Answer:
[tex]\theta = \pm \pi \cdot i[/tex], [tex]\forall i \in \{0,2,4,...\}[/tex]
Step-by-step explanation:
The determination of the maximum can be done with the help of the First and Second Derivative Tests. The first and second derivatives of the function are, respectively:
[tex]r' = -4\cdot \sin \theta[/tex]
[tex]r'' = -4\cdot \cos \theta[/tex]
First Derivative Test
[tex]-4\cdot \sin \theta = 0[/tex]
[tex]\sin \theta = 0[/tex]
Given the periodicity of the function, there are multiple solutions. The set of solutions is represented by:
[tex]\theta = \pm \pi \cdot i[/tex], [tex]\forall i \in \mathbb{N}_{O}[/tex]
Second Derivative Test
There are multiple solutions. If [tex]i[/tex] is an odd number, then cosine is negative and output is positive, which means that associated value is an absolute minimum. Otherwise, if [tex]i[/tex] is zero or an even number, the cosine is positive and output is negative, which means that associated value is an absolute minimum. Consequently, the values of [tex]\theta[/tex] so that [tex]r[/tex] is a maximum are:
[tex]\theta = \pm \pi \cdot i[/tex], [tex]\forall i \in \{0,2,4,...\}[/tex]
A teacup has a radius of 5 centimeters. What is the teacup's diameter? Help please.
Answer:10
Step-by-step explanation:
Radius is half the diameter
Answer:
10 cm
Step-by-step explanation:
the radius is half the diameter so 5x2=10cm
HELP PLEASE
write down a formula for the nth term of these patterns. The first term is n = 1.
14 ,23 ,32 ,41, 50 = nth term = ?????????
-4, -11, -18, -25, -32 = nth term = ???????????
Answer:
1st one= n9+5
2nd one=n×-7+3
WHAT IS 666x666 help me
Answer:
666 x 666 = 443,556
Answer:
443556
Step-by-step explanation:
666 * 666 = 443556
666
x666
-------
443556
Denzel wants to walk to the store from his house but he is not sure how far away it is. Find the distance between his house
(-8, -9) and the store (-4, -10). Each unit is equal to one mile. Round your answer to the nearest mile.
22 miles
4 miles
31 miles
17 miles
Answer:
4 miles
Step-by-step explanation:
Suppose we have two points:
[tex]A = (x_{1}, y_{1})[/tex]
[tex]B = (x_{2}, y_{2})[/tex]
The distance between these points is:
[tex]D = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}[/tex]
In this question:
Points (-8, -9) and (-4, -10).
So the distance is:
[tex]D = \sqrt{(-8 - (-4))^{2} + (-9 - (-10))^{2}} = \sqrt{17} = 4.12[/tex]
The distance is 4.12 miles.
Rounding to the nearest mile, 4 miles.
PICK ME!!
How do you use congruence and similarity criteria to prove relationships in geometric figures?
Answer:
Well, as it turns out, when two figures are similar or congruent, they have certain properties, and these properties can be used to prove relationships between the figures. When two figures are similar figures, they have the following properties: Corresponding angles have equal measure.
Step-by-step explanation:
what is the slope of the equation 3y=9x-6?
Answer:
It's 3
Step-by-step explanation:
Just divide the entire equation by 3 to isolate the y variable on the left side.
y = mx + b (m is the slope)
and in this equation, after you divide by 3, the value of m is 3.
Charlotte have 36 apple,Dylan have 1 apple and Kevin have 56 apple how many apples are left?
Answer:
93 apples?
Step-by-step explanation:
36 + 1 + 56 = 93 apples?
Find the slope: (-1,5) and (2,-3)
Answer:
-2/3
Step-by-step explanation:
Answer:
(-3-5)/(2-(-1))=-8/3
Step-by-step explanation:
How do I solve this problem? I need to find the volume of this composite figure.
Step-by-step explanation:
V = (12*4*5) + (2*3*5) + (5*3*5) + (12*4*5)
V = 240 + 30 + 75 + 240
V = 585 cm^3
What is the value of the 6 In the number 48.061
Answer:
.06 or six hundredths
Step-by-step explanation:
Answer:
Hundredth place
At a camp, kids can choose swimming, art, or music.
40 kids choose swimming, 16 choose art, and 24 choose music.
What is the ratio of kids who choose art to kids who choose swimming?
Answer:
3:5
Step-by-step explanation:
all figures can be divided by 8, so
swimming- 40/8= 5
arts 16/8= 2
music 24/8= 3
therefore, the ratio would be 3:5
Answer:
3/5
Step-by-step explanation:
I took it but got it wrong so i did the math problem and got this 3/5
A spinner with seven equal sized sections was used to play a game It was used 250 times in the first game Of those 250 the arrow landed on section 7 a total of 35 times The same spinner was used 150 times in the second game How many times did the spinner most likely land on section 7 in the second game A. 14 B. 21 C. 30 D. 35
Answer: 21
Step-by-step explanation:
From the question, a spinner with seven equal sized sections was used in playing a game. The spinner was used 250 times in the first game and the arrow landed on section 7 a total of 35 times. This can be expressed as:
= 35/250
= 0.14
The same spinner was also used 150 times in the second game. The number of times the spinner will most likely land on section 7 in the second game will be:
= 0.14 × 150
= 21
The spinner most likely land on section 7 in the second game for 21 times.
5 x 10 to the 6th power is how many times larger than 5 x 10 to the 4th power. PLEASE RESPOND FAST
Answer:
5 x 10 to the 6th power is 5,000,000
5 x 10 to the 4th power is 50,000
5,000,000 / 50,000 = 100
it is 100 times larger
Step-by-step explanation:
eric bought 4 pairs of sports socks for $9. How many pairs of socks can he buy for $13.50.
Answer:
the answer is 6 pair of socks
Step-by-step explanation:
because one pair of socks is 2.25
so 6×2.25 is 13.50
Please help ASAP! I will mark Brainliest! Please READ the question THEN answer CORRECTLY! No guessing!
Answer:
B. The graph contains [tex](1,\frac{1}{10})[/tex].
Step-by-step explanation:
I graphed the equation on the graph below The line goes through the point (1, 1/10).
A lodge rents snowboards for $40/day plus a $20 flat fee for safety gear. Write an equation to represent the relationship between the total cost, c, and number of days renting a snowboard, d.
Answer:
(40+20)^d=c
Step-by-step explanation:
Answer:= let me double check yall
Step-by-step explanation:40+20+c+d
The equation d = 2t + 8 gives d, the total depth in inches of accumulated snow based on t, the time in hours since a storm began. Using this equation, how much snow can be expected to fall with each additional hour?
Answer:
It is expected to fall 2 inches of snow for each additional hour.
Step-by-step explanation:
As we want to find the amount of snow that will fall for each additional hour, we just need to use slope of the equation.
The slope is the value '2' that is together with the variable 't', and it means that if we increase the value of t by 1 unit, the value of d will increase by 2 units.
So we have that for each additional hour, it is expected to fall 2 inches of snow.
What is the result of substituting for y in the bottom equation?
y = x + 3
y = x2 + 2x - 4
Answer:
The correct option is (B).
Step-by-step explanation:
We need to find the result of substituting for y in the bottom equation.
Equation (1) is : [tex]y=x+3[/tex]
Equation (2) is : [tex]y=x^2+2x-4[/tex]
Put the value of y form equation (1) to equation (2) such that,
[tex]x+3=x^2+2x-4[/tex]
It can be seen from the above equation, that option (2) is same as above equation.
Hence, the correct option is (B).
I NEED HELP NOWwwwwwww
Answer:
523 cm^3
Step-by-step explanation:
The volume of a sphere is
V = 4/3 pi r^3
V = 4/3 (3.14) (5)^3
V = 523.33333
Rounding to the nearest whole number
V = 523
Evaluate the following, expressing your result as a simplified fraction:
3
-0.4+
4
Answer:
6.6
Step-by-step explanation:
If the problem is 3-0.4+4, I subtracted 0.4 from 3 which I got 2.6 then added the 4 giving me the answer
Answer:
Step-by-step explanation:
The perimeter of quadrilateral ABCD is 640. The perimeter of quadrilateral LMNO is 144. What is LM
Answer:
LM = 36
Step-by-step explanation:
A quadrilateral is a shape with 4sides. There are different type of quadrilateral such as square, rectangle, trapezium, parallelogram, kite and rhombus.
Perimeter of a quadrilateral is the addition of all 4 sides.
Since the shape is not specified neither is there a diagram, let's assume the quadrilateral is a square.
See attachment for diagram used in solving the question.
Perimeter of square = length+ length+ length+ length
= 4× length
Perimeter of quadrilateral ABCD:
640 = 4×length
Length = 640/4
Length = 160
Perimeter of quadrilateral LMNO:
144 = addition of all 4 lengths
144 = LM + MN + NO +OL
Since we are considering a square all the sides are equal.
LM = MN = NO = OL
144 = 4×LM
LM = 144/4
LM = 36
Can the distributive property be used to rewrite
6 x (8 - 4) ?
Yes
No
If yes, fill in the blanks below.
6 x
8 -
(OⓇD) - (x)
Answer:
I think No
Step-by-step explanation:
The carrying capacity of a biological species in an environment is the maximum population size of the species that the environment can sustain indefinitely, given the food, habitat, water, and other necessities available in the environment. Why is a population that overshoots the carrying capacity can only do so for a limited amount of time?
Answer:
A population that overshoots the carrying capacity can only do so for a limited amount of time because: since the ecosystem already has the maximum number it can take for a given specie, overshooting the ecosystem will not last long as:
1. Competitions for the limited available space and resources will result to increase death rate and emigration from the environment.
2. Birth rate would be controlled as the rate resources are used is greater than they are replenished. This limits productivity among species.
Step-by-step explanation:
The carrying capacity of an environment, in simple terms is the amount of a given specie that the environment can sustain without depleting or degrading the available resources. Population size of an environment increases if birth rate increases and death rate decreases, and if the environment also experience an increase in species coming to live there than they are leaving the environment. In other words, when resources are limited it affects the population size of an environment.
ABC is a straight angle.which equation can be used to find the measure of the unknown angle?
Answer:
Straight angles are all 180 degrees, so it must be an equation that equals 180. I hope that this helps! be saffffeee!
Answer:
140 x 180
Step-by-step explanation:
I don’t know how to do this
Answer:
See attachment
Step-by-step explanation:
80 POINTS! Help with this question please!!!! 80 POINTS!
Answer:
C. Translation 5 units left and 2 units down
Step-by-step explanation:
Let's take a look at A', which is (0, 0). This is the result of A, which is (5, 2) being transformed somehow. Notice that the x-coordinate moved 5 units to the left (from 5 to 0, which means we subtract 5 from 5). And, notice that the y-coordinate moved 2 units down (from 2 to 0, so we subtract 2 from 2).
Look to see if this works for the other two points:
B(6, 1): if we subtract 5 from the x-coordinate 6, we get 6 - 5 = 1, which matches the x-coordinate of the image B'. If we subtract 2 from the y-coordinate of B, which is 1, we get 1 - 2 = -1, which also matches the y-coordinate of B'. So, this works.
C(4, 5): if we subtract 5 from the x-coordinate 4, we get 4 - 5 = -1, which matches the x-coordinate of the image C'. If we subtract 2 from the y-coordinate of C, which is 5, we get 5 - 2 = 3, which also matches the y-coordinate of C'. So, this again works.
Therefore, we know that the transformation is a translation 5 units left and 2 units down, or C.
A picture will be shown below of a graph with the points in the table.
We only need to use (5, 2) and (0, 0) to solve this problem.
We take both points and see what it took for the old point to get to where the new point is (Shown in picture below).
Therefore, the answer is [ C. Translation 5 units left and 2 units down ]
Best of Luck!
The owner of a coffee shop compared the amount of hot coffee per day, in fluid ounces, sold and the daily high temperature, in degrees Fahrenheit, per day. Her data are shown in the scatter plot below. If these data are modeled by the line y = -5.9x + 850, which statement best describes a valid prediction the owner could make?
Picture of the question is attached below.
Answer: B.) For each temperature decrease of 10°F, the shop can expect to sell about 6 fluid ounces more of hot coffee.
Step-by-step explanation:
The model depicted by the line equation:
y = -5.9x + 850 shows a strong negative linear relationship between the amount of hot coffee per day, in fluid ounces, sold and the daily high temperature, in degrees Fahrenheit, per day. This means that the sale of hit coffee decreases with increasing temperature daily, which makes sense. From the plot and line model equation, the shop can expect to sell about 6 fluid ounces less of hot coffee for each temperature ruse of 10F.
-5.9x approximately -6x decrease for every 10F temperature increase.
Picture down below:)
Answer:
the answer is
Step-by-step explanation:
c
Answer:
C
Step-by-step explanation:
help me please i am confused on what to do
Ellen mixed \dfrac1{4}\text{ kg} 4 1 kgstart fraction, 1, divided by, 4, end fraction, start text, space, k, g, end text of flour with \dfrac{2}{9}\text{ kg} 9 2 kgstart fraction, 2, divided by, 9, end fraction, start text, space, k, g, end text of sugar.
Question:
Ellen mixed ¼ kg of flour with ²/9 kg of sugar.
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete. However, question that are likely to be asked are.
- What's the weight of the total mixture in grams
- What percentage of the mixture is sugar
To solve (1);
We simply add both weights together
But first, the units must be converted to grams.
1kg = 1000 grams
So,
¼kg = ¼ * 1000 g
¼kg = 250 g
²/9kg = ²/9 * 1000
²/9kg = 2000/9
²/9kg = 222.2 g
Add these results
Total = 250g + 222.2g
Total = 472 g
The result can be written in different ways
1. 472 grams
2. About 500 grams
If converted back to kg
472 grams = 472/1000 kg
472 grams = 0.472 kg.
So, the result can also be written as
3. 0.472 kg
4. About 0.5kg (½kg)
To solve (2)
What percentage of the mixture is sugar
To do this, we simply divide the size of sugar by the total size of the mixture.
From (1) above
Sugar = 250g
Total = 472g
Percentage of sugar = 250/472
Percentage of sugar = 0.5297
Percentage of sugar = 0.5297 * 100%
Percentage of sugar = 52.97%
Answer:
1/2
Step-by-step explanation:
I did it and it was write right hope it helps
