Answer: 372ft
Step-by-step explanation:
310 divided by 10 equals 31.
31 times 12 = 372
And so it is 372 ft
Solve the equation cos 2 θ = -5 cos θ - 3 on the interval 0 ≤ θ < 2π
Answers must be exact.
Answer:
[tex]\theta =\dfrac{2}{3} \pi ,\;\; \theta =\dfrac{4}{3} \pi[/tex]
Step-by-step explanation:
Given:
[tex]\cos 2\theta=-5 \cos \theta-3, \quad \quad 0 \leq \theta < 2 \pi[/tex]
[tex]\boxed{\begin{minipage}{6.5 cm}\underline{Cos Double Angle Identity}\\\\$\cos (A \pm B)=\cos A \cos B \mp \sin A \sin B$\\\end{minipage}}[/tex]
Use the cos double angle identity to create a quadratic:
[tex]\begin{aligned}\cos 2\theta &=-5 \cos \theta-3\\\cos^2\theta - \sin^2 \theta &=-5 \cos \theta-3\\\cos^2\theta - (1-\cos^2 \theta) &=-5 \cos \theta-3\\2\cos^2\theta - 1 &=-5 \cos \theta-3\\2\cos^2\theta+5 \cos \theta +2 &=0\end{aligned}[/tex]
Factor the quadratic:
[tex]\begin{aligned}2\cos^2\theta+5 \cos \theta +2 &=0\\2\cos^2\theta+4 \cos \theta +\cos \theta +2 &=0\\2\cos \theta(\cos \theta +2)+1(\cos \theta +2) &=0\\(2\cos \theta+1)(\cos \theta +2)&=0\end{aligned}[/tex]
Apply the zero-product property:
[tex]2 \cos \theta + 1 = 0 \implies \cos \theta =-\dfrac{1}{2}[/tex]
[tex]\cos \theta + 2= 0 \implies \cos \theta =-2[/tex]
As -1 ≤ cos θ ≤ 1, cos θ = -2 is undefined.
Therefore, the only valid solution is cos θ = -¹/₂
Therefore:
[tex]\implies \cos \theta =-\dfrac{1}{2}[/tex]
[tex]\implies \theta =\cos^{-1}\left(-\dfrac{1}{2}\right)[/tex]
[tex]\implies \theta =\dfrac{2}{3} \pi +2\pi n,\;\; \dfrac{4}{3} \pi+2\pi n[/tex]
Solutions in the given interval 0 ≤ θ < 2π :
[tex]\theta =\dfrac{2}{3} \pi ,\;\; \theta =\dfrac{4}{3} \pi[/tex]
PLEASE HELP!!!!!!!!! This assignment is already late and last day to turn in is TOMORROW!!!!!!!!!
The value of n and m are 110 and 20 respectively if the equations are 2n + 3m = 280 and 2n + 5m = 320.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Two linear equations are:
2n + 3m = 280
2n + 5m = 320
Using the elimination method:
Because the coefficient for n is the same in both equations
-2m = - 40
m = 20
n = 110
Thus, the value of n and m are 110 and 20 respectively if the equations are 2n + 3m = 280 and 2n + 5m = 320.
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What is the value of x?
Enter your answer in the box.
x =
The side length RQ of the triangle QRT that is 'x' will be 4 units.
What is trigonometry?Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
In triangle ΔRST, the side RT is given by the sine of angle 60°. Then we have
sin 60° = (2√3) / RT
(√3)/(2) = (2√3) / RT
RT = 2 x 2(√3) / (√3)
RT = 4
In triangle ΔQRT, the side QR is given by the tangent of angle 45°. Then we have
tan 45° = RQ / RT
1 = x / 4
x = 4
The side length RQ of the triangle QRT that is 'x' will be 4 units.
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Kiran invested $1,500 in an account paying an interest rate of 81% compounded
continuously. Isaac invested $1,500 in an account paying an interest rate of 7%
compounded daily. After 6 years, how much more money would Kiran have in his
account than Isaac, to the nearest dollar?
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
Kiran has $191254 more amount than Isaac.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
We have,
Kiran:
P = $1500
r = 81%
n = continuously
t = 6 years
A = P [tex]e^{rt}[/tex]
[ e = 2.71828 }
A = 1,500.00 x [tex]2.71828^{0.81\times6}[/tex]
A = $193,536.30
Isaac:
P = $1,500
r = 7%
n = 360
t = 6 years
A = 1500 [tex](1 + 0.07/360)^{360\times6}[/tex]
A = $2,282.85
Now,
The difference between Kiran's and Isaac's amount.
= $193,536.30 - $2,282.85
= $191253.45
= $191254
Thus,
Kiran has $191254 more amount than Isaac.
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Suppose that x and y vary inversely, and x = 30 when y = 2. Find y when x=5.
Answer:
Step-by-step explanation:
1. x is inversely proportional to y
x=k/y
k is the constant of proportionality
x =60/y
2. x=60/y
x=60/12
x=5
Solve the application using polynomials
What is the average number of receipts per quarter at Kingpin Parts?
Answer: The answer is about 57.5
The following are prices for various cars: $22,000, $28,000, $90,000, 22,000, $26,000. What is the median price?
The required median of the prices of the various cars is $26,000.
What is the median?When a dataset is ordered, the median is the value that is exactly in the middle. It is a measure of central tendency that distinguishes between the lowest and top half of data.
here,
Arrange the data set in order,
$22,000, $22,000, $26,000, $28,000, $90,000,
Total number = 5 [ odd numbers ]
Median is given as = n + 1 / 2 th term
= 5 + 1 / 2 th term
= 3 rd term
Thus, as of the given condition, the median of the prices is $26,000.
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeee
Answer:
51.85g
Step-by-step explanation:
At t = 25 years,
A(t) = 200e^-0.054t
A(25) = 200(e^-0.054(25))
= 200(e^-1.35)
= 200(0.2592)
= 51.85
write an equation for a line parallel to y = − 2 x − 3 and passing through the point (3,-3)
Equation of line parallel to y = − 2 x − 3 and passing through the point (3,-3) is y = -2x + 3.
When two lines are called parallel?
Two lines are parallel lines if they do not intersect.
The slopes of the lines are the same.
f(x)= mx + b and g(x)= nx + c are parallel if m = n.
According to the given question:
Given equation of line is y = −2x − 3
If the new line is parallel, then it will have the same slope.
y = -2x + b
Now this line passes through the point (x,y) = (3,-3) so put in the x and y values into the equation above, solve for b
-3 = -2(3) + b
b = 3
Therefore the required equation of line is
y = -2x + 3
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How long will it take 2000 dollars to double if it is invested at 8% interest compounded semi-annually?
The time it will take the 2000 dollar invested at 8% is t= 9.006468342 years
Compound Interest
Compound interest can be define as the addition of interest on the loan to the principal sum of the deposit.
2 = (1+8%) ^t
where t is the time of the year
2= (1 +8%)^t
2 = (1+8/100)^t
2 = ( 1 0.8)^t
Take the log of both sides
log 2 = log 1.08^t
log 2 = t log 1.08
Divide both sides by log 1.08
log 2/ log 1.08 = t
t= 9.006468342 years
Therefore, the time it will take the dollar invested at 8% is t= 9.006468342 years
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Which inequality is represented by the number line?
A.
|2x + 1| ≥ 7
B.
2|x + 1| ≤ 8
C.
|2x − 1| ≥ 9
D.
2|x − 1| ≤ 10
The inequality represented by the graph is |2x − 1| ≥ 9
How to determine the inequality represented by the graph?The number line represents the given parameter
On the number line, we have the following endpoints
x = -4 and x = 5
So, we test the above solutions in the list of options (representing them as an equation)
So, we have
|2x + 1| = 7
When x = -4
|2(-4) + 1| = 7 ⇒ 7 = 7 --- true
When x = 5
|2(5) + 1| = 7 ⇒ 11 = 7 --- false
2|x + 1| ≤ 8
When x = -4
2|(-4) + 1| = 8 ⇒ 6 = 8 --- false
|2x − 1| ≥ 9
When x = -4
|2(-4) - 1| = 9 ⇒ 9 = 9 --- true
When x = 5
|2(5) - 1| = 9 ⇒ 9 = 9 --- true
Hence, the inequality is (c) |2x − 1| ≥ 9
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what multiples to 48 and adds to -12
Effectively what you're asking is to solve this equation
x^2 - 12x + 48 = 0
Compare that to this form
ax^2 + bx + c = 0
to find that
a = 1b = -12c = 48Let's compute the discriminant (aka the stuff under the square root in the quadratic formula).
d = b^2 - 4ac
d = (-12)^2 - 4(1)(48)
d = 144 - 192
d = -48
The discriminant is negative, which tells us that there aren't any real numbered solutions to x^2 - 12x + 48 = 0
Therefore, we have no way to factor x^2 - 12x + 48 over the real numbers. Going back at the problem at hand: there aren't any real numbers that (a) multiply to 48 and (b) add to -12.
The two mystery numbers would be complex numbers in the form a+bi, where i = sqrt(-1). If your teacher hasn't covered these types of numbers yet, then you simply would say "no solution".
Robi has 45 toy cars and 63 motorbike toys. The comparison between the difference and the number of toys that Robi has is
Answer:
the answer is 18!
Step-by-step explanation:
63-45 = 18
just subtract the two values to get your answer. the difference is 18.
Hope this helps!
3. Find the x-intercept of y = 3.
(3,0)
(0,3)
(3,3)
O no x-intercept
Answer:
3
Step-by-step explanation:
x-y =3
To find the x intercept, set y=0
x-0 =3
x=3
Step-by-step explanation:
Answer:
x=(3,0)
Step-by-step explanation:
hope this helps
If southbrook middle schoolbhas 850 students then how mamy students participate in the various number of sports
Answer:
Step-by-step explanation:
67876567
Use close-but-easier numbers to estimate the answer to this problem
78+43
Answer: 121
Step-by-step explanation:
78+43=121
NO LINKS!! Please help me with this problem.
Answers:
Min cost = $464.76
Dimensions = 11.619 feet by 5.164 feet
Each value mentioned above is approximate.
========================================================
Explanation:
x = horizontal dimension
y = vertical dimension
xy = 60
y = 60/x
The amount of outer fencing needed is 2x+2y feet, aka the perimeter of the largest rectangle.
There are 5 vertical inner fences, so we need 5y feet of inner fencing.
Let's set up the cost function.
Cost = 10*(amount of outer fencing) + 5*(amount of inner fencing)
C = 10*(2x+2y) + 5*(5y)
C = 20x+20y+25y
C = 20x+45y
Plug y = 60/x into the cost function.
C = 20x+45y
C = 20x+45(60/x)
C = 20x + (2700/x)
Then use either calculus or a graphing calculator to find the lowest point on the cost curve is roughly located at (11.619, 464.758)
Use the x value x = 11.619 to find its paired y value
y = 60/x
y = 60/11.619
y = 5.16395558998192
y = 5.164
The entire enclosure should be roughly 11.619 feet by 5.164 feet
The total cost is minimized at approximately $464.76
Answer:
11.619 by 5.164 feet$464.76 minimum costStep-by-step explanation:
You want the dimensions and cost of a rectangular enclosure with an area of 60 square feet and 5 internal partitions. The cost of outside fence is $10 per foot, and the cost of partition fence is $5 per foot.
SetupLet x represent the length of the enclosure, and y the width (and the partition length). Then we have ...
xy = 60
10(2x) = cost fencing for length
10(2y) +5(5y) = cost of fencing for width
We know the cost will be minimized when the cost of fence for the length is equal to the cost of fence for the width.
20x = 45(60/x)
Solutionx² = 135 . . . . . . . . . . . multiply by x/20
x = 3√15 ≈ 11.619 . . . .square root
y = 60/(3√15) = (4/3)√15 ≈ 5.164 . . . . . find y
Then the cost is ...
2(10(2x)) = 120√15 ≈ 464.76 . . . . minimum cost
The enclosure is 11.619 by 5.164 feet, for a cost of $464.76.
Carla's uncle owns a pizzeria. Her uncle has 4 pounds of mozzarella cheese. He uses pound of the mozzarella to make a large pizza.
How many large pizzas could Carla's uncle make before running out of mozzarella cheese?
O 3 pizzas
4 pizzas
O 5 pizzas
O 6 pizzas
What does negative 3 over 8 > −1 indicate about the positions of negative 3 over 8 and −1 on the number line? (4 points) a is located on the right of 0, and −1 is located on the left of 0 b is located on the left of 0, and −1 is located on the right of 0 c is located on the left of −1 d is located to the right of −1
The expression - 3/8 > - 1 indicates that the value - 3/8 lies between - 1 and 0 on the number line.
It is located to the left of zero on the number line.
What is a number line?A number line is a one-dimensional horizontal line where we can represent any real number. The origin of the number line is represented by zero left to it are all negative real numbers and right to it are all positive real numbers.
Given, An expression - 3/8 > - 1.
This indicates that the value - 3/8 lies between - 1 and 0 on the number line.
It is located to the left of zero on the number line.
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Maddy is making banana bread. She has 11 bananas. If she uses 3 bananas for each loaf of bread, how many loaves of banana bread can she make?
Answer: She can make 3 full loaves
Step-by-step explanation: 3 x 3 = 9 3 x 4 = 12 you dont have 12 you only have 11
technically you can make 3 [tex]\frac{1}{3}[/tex] loaves but if you are looking for full loaves you can only make 3
25. There are 5 teams in a netball competition. Each team must play each other twice. How many games will team play? A. 10 B. 5 C. 8 D. 4
⛑help again please anyone I got a lot of ⚣ homework to do so I'll ask answers for all of them throughout the night >_<
Answer:
C-8
Step-by-step explanation:
5 games they each play each other they continue if each team wins then they continue to play to 8 games
Answer:
The answer to your problem would be 10
Step-by-step explanation:
There are 5 teams. So, if each team has to play each other twice, 5x2=10.
Each team plays twice....I think I did that right. I'm really sorry if it's not right.
an ice cream factory makes 180 quarts of ice cream in 2 hours.how many quarts willl be made in 12 hours? please send help
PLEASE HURRRY PLSSSSS I NEED ANSWERSSSS
The investments arranged from the least to the greatest amount of interest are:
Investment of $1600 at 5% interest rate for 8 years.
Investment of $1600 at 7% interest rate for 8 years.
Investment of $1600 at 7% interest rate for 12 years.
What is simple interest?Simple interest is the formula that is used to determine the interest that is earned when an amount is investment at an interest rate over a number of years.
Interest earned with simple interest increases linearly over the investment period. This means that the interest earned each year of the investment period is a constant amount.
Simple interest = amount invested x interest rate x year
Simple interest = $1600 x 0.07 x 8 = $896
Simple interest = $1600 x 0.05 x 8 = $640
Simple interest = $1600 x 0.07 x 12 = $1344
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A line intersects the points (4, 12) and (-1, -3). What is the slope of the line in simplest form? m = [?]
Answer: m = 3
Step-by-step explanation:
-3 - 12 = -15
-1 - 4 = -5
[tex]\frac{-15}{-5}[/tex] = 3
HELPPPPP!!!!!!!! 30 POINTSSSS!!!!!
What is the correlation of the data shown?
A. -1
B. -0.5
C. 1
D. 0
The correlation of the data shown on the graph is 1
How to determine the correlation?In this question, the graph represents the given parameter
From the graph, we have the following observations
The x values is on the horizontal axisThe y values is on the vertical axisAs the x values increase, the y values increase (approximately)When the change (increase) in the x values causes a change (increment) in the y values, then the correlation is positive
From the list of options, we have
-1, -0.5 and 0 are not positive values
This means that the correlation is (c) 1
Hence, the correlation of the data is 1
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120 students are signing up for classes. 80 of them are signing up for a Math class (M) and 50 of them are signing up for a Biology
class (B). If 35 of them are signing up for both Math and Biology, how many are signing up for neither Math nor Biology. Hint:
It may help to draw the Venn diagram.
The number of students signing up for neither Math nor Biology is 25.
What are sets and subsets?A set is a collection of well-defined objects.
A subset contains all the elements or a few elements of the given set.
The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.
Given, 120 students are signing up for classes. 80 of them are signing up for a Math class (M) and 50 of them are signing up for a Biology.
We know N(A∪B) = N(A) + N(B) - N(A∩B).
∴ N(M∪B) = 80 + 50 - 35.
N(M∪B) = 95.
So, the number of students signing up for neither Math nor Biology are
(120 - 95) = 25
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4.
20% of what number is 38?
Answer:
190
Step-by-step explanation:
If 38 is 20% then half of 38, 19, is 10%. With that you can divide 19 by 10 and get 1.9. If you take 1.9 and multiply it by 100 you get 190
23a = 391 A. a = 16 B. a = 17 C. a = 8,939 D. a = 8,993
Answer:
Step-by-step explanation:
it is 17 i did the quiz hope it helps
The function g is defined by g(x) = 5+2x/2+x
Find g (4x)
[tex]g(x)=\frac{5+2x}{2+x} \\ \\ \implies g(4x)=\frac{5+2(4x)}{2+4x}=\boxed{\frac{5+8x}{2+4x}}[/tex]