Answers
By definition of tangent,
tan(x) = sin(x) / cos(x)
so if tan(x) < 0, and we're given cos(x) = -1/4 < 0, then it follows that sin(x) > 0.
Recall the Pythagorean identity:
cos²(x) + sin²(x) = 1 → sin(x) = + √(1 - cos²(x))
Then
sin(x) = √(1 - (-1/4)²) = √(15/16) = √(15)/4
Recall the double angle identity:
sin(2x) = 2 sin(x) cos(x)
Then
sin(2x) = 2 • √(15)/4 • (-1/4) = -2√(15)/16 = -√(15)/8
Related Questions
Mr. Omar assigns homework to his class and the homework requires students to
find the prime factorization of 648 using the factor tree method. Kumar wrote the
following. Is he correct? If not, explain why and show the correct method.
Kumar’s solution: 162 X4
Answers
648
/ \
162 4
/ \ / \
81 2 2 2
/ \
9 9
/ \ / \
3 3 3 3
If you poured 15 teaspoons of salt into an empty graduated cylinder, about how many milliliters would it fill?
Answers
Answer:
About 75
Step-by-step explanation:
Answer:
1 cubic millimeter = (about) 0.000202884 us spoons
Then you can use multiplication to solve it.
Step-by-step explanation:
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A farmer grows a particular plant that has a gene that can be manipulated to control the age t at which the plant matures. The number of seeds S(t) produced by a plant maturing at age t is S(t)=−0.3t2+30t+0.2 seeds per mature plant A farmer asks the geneticists to genetically engineer a plant line that accounts for the fact that on his farm, only P(t)=90000t+100, plants mature to age t. What age of maturity should the geneticist select for the plants to maximize the seed production of the farmer's crop?a. Between 130 and 140 days b. Between 120 and 130 days
Answers
Answer:
The correct option is;
Between 40 and 50 days
Step-by-step explanation:
The number of seeds that are produced by a plant maturing at age t, S(t), is given as follows;
S(t) = -0.3·t² + 30·t + 0.2
The proportion of plants maturing at age (t) in the plants to be engineered by the geneticist P(t) = 90000/(t + 100)
The number of seeds produced by the plants = S(t) × P(t) = (-0.3·t² + 30·t + 0.2)×(90000/(t + 100))
To find the maximum number of seeds, we differentiate using an online tool, and equate to zero to get;
d((-0.3·t² + 30·t + 0.2)×(90000/(t + 100)))/dt = (-27000·t² - 5400000·t + 269982000)/(t + 100)² = 0
(-27000·t² - 5400000·t + 269982000)/(t + 100)² = 27000(t - 41.419)(t + 241.419)/(t + 100)² = 0
t = 41.419 or t = -241.419
Therefore, in order to maximize the production of seed of the crops of the farmer, the geneticist should select between 40 and 50 days.
What is the sum of the first eight terms in this series?
2+10+50+250+.....
Answers
Answer:
C.195312
Step-by-step explanation
The sum of geometric sequence 2,10,50... up to 8 terms is 195312. Therefore, option C is the correct answer.
The given geometric sequence is 2+10+50+250+.....
What is the sum of the geometric sequence formula?Sum of the geometric sequence is S = a + ar + ar² +....+ [tex]ar^{n-1}[/tex].
The first term of the series is a and the common ratio is r.
The sum of the geometric sequence formula is [tex]S_{n} =\frac{a(r^{n} -1)}{(r-1)}[/tex] .
Now, a=2
To find r,
r = 10/2
r = 5 and n = 8
S = 2 ([tex]5^{8}[/tex]- 1) / (5 - 1)
S = 2(390625 - 1) / 4
S = (390624) / 2
S = 195312
Therefore, the sum of geometric sequence 2,10,50... up to 8 terms is 195312.
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for which division problems is 54 the quotient write those divison problems in the box
Answers
Answer:
what?
Step-by-step explanation:
The division problems for which 54 is the quotient are, 2430÷45 and 594÷11
What are quotient?The number we obtain when we divide one number by another is the quotient.
Given are the numbers, we need to find which one of them gives the quotient of 54
When we divide 2430÷45, we will get 54
And, 594÷11 = 54
Hence, The division problems for which 54 is the quotient are, 2430÷45 and 594÷11
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Which correctly describes how the graph of the inequality 4x − 2y > 20 is shaded?
Above the solid line
Below the solid line
Above the dashed line
Below the dashed line
Answers
Answer:D Below the Dashed line
Step-by-step explanation:
Just took the test
Answer:
Below the dashed line so the answer is D
Step-by-step explanation:
just finished taking the quiz with this same answer!!
What is the measure of angle a?
A) 54
B) 46
C) 126
D) 136
Answers
Answer:
Step-by-step explanation: 54+54=108
360-108=252 divide by 2
Answer:
C
Step-by-step explanation:
a and 54° are adjacent angles and are supplementary, thus
a = 180 - 54 = 126 → C
Is -23.4 greater or less than 23.4
Answers
Because it’s negative
Answer:
No 23.4 is greater
Step-by-step explanation:
-23.4 is negative so that means it is less than 0
In 1992, Disney created a one-of-a-kind special pin. Each year, the pin’s value appreciates by a constant amount. In 1997, the pin was valued at $350. In 2002, it was valued at $600. Let x be the number of years since 1992 and y be the value of the pin in dollars. Write a linear equation in slope-intercept form that models this situation.
Answers
Answer:
[tex]y = 50x + 50[/tex]
Step-by-step explanation:
Given
x = years since 1992.
y = value of pin
This means that
[tex]x = 1[/tex] ----- in 1992
[tex]x_1 = 6[/tex]; [tex]y_1 = 350[/tex] ---- in 1997
[tex]x_2 = 11;[/tex] [tex]y_2 = 600[/tex] ---- in 2002
Required
Determine the line equation in slope intercept form
First, we need to determine the slope (m) of the line
[tex]m = \frac{y_2 - y_1}{x_2- x_1}[/tex]
[tex]m = \frac{600 - 350}{11- 6}[/tex]
[tex]m = \frac{250}{5}[/tex]
[tex]m = 50[/tex]
The equation is then calculated using:
[tex]y - y_1 = m(x - x_1)[/tex]
Recall that
[tex]x_1 = 6[/tex]; [tex]y_1 = 350[/tex]
[tex]m = 50[/tex]
So, we have:
[tex]y - 350 = 50(x - 6)[/tex]
[tex]y - 350 = 50x - 300[/tex]
[tex]y = 50x - 300 + 350[/tex]
[tex]y = 50x + 50[/tex]
AB=CD what is the property
Answers
The formula for the area of a triangle is A =12bh, in which b represents the length of the base and h represents the height. If a triangle has an area of 232 mm 2 and the height is 16 mm, what is the measure of the base? The measure of the base is mm.
Answers
Answer:
Step-by-step explanation:
Write it out: A = 1/2(bh)
substitute values: 232 = 1/2(16b)
Simplify: 232 = 8b
Divide each side by 8: b = 29
The base is 29 millimeters
Need rn! worth 30
Evaluate the function T(x)=19−x, when x=−3.
a.) 57
b.) 22
c.) 16
d.) −16
Answers
Answer:
b
Step-by-step explanation:
Find the equation of the line that has a slope of 2
and passes through the point (5, -8). Write the
equation in point-slope form.
Answers
Answer:
The equation in the point-slope form will be:
[tex]y-(-8) = 2 (x-5)[/tex]
Step-by-step explanation:
The point-slope form of an equation is written as:
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope, and (x₁, y₁) is a point on the line.
Now, we will substitute the values of m and (x1, y1) in the given equation. Here,
m=2
and
(x1, y1) = (5, -8)
x1 = 5
y1 = -8
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-(-8) = 2 (x-5)[/tex]
Therefore, the equation in the point-slope form will be:
[tex]y-(-8) = 2 (x-5)[/tex]
A Rental Car Agency charges a flat fee of $25 per day plus $0.15 for each mile driven. The total charge for one day's rental was $75.30. Which equation below can be used to solve this problem?
Answers
Answer:
Step-by-step explanation:
75.30-25 for a day leaves 50.30 for mileage.
50.30/.15 per mile= 335.3 miles driven.
75.30>=25+0.15m. m=335.3
Select all lines with a slope of 2/5
Answers
Answer:
C and D
Step-by-step explanation:
Answer:
Pull a mil' in a day, ain't even have the bill
On your pill, everyday I just be sippin' Chamomile
Mass appeal, everybody show up 'cause they know I'm here
Every week, I be on the face, she think it's Cetaphil
Up in my business, pull up in my crib
I got people locked and loaded like they trained for ISIS
Askin' for forgiveness, I never said you have it
Pullin' all these dimes like, do you really want attention?
Step-by-step explanation:
Please only answer if you know the answer
Don’t say dumb stuff or just lie and about the answer or just put Radom words please
Answers
Please help me out with this please
Answers
Answer:
2nd from the bottom
Step-by-step explanation:
A game board with 17 spaces. Start, green, green, star, quesiton mark, question mark, star, question mark, green, cat town, green, green, star, question mark, green, green, star, green, end.
You are playing a board game and your playing piece begins the game at START. You roll a single number cube numbered 1 to 6 to find out how many spaces you can move.
What are the possible outcomes of your first roll?
Answers
Answer:
2/3
Step-by-step explanation:
Solve y = x2-5 for x.
O A. x = +/-5
B. X = y + 5
C. X = +/y+5
O D. x = y-5
Answers
Sara compra 3 naranjas a Q 2.00 cada una. Compra un melón a
Q 12.00 y quiere comprar 4 manzanas, tomando en cuenta que la
docena de manzanas cuesta Q 24.00. ¿Cuánto gastó en total por las 3
naranjas, el melón y las 4 manzanas?
Answers
Respuesta:
29.00
Explicación:
una naranja 3.00
un melón 12.00
una manzana 2.00 (porque una docena equivale 12 artículos; 24/12 es 2)
tres naranjas 3(3.00) = 9.00
un melón 12.00
cuatro manzanas 4(2.00) = 8.00
9.00 +12.00 +8.00
29.00
A shop sells packets of envelopes.
There are 5 envelopes in a small packet.
There are 20 envelopes in a large packet.
There is a total of T envelopes in x small packets and y large packets.
Write down a formula for T in terms of x and y.
Answers
9514 1404 393
Answer:
5x +20y = T
Step-by-step explanation:
There are 5 envelopes in each of x small packets, for a total of 5x envelopes in small packets.
There are 20 envelopes in each of y large packets, for a total of 20y envelopes in large packets.
The total number envelopes is then ...
T = 5x +20y
Polygon R and polygon S are similar. The perimeter of polygon R is 72 cm, and the perimeter of polygon S is 36 cm. If one side of polygon S is 6 cm, what is the length of the corresponding side in polygon R?
Answers
Answer:
the answere is 10
Step-by-step explanation:
explanation- it just is
What is slope intercept form?
O
a + b =C
O y = 3m + b
O
y = mx + b
Answers
Answerc
Step-by-step explanation:
Answer:
Step-by-step explanation: a
what is the value of q in the equation 3(q+4/3) =2
Answers
Step-by-step explanation:
3q+(3×4÷3)=2
3q+4=2
3q=2-4
3q=-1
q=-1÷3
Alex rode his bike 25 kilometers. About how many miles did Alex ride his bike?
Answers
Answer:
Alex rode 15.5343 miles in his bike
Step-by-step explanation:
1 kilometer is 0.621371 miles, multiply 0.621371 with 25. Hope this helps!
Alex rode his bike for 15.535 miles.
What is unit conversion?Unit conversion means the conversion between different units and measurements of the same quantity done by the process of multiplication or division.
Given
Alex rode his bike 25 kilometers
1 kilometer = 0.6214 miles
25 kilometers = 0.6214 × 25 = 15.535 miles
Hence, ride distance is 15.535 miles.
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A class has 5 girls and 9 boys. Select all associated ratios for this class.
A. 5:4
B. 5:14
C. 9:14
D. 14:11
E. 5:4
F. 9:5
G. 4:9
H. 5:9
Answers
A fitness center charges a monthly fee to use the facilities plus $3 for each fitness class. One month Sara took 6 classes and paid $30 for the month. If she paid $48 for the next month how many classes did she take?
Answers
Answer:
12
Step-by-step explanation:
3x6 = 18
30-18 = 12 so the monthly fee is twelve
-----------------------------------------------------------------
48- 12 = 36 (cost of classes)
36/3= 12
Solve the linear equation -3x + 3= 12
Answers
Answer:
x = -3
Step-by-step explanation:
-3x = 9
x = -3
Answer:
x=-3
Step-by-step explanation:
i subtracted 3 from both side then i divdeed -3 from both side of the equation
Estimate the value of the square root
/20
Answers
Answer:
about 5
Step-by-step explanation:
What is the volume of a cone (in cubic inches) with a radius of 3 inches and a height of 6 inches?
Use 3.14 for π. Round your answer to the nearest hundredth.
Answers
Answer:
V≈56.55in³
Step-by-step explanation:
Answer:
56.55
Step-by-step explanation:
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