Answer:
[tex]\cot(x) = -1[/tex] whenever [tex]\displaystyle x = k\, \pi-\frac{\pi}{4}[/tex] radians, where [tex]k[/tex] could be any integer ([tex]k \in \mathbb{Z}[/tex], which includes positive whole numbers, negative whole numbers, and zero.)
Step-by-step explanation:
[tex]x = 45^\circ[/tex] (as in isoscele right triangles) would ensure that [tex]\displaystyle \cot(x) = 1[/tex]. Since cotangent is an odd function, [tex]\cot(-45^\circ) = -1[/tex].
Equivalently, when the angles are expressed in radians, [tex]\cot(-\pi / 4) = -1[/tex].
The cycle of cotangent is [tex]\pi[/tex] (or equivalently, [tex]180^\circ[/tex].) Therefore, if [tex]k[/tex] represents an integer, adding [tex]k\, \pi[/tex] to the input to cotangent would not change the output. In other words:
[tex]\displaystyle \cot\left(k\, \pi - \frac{\pi}{4}\right) = \cot(-\pi / 4) = -1[/tex].
Hence, [tex]\displaystyle x = k\, \pi-\frac{\pi}{4}[/tex] would be a solution to [tex]\cot(x) = -1[/tex] whenever [tex]k[/tex] is an integer.
Since [tex](-\pi / 4)[/tex] is the only solution to this equation in the period [tex](0,\, \pi)[/tex], all real solutions to this equation would be in the form [tex]\displaystyle x = k\, \pi-\frac{\pi}{4}[/tex] (where [tex]k[/tex] is an integer.)
plwjahajsjwjjee helppppp!!
Answer:
30% of total students chose snowboarding as their favorite sport.
Step-by-step explanation:
We know that;
=> Total people = 500
=> Snowboarding people = 105
=> Percentage = unknown, so we can say it as x
So we can set up the equation;
x% · 500 = 105
[tex]\frac{x}{100}[/tex] · 500 = 105
x · 5 = 105
x = 105/5
x = 30
So 30% of total students chose snowboarding as their favorite sport.
Hope this helps!
Jim wants to buy an electric saw marked $98.00. If the salesperson offers him a discount of 15%, how much will he have to pay for the saw?
Answer:
$83.30
Step-by-step explanation:
Find how much he will have to pay by multiplying the price by 0.85, since this will calculate what 85% of the price is (with the 15% discount):
98(0.85)
= 83.3
So, he will have to pay $83.30 for the saw
Bill used a rain gauge to measure how much rain fell, in centimeters (cm), during a
rainfall.
(ANYONE WANNA HELP ME?)
Step-by-step explanation:
done hope this helped you
Find the 9th term of the geometric sequence 5, -25, 125, ...
Answer: 1,953,125
This is one single value and it is just a bit under 2 million.
Or more accurately, it's a bit over 1.9 million.
===========================================================
Explanation:
a = 5 = first termr = -5 = common ratioNote that dividing any term by its previous term gets us the common ratio
r = term2/term1 = -25/5 = -5r = term3/term2 = 125/(-5) = -5The r value must stay the same the entire time, or else the sequence isn't geometric.
The nth term of any geometric sequence is a*(r)^(n-1). With the 'a' and 'r' values we found, we update that to 5(-5)^(n-1)
-----------------
To verify that is the correct nth term expression, plug in various values of n to compare it with the given sequence.
If we tried n = 2 for instance, then we find the 2nd term is
5(-5)^(n-1) = 5(-5)^(2-1) = -25
which matches what your teacher gave you. I'll let you verify the other terms.
-----------------
The last thing we need to do is plug in n = 9 and simplify
5(-5)^(n-1)
5(-5)^(9-1)
5(-5)^8
5(390625)
1,953,125 this is one single value (rather than 3 separate values)
find the exact value of tan A in simplest radical form
Answer:
they might not be the same numbers but you can do it with all of the step-by-step explanations I gave you just with the numbers you have
Step-by-step explanation:
Triangle ABC is a right angle triangle.
From the given right angle triangle,
AB represents the hypotenuse of the right angle triangle.
With m∠A as the reference angle,
AC represents the adjacent side of the right angle triangle.
BC represents the opposite side of the right angle triangle.
To determine tan m∠A, we would apply the tangent trigonometric ratio.
Tan θ = opposite side/adjacent side. Therefore,
Tan A = √32/2 = (√16 × √2)/2
Tan A = (4√2)/2
Tan A = 2√2
2. Caleb wants to tile the floor of his fort, the dimensions are 3mm by 4m. The tiles he
wants to buy come in squares. The perimeter of the tile is 80cm.
How many tiles will Caleb need?
tiles
Answer:
Number of tile need = 300 tiles
Step-by-step explanation:
Given:
Dimensions of floor = 3 m by 4 m
Perimeter of square tile = 80 cm
Find:
Number of tile need
Computation:
Perimeter of square tile = 4(Side)
80 = 4(Side of tile)
Side of tile = 80 / 4
Side of tile = 20 cm
Side of tile = 0.2 meter
Area of tile = 0.2 x 0.2
Area of tile = 0.04
Area of floor = 3 x 4
Side of tile = 12 square meter
Number of tile need = 12 / 0.04
Number of tile need = 300 tiles
5x (2yz + 4y - 3)
Use the distributive property to simplify the expression
Answer:
10xyz + 20xy - 15x
Step-by-step explanation:
5 x ( 2yz + 4 y - 3)
using the Distributive property multiply the each term by 5x
5x × 2yz + 5x × 4y - 5x × -3
calculate the product
10xyz + 20xy - 15x
Answer:
10xyz+20xy-15
Step-by-step explanation:
In 1994, the General Social Survey included a question that asked its participants if they felt that nuclear power plants were extremely/very dangerous to the environment. Out of the 1263 surveyed, 565 said yes. What is the value of the test statistic for this problem
Answer:
Value of the test statistic for this problem = -3.74
Step-by-step explanation:
Here
the sample size n = 1263
and the x = 565
So, the p' -value = 565/1263 = 0.4473
As per the test statistics formula, z value will be evaluated
z = (0.4473-p)/sqrt {p(1-p)/n}
Let us say that p = 0.5
Substituting the given value in above equation, we get -
z = (0.4473-0.5)/sqrt {0.5(1-0.5)/1263}
z = -3.74
The test statistic of the question is; z = -3.74
What is the test statistic?We are given;
Sample size; n = 1263
Number of people that said yes; x = 565
Sample proportion is; p'= 565/1263 = 0.4473
Formula for the test statistic of proportion is;
z = (p' - p)/(√(p(1 - p)/n)
We will assume that population proportion p = 0.5. Thus;
z = (0.4473 - 0.5)/(√(0.5(1 - 0.5)/1263)
z = -3.74
Read more about test statistic at; https://brainly.com/question/4621112
The annual energy consumption of the town where Camilla lives increases at a rate that is proportional at any time to the energy consumption at that time. The town consumed 4.44.44, point, 4 trillion British thermal units (BTUs) initially, and it consumed 5.55.55, point, 5 trillion BTUs annually after 555 years. What is the town's annual energy consumption, in trillionso f BTUs, after 9 years?
Answer:
The town's annual energy consumption will be of 6.57 trillons of BTU after 9 years.
Step-by-step explanation:
The annual energy consumption of the town where Camilla lives increases at a rate that is proportional at any time to the energy consumption at that time.
This means that the consumption after t years is given by the following differential equation:
[tex]\frac{dC}{dt} = kC[/tex]
In which k is the growth rate.
The solution is, applying separation of variables:
[tex]C(t) = C(0)e^{kt}[/tex]
In which C(0) is the initial consumption.
The town consumed 4.4 trillion British thermal units (BTUs) initially.
This means that [tex]C(0) = 4.4[/tex]
So
[tex]C(t) = C(0)e^{kt}[/tex]
[tex]C(t) = 4.4e^{kt}[/tex]
5.5 trillion BTUs annually after 5 years.
This means that [tex]C(5) = 5.5[/tex]. We use this to find k. So
[tex]C(t) = 4.4e^{kt}[/tex]
[tex]5.5 = 4.4e^{5k}[/tex]
[tex]e^{5k} = \frac{5.5}{4.4}[/tex]
[tex]e^{5k} = 1.25[/tex]
[tex]\ln{e^{5k}} = \ln{1.25}[/tex]
[tex]5k = \ln{1.25}[/tex]
[tex]k = \frac{\ln{1.25}}{5}[/tex]
[tex]k = 0.0446[/tex]
So
[tex]C(t) = 4.4e^{0.0446t}[/tex]
After 9 years?
This is C(9). So
[tex]C(9) = 4.4e^{0.0446*9} = 6.57[/tex]
The town's annual energy consumption will be of 6.57 trillons of BTU after 9 years.
Find the equation (in terms of x ) of the line through the points (-3,4) and (1,-8)
Answer:
A(-3,4) B(1,-8)
y-y1/x-x1 =y2-y1/x2-x1
y-4/x--3 = -8-4/1--3
y-4/x+3 = -12/1+3
y-4/x+3 =-12/4
y-4/x+3 = -3
y-4 = -3(x+3)
y-4=-3x-9
y+3x +9-4=
y+3x+5=0
Answer:
y = -3x - 5
Step-by-step explanation:
-3, 4 and 1, -8
1 - -3 = 4
-8 - 4 = -12
[tex]\frac{-12}{4}[/tex] = [tex]\frac{-3}{1}[/tex] = -3
gradient/slope = -3
now substituting in the point -3, 4 to find the y intercept:
4= -3 x -3 + c
4 = 9 + c
-5 = c
y intercept = -5
equation is y = -3x - 5
Write the equation of the circle centered at ( - 4,7) with radius 20?
Answer:
(x + 4)² + (y - 7)² = 20²
Step-by-step explanation:
Graphing form
(x - h)² + (y - k)² = r²
(h, k) is the center = (-4, 7)
r is the radius = 20
-----------------------------------
Plug in the givens
(x + 4)² + (y - 7)² = 20²
Select the two expressions equivalent to 25 .
Answer: 2 primes 1 disinct
Step-by-step explanation:
A triangle has sides 12, 35, and 37. Identify whether the triangle is right, acute, or obtuse.
Answer:
Right triangle
Step-by-step explanation:
Using pythagorean theorem,
[tex]c^2 = a^2 + b^2\\37^2 = 12^2 + 35^2 \\1369 = 144 + 1225\\1369 = 1369[/tex]
Hence satisfied. So it is right triangle.
What is the answer to this equation 4y+3y+2y=
4y + 3y + 2y = 9y
9y is the answer
Plz mark me brainliest
answer is 100% correct
A laptop computer is purchased for $3900. Each year, its value is 75% of its value the year before. After how many years will the laptop computer be worth $700 or less?
Answer:
1200*0.70=840
840*0.70=588
588*0.70=411.60
411.60*0.70=288.12
if you add 5 over 8 + 5 over 8.. how do you simplify it and write it as a mixed number?
Answer:
its equal to 10 over 8
Step-by-step explanation:
then u divide the numerator and denominator by 2 over 2 which will give you 5 over 4
since it's 5 over 4 you 1 whole number which become 1 and 1 over 4
outside the court ard is 120 m“, find the width of the path.
A square garden has an area of 441 m². If the path of uniform width surrounding inside the
garden is 216 m², find the width of the path.
Answer:
Area of a square garden = 2, 500 m².
Length of the side of the garden = √2,500 = 50 m.
Width of the path = 2.5 m.
Path is inside the garden.
Width of the garden that is inside (enclosed) by the path:
50 - 2 * 2.5 = 45 m.
Length of the garden inside by the path : = 45 m.
So the area of garden inside the path = 45 * 45 m²
= 2, 025 m².
Area of the path = 2, 500 - 2, 025
= 475 m².
Cost of laying the path = Rs 25 /m² * 475 m²
= Rs 11, 875.
Step-by-step explanation:
Please help meeeeeeee
Answer:
5040
Step-by-step explanation:
This is a problem of permutation where one has to arrange all the letters of the word taken all at a time. Since in N lettered word if all the letters are different then it can be arranged in N! ways i.e factorial N ways.
In the problem mentioned given
Word : Musical
number of words = 7 (all the words are different)
Number of ways to arrange it = 7!
7*6*5*4*3*2*1 = 5040
Hence 5040 is the answer!
Which of the following functions has a vertical asymptote at x=3?
Answer:
the last one: f(x) = 1/(x-3)
Step-by-step explanation:
Vertical asymptote at x=3 means dividing by zero for x=3. If you examine all denominators with x=3, you find that the last one divides by zero (3-3).
Help me or not i have 10 points to offer
Answer:
I think 42.5
Step-by-step explanation:
About 89% sure
THIS IS WORTH 30 POINTS
1. Point B is located at (-4, -6). Where is the location of B’ after a reflection over the y-axis?
Answer:
your awnser would be [4, −6]
Step-by-step explanation:
hope this helps
Calculate the scale factor of ABC to DEF. Enter answer as a whole number or as a fraction in lowest terms, using the slash mark ( / ) for the fraction bar.
Answer:
3
Step-by-step explanation:
because 3x3= 9 and 4x3=12 and 5x3=15
Mike has a bank account whose balance is represented by A(t)=10,000*3.138^t. Where t is in years. Write the function so it reflects the monthly rate of interest . Around the nearest percent
9514 1404 393
Answer:
A(m) = 10000×1.10^m; 10% monthly interest
Step-by-step explanation:
If t is the time in years and m is the corresponding time in months, then we have ...
m = 12t
t = m/12
So, the balance is ...
A(t) = 10000×3.138^t
A(m) = 10000×3.138^(m/12) = 10000×(3.138^(1/12))^m
A(m) = 10000×1.10^m
The monthly interest rate is 10%.
_____
The monthly growth factor 1.10 is 1 more than the monthly growth rate.
growth rate = growth factor -1 = 1.10 -1 = 0.10 = 10%.
A recipe uses 100 g of flour, 100 g of sugar and 80 g of butter.
8. Damia has 120 g of butter and wants to use it all in this recipe. What total weight of flour and sugar should he use in grams?
9. Damia realizes he only has 60 g of sugar, so can’t use all of his butter. How many grams of butter will he have
left over when he’s finished making the recipe?
Answer for question number 8 is 300 gms.
Can someone help to solve question number 9 in step by step please?
Answer:
600 butter : 2000 flour : 200 sugar : 400 currants = 72 cakes
120 cakes could be made with 1 kg of butter
Step-by-step explanation:
Here, 72 cakes = 6 dozen cakes
( since 12 cake = 1 dozen cake ).
a. First calculate quantity of each ingredient per dozen by dividing each by 1.5 (18/12).
• Butter - 150/1.5 = 100 g per dozen
For 6 dozen :
100g x 6 = 600 g
• Flour - 500/1.5 = 333.33 g per dozen
For 6 dozen :
333.33 g x 6 = 2000 g
• Sugar - 50/1.5 = 33.33 g per dozen
For 6 dozen :
33.33 x 6 = 200 g
• Currants - 100/1.5 = 66.67 g per dozen
For 6 dozen :
66.67 x 6 = 400 g
b. It is given that,
150g butter is required to make = 18 cakes
Then by using unitary method, we get,
1 g of butter is required to make = 18/150 cakes
Since, 1 Kg = 1000 g
Then,
1000 g of butter is required to make = (18/150) × 1000
= 120 cakes
Hence, with 1 kg of butter 120 whole cakes can be made.
Hope this answer helps you :)
Have a great day :)
Mark brainliest
There are______
Pairs of integers satisfying a÷b = -2
Answer:
There are only 1
Pairs of integers satisfying a÷b = -2
Step-by-step explanation:
Answer:
[tex]all \: positive \: integers \: in cluding \: 1[/tex]
so I dont really know how many
Step-by-step explanation:
eg
[tex] \frac{ - 2}{1} \\ \frac{ - 4}{2} \\ \frac{6}{ - 3} \\ = - 2[/tex]
they are all equal to negative 2
Which equation is the inverse of y = x2 + 16?
O y = x2 – 16
y=+√x - 16
y=+NX-16
y = x2 - 4
Hi there!
[tex]\large\boxed{y = \pm \sqrt{x - 16}}[/tex]
To solve for the inverse, swap the x and y variables:
x = y² + 16
Isolate for y by subtracting both sides by 16:
x - 16 = y²
Square root both sides:
√(x - 16) = y
Add the plus/minus sign:
y = ±√(x - 16)
Answer:
c
Step-by-step explanation:
Find the slope of a line passing through the given points.
(-4, 2) and (5,6)
slope =
Answer:
4/9
Step-by-step explanation:
To find slope without a graph, you subtract the 2 y-coords and the 2 x-coords, then divide the y-coord by the x-coord.
The formula is (y²-y¹)/(x²-x¹).
So we just plug in the coordinates.
(6-2)/(5-(-4))
(6-2)/(5+4)
4/9
So the slope is 4/9
---
hope it helps
What is the area of the triangle?
Answer:
c
Step-by-step explanation:
x^2-16=0 solve for all real values of x
Hi there! Use the difference of two squares formula below:
[tex] \large \boxed{ {x}^{2} - {y}^{2} = (x + y)(x - y)}[/tex]
You need to know that what number times itself and get 16. 16 comes from 4×4 or 4².
Then,
[tex] \large{ {x}^{2} - 16 = (x + 4)(x - 4)}[/tex]
[tex] \large{(x + 4)(x - 4) = 0}[/tex]
Solve the equation for all real values of x.
[tex] \large{x = 4, - 4}[/tex]
If you don't like using a formula. You can do this:
[tex] \large{ {x}^{2} - 16 = 0} \\ \large{ {x}^{2} = 16} \\ \large{x = \pm \sqrt{16} } \\ \large{x = \pm 4}[/tex]
If you remember the square root well, the square root of 16 is 4×4. Pull out the two 4's and thus the square root of 16 is 4.
For the square both sides method above (second method), we can define that:
[tex] \large \boxed{ \large{ {x}^{2} = a \longrightarrow x = \pm a }}[/tex]
Answer
x = 4,- 4 (You can answer x = ±4Hey! Can someone please help me with this question? Really appreciate it
Answer:
[tex]d = 0.112* 10^3[/tex]
Step-by-step explanation:
Given
[tex]h = 8.4 * 10^3[/tex]
[tex]d = \sqrt{\frac{3h}{2}}[/tex]
Required
Find d
We have:
[tex]d = \sqrt{\frac{3h}{2}}[/tex]
Substitute: [tex]h = 8.4 * 10^3[/tex]
[tex]d = \sqrt{\frac{3*8.4 * 10^3}{2}}[/tex]
[tex]d = \sqrt{\frac{25.2 * 10^3}{2}}[/tex]
[tex]d = \sqrt{12.6 * 10^3}[/tex]
Express as:
[tex]d = \sqrt{1.26 *10* 10^3}[/tex]
[tex]d = \sqrt{1.26 *10^4}[/tex]
Split
[tex]d = \sqrt{1.26} *\sqrt{10^4}[/tex]
[tex]d = 1.122* 10^2[/tex]
To write in form of: [tex]a * 10^b[/tex]
The value of a must be: [tex]0 \le a \le 1[/tex]
So, we have:
[tex]d = 0.1122* 10 * 10^2[/tex]
[tex]d = 0.1122* 10^3[/tex]
Approximate
[tex]d = 0.112* 10^3[/tex]