(tan²(θ) cos²(θ) - 1) / (1 + cos(2θ))
Recall that
tan(θ) = sin(θ) / cos(θ)
so cos²(θ) cancels with the cos²(θ) in the tan²(θ) term:
(sin²(θ) - 1) / (1 + cos(2θ))
Recall the double angle identity for cosine,
cos(2θ) = 2 cos²(θ) - 1
so the 1 in the denominator also vanishes:
(sin²(θ) - 1) / (2 cos²(θ))
Recall the Pythagorean identity,
cos²(θ) + sin²(θ) = 1
which means
sin²(θ) - 1 = -cos²(θ):
-cos²(θ) / (2 cos²(θ))
Cancel the cos²(θ) terms to end up with
(tan²(θ) cos²(θ) - 1) / (1 + cos(2θ)) = -1/2
Explain how the vertical line test was robes that a relation is not a function.
Using a calculator, find the decimal equivalent for the fraction 416888.
Answer:
0.46846846846
Step-by-step explanation:
if fraction was 416/888 thats the answer....
Suppose you have 9 tubes of paint. How many distinct color groupings can you make with your paint?
9514 1404 393
Answer:
511
Step-by-step explanation:
Each tube can be included in the mix, or not. There are 2^9 = 512 possible subsets of a set of 9 objects, including the complete set and the empty set. The empty set will not make a color, so there are ...
2^9 - 1 = 511 distinct color groupings that can be made
__
The assumption in the above answer is that no tube color can be made by any combination of other tube colors.* We also assume that the choice of tubes is what makes a "color grouping", and that the colors within that grouping made by using different ratios of paint quantities are not counted separately.
Examine the graph.
Select each interval where the graph is decreasing.
a.−4b. 3c.2d.−1
The research question is: Do the data provide evidence that the treatments affect the mean LDL level in this population
Answer:
hello your question is incomplete attached below is the complete question
answer : The population mean LDL level after six months is same for all four treatments
Step-by-step explanation:
A null hypothesis represents a no difference in the question. therefore the correct option is The population mean LDL level after six months is same for all four treatments
7 divided by 783 ttsggsgsgsvs
Answer: 0.008939
If you meant to put the opposite, your answer is 111.8571.
If f is the function defined by f(x) = 3x^5 - 5x^4, what are all the x coordinates of points of inflection for the graph of f?
a. -1
b. 0
c. 1
d. 0 and 1
e. -1, 0, and 1
Answer:
D: 0 and 1
Step-by-step explanation:
Function is defined by;
f(x) = 3x^(5) - 5x⁴
Now, an inflection point will be a point on the graph where the inflection or concavity changes.
Thus, let's find the derivatives until we get there;
f'(x) = 15x⁴ - 20x³
f''(x) = 60x³ - 60x²
So factorizing gives;
f''(x) = 60x²(x - 1)
At f''(x) = 0, we have; x = 0 or x = 1
Thus, the x coordinates of points of inflection are 0 & 1
HELLPPPPPUIPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
6
Step-by-step explanation:
6 dont put that down
if the probability that it will rain tomorrow is 1/6 what is the probability that it will not rain tomorrow
Answer:
.4
Step-by-step explanation: Subtract 0.6 from 1.
1-0.6=0.4
There is a 0.4 chance that it will not rain tomorrow.
Step-by-step explanation: Im sorry if this isn't right
PLEASE HELP!! 50 points MATH
Answer:
1) No
2) yes
3) no
Step-by-step explanation:
1)
[tex] \sqrt{5} [/tex]
It cannot be simplified
2)
[tex] \sqrt[3]{8} [/tex]
[tex] \sqrt[3]{(2) {}^{3} } [/tex]
[tex]2[/tex]
It can be simplified
3)
[tex] \sqrt{3} + 5[/tex]
It cannot be simplified
Which of the following give a decimal answer whose non-zero digits repeat infinitely many times ? Select all that apply .
1. 12/8
2. 3/7
3. 7/9
4. 3/2
5.3/11
What is the INPUT when the OUTPUT is 12?
Answer:
I think the answer is 4
solve the system using the elimination method. write solution as a orders pair.
3x+2y=22
-x+4y=22
please help!!!
Answer:
4x-2y=0
Step-by-step explanation:
Ok
so you need to subtract
(3x+2y=22)-(-x+4y=22)
Use distributive property and take away parenthesis
3x+2y=22+x-4y=-22
----------------------------
3x+2y=22
x-4y=-22
------------------------------
4x-2y=0
Brainliest Please
Answer:
( [tex]\frac{22}{7}[/tex] , [tex]\frac{44}{7}[/tex] )
Step-by-step explanation:
3x + 2y = 22 ....... (1)
- x+ 4y = 22 ........ (2)
3 × (2) + (1)
(3x - 3x) + (2y + 12y) = 22 + 66 ( variable "x" is eliminated )
14y = 88
y = [tex]\frac{44}{7}[/tex]
- x + 4( [tex]\frac{44}{7}[/tex] ) = 22
x = [tex]\frac{176}{7}[/tex] - [tex]\frac{154}{7}[/tex] = [tex]\frac{22}{7}[/tex]
( [tex]\frac{22}{7}[/tex] , [tex]\frac{44}{7}[/tex] )
Tina is saving to buy a notebook computer. She has two options. The first option is to put $400 away initially and save $10 every month. The second option is to put $300 away initially and save $30 every month. After how many months would Tina save the same amount using either option? How much would she save with either option?
Answer:
After 5 months, both options will have saved 450$
Step-by-step explanation:
The first option can be modeled with the expression
400 + 10x
The second option can be modeled with the expression
300 + 30x
The variable x represents the months so in order to find the month where Tina saves the same amount, we set the expressions equal to each other.
400 + 10x = 300 + 30x
solve for x
20x = 100
x = 5
After 5 months, Tina will save the same amount of money which is
400 + 10*5 = $450
Rohan and Sara have equal amounts invested in their respective portfolios. Both have invested in a popular international company. Their investments are listed in the table. Recent data shows a decrease in the international company’s share price. Which statement about this scenario is correct?
Rohan’s Investments company stocks, bonds, mutual funds, domestic stocks, and international stocks
Sara’s Investments international stocks
A.
Rohan’s portfolio will be affected the most because he has too many assets in his portfolio.
B.
Neither portfolio will be significantly affected because both have a good mix of assets.
C.
Sara’s portfolio will be affected more because it’s limited to international stocks.
D.
Both portfolios will be equally affected because both have an equal number of international stocks.
Answer:
C
Step-by-step explanation:
Sara only has international stocks in her portfolio
The correct statement about the scenario is; Sara’s portfolio will be affected more because it’s limited to international stocks.
How to Interpret Investment Schemes?We are told that;
Amount invested by Rohan and Sara are equal amounts.
They both have now invested in an international company that is popular. Also, recent data shows a decrease in the share price of the international company.
From their respective investments in the data table given as seen online, we can say that the correct statement is Option C.
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Solve for the value of y.
(4y+7)
(3y+5)
Answer: The value of y is 24.
Step-by-step explanation:
. A right cylindrical drum is to hold 7.35 cubic feet of liquid. Find the dimensions (radius of the base and height) of the drum which would minimize the surface area. What is the minimum surface area
Answer:
[tex]r=1.05\ \text{ft}[/tex]
[tex]h=2.12\ \text{ft}[/tex]
[tex]20.91\ \text{ft}^3[/tex]
Step-by-step explanation:
r = Radius
h = Height
Volume of cylinder = [tex]7.35\ \text{ft}^3[/tex]
[tex]V=\pi r^2h\\\Rightarrow h=\dfrac{V}{\pi r^2}\\\Rightarrow h=\dfrac{7.35}{\pi r^2}[/tex]
Surface area is given by
[tex]A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi r^2+2\pi r\dfrac{7.35}{\pi r^2}\\\Rightarrow A=2\pi r^2+\dfrac{14.7}{r}[/tex]
Differentiating with respect to radius we get
[tex]\dfrac{dA}{dr}=4\pi r-\dfrac{14.7}{r^2}[/tex]
Equating with zero we get
[tex]0=4\pi r-\dfrac{14.7}{r^2}\\\Rightarrow 4\pi r=\dfrac{14.7}{r^2}\\\Rightarrow r^3=\dfrac{14.7}{4\pi}\\\Rightarrow r=(\dfrac{14.7}{4\pi})^{\dfrac{1}{3}}\\\Rightarrow r=1.05[/tex]
[tex]\dfrac{d^2A}{dr^2}=4\pi-2\times \dfrac{14.7}{r^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=4\pi+2\times \dfrac{14.7}{1.05^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=37.96>0[/tex]
So, the value of the function is minimum at [tex]r=1.05[/tex]
[tex]h=\dfrac{7.35}{\pi r^2}=\dfrac{7.35}{\pi 1.05^2}\\\Rightarrow h=2.12[/tex]
So, the radius and height which would minimize the surface area is 1.05 feet and 2.12 feet respectively.
Surface area
[tex]A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi \times 1.05^2+2\pi 1.05\times 2.12\\\Rightarrow A=20.91\ \text{ft}^3[/tex]
The minimum surface area is [tex]20.91\ \text{ft}^3[/tex].
4 of 5
A student performed the following construction for the angle bisector of ZDAE. is the student's construction correct?
Yes. The student's construction is correct because circle A and circle D are the same size.
O No. The student's construction is not correct because circle D and circle E are not the same size.
Yes. The student's construction is correct because EH = DH
O No. The student's construction is not correct because AHDH.
The correct option is b). No. The student's construction is not correct because circle D and circle E are not the same size.
What is meant by angle bisector?An angle bisector is a ray, segment, or line which divides a provided angle into two equal-sized angles. The term bisector or bisection refers to the process of dividing something into two equal parts.
In geometry, the angle bisector is the ray, line, or segment that divides a provided angle into two equal parts. An angle bisector, for example, will divide a 60-degree angle into two 30-degree angles. In other words, it separates an angle into two congruent smaller angles.Now, as per the given question;
If line AH is the angle bisector of angle DAE, circle D as well as circle E should be the same size to ensure triangle ΔHDA ≅ Δ HEA, from which ∠ DAH= ∠EAH is deduced. Angle bisector properties
Thus, the student's construction again for angle bisector of DAE is incorrect because circle D or even circle E aren't the same size.
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A bean plant grows at a constant rate for a month. After 10 days, the plant is 35 centimeters tall. After 20 days, the plant is 55 centimeters tall. Which equation models the height of the plant, y, after x days?
Answer: Good afternoon fellow student, to answer your question
y - 35 = 2(x - 10)
Step-by-step explanation:
Let
y-----> the height of the plant
x ----> the number of days
Find the slope
we have the points
(10,35)
The slope is equal to
m= (55-35)/(20-10)
m= 2
Find the equation of the line into point slope form
y- y1 = m(x - x1)
we have
m= 2 and point (10,35)
y - 35 = 2(x - 10)
I need a legit answer with just a little explanation please it would mean alot to me
Answer: C.
Step-by-step explanation: Plug in x in the formula. Solve for each y by plugging in each x in the formula and seeing if it works. This took me like 3 min to solve
complete each function table. Then state the Domain and range of the function.
Answer:
Last option (c) on the list of answers
Step-by-step explanation:
f(x) = { -10, -9, -2, 3}
Domain = {-3, -2, 5, 10}
Range = {-10, -9, -2, 3}
yea so like anyone know this
Answer:
=13p+7
Step-by-step explanation:
Let's simplify step-by-step.
5p+11+8p−4
=5p+11+8p+−4
Combine Like Terms:
=5p+11+8p+−4
=(5p+8p)+(11+−4)
=13p+7
Answer:
D
Step-by-step explanation:
if i am not mistaken you would add the common multiples with each other which would be 5p+8p and 11+(-4) which would equal 13p+7. I'm sorry if I'm incorrect
Identify how many rulers Rome had between A.D.180 and A.D.284.
Answer:
29
Step-by-step explanation:
The population in the trapezoid-shaped region shown is about 7000 people. How many people are there per square mile?
Answer:
250
Step-by-step explanation:
14 x 4 = 56
56 divided by 2 = 28
7000 divided by 28 = 250I’ll give brain plesse helppppp
Answer:
Step-by-step explanation: First, you isolate x, meaning only x can be on one side. you subtract 3 from both sides, getting x<4- x is less than four.
there are two graphs showing x less than four, but since this is less than and not less than/equal to, your answer is the fourth graph, where the point is open and not closed.
Answer:
Last choice,
open circle on 4 arrow going left.
Step-by-step explanation:
X + 3 < 7
x < 4
The basketball team took 20 free throws in the game and made 65% of them how many free throws did they make?
Answer:
its 13
Step-by-step explanation:
Solve using elimination.
- 9x + 2y = 5
-9x + y = -2
Answer:
(1 , 7)
Step-by-step explanation:
Solve the given equation: 10|2x-4|=40
Please answer step by step
Answer:
step by step you said answer step by step that's your answer
Step-by-step explanation:
step by step you said answer step by step that's your answer
Drag all of the steps necessary into the box to find the product of 2 . 7 × 6 . 4 using partial products.
The product of the numbers 2.7 x 6.4 using partial products is 17.28
How to calculate the value?In order to get the product of the values using partial products, we will use the concept of repeated addition as shown:
2.7 x 6.4
For 2.7 = 2.0 + 0.7
6.4 = 6.0 + 0.4
Substituting the sum into the product, we will have:
2.7 x 6.4 = (2.0 + 0.7) x (6.0 +0.4)
2.7 x 6.4 = 2.0(6.0) + 2(0.4) + 0.7(6) + 0.7(0.4)
2.7 x 6.4 = 12 + 0.8 + 4.2 + 0.28
2.7 x 6.4 = 17.28
Therefore, the value is 17.28.
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Two machines just completed projects at the same time. Machine A complete a project every 1.25 minutes. Machine B completes a project every 4.5 minutes. How long will it be until both machines complete a project at the same time again?
Answer:
5.75
Step-by-step explanation:
1.25 +4.5 =5.75(the time =the addition of the both times)