Answers
9514 1404 393
Answer:
x = 10·cos(θ) -4·cot(θ)
Step-by-step explanation:
Apparently, we are to assume that the horizontal lines are parallel to each other.
The relevant trig relations are ...
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
If the junction point in the middle of AB is labeled X, then we have ...
sin(θ) = 4/BX ⇒ BX = 4/sin(θ)
cos(θ) = x/XA ⇒ XA = x/cos(θ)
Then ...
BX +XA = AB = 10
Substituting for BX and XA using the above relations, we get
4/sin(θ) +x/cos(θ) = 10
Solving for x gives ...
x = (10 -4/sin(θ))·cos(θ)
x = 10·cos(θ) -4·cot(θ) . . . . . simplify
_____
We used the identity ...
cot(θ) = cos(θ)/sin(θ)
Related Questions
What is a solution to the system? y = x^2 + 2x - 15 y – 4x = -12
Answers
9514 1404 393
Answer:
(x, y) = (-1, -16) or (3, 0)
Step-by-step explanation:
Perhaps you want to solve the system of equations ...
y = x^2 +2x -15y -4x = -12Substituting the first expression for y into the second equation gives ...
x^2 +2x -15 -4x = -12
x^2 -2x -3 = 0 . . . . . . . . add 12
(x -3)(x +1) = 0 . . . . . . . factor
Solutions are the values of x that make the factors zero: x = 3, x = -1.
The corresponding values of y are ...
y = -12 +4x
y = -12 +4{-1, 3} = -12 +{-4, 12} = {-16, 0}
The solutions to the system are ...
(x, y) = (-1, -16) or (3, 0)
If the switches at 2, 3, 4, and 5 are independently closed or open with probabilities 0.1 (for closed) and 0.9 (for open), what is the probability of a closed path between the input line on the left and the output line on the right
Answers
Complete Question
The Complete Question is attached below
Answer:
[tex]P(X)=0.0163[/tex]
Step-by-step explanation:
From the question we are told that
Probability of open [tex]P(x)O=0.9[/tex]
Probability of open [tex]P(x)C=0.1[/tex]
Generally the equation for Probability of a closed path between the input line on the left and the output line on the right is mathematically given by
[tex]P(X)=(P(3\&5)C*P(2\&4)C)+(P(2\&4)O+P(2\&4)C*P(1\&3)O)+(P(1\&3)C-P(3\&5)C*P(2\&4)C)[/tex]
[tex]P(X)= 0.1*0.1*(0.1*0.1+0.9*0.9 ) + 0.1*0.1*(0.9*0.9 + 0.1*0.1) - 0.1*0.1*0.1*0.1[/tex]
[tex]P(X)=0.0163[/tex]
the ratio of two complementary angles is 8:17. find the measure of the smallest angle.
Answers
Answer:
28.8
Step-by-step explanation:
Multiply each by x
8x : 17x
Complementary angles add to 90
8x+17x = 90
25x = 90
Divide each side by 25
25x/25 = 90/25
x=3.6
The smallest angle is 8x
8*3.6 =28.8
x
and
y
. We know that
x
+
y
=
90
. For this equation, let's assume
y
is the bigger angle.
y
would equal 8:7x, or to make it simpler,
8
7
x
. We can plug in
8
7
x
for
y
in the original equation to get
x
+
8
7
x
=
90
. Combining like terms, and then saying that
x
=
7
7
, we get
15
7
x
=
90
. We then divide
15
7
on both sides, and get
x
=
42
. In the equation,
y
=
8
7
x
, we add in 42 which makes
y
=
48
. That's how we find out our answer.
Need help on this one (listing BRAINLIST and giving points) =)
Answers
I hope this is help full to you
how to convert 15 cm to mm
Answers
15cm x 10 = 150mm
PLEASE HELP ASAPPP!!!!!
Three coins are flipped. What is the probability that there will be two tails and one head?
Answers
If f(x)= 10 sin(x) – 3 then f (30%) = ?
A) - square root 3/2 -3
B.) 2
C.) -5/2
D.) 4/3 - square root 3/2
Answers
Answer:
The value of f(30) is equal to 2.
Step-by-step explanation:
The given expression is :
[tex]f(x)= 10 \sin(x) - 3[/tex]
We need to find the value of f(30)
Put x = 30 in above expression.
So,
[tex]f(x)= 10 \sin(30) - 3\\\\=10\times \dfrac{1}{2}-3\\\\=5-3\\\\=2[/tex]
Hence, the value of f(30) is equal to 2.
The height of a triangle is 7 feet greater than the base. the area of the triangle is 247 ft.² find the length of the base and the height of the triangle
Answers
Answer:
Base = 19
Height = 26
Step-by-step explanation:
Given :
Height, h = base, b + 7 feets
The area of triangle, A = 247 ft²
The area of a triangle is given by :
A = 1/2 * base * height
247 = 1/2 * b * (b + 7)
247 = 0.5 * b * (b + 7)
247 = 0.5b² + 3.5b
0.5b² + 3.5b - 247 = 0
Solving the quadratic equation ; using the quadratic equation solver, the roots are :
b = -26 or b = 19
Length of base can't be negative :
Hence,
Base, b = 19
Height, h = base + 7 = 19 + 7 = 26
I need help on C......
Answers
Step-by-step explanation:
[tex]B=100e^{0.592t}[/tex]
c) To solve for t, take the natural logarithm of the above equation:
[tex]\dfrac{B}{100}=e^{0.592t}[/tex]
[tex]\Rightarrow \ln \left(\dfrac{B}{100} \right) = \ln e^{(0.592t)}=(0.592t)\ln e[/tex]
Recall that [tex]\ln e = 1[/tex] so we can rewrite the equation above as
[tex]0.592t = \ln \left(\dfrac{B}{100} \right)[/tex]
Finally, solving for t, we get
[tex]t = \frac{1}{0.592} \ln \left(\dfrac{B}{100} \right)[/tex]
which measure of central tendency best describes the situation, the ages of 7 people who auditioned for a role in a play: 17,20,22,12,15,12,21
Answers
Answer:
Both the mean and median and they both gives a measure of 17
Step-by-step explanation:
Given the data about the ages of 7 people :
17,20,22,12,15,12,21
Ordered data: 12, 12, 15, 17, 20, 21, 22
To find the median :
Median = 1/2 * (n+1)th term
n = number of observations = 7
Median = 1/2(7+1)th term
Median = 1/2 *8 = 4th term = 17
Mean = Σx / n = (sum of ages) / number of observations
Mean = 119 / 7 = 17
:
Help!!!! 20 points!!!!!!’
Answers
Answer:
option c is the correct answer
first take y raised to the power 4 common then cancel its power by y raised to the power 3
you get your answer
What inequality does the number line graph represent
Answers
Answer:
5x + 3 ≥ 18
Step-by-step explanation:
when solved, the inequality is x ≥ 3
x ≥ 3 indicates all values greater than 3, including 3, should be in the solution set
PLS HELP ASAP. NO LINKS
When z= 9, the value of z2 + 1 is
Answers
substitute z for 9
9^2 = 81+ 1= 82
1,Convert 24 hours to sec
Answers
Answer:
86400 sec
Step-by-step explanation:
24 hour⇒ sec
1 hr = 3600 sec
So,
24×3600
= 86400 sec
Which statement is true about the equations -3x 4y = 12 and #*-}y=I?
O The system of the equations has exactly one solution at (-8, 3).
O The system of the equations has exactly one solution at (-4, 3).
O The system of the equations has no solution; the two lines are parallel.
The system of the equations has an infinite number of solutions represented by either equation.
Answers
Frank earns 56,600$ one year and receives a 9 % raise in salary. What is his new salary?
Answers
Answer:
His new salary would be $61,694
Step-by-step explanation:
Cuánto es 1/4 mas 1/4
Answers
Answer:
0.5
Step-by-step explanation:
PLEAZSEE HELP MEEEJEHSHD
Answers
Answer:
First gap:
√1000/16
= 8 seconds
Second gap:
Rearrange formula:
√d = 4t
40=√d
d = 6 meters.
Find the perimeter of the figure.
Answers
Answer:
45 inches (choice B)
Step-by-step explanation:
The perimeter is the sum of all of the sides of a shape. Since the sides are given this problem is fairly easier than other problems. You simply have to add the numbers together.
8 + 3 + 3 + 6 + 6 + 19 = 45 inches
Answer:
45 in.
Step-by-step explanation:
Perimeter = 8 + 3 + 6 + 19 + 6 + 3
= 45.
HELP ME PLZ WILL MARK U AS BRAINLIEST
Answers
Answer:
yes
Step-by-step explanation:
the difference of mean is 10.5
the mean for Mrs.S was 26.7 while for Mr.C it was 37.2.
using this info we can infer that Mr.C uses 10-11 more textbooks monthly
A fuel pump at a gasoline station doesn't always dispense the exact amount displayed on the meter. When the
meter reads 1.000 L, the amount of fuel a certain pump dispenses is normally distributed with a mean of 1 L
and standard deviation of 0.05 L. Let X = the amount dispensed in a random trial when the meter reads
1.000 L
Find P(X < 1).
Answers
Answer:
P(X < 1) = 0.5
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 1 L and standard deviation of 0.05 L.
This means that [tex]\mu = 1, \sigma = 0.05[/tex]
Find P(X < 1).
This is the p-value of Z when X = 1. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1 - 1}{0.05}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a p-value of 0.5. Thus
P(X < 1) = 0.5
1. p-4= -9+p
2. 4m-4= 4m
Extra Credit, need help
Answers
Answer:
1. No solution
2. No solution
Step-by-step explanation:
1. p-4=-9+p
-4=-9
No solution
2. 4m-4=4m
-4=0
No solution
If this helps please mark as brainliest
What is the difference between function and operator in math?
Answers
Step-by-step explanation:
In mathematics, a function is a mapping from set A to a set B that has a unique output for any given input. “Operators” or “operations” are typically defined as a special type of function.
y=10x/3+19 find the y-intercept
Answers
Answer:
(0, 19)
Step-by-step explanation:
In slope-intercept form, the constant at the end of the equation is the value of the y-intercept.
You can also solve for the y-intercept by letting x = 0. This is because, at the point where the line crosses the y-axis, x will be 0.
y = 10(0)/3 + 19
y = 0 + 19
y = 19
Therefore, the y-intercept is (0, 19).
The y-intercept is (0, 19).
What is the y-intercept?The y-intercept is the point where the graph intersects the y-axis.
Given is an equation of a line, y = 10x/3+19
To solve for the y-intercept,
Put x = 0. This is because, at the point where the line crosses the y-axis, x will be 0.
y = 10(0)/3 + 19
y = 0 + 19
y = 19
Therefore, the y-intercept is (0, 19).
For more references on y-intercept, click;
https://brainly.com/question/14180189
#SPJ2
Customer: "A previous representative told me that I would receive a 17% discount on my $123.76 service plan. How much is the discount?" Representative: "You will receive a discount of __________
Answers
Savings: $22.30
You will receive a discount of $22.30
Answer:
$21.04
Step-by-step explanation:
123.76 x 17% = 21.0392 = 21.04
SAT Scores The national average SAT score (for verbal and math) is 1028. Assume a normal distribution with o=92.
0
Round intermediate : -value calculations to two decimal places.
What is the 95th percentile score? Round the answer to the nearest whole number,
The 95th percentile score is ?
Answers
Answer:
Similar to your other question. Now, you're looking for the score such that this time, 0.99 corresponds to a z-score of approximately, which means
Identify a pair of parallel lines in the given figure.
a)p and s
b)r and s
c)r and q
d)r and p
Answers
What is the unit rate for the following point?
(7, 1 3/4)
Answers
Answer:
Step-by-step explanation:
7
What is the value of m
Answers
Answer:
B=34, A=56
Step-by-step explanation:
56 + 90 + B = 180
=) B=34
A is head to head with 56°.
Which of the following will most likely produce sample proportions that are
normally distributed?
A. Many samples of 34 coin flips
B. Many samples of 14 coin flips
C. Many samples of 19 coin flips
D. Many samples of 9 coin flips