Answer:
no
Step-by-step explanation:
no because some numbers could be negative and most number lines also contain 0. whole numbers are positive, non decimal/fractional, real numbers
 Use trigonometric identities to solve each equation within the given domain
sec(x) cos(3x) = 0 from [- x /2 , x /2]
Answer:
Either [tex]x = (-\pi / 6)[/tex] or [tex]x = (\pi / 6)[/tex].
Step-by-step explanation:
Angle sum identity for cosine:
[tex]\cos(a + b) = \cos(a)\, \cos(b) - \sin(a) \, \sin(b)[/tex].
Double-angle identity for cosine and sine:
[tex]\begin{aligned}& \cos(2\, a)\\ &= \cos^{2}(a) - \sin^{2} (a) \\ &= (\cos^{2}(a) + \sin^{2}(a) - 2\, \sin^{2}(a) \\ &= 1 - 2\, \sin^{2}(a)\end{aligned}[/tex].
[tex]\sin(2\, a) = 2\, \cos(a) \, \sin(a)[/tex].
The secant of an angle is the inverse reciprocal of the cosine of that angle:
[tex]\displaystyle \text{$\sec(x) = \frac{1}{\cos(x)}$ if $\cos(x) \ne 0$}[/tex].
Apply these identities to rewrite the left-hand side of the equation.
[tex]\begin{aligned} & \sec(x) \, \cos(3\, x) \\ =\; & \frac{1}{\cos(x)} \cdot \cos(3\, x) \\ =\; & \frac{1}{\cos(x)} \cdot (\cos(x)\, \cos(2\, x) - \sin(x)\, \sin(2\, x)) \\ =\; &\cos(2\, x) \\ & - \frac{1}{\cos(x)} \cdot (\sin(x)\, \sin(2\, x)) \\ =\; & \cos(2\, x)\\ & - \frac{1}{\cos(x)} \cdot (\sin(x) \cdot (2\, \sin(x)\, \cos(x))) \\ =\; & \cos(2\, x) - 2\, \sin^{2}(x) \\ =\; & (1 - 2\, \sin^{2}(x)) - 2\, \sin^{2}(x) \\ =\; &1 - 4\, \sin^{2}(x) \end{aligned}[/tex].
Solve the rewritten equation:
[tex]\displaystyle \sin^{2}(x) = \frac{1}{4}[/tex].
Either [tex]\sin(x) = (1/2)[/tex] or [tex]\sin(x) = (-1/2)[/tex].
The question required that [tex](-\pi / 2) \le x \le (\pi / 2)[/tex]. The sine function is one-to-one over this range. In other words, for each [tex]y[/tex] between [tex](-1)[/tex] and [tex]1[/tex], there is exactly one [tex]x[/tex] between [tex](-\pi / 2)[/tex] and [tex](\pi / 2)[/tex] such that [tex]\sin(x) = y[/tex].
If [tex]\sin(x) = (-1/2)[/tex] and [tex](-\pi / 2) \le x \le (\pi / 2)[/tex], then [tex]x = (-\pi / 6)[/tex].
Otherwise, if [tex]\sin(x) = (1/2)[/tex] and [tex](-\pi / 2) \le x \le (\pi / 2)[/tex], then [tex]x = (\pi / 6)[/tex],
Verify that [tex]\cos(x) \ne 0[/tex] for either of the two [tex]x[/tex] values, such that the [tex]\sec(x)[/tex] in the original equation takes a real value.
precalculus question please help
Answer:
It is the 1st one x=6, y=2
Step-by-step explanation:
you find this out by comparing the degrees in the numerator and the denominator. Have a nice day!!!
Hel me please!
Find two points from this graph.
Answer:
-4,-8 : 8,8
Step-by-step explanation:
help plssssssssssssssssssssssssssssssssssssz
Answer:
2x+y=-10
Step-by-step explanation:
Which of the following best represents the solution to this system (3x+2y<2
Answer:
y < (2 - 3x)/2.
Step-by-step explanation:
(3x+2y)<2
2y < 2 - 3x
y < (2 - 3x)/2
The length and breadth of a rectangles are in the ratio 8:5. If its perimeter is 104cm, find the length of the rectangle
20.8 cm
so sorry if incorrect :(
HELP PLEaseeeeeeeeeeeee thank youi
Answer:
d=4.5t
Step-by-step explanation:
in two hours, Francine went 9 miles
9/2=4.5
the distance equals 4.5 times each cycling time.
d=4.5t
What equation in Slope-Intercept Form represents the line that passes through the points ( -3,3) and ( 1,2)?
Are the two lines parallel?
If so, then what is the slope?
Yes, and the slope is 2.
Yes, and the slope is 5/2
res, and the slope is 2/5
No, They are not parallel
Answer and Step-by-step explanation:
(3rd option) The two lines are parallel, and they have a slope of [tex]\frac{2}{5}[/tex].
First, we can see that the two lines look parallel (meaning that if you were to go beyond what the graph shows (unless the graph shows an intersection), the lines at no point will intersect).
Second, If you found the slope of each line as well, (slope = rise over run, count up and then count right in this scenario from any point), they are the same, meaning they must be parallel to each other.
#teamtrees #PAW (Plant And Water)
I hope this helps!
[tex]3\sqrt[n]{x} 125[/tex]
Answer:
375[tex]\sqrt[n]{x}[/tex]
Step-by-step explanation:
If the f(x)=2x-1 and g(x)=x^2-1 find what the g(f(a-1)) is
Answer:
GOOD LUCK ON YOUR TEST YOU WILL DO GOOD
Step-by-step explanation:
Please someone brilliant answer this!!!
Eighteen plumbers can install 540 water lines in six weeks. How long will it take twelve plumbers to install the same number of lines?
It will take twelve (12) plumbers 9 weeks to install the same number of lines
From the question,
We have that, 18 plumbers can install 540 water lines in 6 weeks,
To determine how long it will take 12 plumbers to install the same number of lines,
First, we will determine how long it will take 1 plumber.
If 18 plumbers can install 540 water lines in 6 weeks
Then,
1 plumber will install 540 water lines in 18 × 6 weeks
18 × 6 weeks = 108 weeks
∴ It will take 1 plumber 108 weeks to install 540 water lines
Now, for the number of weeks it will take 12 plumbers
If 1 plumber can install 540 water lines in 108 weeks
Then,
12 plumbers will install 540 water lines in [tex]\frac{108}{12}[/tex] weeks
[tex]\frac{108}{12} = 9 \ weeks[/tex]
Hence, it will take twelve (12) plumbers 9 weeks to install the same number of lines
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factor (x-3)²+4(x-3)
Answer:
[tex] {(x - 3)}^{2} + 4(x - 3) \\ = (x - 3)((x - 3) + 4) \\ (x - 3)(x - 3+ 4) \\ = (x - 3)(x + 1)[/tex]
(x - 3) is common factor
Imagine you are multiplying or dividing each term by the common factor
[tex] {(x - 3)}^{2} + 4(x - 3) \\ \frac{{(x - 3)}^{2}}{(x - 3)}+(x-3)4\frac{(x - 3)}{(x - 3)}\\(x-3)((x-3)+4)[/tex]
Ordered pairs are ordered as (x,y) What is the constant of proportionality
for the ordered pair (-2,18)?
I need help!!! Can you figure this out?
Answer:
128 degrees
Step-by-step explanation:
38+90=128
845 + 68 =.....
Answer:
777
Step-by-step explanation:
Answer:
913
good luck <3
20% of the tickets sold at a water park were child tickets. If the park sold 50 tickets in all,
how many child tickets did it sell?
tickets
Answer:
= 10 tickets
Step-by-step explanation:
= 20% × 50
= 20/100 × 50
= 1000/100
= 10
$400 at 6.3% for 4 years. Find the simple interest
Answer:
the amount of interest is $100.80
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 6.3%/100 = 0.063 per year,
then, solving our equation
I = 400 × 0.063 × 4 = 100.8
I = $ 100.80
The simple interest accumulated
on a principal of $ 400.00
at a rate of 6.3% per year
for 4 years is $ 100.80.
BRAINLIEST PLEASE!
Which equation represents a proportional relationship?
A. 1/4x + y = 10
B. y = 1/4x
C. y = 1/3x + 1
the acute angles of the right isocoles triangle are congruent you rotate the triangle 135 counterclockwise about the origin
Answer:
45°
4 units
Step-by-step explanation:
Rotation changes nothing about the geometric relationships within the figure. Angle measures are unchanged; side lengths are unchanged.
The acute angles of an isosceles right triangle are (180° -90°)/2 = 45°. This is true regardless of the orientation of the triangle with respect to any coordinate axes.
The measures of the legs of your triangle are 0 -(-4) = 4 = (1 - (-3)). Rotating the figure any amount in any direction around any center doesn't change that.
Larry works for a tree farmer and needs to plant new saplings (young trees). He can plant 27 saplings per hour. He needs to plant 178 total saplings and has already planted 16 saplings.
Which equation and answer shows the number of hours (h) it will take for him to plant the rest of the saplings?
Answer:
27h+16=178 I believe would work as an equation for this problem
Step-by-step explanation:
The required time to plant the rest of the saplings is 6 hours, and 27 + 16 = 178 is the required expression.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Let the number of hours be h,
He can plant 27 saplings per hour.
He needs to plant 178 total saplings and has already planted 16 saplings.
So, according to the quesiton,
27h + 16 = 178,
27h = 162
h = 162/27
h = 6
Thus, the required time to plant the rest of the saplings is 6 hours,
Learn more about models here:
https://brainly.com/question/22591166
#SPJ2
Given f(x) = 5x + 32, find the following.pls don't send me a link to something and. pls pls help me this is due today and I'm still struggling with it
Answer:
thank you for points....
A bouncy ball is dropped. The function h(n)=300(3/4)^n−1 models the maximum height of the ball, in centimeters, after its nth bounce.
Select EACH true statement about the scenario.
[] The function represents a geometric sequence.
[] The first term in the sequence is 300.
[] The height of the ball after the first bounce is 300 cm.
[] The ball is dropped from a height of 300 cm.
*Multiple Choice*
The true statements about the scenario are;
The function represents a geometric sequence. The first term in the sequence is 300.The standard form of a geometric sequence is expressed as:
[tex]Tn = ar^{n-1}[/tex]
a is the first term
r is the common ratio
n is the number of terms
Given the expression [tex]h(n)=300(\frac{3}{4} )^{n-1}[/tex]
Compare and contrast
a = 300
This shows that the first term of the sequence is 300.
Also, a function represents a geometric sequence
Hence the true statements about the scenario are;
The function represents a geometric sequence. The first term in the sequence is 300.Learn more here: https://brainly.com/question/9300199
{(-4,3), (5,-9), (11,4), (9,6), (5,-3), (8,-9), (1,4)}
Function / Not a Function
is not a function.
The relation is not a function.
Step-by-step explanation:
If line AB is congruent to line CD then CD is congruent to AB what property
can someone check these for me? lmk if they are wrong and how to correct them please
Answer:
the 1. is y = (5/4)x + 6 and 2 . is y = 20x+10, so you are right, both of them correct
B.
B.
6.4 cm
114 cm
15 cm
1.5 cm
8 cm
-
Find volume
Answer:
143.4
Step-by-step explanation:
The airline tickets to Jamaica that you want to buy just went on sale. They were originally $1100 and the sale price is $600. What percentage is the original price marked down?
Step-by-step explanation:
100% = $1100
1% = 100%/100 = 1100/100 = 11
how many % are $600 ?
that is how often does 1% fit into $600 ?
600 / 11 = 54.545454... %
rounded that means 55%.
so, the making down percentage is then the difference
100% - 55% = 45%
Which number is less than 8/3
Answer:
A I belive
Step-by-step explanation:
Just divide the top number with the bottom
Allison is going to the post office to buy 34cent stamps and 3 cent adjustment stamps. Since the current postage rate is 49 cent she will need 5 times as many 3 cent adjusment stamps as 34 cent stamps. If she has $12.25 to spend, what is the largest number of 34 cent stamps she can buy?
Determine the largest number of 34 cent stamps she can buy
The largest number of 34 cent stamps she can buy is 30
Given:
Total money = $12.25
let
x = 34 cent stamp
y = 3 cent stamp
34 cent stamp = 5 × 3 cent stamp
x + y = 0.49
x = 5y
0.34x + 0.3y = 12.25
0.35(5y) + 0.3y = 12.25
1.75y + 0.3y = 12.25
2.05y = 12.25
y = 12.25/2.05
y = 5.9756097560975
approximately, y = 6
Recall,
x = 5y
x = 5(6)
x = 30
Therefore, the largest number of 34 cent stamps she can buy is 30
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