Answer:
[tex]t_{1} = 0.422\pi \pm \pi\cdot i[/tex], [tex]\forall \,i \in \mathbb{N}_{O}[/tex]
[tex]t_{2} = 1.422\pi \pm \pi\cdot i[/tex], [tex]\forall \,i \in \mathbb{N}_{O}[/tex]
Step-by-step explanation:
In the case of parametric equations, the slope of the curve is equal to:
[tex]\frac{dy}{dx} = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }[/tex]
Where [tex]\frac{dx}{dt}[/tex] and [tex]\frac{dy}{dt}[/tex] are the first derivatives of [tex]x[/tex] and [tex]y[/tex] regarding [tex]t[/tex]. Let be [tex]x(t) =2\cdot \cos t[/tex] and [tex]y(t) = 8\cdot \sin t[/tex], their first derivatives are found:
[tex]\frac{dx}{dt} = -2\cdot \sin t[/tex] and [tex]\frac{dy}{dt} = 8\cdot \cos t[/tex]
Thus, equation for the slope is:
[tex]\frac{dy}{dx} = -\frac{8\cdot \cos t}{2\cdot \sin t}[/tex]
[tex]\frac{dy}{dx} = -\frac{4}{\tan t}[/tex]
If [tex]\frac{dy}{dx} = -1[/tex], then:
[tex]-1 = -\frac{4}{\tan t}[/tex]
[tex]\tan t = 4[/tex]
Tangent is positive at 1st quadrant and is a function with a periodicity of [tex]\pi[/tex], the set of solutions are:
[tex]t_{1} = 0.422\pi \pm \pi\cdot i[/tex], [tex]\forall \,i \in \mathbb{N}_{O}[/tex]
[tex]t_{2} = 1.422\pi \pm \pi\cdot i[/tex], [tex]\forall \,i \in \mathbb{N}_{O}[/tex]
Name the property of equality that justifies going from 3x+6x to (3+6)x
Write 843,208,732,833 in word form
Answer:
Hey!
Your answer is Eight-hundred and forty-three billion, two-hundred and eight million, seven-hundred and thirty-two thousand, eight-hundred and thirty-three.
HOPE THIS HELPS!
Se tiene dos números, a y b . Si se sabe que el producto de ambos es 676 y el cociente de b entre a es 4 , determina la suma de dichos números
Answer:
a = 13
b = 52
a + b = 65
Step-by-step explanation:
a*b = 676
b/a = 4
b = 4a
a*4a = 676
4a² = 676
a² = 676/4
a² = 169
a = 13
b = 4a
b = 4(13)
b = 52
a + b
13 + 52
65
The area of a rectangular wall of a barn is 16 square feet. Its length is 4 feet longer than twice its width. Find the length and width of the wall of the barn.
Answer:
width = 2 ft
length = 8 ft
Step-by-step explanation:
area = L x W
area = 16 ft^2
width = x
length = 2x+4
width = 2 ft
length = 2(2)+4
length = 4+4
length = 8 ft
area = 8 x 2 = 16 ft^2
William started a game with twice as many poker chips as Victoria. William gave 20 of his chips to Victoria, and he still had 10 more chips than her. How many chips did William start with?
William started with 60 poker chips.
William started with 60 poker chips
Which equation correctly shows the multiplication of the means and extremes in the proportion 7.2∕9.6 = 21.6∕28.8?
Answer:
7.2 × 28.8 = 9. 6 × 21.6
Step-by-step explanation:
Given the equation:
7.2∕9.6 = 21.6∕28.8
The equation which provides the multiplication of the means and the extremes in the equation provided above can be obtained through cross multiplication of the two ratios or proportion.
(7.2 / 9.6) = (21.6 / 28.8)
L. H. S = R. H. S
(numerator of L. H. S * denominator of R. H. S) = (denominator of L. H. S * numerator of R. H. S)
Hence, we have ;
7.2 × 28.8 = 9. 6 × 21.6
Using the translation (x,y) --> (x+1,y-3), what is the image of A (-1,7)
Answer:
A'(0,4)
Step-by-step explanation:
You would just add 1 to the x and subtract 3 form the y and you would get A prime or A'(0,4) so that would be your answer
A(-1,7)--> (-1+1,7-3)
(0,4)
Sarah and John are running clockwise around a circular track with radius 25 meters. They start at the same position, and Sarah runs at 2.7 m/s while John runs at 2.2 m/s. How far away from their starting point are they when Sarah catches up and passes John for the first time after the start?
Answer:
62.8 m
Step-by-step explanation:
The length of one lap is ...
C = 2πr = 2π(25 m) = 50π m ≈ 157.08 m
Sarah is gaining ground on John at the rate of 2.7 m/s -2.2 m/s = 0.5 m/s. So it will take Sarah ...
157.08 m/(0.5 m/s) = 314.16 s
to run 1 lap farther than John does.
It takes Sarah ...
157.08 m/(2.7 m/s) = 58.18 s
to run 1 lap, so in the time it takes her to catch John, she will have run ...
314.16 s/(58.18 s/lap) = 5.4 laps
She (and John) will be 0.4 laps from their start when they meet again. That distance is ...
(0.4)(157.08 m) = 62.8 m
Sarah will catch and pass John 62.8 meters from their starting position.
Will mark brainliest, 60 points
Answer:
[tex] \boxed{ \bold{ \sf{ \: 1. \: \: \: \: \: 198}}}[/tex]
[tex] \boxed{ \bold{ \sf{2. \: \: \: \: \: - 8}}}[/tex]
[tex] \boxed{ \bold{ \sf{ 3. \: \: \: \: \: \frac{64}{343} }}}[/tex]
Step-by-step explanation:
1. Given, u = 20 , x = 4 , y = 7 , z = 10
[tex] \sf{ \frac{u}{z} + x {y}^{2} }[/tex]
⇒[tex] \sf{ \frac{20}{10} + 4 \times {7}^{2} }[/tex]
⇒[tex] \sf{ \frac{20}{10} + 4 \times 49}[/tex]
⇒[tex] \sf{ \frac{20}{10} + 196}[/tex]
⇒[tex] \sf{ \frac{20 + 196 \times 10}{10} }[/tex]
⇒[tex] \sf{ \frac{20 + 1960}{10} }[/tex]
⇒[tex] \sf{ \frac{1980}{10} }[/tex]
⇒[tex] \sf{198}[/tex]
2. [tex] \sf{4( - 2)}[/tex]
Multiplying or dividing a positive integer by any negative integer gives a negative integer
= - 8
3. [tex] \sf{( \frac{4}{7} ) ^{3} }[/tex]
⇒[tex] \sf{( \frac{ {4}^{3} }{ {7}^{3} } })[/tex]
⇒[tex] \sf{ \frac{4 \times 4 \times 4 }{7 \times 7 \times 7}} [/tex]
⇒[tex] \sf{ \frac{64}{343} }[/tex]
Hope I helped!
Best regards! :D
Answer:
[tex]\Huge \boxed{\mathrm{18. \ \ \ 198}} \\\\\\ \Huge \boxed{\mathrm{19. \ \ \ -8}} \\\\\\ \Huge \boxed{\mathrm{20. \ \ \ \frac{64}{343} }}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
18.[tex]\displaystyle \frac{u}{z} +xy^2[/tex]
u = 20, x = 4, y = 7, and z = 10.
[tex]\Rightarrow \displaystyle \frac{20}{10} +(4)(7)^2[/tex]
[tex]\Rightarrow \displaystyle 2+(4)(49)[/tex]
[tex]\Rightarrow 2+196[/tex]
[tex]\Rightarrow 198[/tex]
19.[tex]4(-2)[/tex]
Rewriting.
[tex]\Rightarrow -(4*2)[/tex]
Multiplying.
[tex]\Rightarrow -8[/tex]
20.[tex]\displaystyle ( \frac{4}{7} )^3[/tex]
Distributing the cube sign to the numerator and the denominator.
[tex]\Rightarrow \displaystyle \frac{4^3 }{7^3 }[/tex]
[tex]\Rightarrow \displaystyle \frac{64}{343}[/tex]
[tex]\rule[225]{225}{2}[/tex]
according to Cavaliers principal, a right cylinder and a right rectangular prism can never have the same volume because they have different shapes.
a. True
b. False
==================================================
Explanation:
If you have the two 3D solids with cross sections of equal area, and they are of the same height, then it can be proven the two volumes are the same. So it is possible for a cylinder and triangular prism to have the same volume.
An example would be that imagine you had a stack of pennies to form a large cylinder. The volume is found by computing the area of one penny's face (aka area of a circle) multiplied by the height of the stack.
Now imagine moving the stack to form a strange curve of any sort you want. The pillar has a bend in it now. It's no longer a perfect cylinder, but we still have the same volume since we haven't destroyed any of the pennies.
All we've done is move things around. The small pieces all have the same volume, so the total volume is still the same as well. So this is one application of Cavalieri's principle.
Can you help me with this I’ll give you a brain list
Answer:
the answer is c or the third line
Step-by-step explanation:
lets see all choices by solving them
The first line 5+2-(-8) Now we should follow the bodmas rule 5 + 2 + 8 because - ( - ) become +so the answer is 13 means not negative
2. The second line 5-8-(-6)
Also now we should follow the bodmas rule
5 - 8 + 6 because - ( - ) become +- 3 + 6
3 the answer is 3 so it means not negative
3. The third line 6+6-17
Now it is simple we solve it
6 + 6 - 1712 - 17
-5 the answer is -5 means negative
4. The fourth line 6-4-(-8)
Again we need bodmas rule
6 - 4 + 8 because - ( - ) become +-2 + 8
6 the answer is 6 means not negative
I hope u like it
Simplify 3•2x. What is the coefficient?
2
3
6
X
Answer:
6x
Step-by-step explanation:
coefficient is 6
If a barrel has the capacity to hold 75 gallons how many gallons does it contain when it is 3/5 full
Answer:
45 gallons
Step-by-step explanation:
Take the total number of gallons and multiply by the fraction it is holding
75 *3/5
75/5 *3
15*3
45
Answer: 45 gallons
Step-by-step explanation: Using proportions, I did ?/75 = 3/5. I cross multiplied so 75 x 3 = 225 divided by 5 = 45.
a rescue company determined that 90 out of 100 calls they received were true emergencies. which describes the fraction of their calls that were true emergencies.
Step-by-step explanation:
It is given that,
A rescue company determined that 90 out of 100 calls rescue company determined that 90 out of 100 calls. We need to find the fraction of their calls that were true emergencies.
Fractions can be written as true value on the denominator and the part of it on the numerator.
The required value is : [tex]\dfrac{90}{100}=\dfrac{9}{10}[/tex]
So, (9/10) describes the fraction of their calls that were true emergencies.
Help! Please! You can just give answers if want to make It faster.
Answer:
X' = (-3 , -5)
Y' = (-1, -1)
Z' = (4, -8)
General rule: (x,y) = (y, -x)
I am 1 brainly away from the next rank, your help would be appreciated
Simplify each expression using the order of operations. Then, match the expression (term) on the left with its solution (definition) on the right. (4 points) Group of answer choices 42 + 3 − 2(3) [ Choose ] 22 ⋅ 8 ÷ 2 + 2 [ Choose ] (42 + 16) + 12 [ Choose ] 8 ⋅ 32 + 3 [ Choose ]
Answer:
39, 90, 70, 259
Step-by-step explanation:
1 ).................................................
42 + 3 − 2(3) = 42 + 3 - 6 = 45 - 6 = 392) .................................................
22 ⋅ 8 ÷ 2 + 2 = 176 ÷ 2 + 2 = 88 + 2 = 903) .................................................
(42 + 16) + 12 = 58 + 12 = 704) .................................................
8 ⋅ 32 + 3 = 256 + 3 = 259if a bag of balloons consists of 47 white balloons, 5 yellow balloons, and 10 black balloons, what is the probability that a balloon chosen randonly from the bag will be black?
Answer:
10/62, 5/31, or 16.129%
Step-by-step explanation:
First you have to add all of the balloon colors together to get the entire sample size.
47 + 5 + 10 = 62
Next, you need to know the how many of the balloon colors you what the probabilty for that are in the sample size.
10 black balloons.
Finally, you divide the number of black balloons by total balloons to find the probability of randomly choosing one.
10/62 = 5/31 or 16.129%
I hope this helps!
-TheBusinessMan
write a sentence as an equation
the product of t and 15 , minus 94 is the same as 103
Answer:
15t-94=103
Step-by-step explanation:
hav a nice day
Answer:
You already wrote the sentence, so im guessing that you want the equation...
(15)(t) - 94 = 103
Set up the equation for the area of a triangle in
you graphing calculator. Define the variables and
use the sliders to find the areas of the triangles
below.
Answer:
The person above me is right, and the answer for the second part is "somewhat similar".
Step-by-step explanation:
Edge 2021.
Ellie takes her dog, Jack, for a 3 mile walk each day. On the first part of the walk, they go 2 mph. Then for the second part of their walk, they go 3 mph but for half the time that they went 2 mph. How long was their walk in hours?
Answer:
the entire walk is 9/7 hours i think
Please help, I don't understand
Answer:
C. √37-√26 = 0.98
Step-by-step explanation:
[tex]\sqrt{37}-\sqrt{26}\\\mathrm{Refine\:to\:a\:decimal\:form}\\= 0.98374\dots[/tex]
Which of the following is NOT a formula for determining complementary probability?
Question:
Which of the following is NOT a formula for determining complementary probability?
A. P(outcome) = 1- P(-outcome)
B. P(outcome) - P(-outcome) = 1
C. P(outcome) + P(-outcome) =1
D. P(-outcome) = 1 - P(outcome)
Answer:
[tex]P(outcome) - P(-outcome) = 1[/tex]
Step-by-step explanation:
Required
Determine which option is not a formula of complementary probabilities
From the list of given options, the complementary probabilities are P(outcome) and P(-outcome)
In probability;
[tex]P(outcome) + P(-outcome) = 1[/tex] --- Equation 1
Subtract P(outcome) from both sides
[tex]P(outcome) - P(outcome) + P(outcome) = 1 - P(outcome)[/tex]
[tex]P(-outcome) = 1 - P(outcome)[/tex] ------ Equation 2
Subtract P(-outcome) from both sides of equation 1
[tex]P(outcome) + P(-outcome) - P(-outcome) = 1 - P(-outcome)[/tex]
[tex]P(outcome) = 1 - P(-outcome)[/tex]
Equation 1, 2 and 3 represents options A, C and D
While option B is out of place
Hence, option B is not a formula of complementary probability
Michael paid $16.40 for 20.5 centimeters of wire. Find the unit price in dollars per centimeter. If necessary round your answer to the nearest cent.
Answer:
$0.80
Step-by-step explanation:
$16.40 ÷ 20.5 = 0.80
You can check your work by doing :
20.5 cm of wire × $0.80 = $16.40
The unit price of the wire which Michael bought 20.5 cm for $16.40 is $0.8.
What is The Unit price?The price of a product offered in more or fewer than one unit is referred to as the unit price. The "unit pricing" of a food package informs you of the price per pound, quart, or another unit of weight or volume. Normally, it is displayed underneath the food on the shelf. The item price (total price) and unit price (unit price) for the food item are both displayed on the shelf tag. When shoppers are taught how to use unit price information in supermarkets, research reveals that they can save about 17–18%, but over time, this number decreases.
Given:
The price for the length of 20.5-centimeter wire, a = $16.40,
Calculate the price of 1 cm wire by dividing the total price by the length of the wire,
So unit price = 16.40 ÷ 20.5
Unit price = $0.8
Therefore, the unit price of the wire is $0.8.
To know more about unit price:
https://brainly.com/question/10503561
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Convert the decimal below to a fraction in simplest form.
0.131
Answer:
Submit Answer
Answer:
131/100 is the fraction in the simplest form
Answer:
131/1000
Step-by-step explanation:
This is the simplest form as a fraction
For any set B, the null set, ∅, is a proper subset of B TRUE OR FALSE
Answer:
t
Step-by-step explanation:
A store sells paint sets. Each paint set costs the same amount. During a sale, the store reduces the price of each paint set by $1.50. Logan spends
$13.47 on 3 paint sets at the sale price.
What was the price of I paint set before the sale?
Answer:
the price of I paint set before the sale was $5.99
Step-by-step explanation:
Selling price of 3 paint sets = $13.47
To get selling price of 1 set
we divide both LHS and RHS by 3
Selling price of 3/3 = 1 paint sets = $13.47/3 = $4.49
Thus, selling price of 1 paint set after sale is $4.49
Given that
the store reduces the price of each paint set by $1.50
Let the price before sale be x
selling price of 1 paint set after sale = price before sale - $1.50
$4.49 = $x - $.150
$x = $4.49 + $1.50 = $5.99
Thus, the price of I paint set before the sale was $5.99
[tex](3+\sqrt{7})(3-\sqrt{7})[/tex]
Answer:
The answer should be 2 but it won't let me post it with less than twenty characters so yeah
find the variable 5x+8=3x
Answer:
-4 =x
Step-by-step explanation:
5x+8=3x
Subtract 5x from each side
5x-5x+8=3x-5x
8 = -2x
Divide by -2
8/-2 = -2x/-2
-4 =x
find the perimeter and area of each figure below.
Two cyclists, 40 miles apart, start riding toward each other at the same time. One cycles 3 times as fast
as the other. If they meet 2
hours later, what is the speed (in mi/h) of the faster cyclist?
Answer:
15 mph
Step-by-step explanation:
The cyclists will cover distance at a rate proportional to their speed. So, the distance ratio is ...
faster cyclist distance : slower cyclist distance = 3 : 1
Then the faster cyclist covers 3 : (3+1) = 3/4 of the total distance, or (3/4)(40 mi) = 30 mi.
That distance took 2 hours for the faster cyclist, so the speed was ...
speed = distance/time = 30 mi/(2 h) = 15 mi/h