.
1,500 - 225 = $1,275
Therefore, after one year, the car will be worth $1,275.
Hope this helps! :D
Who has
✨ A n x i e t y ✨
Answer:
yupyup
Step-by-step explanation:
been having it for years now
Write this fraction in an equation using words: 2/3
Answer:
two-thirds plus five=five and two-thirds
Step-by-step explanation:
Select all simplified expressions of 3^4 divided by 3^9
A group of friends went fishing. They each caught 20 fish but not all of them were keepers. Which person was able to keep 3/5 of the fish that he or she caught?
Answer:
Those who were able to keep 12 fishes
Step-by-step explanation:
Given
Total = 20 (each)
Required
Which was able to keep 3/5
First, we need to calculate 3/5 of the total number of fishes
Fish = 3/5 * 20
Fish = (3 * 20)/5
Fish = 60/5
Fish = 12
From the calculation above, only those who keep 12 of the 20 fishes were able to keep 3/5 of their fishes
A poster of the detroit lions football players uses a scale of 4 inches= 3 feet. If quarterback Matthew stafford is 8 1/2 inches tall on the poster, find his actual height.
Answer:
The actual height = 6.38 feet
Step-by-step explanation:
Given that a poster of the detroit lions football players uses a scale
of 4 inches = 3 feet
so
1 inch = 3/4 feetGiven that the poster's length:
[tex]8\frac{1}{2}=\frac{17}{2}=8.5[/tex] inch
We need to determine the actual height if quarterback Matthew Stafford is 8 1/2 inches tall on the poster.As 1 inch = 3/4 feetThus, we need to multiply 8.5 inches by 3/4 to determine the actual height of the player.
Actual height = 8.5 × 3/4 feet
= 6.38 feet
Therefore, the actual height = 6.38 feet
What is another way to express 48 + 32?
(a) 6(8+6)
(b) 16(3 + 2)
(c) 3(16 + 11)
(d) 12(4 + 3)
Answer:d
Step-by-step explanation: tufryvztgv
A store had 5 packs of paper for $7.80. How much would it cost if you were to buy 3 packs
$1.56
$2.19
$7.80
$4.68
Given the set of test scores: 42, 72, 74, 78, 80, 80, 85, 88, 92. If the outlier is removed, which statement is true? Select all that apply.
Choose all that apply:
The standard deviation decreases.
The mean increases.
The median decreases.
The range increases.
Answer:
Standard deviation decreases and mean increases
Step-by-step explanation:
The test scores are:
42, 72, 74, 78, 80, 80, 85, 88, 92
Mean = (42 + 72 + 74 + 78 + 80 + 80 + 85 + 88 + 92)/9 = 76.77
Median is 5th term which is 80
Range is highest score - lowest score = 92 - 42 = 50
Standard deviation from an online calculator gives 13.69
Now,we want to know what happens to those values when the outlier is removed. The outlier in this case is 42 because it is not consistent with other scores which range from 72 - 92.
Thus,the new set of scores are;
72, 74, 78, 80, 80, 85, 88, 92
New Mean = (72 + 74 + 78 + 80 + 80 + 85 + 88 + 92)/8 = 81.125
New Median will be the average of the 4th and 5th term which is (80 + 80)/2 = 80
New Range = 92 - 72 = 20
New Standard deviation from an online calculator gives 6.39
From the comparison above when the outlier is removed, we can say that;
- Mean increases
- remains the same
- Range decreases
- standard deviation decreases
Will you please help me with this problem
Answer:
A
Step-by-step explanation:
if you want the step by step, let me know (:
Answer:
a
Step-by-step explanation:
derivative of (a^x/Log a)?
[tex]\sf{\dfrac{a^x}{log(a)} }[/tex]
(OR)[tex]\sf{\dfrac{a^x}{ln(a)} }[/tex]
[tex]\large\bold{\underline{\underline{Solution:-}}}[/tex][tex]\sf{Let\ y=\dfrac{a^x}{ln(a)} }[/tex]
[tex]\sf{=\dfrac{d}{dx}\bigg[\dfrac{a^x}{ln(a)} \bigg] }[/tex]
(Linear differentiation)[tex]\sf{=\dfrac{1}{ln(a)}.\dfrac{d}{dx}(a^x) }[/tex]
[tex]\sf{=\dfrac{ln(a)a^x}{ln(a)} }[/tex]
[tex]\boxed{\sf{=a^x}}[/tex]
[tex]\large\bold{\underline{\underline{Applied:-}}}[/tex]✭ Linear differentiation→ [tex]\sf{[a.b(x)+c.d(x)]'=a.b'(x)+c.d'(x)}[/tex]
✭ Exponential function rule
→ [tex]\sf{(a^x)'=ln(a).a^x}[/tex]
Answer:
a^x.
Step-by-step explanation:
y = a^x / log a
Assuming the log is to the base e:
y = (1/ log a) * a^x
Derivative of a^x:
Let u = a^x
log u = log a^x
log u = x log a
1/u * du/dx = log a
du/dx = = u * log a
y = (1 / log a) * u
so dy/du = 1/log a
and dy/dx = dy/du * du/dx
= (1/log a )* log a u
= u
= a^x.
A) Find the distance of line segment PR. Round answer to the nearest tenth. B) Find the distance around the park (perimeter).
Answer:
A. [tex] PR = 80.6 yd [/tex]
B. Perimeter = 190.6 yd
Step-by-step explanation:
A. Distance between P(10, 50) and R(80, 10):
[tex] PR = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
[tex] PR = \sqrt{(80 - 10)^2 + (10 - 50)^2} [/tex]
[tex] PR = \sqrt{(70)^2 + (-40)^2} [/tex]
[tex] PR = \sqrt{4,900 + 1,600} [/tex]
[tex] PR = \sqrt{6,500} [/tex]
[tex] PR = 80.6 yd [/tex] (nearest tenth)
B. Distance around the park = Perimeter = PR + PQ + QR
PR = 80.6 yd
PQ = |50 - 10| = 40 yd
QR = |80 - 10| = 70 yd
Perimeter = 80.6 + 40 + 70
Perimeter = 190.6 yd
Select the two correct factors of the polynomial:
Answer:
(x + 6)
(x - 7)
Step-by-step explanation:
To factor the polynomial in form [tex]x^{2} +bx+c[/tex] find two factors of C that have a sum of B
B = -1
C = -42
Factors of 42:
1, 2, 3, 6, 7, 14, 21, 42
6 and -7 multiply to -42 and add to -1
Write in factored form:
(x + 6)(x - 7)
Answer:
(x - 7)(x + 6)
Step-by-step explanation:
Given
x² - x - 42
Consider the factors of the constant term (- 42) which sum to give the coefficient of the x- term (- 1)
The factors are - 7 and + 6 , since
- 7 × 6 = - 42 and - 7 + 6 = - 1 , thus
x² - x - 42 = (x - 7)(x + 6)
(6,5), 7x-3y=5 find the equation of the line that contains the given point and is parallel to the line. write the equation in slope intercept form
Answer:
y = (7/3)x - 9
Step-by-step explanation:
1. Convert given equation to y=mx+b form --> y = (7/3)x - 5/3
2. Equation of new line --> y = (7/3)x + b
Note: 7/3 is the slope and for lines to be parallel they need the same slope so both equations have 7/3.3. Plug in given values --> 5 = (7/3)(6) + b
4. Solve for b --> b = 5 - 14 b = -9
5. New line --> y = (7/3)x - 9
What is the equation of the line through (2,-4) and (0,4)?
Answer:
y = -1/4x + 4
Step-by-step explanation:
y2-y1/x2-x1
You are giving a rectangle with dimensions of: length = 60 inches and width = 4j. The perimeter of the rectangle is 400 inches. What is the values of j?
Answer:
perimeter is sum of all four sides; two of which are '4j' and other two are 60 inches each
Step-by-step explanation:
P= 2(4j) + 2(60)
We know perimeter is 400 inches
400 = 8j + 120
8j = 280
j = 35
A pair of designer sneakers was purchased for $100. Since they were purchased, their price has increased by 15%. What is the new price?
Answer:
115
Step-by-step explanation:
When flipping a coin, the probability of getting tails is 50% and heads 50%. What is the probability of getting heads
or tails?
50%
60%
75%
100%
Answer:
50%
Step-by-step explanation:
Most people assume the toss of a coin is always a 50/50 probability, with a 50 percent chance it lands on heads, and a 50 percent chance it lands on tails
Answer:
100%
Step-by-step explanation:
There is a 50% chance of getting heads, and 50% chance of getting tails.
If these two options are added together, you get 100%. There are only two options on a coin flip anyways, so the probability of getting heads or tails would be 100%.
PLEASE HELP FAST AS A MIXED RADICAL READ IT CARFULLY BRAINLIST!
Answer:
[tex]2\sqrt[3]{2}[/tex]
Step-by-step explanation:
This is equal to [tex]\sqrt[3]{8} * \sqrt[3]{2} = 2\sqrt[3]{2}[/tex]
The large rectangle below represents one whole.
A large rectangle with 25 equal sections, 11 of which are shaded
What percent is represented by the shaded area?
44%
I hope this helped!!!
Answer:
ummmmmmmmm 44?
Step-by-step explanation:
30 Points. i fr need to pass this test i dont feel like taking it again my senior year
Answer:
3x^3+2x^2+2x+5
Step-by-step explanation:
The answer is A