Solve the following equation exactly. Use an inverse function when appropriate.
√x³ - 100 = 5

Answers

Answer 1

Answer:

Starting with the given equation:

√x³ - 100 = 5

Adding 100 to both sides:

√x³ = 105

Squaring both sides:

x³ = 11025

Taking the cube root of both sides:

x = 15

Therefore, the exact solution to the given equation is x = 15.

Note that no inverse functions were needed to solve this equation

Step-by-step explanation:


Related Questions

Consider the set of vectors x, x + 3x^2, x^3, x^2 ∈ P[x]. Does
this set span P[x]?

Answers

No, the set of vectors x, x + 3x², x³, x² does not span P[x].

To span P[x], a set of vectors must be able to generate any polynomial in P[x] through a linear combination of the vectors in the set. However, the set given only includes polynomials of degree 1, 2, and 3. This means that it cannot generate polynomials of degree 0 (constants) or polynomials of degree 4 or higher.

For example, the polynomial 5 cannot be generated from a linear combination of the vectors in the set, as there are no constants in the set. Similarly, the polynomial x⁴ cannot be generated, as there are no vectors of degree 4 or higher in the set.

Therefore, the set of vectors x, x + 3x², x³, x² does not span P[x].

Learn more about span at https://brainly.com/question/14869582?

#SPJ11

when Aaron runs the 400 m dash is finishing times are normally distributed with a mean of 80 seconds and a standard deviation of 2.5 seconds using the elliptical rule determine the interval of times that represent the middle 99.7% of his finishing times in the 400 m race.

Answers

So, by resolving the given, we obtain the result: As a result, the range of standard deviation timings between 72.5 and 87.5 seconds is the middle 99.7% of Aaron's 400 m finishing speeds.

What is standard deviation?

A statistic called standard deviation may be used to represent the variability or variation of a collection of statistics. A low standard deviation means that the values often tend to be closer to the set mean, whereas a large standard deviation shows that the values are widely spread. The standard deviation is an indicator of how far the data are from the mean (or ). The data tend to cluster around the mean when the standard deviation is small, and are more scattered when it is big. Standard deviation is the average degree of variability in the data collection. It displays each score's standard deviation from the mean.  

We can thus get the z-scores that correspond to the bottom and upper bounds of this range using the z-score calculation formula:

Lower bound: z = (x - )/z = (x - 80)/z = 2.5 z = -3

The maximum value is z = (x - ) / z = (x - 80) / 2.5 z = 3.

The area under the curve between z = -3 and z = 3 can be calculated using a calculator or a conventional normal distribution table.

The minimum value is z = -3 (x - 80) / 2.5 = -3 x - 80 = -7.5 x = 72.5.

z = 3 (x - 80) / 2.5 = 3 x - 80 = 7.5 x = 87.5 is the upper limit.

As a result, the range of timings between 72.5 and 87.5 seconds is the middle 99.7% of Aaron's 400 m finishing speeds.

To know more about standard deviation visit:

https://brainly.com/question/23907081

#SPJ1

1. he marks of Calculus I in the final examination in a private college are normally distributed with a mean of 45 marks and a standard deviation of 10 marks. (a) If a student is chosen at random, find the probability that his/her mark is less than 52. 0.75$ (b) If the college has 220 students who sat for the examination, find the number of students whose marks are between 45 and 55. 75 (c) Find the percentage of students whose marks exceed 40. 69.15%
2. A survey on the study habits of 1000 HSM students shows that 550 use reference books, 750 have regular study times and all those who use reference books have regular study time. A HSM student is chosen at random; what is the probability that the student
a) only has regular study time?
b) either has a regular study time or uses
reference books?
c) neither studies regularly nor uses reference
books?

Answers

1. (a)  Using a z-table, we can find the probability corresponding to this z-score, which is 0.758. Therefore, the probability that a student's mark is less than 52 is 0.758. (b) To find the number of students whose marks are between 45 and 55, we need to calculate the z-scores for 45 and 55 . The z-score for 45 is (45 - 45) / 10 = 0, and the z-score for 55 is (55 - 45) / 10 = 1.  (c)  The probability corresponding to this z-score is 0.3085. Therefore, the percentage of students whose marks exceed 40 is 1 - 0.3085 = 0.6915, or 69.15%. 2. (a)  So, the probability that a student only has regular study time is 750/1000 - 550/1000 = 200/1000 = 0.2. (b) The probability that a student either has a regular study time or uses reference books is 750/1000 + 550/1000 - 550/1000 = 750/1000 = 0.75. (c) The probability that a student neither studies regularly nor uses reference books is 1 - 0.75 = 0.25.

Therefore, the probability that a student's mark is between 45 and 55 is 0.8413 - 0.3413 = 0.5. Since there are 220 students in the college, the number of students whose marks are between 45 and 55 is 0.5 * 220 = 110.

To find the probability that a student's mark is less than 52, we need to calculate the z-score for 52 using the formula z = (x - μ) / σ, where x is the value we are interested in, μ is the mean, and σ is the standard deviation. So, z = (52 - 45) / 10 = 0.7.

Know more about probability here:

https://brainly.com/question/30034780

#SPJ11

OAB is a sector of a circle as shown below.
Work out the length of the arc AB.
Give your answer in millimetres (mm) to
1 d.p.
IMPORTANT

Answers

The length of the arc AB is 44.7 mm

What is the length of an arc?

A sector is a part of a given circle which is bounded by two radii and an arc. The length of an arc is simply the path of the incomplete circle.

The length of an arc can be determined by:

length of an arc = θ/ 360 2πr

Where is the measure of the central angle, and r is the radius of the circle.

From the diagram given,

The length of arc AB =  θ/ 360 2πr

                                   = 61/ 360*2*22/7*42

                                   = 44.7333

The length of arc AB is 44.7 mm.

Learn more about the length of an arc at https://brainly.com/question/28108430

#SPJ1

what is 11.5 + 10.5 in math

Answers

Answer:

22

Step-by-step explanation:

10+11=21

.05+.05=1

1+21=22

Type the correct answer in the box.
(Graphs)
Graph [] describes exponential decay.

Answers

So, what's the Question to write an answer for it?

Use simple interest to find the ending balance.
$7,900 at 1.9% for 2 & 3/4 years

Answers

Answer:

To calculate the ending balance, we can use the following formula:

Ending Balance = Principal x (1 + Interest Rate x Time)

Given:

Principal = $7,900

Interest Rate = 1.9%

Time = 2 3/4 years

Therefore,

Ending Balance = $7,900 x (1 + 0.019 x 2.75) = $8,084.60

Answer: 8319.66994

Step-by-step explanation:

your initial x your interest all raised to your time interval.

7,900(1+.019)^2.75

8900 dollars is placed in a savings account with an annual interest rate of 3.3% if no money is added or removed from the account which equation represents how much will be in the account after 4 years

Answers

Answer: 10134.2425

Step-by-step explanation:

Your initial number, 8900, is multiplied by 1+.033 because your percent and your adding money. It all is then raised to the power of 4. Your equation will be 8900(1+.033)^4 Your percentage is always moved two decimal points to the left all multiplied by the amount of years.

565 545 245 450 350How much money will they save monthly by the move to Oakland?

Answers

Benito and his family will save $1,315 by the move to Oakland.

Savings in house = $1200 - $565

                               = $635

Savings in food = $655 - $545

                          = $110

Saving in health care = $495 - $245

                                   = $250

Saving in taxes  = $625 - $450

                          = $175

Saving in necessities = $495 - $350

                                   = $145

Total saving = $635 + $110 + $250 + $175 + $145

                    = $1,315.

Hence, Benito and his family will save $1,315 by the move to Oakland.

To learn more about savings, refer to:

https://brainly.com/question/15279000

#SPJ4

Your question is incomplete, the complete question is:

Benito's family is thinking of relocating from Los Angeles to Oakland to save money. They set up a budget comparing the cost of living for both cities.

Oakland     Los Angeles  

Cost Housing       $565        $1200

Food                     $545        $655

Health Care         $245        $495

Taxes                    $450         $625

Other Necessities $350        $495

How much money will they save monthly by the move to Oakland? $1315, $1560, $1665, or $1765?

Please please help me! This is due ASAP
sin 200 degrees cos 80 degrees- cos 200 degrees sin 80 degrees

Thank you!!

Answers

Answer:

0.866

Step-by-step explanation:

sin (200) = −0.34202014

cos (80) = 0.17364817

-

cos (200) = −0.93969262

sin (80) = 0.98480775

=

0.86602540338, or 0.866

If the figures below are similar, find the scale factor of Figure B to Figure A.

A. 3/16
B. 20/3
C. 16/3
D. 3
E. 3/20
F. 1/3

Answers

I think I should be e hope this helped !

a printer makes more than three copies of labels every hour graph the number of books made in 2 hours.

Answers

Gives us more instructions and explanations of this question. Kind of confusing this question

Jayden made 5% of his free throws over the season. If he shot 120 free throws, how many did he make? Divide/scale down to solve for the missing percent.

Answers

Answer:6

Step-by-step explanation:If jayden made 5% of his free throws and he shot 120 free throws you have to find 5% of 120.

5% of 120 = 6  

So Jayden shot a total of 6 free throws during the season

degree 4 polynomial with zeroes 4 and -(6)/(5) (each with multiplicity 1) and 0 (with multiplicity 2)

Answers

The degree 4 polynomial with the given zeroes is P(x) = x^4-(94/5)x^3-(24/5)x^2.

A degree 4 polynomial with the given zeroes can be represented as:


P(x) = (x-4)(x+(6)/(5))(x-0)^2


Simplifying the polynomial gives:


P(x) = (x-4)(x+(6)/(5))(x^2)


P(x) = (5x-20)(x+(6)/(5))(x^2)


P(x) = (5x^2-20x+(6x)/(5)-24/(5))(x^2)


P(x) = (25x^2-100x+6x-24)/(5)(x^2)


P(x) = (25x^2-94x-24)/(5)(x^2)


P(x) = (5x^4-94x^3-24x^2)/(5)


P(x) = x^4-(94/5)x^3-(24/5)x^2


So the degree 4 polynomial with the given zeroes is P(x) = x^4-(94/5)x^3-(24/5)x^2.

For more about polynomial:

https://brainly.com/question/11536910

#SPJ11

If 1/6 of a gallon of milk is shared equally between three friends how much milk will each friend get

Answers

the friends receive one eighteenth each

A young group and their leaders visited mammoth cave. two adults and five students in one been paid $77 for the hand avenue tour of the cave. Two adults and seven segments
students in the second van pair $95 for the same tour. Find the adults price and the student pieces
price of the tour.

Answers

The price for adults to visit the mammoth cave is $16 and the price for students is $9.

What is the adult and students price?

The first step is to form a system of equations that represent the information in the question.

2a + 5s = 77 equation 1

2a + 7s = 95 equation 2

Where:

a = price of one adult

s = price of one student

The elimination method would be used to solve the equations.

Subtract equation 1 from equation 2:

2s = 18

Divide both sides of the equation by 2

s = 18/2

s = $9

Substitute for s in equation 1:

2a + 5(9) = 77

2a + 45 = 77

2a = 77 - 45

2a = 32

a = 32 / 2

a = 16

To learn more about system of equations, please check: https://brainly.com/question/25875552

#SPJ1

Escribir la ecuación cuadrática con raíces 1 y 5, y con coeficiente principal 2.

(Utilizar la letra x para representar la variable. )

Answers

The quadratic equation with roots 1 and 5 and leading coefficient 2 is 2x^2 - 12x + 10 = 0

To write the quadratic equation with roots 1 and 5 and leading coefficient 2, we can use the fact that the general form of a quadratic equation is:

ax^2 + bx + c = 0

where a, b, and c are constants.

Since the roots are 1 and 5, we know that the factors of the quadratic equation are:

(x - 1) and (x - 5)

Multiplying these factors together, we get:

(x - 1)(x - 5) = x^2 - 6x + 5

To satisfy the condition of having a leading coefficient of 2, we can simply multiply the entire equation by 2

2(x^2 - 6x + 5) = 2x^2 - 12x + 10

Learn more about quadratic equation here

brainly.com/question/639492

#SPJ4

Which Value Of X Will Make The Expression?

Answers

Answer:

2 and -2

Step-by-step explanation:

For the expression to be equal to 0, it means it has to be undefined, so all we need do, is equate the denominator to 0, since any number divided by 0 = 0

Therefore,

5x² - 20 = 0

5x² = 0 + 20

5x² = 20

Divide both sides by 5,

x² = 20/5

x² = 4

Square root both sides,

x² = √4

x = ±2

Please mark brainliest.

Thanks.

A washing machine holds 10 gallons of water and drains 8 of the gallons in 2 minutes. What was the average flow through the pipe in 2 minutes?
gallons/min

Answers

8 gallons because u have 10 and it drains 8 in 2min so if it is asking you what is the average flow through the pipes in 2min it would be 8 gallons

The answer is 8

I paid $9.54 for 1.2 pounds of fresh fish.
How much did the fresh fish cost per pound?

Answers

$7.95 is the correct answer

Which of the following gives the correct range for the graph? −2 ≤ x ≤ 5

Answers

For the functiοn, the range is deduced tο be [-2, 5].

What is the range of data?

The range οf data is defined as a measure of the difference between the maximum value of data and the minimum value οf data.

The rangeοf a graph refers to the set of all possible output values, or the y-values, οf the function represented by the graph.

The given range of −2 ≤ x ≤ 5 actually represents the domain of the function, or the set οf all possible input values, or the x-values, fοr which the function is defined.

Sο, the range can also be written as [-2, 5] for the given set of data.

Therefore, the range is οbtained as [-2, 5].

To learn more abοut range from the given link

https://brainly.com/question/28135761

#SPJ1

A new town developed in Wyoming due to mineral activity. It began with 150 workers/managers moving in, so in year zero its population was 150, after one year, 620 people lived in the new city. After two years, 1170 people inhabited the town, and by the end of the third year, the population was 1950. Find a linear regression that fits this data and predict the towns population by year 12.( what is the r^2 value?) what is the equation of the line? the r value? and prediction of population in year 12?

Answers

The equation of the line is y = 780x + 150, r² value  is 0.186, the r value is 0.431, and the predicted population in year 12 is 9450.

To find a linear regression that fits this data, we need to use the following formula:
y = mx + b
where y is the population, x is the number of years, m is the slope, and b is the y-intercept.

We can use the data given to find the slope (m) and the y-intercept (b). The slope can be found by calculating the difference in the population between two consecutive years and dividing it by the difference in the number of years. The y-intercept can be found by plugging in the values of x and y into the equation and solving for b.

Using the data given, we can find the slope and y-intercept as follows:

m = (1950 - 1170) / (3 - 2) = 780
b = 150 - (0)(780) = 150

Therefore, the equation of the line is:
y = 780x + 150

To find the r² value, we can use the formula:
r² = 1 - (SSres / SStot)

where SSres is the sum of squares of residuals and SStot is the total sum of squares.

SSres = (150 - 150)² + (620 - 930)² + (1170 - 1710)² + (1950 - 2490)² = 2,484,400
SStot = (150 - 1222.5)² + (620 - 1222.5)² + (1170 - 1222.5)² + (1950 - 1222.5)² = 3,051,875

r² = 1 - (2,484,400 / 3,051,875) = 0.186

The r value can be found by taking the square root of the r²value:
r = √0.186 = 0.431

To predict the population in year 12, we can plug in the value of x into the equation of the line:
y = 780(12) + 150 = 9450

Therefore, the predicted population in year 12 is 9450.


Learn more about equation at https://brainly.com/question/11186716?

#SPJ11

Which equation can be used to find the area of the figure below?





F.A = (10⋅82
)+
(16⋅8
)
G.A = (6⋅82
)+
(10⋅8
)
H.A = (6⋅82
)+
(6⋅8
)
J.A = (6⋅8
)+
(10⋅8
)

Answers

The equation that can be used to find the area of the figure below is: (10)(8) + (1/2)(6)(8).

What is area of composite figure?

The area of mixed shapes is the area that is covered by any hybrid shape. The composite shape is a shape created by joining a small number of polygons to create the desired shape. These forms or figures can be constructed from a variety of shapes, including triangles, squares, quadrilaterals, etc. To calculate the area of a composite object, divide it into simple shapes such a square, triangle, rectangle, or hexagon.

A composite form is essentially a combination of fundamental shapes. A "composite" or "complex" shape is another name for it.

The area of the rectangle is given as:

A = (l)(w)

A = 10(8)

A = 80 sq. units

The area of the triangle is:

A = 1/2(b)(h)

In the figure:

b = 16 - 10 = 6 and h = 8.

A = 1/2(6)(8)

A = 24 sq. units

The total area of the figure is:

Area = area of rectangle + area of triangle

Area = 80 + 24

Area = 104 sq. units

Hence, the equation that can be used to find the area of the figure below is: (10)(8) + (1/2)(6)(8).

Learn more about area here:

https://brainly.com/question/11952845

#SPJ1

Hi! Please help! question attached tysm x​

Answers

so the rate is per annum, so compounding period is 1 per year, hmmm we could use 1 or 2 years to get "r", hmmm let's use 2.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \pounds 5903.13\\ P=\textit{original amount deposited}\dotfill &\pounds 5500\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases}[/tex]

[tex]5903.13 = 5500\left(1+\frac{\frac{r}{100}}{1}\right)^{1\cdot 2} \implies \cfrac{5903.13}{5500}=\left( 1+\cfrac{r}{100} \right)^2 \\\\\\ \sqrt{\cfrac{5903.13}{5500}}=\cfrac{100+r}{100}\implies 100\sqrt{\cfrac{5903.13}{5500}}=100+r \\\\\\ 100\sqrt{\cfrac{5903.13}{5500}}-100=r\implies \stackrel{ \% ~ ~~ ~ }{\boxed{3.6\approx r}}[/tex]

HELP ASAP PLSSSSS
Complete the frequency table:


Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 60
Age 15 and above 65 195
Column totals 152 110 98 360


How many students age 15 and above take a car to school?
18
38
50
87

Answers

The correct option is (b) i.e. there are 38 students age 15 and above who take a car to school.

What is a linear equation?

A linear equation is one in which the maximum power of the variable is one. Mathematically, an equation of the type axe + b = 0 or axe + by + c = 0, where a, b, and c are real integers and x and y are variables of maximum power one.

We know that,

Students under age 15 who prefer walk/bike + Students age 15 and above who prefer walk/bike = total of column

So, Students under age 15 who prefer walk/bike

   = total of column - Students age 15 and above who prefer walk/bike

   = 152 - 65

   = 87.

Now, total of rows = total of columns

       Row 1 + Row 2 = 360

      Row 1 = 360 - Row 2

                 =360-195

                 = 165.

Now, Students under age 15 who prefer bus + Students under age 15 who prefer walk/bike + Students under age 15 who prefer car = Row table

So, Students under age 15 who prefer bus

    = 165 - 60 - 87

    = 18.

Similarly,

Students under age 15 who prefer bus + Students 15 and above who prefer bus  = column total

So, Students 15 and above who prefer bus  = 110 - 18

                                                                         = 92.

Finally, students age 15 and above take a car to school

           = 195 - 92 - 65

           = 38.

To learn more about Linear equations, visit the link:

https://brainly.com/question/2030026

#SPJ1

Use interval notation to write the intervals over which f is a) increasing, b)
decreasing, and c) constant.
-5-4-3-2-1
S
f
3+
CN
1+
-1-
-2+
-3+
-4-
-5+
1 2 3 4 5 X

Answers

Answer: (a) From the graph, we can see that the function f is increasing on the interval [-5, -1), (-2, 2), and (3, 5]. Therefore, we can write the increasing intervals in interval notation as:

[-5, -1) ∪ (-2, 2) ∪ (3, 5]

(b) From the graph, we can see that the function f is decreasing on the interval (-1, 1) and (2, 3]. Therefore, we can write the decreasing intervals in interval notation as:

(-1, 1) ∪ (2, 3]

(c) From the graph, we can see that the function f is constant on the interval [-4, -3]. Therefore, we can write the constant interval in interval notation as:

[-4, -3]

Step-by-step explanation:

Suppose that researcher; using data on class size (CS) and average test scores (S) from 100 third-grade classes, estimates the OLS regression: S = 520. 4 5. 82 CS, (20. 4) (2. 21) Rz = 0. 08, SER = 11. 5 a) A classroom has 22 students What is the regression prediction for that classroom average test score?b) Last year classroom had 19 students and this year it has 23 students What is the regression's prediction for the change in the classroom average test score? c) The sample average class size across 100 classrooms is 21. 4. What is the sample average ofthe test scores across the 100 classrooms? d) Interpret the R? measure. Is it large Or small? What does it mean? e) What is the magnitude of the coefficient of correlation in this model? Interpret the R? measure the context of the correlation coefficient: What is the difference in the interpretation of the twO measures of the linear association of the tWo random variables? f) What is the sample standard deviation of test scores across the 100 classrooms? Hint: Use the formula for the standard error of the regression (SER) to get the sum of squared residuals:

Answers

a) The regression prediction for a classroom with 22 students is 651.24.

b) The predicted change in the classroom's average test score for a change from 19 to 23 students is 23.28.

c) The sample average of the test scores across the 100 classrooms is approximately 639.88.

d) The R-squared (R²) measure is 0.08, which indicates a relatively small amount of variation in test scores is explained by variation in class size.

e) The magnitude of the coefficient of correlation (r) is 0.283, indicating a weak positive linear association between class size and test scores.

f) The sample standard deviation of test scores across the 100 classrooms is approximately 11.28.

a) If a classroom has 22 students, then the regression prediction for that classroom's average test score would be:

S = 520.4 + 5.82(22) = 651.24

b) If last year a classroom had 19 students and this year it has 23 students, then the predicted change in the classroom's average test score would be:

ΔS = 5.82(23-19) = 23.28

Note that this calculation assumes that the other factors affecting test scores remain the same, which may not be realistic.

c) The sample average class size across 100 classrooms is 21.4. To find the sample average of the test scores across the 100 classrooms, we simply plug in the average class size into the regression equation:

S = 520.4 + 5.82(21.4) = 639.88

Therefore, the sample average of the test scores across the 100 classrooms is approximately 639.88.

d) The R-squared (R²) measure in this model is 0.08. This is a relatively small value, which means that only 8% of the variation in test scores can be explained by variation in class size. The remaining 92% of the variation is due to other factors that are not captured by the regression model.

e) The magnitude of the coefficient of correlation (r) in this model can be found by taking the square root of R²:

r = √0.08 = 0.283

The interpretation of r is that there is a weak positive linear association between class size and test scores. This means that as class size increases, test scores tend to increase slightly, but the relationship is not very strong.

The difference between R² and r is that R² measures the proportion of variance in the dependent variable (test scores) that is explained by the independent variable (class size) and any other variables in the model, while r measures the strength and direction of the linear association between the two variables.

f) The standard error of the regression (SER) is given as 11.5. This represents the average amount of variation in test scores that is not explained by the regression model. The sample standard deviation of test scores can be estimated by multiplying SER by the square root of (1 - R²) and dividing by the square root of the number of observations:

s = SER × √(1 - R²) / √n

= 11.5 × √(1 - 0.08) / √100

= 11.28

Learn more about standard deviation here

brainly.com/question/14853042

#SPJ4

URGENT: Can you find the perimeter of each polygon and type the correct code? Please remember to type in ALL CAPS with no spaces.
PLEASEEEE HELPPP NOW!!!

Answers

Perimeter of trapezoid is 35x+2, Perimeter of square is 16x-32, Perimeter of Pentagon is 10x-20 and Perimeter of rhombus is 28x+8.

What is Polygon?

A polygon is a plane figure made up of line segments connected to form a closed polygonal chain.

Perimeter of trapezoid=9x+4+7x+8+12x-2+7x-8

Add the like terms

35x+2

Perimeter of trapezoid is 35x+2

Perimeter of square= 4(4x-8)

=16x-32

Perimeter of Pentagon=5(2x-4)

=10x-20

Perimeter of rhombus=4(7x+2)

=28x+8

Hence, Perimeter of trapezoid is 35x+2, Perimeter of square is 16x-32, Perimeter of Pentagon is 10x-20 and Perimeter of rhombus is 28x+8.

To learn more on Polygon click:

https://brainly.com/question/24464711

#SPJ1

Please help, I don't know how to do this!!!

Answers

the height of the antenna is approximately 24 meters.

What is the right-angle triangle?

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

From the diagram, we see that we need to find the distance d and the height h. We can use the tangent function to find these values.

First, let's find d:

tan(θ) = h / (d + 1.51)

Rearranging, we get:

d = (h / tan(θ)) - 1.51

Next, let's find h:

tan(θ') = h / d

Substituting the expression for d that we found above, we get:

tan(θ') = h / ((h / tan(θ)) - 1.51)

Multiplying both sides by (h/tan(θ1)) - 1.51 and simplifying, we get:

h = (29 * tan(θ') * tan(θ)) / (tan(θ') - tan(θ))

Now we can plug in the values for the angles and solve for h:

h = (29 * tan(31°) * tan(17°)) / (tan(31°) - tan(17°))

h ≈ 24

So the height of the antenna is approximately 24 meters.

Learn more about right-angle triangles here:

https://brainly.com/question/3770177

#SPJ1

If the matrix A = [a1 a2 a3 a4 a5]
has reduced row echelon form
[ 1 -1 0 0 2 ]
[ 0 0 1 0 3 ]
[ 0 0 0 1 1 ]
[ 0 0 0 0 0 ]
then a basis for Col(A) is [ __ __ __ ].
(Note that a1, a2, a3, a4 and a5 are t

Answers

If the matrix A = [a1 a2 a3 a4 a5] has reduced row echelon form [1−10​2​][00031​][00001​][00000​], then a basis for Col(A) is [a1−a2a3a4].

Reduced row echelon form is a way of representing a matrix that has been transformed into a more simplified version. It is commonly used in linear algebra and has many applications.

The columns of a matrix that contain at least one non-zero element in the reduced row echelon form are known as pivot columns. Pivot columns can be used to form a basis for the column space of the matrix.

The number of pivot columns determines the rank of the matrix. Since in the given matrix A has three pivot columns, therefore, the rank of the matrix is 3. Since there are three pivot columns in the reduced row echelon form, a basis for Col(A) must consist of the first three columns of A.

Hence, the required basis for Col(A) is [a1−a2a3a4].

To know more about matrix here:

https://brainly.com/question/28180105

#SPJ11

Other Questions
A mid-sized graphic design company has a position for a graphic design artist. The hiring panel has narrowed the candidates down to three.Candidate A is a recent college graduate. He has a degree in digital design and experience using Adobes photo design software. Candidate A has strong opinions about his design process and argued with the interview panel at length about their critique of his portfolio.Candidate B has just completed an internship at a large graphic design corporation. She has experience using some of the latest design software, but her work has always been in collaboration with others. She has never completed a design job on her own.Candidate C has worked in corporate advertising for the past ten years. She has experience in design, but her methods of production are more traditional. She does not have experience with the latest design software, nor is she very interested in learning it.Which candidate would most likely be hired for this position?Responsescandidate Acandidate Acandidate Ccandidate Ccandidate Bcandidate BNone--for education-- For each value of x, determine whether it is a solution to 13 < 2x+3. Is it a solution? 10+3 to the power of 3/9=?PLEASE HELP!! Required informationExercise 7-3 Predicting future cash flow (LO 7-2)Skip to question[The following information applies to the questions displayed below.]Shelter Products sells portable livestock shelters to hog producers in the Central and Midwest regions of the United States. The terms of sale require cash payment within 30 days, and most customers take full advantage of this payment option. Sales are somewhat seasonal, as indicated by the following table of monthly sales, accounts receivable, and cash receipts information. Accounts receivable figures are as of the month end, and December credit sales and cash collections are omitted for brevity. Dec Jan Feb Mar Apr May JuneCredit sales $ 38,000 $ 24,000 $ 45,000 $ 56,000 $ 63,000 $ 42,000Accounts receivable $ 15,000 36,000 23,000 42,000 55,500 61,000 41,000Cash collections 17,000 37,000 26,000 42,500 57,500 62,000Requirement 22. Briefly explain why current period accrual earnings may be a better predictor of future operating cash flow than is current period operating cash flow. Question 1 (20 marks) Consider the following transportation tableau with three origins and three destinations. To From Windhoek Gobabis Walvis Bay Supply Rundu 4 10 6 100 Oshakati 8 16 6 300 Katima Mulilo 14 18 10 300 Demand 200 300 200 Required Marks Sub total Total Use the Vogel Approximation method (VAM) to find an initial feasible solution? 20 20 To 1. You have a meal high in protein and fat. Explain what occurs to both protein and fats when they enter your: in. stomach in. small intestines I need help, I struggle with tax rate or interest rate problems To determine the number of squirrels in a conservation area, a researcher catches and marks squirrels. Then the researcher releases them. Later squirrels are caught and it is found that of them are tagged. About how many squirrels are in the conservation area? If p-hat is equal to. 65, then the complement (q-hat) is equal to For f(x)=Vx and g(x) = 3x+5, find the following composite functions and state the domain of each (a) fog (b) gof (c) fof(d) gog(a) (f o g)(x) = ____ (Simply your answer) Can you help me put this in order please i know henning Bramd go first but i need this quick Two forces of 68 pounds and 64 pounds act simultaneously on an object. The anglebetween the two forces is 76. Find the magnitude of the resultant, to the nearestpound. Find the measure of the angle between the resultant and the larger force, tothe nearest degree. Let A = {1, 2, 3, 4, 5} B = {1, 3, 5} C = {4, 6}. Find the cardinality of the given set.34. n(B)36. n(A C) contractionsWrite the correct contraction for each set of words. Please help me with homework Create a rational expression with the following constraints Your rational expression must: have a binomial in the numerator roduce to: (1)/(2x-3) Tennessees nickname as the Perfect 36 comes from its support of which progressive issue?A. antitrust legislationB. conservationC. prohibitionD. womens suffrage 45.0J of work is done on a 1.50kg ball at rest. What is the velocity of the ball?30.0m/s5.48m/s60.0m/s7.75m/s ind all of the solutions of the polynomial equation: 4x^(4)-13x^(3)-21x^(2)+78x-18=0 Which invention helped the Chinese solve the problem of needing more money fortrade?gunpowdermagnetic compassesprintingsteel