The sample that has a greater mass is given as follows:
The sample of rock.
The sample of rock has a mass that is 5000 times the mass of the sample of dry sponge.
What is scientific notation?A number in scientific notation is given by the notation presented as follows:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1, justifying the open interval at 10.
To obtain which amount is greater, we must verify the bases when the exponent is the same, hence:
Rock: 1 x 10¹ kg = 10 kg.Sponge: 2 x 10^-3 kg = 0.2 x 10^-2 kg = 0.02 x 10^-1 kg = 0.002 kg.Hence the rock has the greater mass, and the ratio is given as follows:
10/0.002 = 5000.
More can be learned about scientific notation at https://brainly.com/question/5756316
#SPJ1
Jacob is planting flowers for his grandmother. This morning, he spent an hour planting annuals and an hour planting perennials, but he planted more annuals than perennials. This afternoon, he has the same number of annuals and perennials left to plant. Which will likely take him more time to plant?
It is likely that it will take Jacob more time to plant the perennials than the annuals.
What is time?Time is an abstract concept that is not tangible and cannot be seen, touched, or heard. It is a measure of the passage of events and is used to set and track schedules, create goals, and even measure the lifespan of an individual. Time is a precious commodity that cannot be replaced or taken back. Once it has passed, it is gone forever. Time is also a powerful force that can bring us joy and sorrow, success and failure. It is a constant reminder of how quickly our lives can change and how important it is to make the most of every moment.
Perennials require more attention when planting because they have a longer lifespan and are meant to come back year after year. Annuals, on the other hand, only last for one season. Therefore, they require less attention when planting. Jacob will need to make sure that he carefully places the perennials in the soil, as well as taking care to not damage the roots. He may also need to take extra time to trim any overgrowth from the plants. This extra care and attention will likely take more time than it would to plant the annuals.
To know more about time click-
https://brainly.com/question/1933707
#SPJ1
Bob's gift shop sold a record number of cards for Mother's Day. One salesman sold 44 cards, which was 10% of the cards sold for Mother's Day. How many cards were sold for Mother's Day?
Using the equation 0.1x = 44, the total number of cards sold for Mother's Day was 440.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
Let's call the total number of cards sold for Mother's Day "x".
We know that one salesman sold 10% of these cards. or
Converting the percentage to decimal = 10 / 100 = 0.1
So, 0.1x, is equal to 44 cards.
We can set up an equation to solve for x -
0.1x = 44
To isolate x, we can divide both sides of the equation by 0.1 -
x = 440
Therefore, the total number of cards sold for Mother's Day was 440.
To learn more about equation from the given link
https://brainly.com/question/28871326
#SPJ1
HELP ASAP!!!!!!!!!!!!!
What are all the zeros of the polynomial function
[tex]f(x)=3x^{3} -5x^{2} -10x-6[/tex]
The zeros of the polynomial function f(x) are 3, -[(2 -i√2) / 3] and -[(2 + i√2) / 3]
What is the zero of the functionTo find the zeros of the polynomial function f(x), we need to find the values of x for which f(x) = 0.
We can start by factoring out a common factor of 3x^2 from the polynomial:
f(x) = 3x^3 - 5x^2 - 10x - 6
f(x) = 3x^2(x - 5/3) - 2(5x + 3)
Now, we can set each factor equal to zero and solve for x:
3x^2(x - 5/3) - 2(5x + 3) = 0
3x^3 - 5x^2 - 10x - 6 = 0
x = 3, -[(2 -i√2) / 3], -[(2 + i√2) / 3]
Learn more on zeros of function here;
https://brainly.com/question/20901045
https://brainly.com/question/2833285
#SPJ1
Let f(x)=4x+7 and g(x)=3x-2 find (f.g)(-6)
There are `11` dancers in a performance. Their ages (in years) are: `5.5`, `6`, `6`, `6.5`, `7`, `7.5`, `8`, `8`, `8.5`, `9`, `9` 1. Determine the first quartile, median, and third quartile of the dancers' ages. 2. Drag the movable points to label them on the box plot.
The first quartile is 6, the median is 7.5 and the third quartile is 8.5. The box plot has been attached below.
What is a median?
A data set can be described more accurately than its average by using the median, which is the midpoint of an ordered, ascending or descending list of integers.
The data is given as 5.5, 6, 6, 6.5, 7, 7.5, 8, 8, 8.5, 9, 9.
From this, we get the first quartile to be 6.
The median is 7.5 and the third quartile is 8.5.
The box plot of the data has been plotted and attached below.
Hence, the required solution has been obtained.
Learn more about median from the given link
brainly.com/question/16408033
#SPJ1
Question: There are 11 dancers in a performance. Their ages (in years) are: 5.5, 6, 6, 6.5, 7, 7.5, 8, 8, 8.5, 9, 9.
1. Determine the first quartile, median, and third quartile of the dancers' ages.
2. Drag the movable points to label them on the box plot.
A mathematician is analyzing an email message. Out of the first 100 characters, the letter e appears 13 times. The email message is 1,100 characters in length. Based on the information, how many of the characters should be a letter e?
The mathematician should expect to see the letter e appear 143 times in the 1,100 character email message.
What is proportion?It is a ratio of the count of the specific outcome or event to the total number of observations in the sample or population. Proportion is often expressed as a percentage or fraction and can be used to make inferences about the population based on the sample.
According to question:If the letter e appears 13 times out of the first 100 characters, we can assume that the proportion of e's to the total characters is constant throughout the entire message.
Let x be the number of times the letter e appears in the 1,100 character message. Then, we can set up a proportion:
13/100 = x/1100
Solving for x, we get:
x = (13/100) * 1100 = 143
Therefore, the mathematician should expect to see the letter e appear 143 times in the 1,100 character email message.
To know more about proportion visit:
https://brainly.com/question/29765554
#SPJ1
why is the trapezoid doubled and flipped to create a parallelogram
Answer:
Step-by-step explanation:
The Weinis Loves cookies
The height of the parallelogram is the same as the height of the trapezoid
Why?
Doubling the trapezoid and then halving the resulting area
As was true with the triangle, but its base is the sum of the two bases of the trapezoid.
1800 is invested at 4% compound intreast per year
It will take approximately 2.5 years for the investment to be worth £2000.
How to find amount increase in desired year?To solve this problem, we can use the formula for compound interest:
[tex]$A = P(1 + r/n)^{nt}$[/tex]
where:
A is the amount of money after t years
P is the principal amount (the initial investment)
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the number of years
We can rearrange this formula to solve for t;
[tex]$t = \frac{\log(A/P)}{\log(1 + r/n)}\div n$[/tex]
Substituting the given values, we get;
[tex]$t = \frac{\log(2000/1800)}{\log(1 + 0.04/1)}\div 1$[/tex]
Simplifying, we get:
[tex]$t = \frac{\log(1.11111)}{\log(1.04)}\approx 3.03[/tex][tex]$t = \frac{\log(1.11111)}{\log(1.04)}\approx 2.69[/tex] years
Therefore, it will take approximately 2.5 years for the investment to be worth £2000.
To know more about Compound interest visit:
brainly.com/question/25309651
#SPJ9
Complete question:
1800 is invested at 4% compound intreast per year
answer as an integer or as a decimal rounded to the nearest tenth
Answer: x=120
Step-by-step explanation:
If it is a regular polygon then the sum of internal angles is 180 degrees. Each angle should be 60. Since a straight line is 180, 180 - 60 would equal x!
Answer: 120
Step-by-step explanation: A triangle has a sum of 180°. A regular polygon has equal angles, so you divide 180 by 3, getting 60. Next x is supplementary to the adjacent angle, so you must do 180-60, yielding 120° as x.
Mrs. Hubert gave a test to her chemistry class. 20% of the students failed. Of those students who failed, 10% are going to do retake. If she teaches 150 students, how many will do a retake?
Answer:
3 students will retake the test
Step-by-step explanation:
20% of 150 students is 30
(20÷100)×150=30 students
Now we need to find the 10% of the 30 students who failed.
(10÷100)×30=3 students
we can check this by Subtracting that 20% who failed from 100%(the total in class). So that will be 80%. Now that 80% is the number of students who passed.
And in order to find the number of students who passed we say:
(80÷100)×150= 120
all you need to do now is, subtract that 120 from 150, then find the 10% of the answer.
Question 1-2
The functions j(x) = 2(x + 3)² — 10 and k(x) = 2x² + 12x + c are equivalent.
What is the value of c?
Answer:
c = 18
Step-by-step explanation:
expand the factor in j(x) and compare like terms with k(x)
j(x) = 2(x + 3)² ← expand factor using FOIL
= 2(x² + 6x + 9) ← distribute parenthesis by 2
= 2x² + 12x + 18
compare to k(x) = 2x² + 12x + c
the 2 expressions are equivalent when c = 18
Please answer the question and explain how to do it step by step.
Parker is wrong, as the volume of the cube container is obtained as [tex]\frac{1}{512} t^9u^{12}[/tex].
What is volume?
Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
The volume of a cube is given by the formula V = s³, where s is the length of one side of the cube.
In this case, the length of the container is given as [tex]\frac{1}{8} t^3u^4[/tex].
To find the volume of the cube, we need to cube this length -
[tex]V=\big(\frac{1}{8} t^3u^4\big)^3[/tex]
Simplifying this expression using the rules of exponents, we get -
[tex]V=\big(\frac{1}{8}\big)^3 \times (t^3)^3 \times (u^4)^3[/tex]
[tex]V =\frac{1}{512} t^9u^{12}[/tex]
So, the actual volume of the container is [tex]\frac{1}{512} t^9u^{12}[/tex], not [tex]\frac{1}{12} t^9u^{12}[/tex] as Parker said.
Therefore, Parker is incorrect.
To learn more about volume from the given link
https://brainly.com/question/1972490
#SPJ1
Write an equation in slope-intercept form of the line with the given characteristics
perpendicular to y=-3x+1; passes through (2,2)
Answer:
The equation in slope-intercept form of the line perpendicular to y = -3x + 1 and passing through (2, 2) is y = (1/3)x + 4/3.
Step-by-step explanation:
To find the equation of the line perpendicular to y = -3x + 1 and passing through the point (2, 2), we first need to determine the slope of the line we are looking for.
The slope of any line perpendicular to y = -3x + 1 will be the negative reciprocal of the slope of y = -3x + 1. The slope of y = -3x + 1 is -3, so the slope of the line we want is the negative reciprocal of -3, which is 1/3.
So the slope of the line we want is 1/3. We also know that the line passes through the point (2, 2). We can now use the point-slope form of the equation of a line to find the equation of the line we want:
y - y1 = m(x - x1)
where m is the slope of the line, and (x1, y1) is the point the line passes through.
Substituting m = 1/3, x1 = 2, and y1 = 2, we get:
y - 2 = (1/3)(x - 2)
Multiplying both sides by 3, we get:
3y - 6 = x - 2
Subtracting x from both sides, we get:
-x + 3y = 4
So the equation of the line perpendicular to y = -3x + 1 and passing through the point (2, 2) is -x + 3y = 4, which is in standard form. We can also write it in slope-intercept form:
3y = x + 4
y = (1/3)x + 4/3
So the equation of the line we want in slope-intercept form is y = (1/3)x + 4/3.
Hope this helps you! Sorry if it doesn't. If you need more help, ask me! :]
What is the length of the adjacent side of this right-angled triangle, relative to a) the 71° angle? b) the 19° angle? 1.2 cm 71" 3.7 cm 3.5 cm 19
Answer: a) 19 degree
b) 71degree
Step-by-step explanation:
Please help! A teacher records and graphs the average grade of a student at the end of each week over a 3-month period. If x represents the number of weeks since the teacher began recording the student’s grade, and y represents the student’s grade, which best represents the scales that would be used for the graph?
A. The x-axis could be labeled from 0 to 3 with a scale of 1, and the y-axis could be labeled from 0 to 100 with a scale of 1.
B. The x-axis could be labeled from 0 to 12 with a scale of 1, and the y-axis could be labeled from 0 to 10 with a scale of 1.
C. The x-axis could be labeled from 0 to 12 with a scale of 1, and the y-axis could be labeled from 0 to 100 with a scale of 10.
D. The x-axis could be labeled from 0 to 100 with a scale of 10, and the y-axis could be labeled from 0 to 12 with a scale of 1.
The graph's scales could be represented by the x-axis, which could be labelled from 0 to 12 with a scale of 1, and the y-axis, which could be labelled from 0 to 100 with a scale of 10.
What is the x-axis scale?The horizontal scale used in a graph is called the X axis. Measurements on the coordinate plane are made using it as a reference line. The position of an object on that plane is described by its distance from the x and y axes.
What is the data's X and Y axis scale?All potential data that can be graphed is represented by the numbers on the X and Y axes. Each number here is different by ten. Scale is the name for this. On a coordinate grid, scale is the distance between each square.
To know more about graph's scales visit:-
https://brainly.com/question/30874892
#SPJ1
true or false: when dealing with fixed effects, a de-meaned model approach is superior to the lsdv approach because the de-meaned model gives us more accurate coefficient estimates.
The statement that "when dealing with fixed effects, a de-meaned model approach is superior to the lsdv approach because the de-meaned model gives us more accurate coefficient estimates" is true.
Fixed effects are a type of regression technique used to understand the effect of a single variable across different groups (such as across countries, across states, across individuals, etc.) by comparing the variance of the variable within each group to the variance of the variable across all groups.
When conducting a fixed effects regression, researchers must choose between the least squares dummy variable (LSDV) and de-meaned model approaches.Both models produce unbiased estimates of the coefficients, but the LSDV model has an advantage in that it provides more flexibility when dealing with interactions between fixed effects and time-varying covariates. On the other hand, the de-meaned model is preferred for reasons of computational efficiency and it can handle certain types of data that the LSDV model cannot (such as panel data with a small number of time periods).
for such more question on Fixed effects
https://brainly.com/question/29563847
#SPJ11
which of the following is a characteristic of an experiment where the binomial probability distribution is applicable? group of answer choices the trials are dependent on each other the experiment has at least two possible outcomes the probabilities of the outcomes changes from one trial exactly two outcomes are possible on each trial
The characteristic of an experiment where the binomial probability distribution is applicable is that exactly two outcomes are possible on each trial.
What is the binomial probability distribution?
The binomial probability distribution is a probability model that is used to evaluate the probability of having an exact number of successes in a particular number of independent trials that have two possible outcomes (success and failure).
The characteristics of an experiment where the binomial probability distribution is applicable are as follows: It is an experiment that comprises a set of trials with a fixed number of independent trials.
It has only two outcomes, namely success and failure. The trials are independent of each other.
The probability of success is constant for each trial of the experiment.
The binomial distribution has a discrete set of outcomes. Each of these outcomes is measured by a single random variable that takes on only one of two possible values. Exactly two outcomes are possible on each trial. The experiment is a random variable that can be counted by counting the number of successes (X) in n trials.
To know more about binomial probability distribution: https://brainly.com/question/29163389
#SPJ11
Help on a homework assignment
1. Definition of Congruence:∠ RSU ≅ ∠ VST
2. Definition of Congruence: m∠ RSU = m∠ VST
3. Angle Addition Postulate: m∠ RSU + m∠ USV = m/RSV
4. Angle Addition Postulate: m∠ VST + m∠ USV = m∠ UST
5. Transitive Property: m∠ RSU + m∠ USV = m∠ UST
6. Substitution Property: m∠ RSV = m∠ UST
7. Definition of Congruence: ∠ RSV ≅ ∠ UST
What is the transitive property?In mathematics, a relation R on a set X is said to have a transitive property if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates a to c.
This is shown in the case of number 6 where :
m∠ RSU + m∠ USV = m∠ UST
The transitive property is also shown in equality states where all values of a, b, and c, if a = b, and b = c, then a = c.
Learn more about the transitive property at: https://brainly.com/question/2437149
#SPJ1
I need the answer ASAP. Please can someone help with all the steps for both parts? Please :)
The value of angle E and angle F are both 22.8°
What is circle geometry?Circle theorem includes the concept of tangents, sectors, angles, the chord of a circle and proofs. A circle is the locus of all points in a plane which are equidistant from a fixed point.
The theorem that states that the angle at the center is twice the angle at the circumference is applied in this scenario.
angle P = angle of arc DG = 45.6°
therefore angle E = 1/2 angle of arc DG
= 1/2 × 45.6
= 22.8°
angle E = angle F = 22.8° . This because angle in the same segment are equal.
therefore angle E = angle F = 22.8°
learn more about circle geometry from
https://brainly.com/question/24375372
#SPJ1
Use the distance formula (d = √(x2 − ₁)² + (32 − y₁)²) to find the distance from the
center of a circle (-2, 4) to a point on the circle (3, 1).
A.√16≈ 4
B.√50 7.07
C.26≈ 5.10
D.34≈ 5.83
Therefore , the solution of the given problem of circle comes out to be option D 34 = 5.83.
what is a circle?A circle is formed by every region of a plane that is a certain distance from this extra spot (center). Thus, it is made up of curved areas that are spaced apart and divided by a surface. It also revolves equally it around centre from all directions. In a circular, limited double sphere, every pair of endpoints is uniformly separated from the "centre." By weaving a thread through a circle, one can create a line that leads to circular symmetry.
Here,
The following algorithm can be used to calculate the separation between two points:
=> d = √(x2 − x₁)² + (y2 − y₁)²
Here, a circle's centre is at (-2, 4), and a spot on the circle is at (3, 1). We thus have:
=> d = √(3 − (-2))² + (1 − 4)²
=> √(5)² + (-3)²
=> √25 + 9
=> √34 ≈ 5.83
As a result, 5.83 metres (or yards) is roughly how far the circular's centre is from the point on the circle. Therefore, the response is (D) 34 5.83.
To know more about circle visit:
https://brainly.com/question/29142813
#SPJ1
19. Find the area of the square whose:
a) Side = 18 cm
The area of the square with given side 18 cm is 324 square cm.
Why is the equation for a square's area Side x Side?The equation for a square's surface area A square is a quadrilateral with four equal sides and four right angles, which is how Side x Side is obtained. By multiplying one side's length by the other side's length, which is likewise the same length, one may get the area of a square, which is the amount of space within the square. As a result, Side x Side is the formula for calculating a square's area.
Given that the length of the side of square = 18cm.
The area of the square is given as:
A = (s)(s)
Substituting the value we have:
Area = 324 square cm
Hence, the area of the square is 324 square cm.
Learn more about area of square here:
https://brainly.com/question/30556035
#SPJ1
Find the area of the trapezoid to the nearest tenth.
pls help me I keep getting wrong
The area of the given trapezoid above would be = 1.2m²
How to calculate the area of the given trapezoid?A trapezoid is defined as a quadrilateral that has four sides with a pair of parallel sides.
To calculate the area of the trapezoid the formula below should be used. That is;
Area = 1/2 (a+b) h
where;
a= 1.7m
b = 0.7m
h = sin∅ = opposite/hypotenuse
where;
opposite = ?
hypotenuse =1.4
sin 45° = h/1.4
h= 0.707106781 ×1.4
h = 1m
Area= 1/2 (1.7+0.7) × 1
= 1.2 m²
Learn more about area here:
https://brainly.com/question/28020161
#SPJ1
Which would be included in a probability model for rolling a cube with faces numbered 1 through 6. Select all that apply. A. Sample space: 1, 2, 3, 4, 5, 6 B. P(1) =16 C. P(2) =26 D. P(6) =16 E. The outcomes of the trial: 2, 2, 2, 5, 3, 2, 6, 5, 6, 1
Answer:
A. Sample space: 1, 2, 3, 4, 5, 6
D. P(6) = 1/6
Step-by-step explanation:
Option B and C are not possible because the probability of rolling any particular number on a fair six-sided cube is always 1/6. Option E describes the outcomes of 10 trials, which is not the probability model.
Find the distance between the points (9,10)and (-6,-6) round to the nearest tenth
An aquarium can be modeled as a right rectangular prism and it can hold 1368 cubic
inches of water when it is full. Its length is 19 in and width is 9 in. Find the height of
the aquarium in inches. Round your answer to the nearest tenth if necessary.
The height of the rectangular prism of aquarium is 8 inches.
What is right rectangular prism?A right rectangular prism is a six-sided, three-dimensional geometric figure. The term "rectangular parallelepiped" is another name for it. Three pairs of congruent faces, each pair of which is parallel to the other, make up a right rectangular prism. In addition, it contains four vertices and three pairs of congruent edges. In a right rectangular prism, the opposing faces are parallel and congruent rectangles, and the angles separating the faces are all right angles. Multiplying the prism's length, width, and height yields the volume of a right rectangular prism.
Given that, the length is 19 in and width is 9 in and it can hold 1368 cubic inches of water.
The volume of a rectangle is given as:
V = lwh
Substitute the values:
1368 = 19(9)(h)
h = 1368/(19*9) ≈ 8 inches
Hence, the height of the rectangular prism of aquarium is 8 inches.
Learn more about right rectangular prism here:
https://brainly.com/question/3248292
#SPJ1
What equation can be used to represent the relationship shown in the graph?
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{7}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{7}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{2}}} \implies \cfrac{ 2 }{ 2 } \implies 1[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{ 1}(x-\stackrel{x_1}{2}) \\\\\\ y-5=x-2\implies {\Large \begin{array}{llll} y=x+3 \end{array}}[/tex]
Evaluate the expression for a = 3.8, a = 7, and a - 7.2
The expression a ÷ 4 is equal to __ a = 3.8
Given:-
[tex] \sf \: a = 3.8 , 7 , -7.2[/tex][tex] \: [/tex]
[tex] \sf \: a ÷ 4 ---eqⁿ[/tex][tex] \: [/tex]
Solution:-
[tex] \underline{ \: \sf{[a = 3.8] \: }}[/tex]
[tex] \: [/tex]
[tex] \sf \: a ÷ 4[/tex][tex] \: [/tex]
[tex] \textsf{put the value of a = 3.8}[/tex]
[tex] \: [/tex]
[tex] \sf \: 3.8 ÷ 4 [/tex][tex] \: [/tex]
[tex] \boxed{ \sf{ \purple{0.94}}}[/tex][tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━━━━
[tex] \underline{ \sf \: [a = 7]\: }[/tex]
[tex] \: [/tex]
[tex] \sf \: a ÷ 4[/tex][tex] \: [/tex]
[tex] \textsf{ \: put the value of a = 7 \: }[/tex]
[tex] \: [/tex]
[tex] \sf \: 7 ÷ 4[/tex][tex] \: [/tex]
[tex] \boxed {\sf \red{1.75}}[/tex][tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━━━━
[tex] \underline{ \sf{[a = -7.2]}}[/tex]
[tex] \: [/tex]
[tex] \sf \: a ÷ 4[/tex][tex] \: [/tex]
[tex] \textsf{ \: put the value of a = -7.2 \: }[/tex]
[tex] \: [/tex]
[tex] \sf \: -7.2 ÷ 4[/tex][tex] \: [/tex]
[tex] \boxed{ \sf \green{-1.8}}[/tex][tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━━━━
hope it helps! :)
if 2tanx-1=0 and cos<0 solve √5cosx+4/sin2x
From the equation 2tanx - 1 = 0, we can find the value of tangent of x as follows:
2tanx - 1 = 0
2tanx = 1
tanx = 1/2
x = arctan(1/2) + nπ, where n is an integer
Now we need to solve √5cosx+4/sin2x, given that cos(x) < 0.
Since cos(x) < 0 and tan(x) = sin(x)/cos(x) = 1/2, we can use the Pythagorean identity to find sin(x):
sin^2(x) + cos^2(x) = 1
sin^2(x) + (-cos(x))^2 = 1
sin^2(x) = 1 - cos^2(x)
sin(x) = -√(1 - cos^2(x))
Substituting this into the expression we want to evaluate:
√5cos(x) + 4/sin^2(x) = √5cos(x) + 4/(-√(1 - cos^2(x)))^2
= √5cos(x) + 4/(1 - cos^2(x))
To simplify this expression further, we can use the identity sec^2(x) = 1 + tan^2(x) to find cos^2(x):
sec^2(x) = 1 + tan^2(x)
1/cos^2(x) = 1 + (1/2)^2
1/cos^2(x) = 5/4
cos^2(x) = 4/5
cos(x) = ±2/√5
Since cos(x) is negative, we have cos(x) = -2/√5.
Substituting this value into the expression we want to evaluate:
√5cos(x) + 4/(1 - cos^2(x)) = √5(-2/√5) + 4/(1 - (-2/√5)^2)
= -2 + 4/(1 - 4/5)
= -2 + 20
= 18
Therefore, the solution to √5cos(x) + 4/sin^2(x) given 2tan(x) - 1 = 0 and cos(x) < 0 is 18.
the graph shows that you are traveling at a constant rate three of the statements are true, which is not
Answer: False= Your speed is 135 mph
Step-by-step explanation:
The graph shows you have traveled 90 miles in 1.5 hours.
90miles * 2/3 = 60miles
1.5hours * 2/3 = 1 hour
1 hour : 60 miles = 60mph NOT 135mph
John earns twice as much as his wife Grace. Write down an expression for the difference between their earnings.
An expression for the difference between their earnings is 2G - G.
How to write an equation to model this situation?In order to write a linear equation to describe this situation, we would assign variables to John's earnings and Grace's earnings respectively, and then translate the word problem into a linear equation as follows:
Let the variable J represent John's earnings .Let the variable G represent Grace's earnings.Since John earns twice as much as his wife Grace, a linear equation that models the situation is given by:
J = 2G
100 = 50
For the difference between their earnings, we have the following:
Difference = J - G
Difference = 2G - G
Read more on expression here: brainly.com/question/25767785
#SPJ1