Answer:
[tex]\displaystyle \cos\left(-\frac{7\,\pi}{12}\right) = \frac{\sqrt{2} - \sqrt{6}}{4}[/tex].
Step-by-step explanation:
Convert the angle [tex]\displaystyle \left(-\frac{7\, \pi}{12}\right)[/tex] to degrees:
[tex]\displaystyle \left(-\frac{7\, \pi}{12}\right) = \left(-\frac{7\, \pi}{12}\right) \times \frac{180^\circ}{\pi} = -105^\circ[/tex].
Note, that [tex]\left(-105^\circ\right)[/tex] is the sum of two common angles: [tex]\left(-45^\circ\right)[/tex] and [tex]\left(-60^\circ\right)[/tex].
[tex]\displaystyle \cos\left(-45^\circ\right) = \cos\left(45^\circ\right) = \frac{\sqrt{2}}{2}[/tex].[tex]\displaystyle \cos\left(-60^\circ\right) = \cos\left(60^\circ\right) = \frac{1}{2}[/tex].[tex]\displaystyle \sin\left(-45^\circ\right) = -\sin\left(45^\circ\right) = -\frac{\sqrt{2}}{2}[/tex].[tex]\displaystyle \sin\left(-60^\circ\right) = -\sin\left(60^\circ\right) = -\frac{\sqrt{3}}{2}[/tex].By the sum-angle identity of cosine:
[tex]\cos(A + B) = \cos(A)\cdot \cos(B) - \sin(A) \cdot \sin(B)[/tex].
Apply the sum formula for cosine to find the exact value of [tex]\cos\left(-105^\circ \right)[/tex].
[tex]\begin{aligned}\cos\left(-105^\circ \right) &= \cos\left(\left(-45^\circ\right) + \left(-60^\circ\right)\right) \\ &= \cos\left(-45^\circ\right) \cdot \cos\left(-60^\circ\right)\right) - \sin\left(-45^\circ\right) \cdot \sin\left(-60^\circ\right)\right) \\ &= \frac{\sqrt{2}}{2} \times \frac{1}{2} - \left(-\frac{\sqrt{2}}{2}\right)\times \left(-\frac{\sqrt{3}}{2}\right) = \frac{\sqrt{2} - \sqrt{6}}{4}\end{aligned}[/tex].
[tex]\displaystyle \left(-\frac{7\, \pi}{12}\right) = \left(-\frac{7\, \pi}{12}\right) \times \frac{180^\circ}{\pi} = -105^\circ[/tex]. In other words, [tex]\displaystyle \left(-\frac{7\, \pi}{12}\right)[/tex] and [tex]\left(-105^\circ\right)[/tex] correspond to the same angle. Therefore, the cosine of [tex]\displaystyle \left(-\frac{7\, \pi}{12}\right)\![/tex] would be equal to the cosine of [tex]\left(-105^\circ\right)\![/tex].
[tex]\displaystyle \cos\left(-\frac{7\,\pi}{12}\right) = \cos\left(-105^\circ\right) = \frac{\sqrt{2} - \sqrt{6}}{4}[/tex].
The cost of a new laptop is $750 which generates a sales tax amount of 37.50. What is the sales tax rate.
Answer:
5 percent.
Step-by-step explanation:
Divide tax by the cost to see the percentage of the tax.
750/37.50=0.05
5 percent.
The ratio of caretakers to childeren is _:_. If 24 more children are added, they should hire _ more caretakers to maintain the ratio of caretakers to children.
Answer:
The first is 1:6 and the second one is 4
Step-by-step explanation:
can u pls help me with this question
Answer:
b
Step-by-step explanation:
Question
9. Deb ordered a set of red and yellow pins. She received 220 pins, and 40% of them were red. How many yellow pins did Deb
receive?
I’ve never been good with math, can u help?
Please help me will give brainliest for the person that answers it correctly.
Answer:
This graph has a slop of 0
Step-by-step explanation
see the included picture of the graph
Find the next three terms of the sequence: 33, 25, 18, 12, …….
a) 7, 2, -1
b) 8, 3, 0
c) 7, 3, 0
d) 6, 2, -1
pls help and show work
The required terms are 7, 3 and 0. The correct option is (c).
What is an arithmetic sequence?
An arithmetic sequence is a kind of sequence of numbers where the difference of any two consecutive terms are the same.
This difference is known as the common difference of the sequence.
The given sequence is as below,
33, 25, 18, 12, …….
The difference between the consecutive terms is given as,
D₁ = 25 - 33
= -8
D₂ = 18 - 25
= -7
D₃ = 12 - 18
= -6
It is clear that the difference between the consecutive terms are in arithmetic progression.
Thus, the next differences can be found as,
D₄ = -6 + 1
= -5
D₅ = -5 + 1
= -4
And, D₆ = -4 + 1
= -3
The next three terms of the sequence can be written as,
12 - 5 =7, 7 - 4 = 3, 3 - 3 = 0.
Hence, the next three terms of the given sequence are 7, 3 and 0.
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Please help I will love you forever!!! This test is timed thank you in advanced <3
Answer: For my opinion, I think it's either A or B.
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
$500 + $100x > 1200
x represents the months
What is the degree of the polynomial, 2y23+3x25-16x26?
25
23
26
16
Please help me! I’ve been trying to find this for an hour );
Answer:
I got (4x+3)(3x+1)
Hope I help Please mark me BrainIIest please and thank you :)
Step-by-step explanation:
The APR on my credit card is 16.8%. What is the monthly interest rate?
I WILL GIVE BRAINLIEST
Tell whether the following equations represent a linear function.
10x + 2y = 4
−x² + 3y = 19
6x + 1/2y = 3
Answer:
Tell whether the following equations represent a linear function.
10x + 2y = 4--linear equation✓
−x² + 3y = 19--quadratic equation
6x + 1/2y = 3--linear equation✓
David cycled 4 laps on a bicycle path surrounding a lake. Each lap was the same length. If he cycled a total of 13.2 mi, what was the length of each lap around the lake? Write your answer in feet.
it's probably 17424 feet
Shirley starts with $85 in the bank and saves $15 every 2 months. Joshua starts with
$212.50 and spends $20 every 3 months.
Answer:
Shirley would have $115 and Joshua ends up with 152.5
Step-by-step explanation:
85+15+15=115
212.50-20-20-20-152.5
Find the x-and y-intercepts.
2x – 3y = -6
Answer:
y intercept is 2 x =-3
Step-by-step explanation:
2x-3y=-6
subtract 2
-3y=-2×-6
divide by -3
y=2/3+2
×
0=2/3x+2
-2=2/3×
-3=x
Lola plans to visit her friend in another state. The distance to her friend is
1297 miles. If she leaves on Friday and drives 7 hours at a time at 60 mph,
when will she get there?
Answer: In three days
Step-by-step explanation:
Help me out here pleaseeeeeeeeeeeeeeeeeee
Answer:
im 90% sure its A
Step-by-step explanation:
Is this a function please help I’m failing
Answer:
No
Step-by-step explanation:
This relation is not a function. This line has repeating x-values, it only has one so each y-value cannot have a unique x-value. For this reason, no vertical line will ever be a function.
What is the slope of the line shown below?
Answer:
m=-2
Step-by-step explanation:
Whats the correct answer need help right now
I’ll be giving extra points(brainliest)
Answer:
The correct answer would be D. It would not be a linear function because the rate of change is not constant.
Step-by-step explanation:
The rate of change is not constant since it is not adding by a same number each time.
y=1/x-2+1 the domain and range of this function
Answer:
Domain=(-infinity,0)
Range: (-infinity,-1)
Step-by-step explanation:
Find the domain by finding where the equation is defined. The range is the set of values that correspond with the domain.
f(x)=7x+6÷x²-x
help pls :)
answer:
y=(x+7/2)^2-73/4
In the diagram, LaTeX: \Delta ABC\cong\Delta DFE
Δ
A
B
C
≅
Δ
D
F
E
. Find the values of x and y.
Answer:
x = 13
y = 8
Step-by-step explanation:
Solve the equation in the interval [0,360). Use an algebraic method.
Answer:
70.9,109.1,204.0,336.0
Step-by-step explanation:
The solution set for the equation 6sin² θ - 7 sinθ - 5 = 0 in the interval [0,360)is {θ∈ [0,360)∣θ = 230.48 ,309.521}
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The given equation is 6sin² θ - 7 sinθ = 5
Lets arrange in an order
6sin² θ - 7 sinθ - 5 = 0
a=6, b=-7 and c = -5
sinθ = 7±√49+120/12
Simplifying under the square root:
sinθ =7±17/12
Taking the positive solution first
sinθ =24/12
sinθ =2 (Not valid)
Now let's try the negative solution:
sinθ =7-17/12
sinθ =-10/12
sinθ =-5/6
θ= sin⁻¹(-5/6)
θ= −50.48⁰ ,−129.52⁰
we need to restrict our solution to the given interval [0,360), so we add 360 degrees to the negative angle:
θ=360−50.48 = 309.52 and 360 −129.52 =230.48
Therefore, the solution set for the equation 6sin² θ - 7 sinθ - 5 = 0 in the interval [0,360)is {θ∈ [0,360)∣θ = 230.48 ,309.521}
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Convert 0.1 lb/day to oz/week
1 pound = 16 ounces
1 week = 7 days
0.1 x 7 = 0.7 pounds per week
0.7 x 16 = 11.2 ounces
0.1 lb/ day converts to 11.2 ounces / week
14) Find the product of seven times five and two
thousandths.
Answer:
35.015
Step-by-step explanation:
see attached image
Tell whether (1,-1) is a solution of y
9x - 10
Answer:
yes, it is
Step-by-step explanation:
plug in the point (1, -1) (x,y) into the equation y = 9x - 10
-1 = 9(1)-10
-1 = 9-10
-1=-1
What type of dance does a geometry teacher like
Answer:
line dancing, square dancing, etc
Step-by-step explanation:
Answer: square dancing, circle dancing, line dancing.
Hope this helps... Stay safe and have a great day/night!!! :D
The concentration C of certain drug in a patient's bloodstream t hours after injection is given by
C(t)= t/3t^2+5
Required:
a. Find the horizontal asymptote of C(t). (Answer must be in slope-intercept form.)
b. Determins what happens to the concentration of the drug as t increases. As t increases, what value will c(t) approach.
c. Determine the time at which the concentration is highest.
Answer:
a) The horizontal asymptote of [tex]C(t)[/tex] is [tex]c = 0[/tex].
b) When t increases, both the numerator and denominator increases, but given that the grade of the polynomial of the denominator is greater than the grade of the polynomial of the numerator, then the concentration of the drug converges to zero when time diverges to the infinity. There is a monotonous decrease behavior.
c) The time at which the concentration is highest is approximately 1.291 hours after injection.
Step-by-step explanation:
a) The horizontal asymptote of [tex]C(t)[/tex] is the horizontal line, to which the function converges when [tex]t[/tex] diverges to the infinity. That is:
[tex]c = \lim _{t\to +\infty} \frac{t}{3\cdot t^{2}+5}[/tex] (1)
[tex]c = \lim_{t\to +\infty}\left(\frac{t}{3\cdot t^{2}+5} \right)\cdot \left(\frac{t^{2}}{t^{2}} \right)[/tex]
[tex]c = \lim_{t\to +\infty}\frac{\frac{t}{t^{2}} }{\frac{3\cdot t^{2}+5}{t^{2}} }[/tex]
[tex]c = \lim_{t\to +\infty} \frac{\frac{1}{t} }{3+\frac{5}{t^{2}} }[/tex]
[tex]c = \frac{\lim_{t\to +\infty}\frac{1}{t} }{\lim_{t\to +\infty}3+\lim_{t\to +\infty}\frac{5}{t^{2}} }[/tex]
[tex]c = \frac{0}{3+0}[/tex]
[tex]c = 0[/tex]
The horizontal asymptote of [tex]C(t)[/tex] is [tex]c = 0[/tex].
b) When t increases, both the numerator and denominator increases, but given that the grade of the polynomial of the denominator is greater than the grade of the polynomial of the numerator, then the concentration of the drug converges to zero when time diverges to the infinity. There is a monotonous decrease behavior.
c) From Calculus we understand that maximum concentration can be found by means of the First and Second Derivative Tests.
First Derivative Test
The first derivative of the function is:
[tex]C'(t) = \frac{(3\cdot t^{2}+5)-t\cdot (6\cdot t)}{(3\cdot t^{2}+5)^{2}}[/tex]
[tex]C'(t) = \frac{1}{3\cdot t^{2}+5}-\frac{6\cdot t^{2}}{(3\cdot t^{2}+5)^{2}}[/tex]
[tex]C'(t) = \frac{1}{3\cdot t^{2}+5}\cdot \left(1-\frac{6\cdot t^{2}}{3\cdot t^{2}+5} \right)[/tex]
Now we equalize the expression to zero:
[tex]\frac{1}{3\cdot t^{2}+5}\cdot \left(1-\frac{6\cdot t^{2}}{3\cdot t^{2}+5} \right) = 0[/tex]
[tex]1-\frac{6\cdot t^{2}}{3\cdot t^{2}+5} = 0[/tex]
[tex]\frac{3\cdot t^{2}+5-6\cdot t^{2}}{3\cdot t^{2}+5} = 0[/tex]
[tex]5-3\cdot t^{2} = 0[/tex]
[tex]t = \sqrt{\frac{5}{3} }\,h[/tex]
[tex]t \approx 1.291\,h[/tex]
The critical point occurs approximately at 1.291 hours after injection.
Second Derivative Test
The second derivative of the function is:
[tex]C''(t) = -\frac{6\cdot t}{(3\cdot t^{2}+5)^{2}}-\frac{(12\cdot t)\cdot (3\cdot t^{2}+5)^{2}-2\cdot (3\cdot t^{2}+5)\cdot (6\cdot t)\cdot (6\cdot t^{2})}{(3\cdot t^{2}+5)^{4}}[/tex]
[tex]C''(t) = -\frac{6\cdot t}{(3\cdot t^{2}+5)^{2}}- \frac{12\cdot t}{(3\cdot t^{2}+5)^{2}}+\frac{72\cdot t^{3}}{(3\cdot t^{2}+5)^{3}}[/tex]
[tex]C''(t) = -\frac{18\cdot t}{(3\cdot t^{2}+5)^{2}}+\frac{72\cdot t^{3}}{(3\cdot t^{2}+5)^{3}}[/tex]
If we know that [tex]t \approx 1.291\,h[/tex], then the value of the second derivative is:
[tex]C''(1.291\,h) = -0.077[/tex]
Which means that the critical point is an absolute maximum.
The time at which the concentration is highest is approximately 1.291 hours after injection.
change 0.18 into a ratio
5. Mrs. Hoskins is going to plant her new
gorden. She purchases 4 tomato plants for
$2.59 each, a package of watermelon seeds
for $1.87, and adapeno plant for $3.88. How
much will Mrs. Hoskins spend on seeds and
plants for her new garden?
The solution is $ 16.11
The total amount of money spend by Mrs.Hopkins on seeds and plants is given by the equation A = $ 16.11
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the cost of each tomato plant be = $ 2.59
The number of tomato plant = 4
The cost of 4 tomato plant = 4 x 2.59
The cost of 4 tomato plant = $ 10.36
Now ,
The cost of watermelon seeds = $ 1.87
The cost of adapeno plant = $ 3.88
So , the equation will be
The total amount of money A = cost of 4 tomato plant + cost of watermelon seeds + cost of adapeno plant
Substituting the values in the equation , we get
The total amount of money A = 10.36 + 1.87 + 3.88
The total amount of money A = $ 16.11
Therefore , the value of A is $ 16.11
Hence , the total amount of money is $ 16.11
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