Solve each of the following right triangles. Round angle measures to the nearest degree and segment lengths to the nearest tenth. Angle C is the right angle of the triangle
Answers
AC=23.
BA=55.2
Related Questions
A tank holds 1,000 gallons of syrup. Danielle filled 65 5-gallon cans with syrup. How much syrup was left in the tank when she finished? 3. Draw a picture or a chart that shows the information and the question.
675 gallons
935 gallons
325 gallons
350 gallons
Answers
Draw a picture of someone taking away 325 gallons of syrup from a 1000 gallon bin.
Hope that helped;)
Answer:
the answer is 675
Step-by-step explanation:
1. there is a tank with 1000 gallons, and we have 65 cans with a capacity of 5 gallons, so if we multiply the 65 cans with the capacity we would have as result
65 x 5 = 325
2- already having the value of gallons used (325) we can subtract this difference to the 1000 gallons that were in the tank at first.
1000 - 325 = 675
Find the lateral area for the regular pyramid.
L. A. =
Answers
Al = (4) * (1/2) * (b) * (h)
Where,
b: base of the triangle
h: height of the triangle
Al = (4) * (1/2) * (2) * (root ((1) ^ 2 + (3) ^ 2))
Al = (4) * (root (1 + 9))
Al = 4raiz (10) units ^ 2
Answer:
Al = 4raiz (10) units ^ 2
Al = (4) * (1/2) * (b) * (h)
Where, b= base of the triangle h=height of the triangle Al = (4) * (1/2) * (2) * (root ((1) ^ 2 + (3) ^ 2)) Al = (4) * (root (1 + 9)) Al = 4raiz (10) units ^ 2
Mrs. Jones Algebra 2 class scored very well on yesterday's quiz. With one exception, everyone received an A. Within how many standard deviations from the mean do all the quiz grades fall?
91, 92, 94, 88, 96, 99, 91, 93, 94, 97, 95, 97
A. 1
B. 2
C. 4
D. 3
Answers
Explanation:
1) Find the mean:
mean = sum of the values / number of data
The number of data is 12, so:
mean = (91 + 92 + 94 + 88 + 96 + 99 + 91 + 93 + 94 + 97 + 95 + 97) / 12
mean = 1127 /12 = 93.917
2) Find the variance:
variance = sum of squares of the differences between each data and the media, divided by thenumber of data - 1
variance = (106.97)/(12-1) = 106.97 / 11 = 9.720
3) Find the standard deviation
standard deviation = square root of variance = √(9.720) = 3.118
4) Find the difference of the maximum and the minimun grades with the media:
maximum grade: 99 - 93.917 = 5.083
Find how many standard deviations that is: 5.083 / 3.118 = 1.63
minimum grade: |88 - 93.917| = 5.917
Find how many standard deviations that is: 5.917 / 3.118 = 1.9
5) Conclusion: all the quiz grades falls inside 2 standard deviations form the mean.
Given that the values in the table represent the graph of a continuous function, y has at least how many zeros? HELLLLP!!!!!!!!!
Answers
We have the following sign changes:
x y
-2.4 0.69
-1.8 -0.39
-1.2 0.24
0 0
0.6 -0.46
1.2 -0.24
1.8 0.39
2.4 -0.69
Therefore, the number of zeros is:
5
Answer:
5
Solution:
x y
-2.4 0.69
-1.8 -0.39
-1.2 0.24
0 0
0.6 -0.46
1.2 -0.24
1.8 0.39
2.4 -0.69
So there will be 5zeros.
Someone please help me?
Answers
remove the ^2's from the left side:
(x-3) +(y+5) = sqrt(25)
(x-3) +(y+5) = 5
radius = 5
now solve for zero 's on the left side:
x-3 = 0 x = 3 (3-3=0)
y+5 = 0 y = -5 (-5 +5=0)
so center = (3,-5) and radius is 5
Answer is last one.
Which accurately shows how to use inverse operations to find the value of a in a + 5 = 14?
Answers
a+5=14
using the additive inverse property we shall have:
a+5+(-5)=14+(-5)
simplifying the above we get:
a+5-5=14-5
a+0=9
thus
a=9
A jar contains 133 pennies.A bigger jar contains 1 2/7 times as many.What is the value of the pennies in the bigger jar?
Answers
133 divided by seven is 19, (that's one-seventh right there) so multiply 19 by two to get 38, then add that to 133 (your "one")
What is the gcf of 3x^2 and 7y
Answers
Unless we have a relationship defined between x and y there is no common factor apart from 1.
hope it helps
~Reema
What are the x intercepts of this function f(x) =2x^2-7x-4?
Answers
2x² - 8x + x - 4 = 0
2x(x - 4) + 1(x - 4) = 0
(2x + 1)(x - 4) = 0
Set each binomial equal to zero.
2x + 1 = 0
2x = - 1
x = - 1/2
x - 4 = 0
x = 4
Your x-intercepts are x = - 1/2, 4 or (- 1/2, 0) and (4, 0)
A bag contains a variety of different-colored marbles. If P(red) = , P(green) = , and P(red and green) = , which statement is true?
Answers
Answer:
The answer is A. The events are independent because P(red) • P(green) = P(red and green).
Answer:
A. The events are independent because P(red) • P(green) = P(red and green).
Step-by-step explanation:
EDGE 2021 AQR
Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = 3 - 4 sin θ
Answers
Explanation:
The equation r = 3 - 4 sin θ may be graphed using cartesian coordinates (i.e. x and y) or polar coordinates.
The logical way is to graph in polar coordinates. I did it using a graphing software and obtained the attached graph.
Also, I attached the graph in cartesian coordinates.
Here you have a table that you can build by your self and use the pairs to draw the graph (either cartesian or polar coordinates).
θ (rad) r = 3 - 4 sin θ
0 3
π/8 2.61731657
π/4 2.29289322
3π/8 2.07612047
π/2 2
5π/8 2.07612047
3π/4 2.29289322
7π/8 2.61731657
π 3
9π/8 3.38268343
5π/4 3.70710678
11π/8 3.92387953
3π/2 4
13π/8 3.92387953
7π/4 3.70710678
15π/8 3.38268343
2π 3
In both of the attached graphs you can see that the left side is equal to the right side, but the upper side is not equal to the bottom side.
Therefore, the graph is symmetric about the y-axis.
Answer:
y-axis... just look at the graph on desmos.com
a quarterback for the seattle seahawks completes 54% of his passes. let the random variablle x be the number of passes completed in 20 attempts. conduct a stimulation of the 20 attempts using the following random digits. be sure to state how your assign your didgits
Answers
"A quarterback for the Seattle Seahawks completes 54% of his passes. Let random variable X be the number of passes completed in 20 attempts. Conduct a simulation of the 200 attempts using the following random digits. Be sure to state how you assign your digits. 98726 10983 56239 42042 76520 68276 58239 48729 84912 87491
a) What proportions of passes were completed?
b) How does this compare with what “should have happened” theoretically?"
First, take 100 numbers, i.e. from 00 to 99, and set that the first 54% are completed passes, therefore from 00 to 53, and the remaining 46% are not completed passes, therefore from 54 to 99.
Now, divide the random digits until you compose 20 numbers: 98, 72, 61, 09, 83, 56, 23, 94, 20, 42, 76, 52, 06, 82, 76, 58, 23, 94, 87, 29.
Then, divide the numbers into the two set categories:
completed: 09, 23, 20, 42, 52, 06, 23, 94, 87 = 9 outcomes
not completed: 98, 72, 61, 83, 56, 94, 76, 82, 76, 58, 29 = 11 outcomes
A) Therefore, from the random digits you get 9/20 = 45% of completed passes and 11/20 = 55% of not completed passes.
B) Using the random digits, the simulation gave an outcome exactly opposite to what we expected.
Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number.
Answers
Lateral area = (2 + 7 + 7.28) x 31 = 16.28 x 31 = 505 m²
Surface area = 2(1/2 x 2 x 7) + 505 = 519 m²
Answer: Lateral area = 505 m² ; Surface area = 519 m²
A sample of 16 from a population produced a mean of 85.4 and a standard deviation of 14.8. a sample of 18 from another population produced a mean of 74.9 and a standard deviation of 16.0. assume that the two populations are normally distributed and the standard deviations of the two populations are equal. the null hypothesis is that the two population means are equal, while the alternative hypothesis is that the mean of the first population is different than the mean of the second population. the significance level is 1%.
Answers
Solution: The test statistic under the null hypothesis is:
[tex]t=\frac{\bar{x_{1}}-\bar{x_{2}}}{s_{p}\sqrt{(\frac{1}{n_{1}})+(\frac{1}{n_{2}})}}[/tex]
Where:
[tex]s_{p} = \sqrt{\frac{(n_{1}-1)s^{2}_{1}+(n_{2}-1)s^{2}_{2}}{n_{1}+n_{2}-2} }[/tex]
[tex]s_{p} = \sqrt{\frac{(16-1)14.8^{2}+(18-1)16^{2}}{16+18-2} }[/tex]
[tex]=15.45[/tex]
[tex]\therefore t=\frac{85.4-74.9}{15.45\sqrt{(\frac{1}{16})+(\frac{1}{18})}}[/tex]
[tex]=\frac{10.5}{5.31}[/tex]
[tex]=1.98[/tex]
Now, to find the critical values, we need to use the t distribution table at 0.01 significance level for [tex]df=n_{1} + n_{2} -2 = 16+18-2=32[/tex] and is given below:
[tex]t_{critical}=-2.738,2.738[/tex]
Since the t statistic is less than the t critical value, we therefore fail to reject the null hypothesis and conclude that the two population means are equal.
A grocer stacks oranges in a four-sided pyramid that is 7 layers high. How many oranges are in the pile?
A.504 B.840 C.140 D.120
Answers
Answer:
Option C. 140
Step-by-step explanation:
Base of a pyramid which has four triangular sides is four sided.
If pyramid contains seven layers of oranges then the layer at the bottom will have 7 oranges.
Since base is a square then other side of the square base will have the same number of oranges = 7.
Therefore number of oranges at the first layer will be = 7×7
Similarly other layers above this layer will have the same sequence
6×6, 5×5, 4×4, 3×3, 2×2, 1×1
Therefore total number of oranges = 7×7 + 6×6 + 5×5 + 4×4 + 3×3 + 2×2 + 1×1 = 49 + 36 + 25 + 16 + 9 + 4 + 1 = 140
Option C. 140 is the answer.
A grocer stacks oranges in a four-sided pyramid that is 7 layers high. Many oranges are in the pile are C.140
Further explanationThe orange is the fruit of the citrus species Citrus and sinensis in the family Rutaceae, native to China. Orange is also called sweet orange, to distinguish it from the related Citrus and aurantium, referred to as bitter orange.
The proper name of four-sided pyramid is a "tetrahedron". The tetrahedron has the extra interesting property of having all four triangular sides congruent
1st Layer: The 1st layer contains only 1 orange so it has only 1 orange
2nd layer: The 2nd layer has total 4 oranges. Calculation: [tex]2*2=4[/tex]
3rd layer: The 3rd layer has total 9 oranges. Calculation: [tex]3 * 3 = 9[/tex]
4th Layer: The 4th layer has total 16 oranges. Calculation: [tex]4 * 4 = 16[/tex].
5th layer: The 5th layer has total 25 oranges. Calculation: [tex]5 * 5 = 25[/tex]
6th layer: The 6th layer has total 36 oranges. Calculation: [tex]6 * 6 = 36[/tex]
7th layer: The 7th layer has total 49 oranges. Calculation: [tex]7 * 7 = 49[/tex].
Sum of all layers:
[tex]1+4+9+16+25+36+49 = 140[/tex]
Learn moreLearn more about oranges https://brainly.com/question/10744522Learn more about pyramid https://brainly.com/question/10262815Learn more about pile https://brainly.com/question/9094265Answer detailsGrade: 9
Subject: mathematics
Chapter: pyramid
Keywords: oranges, pyramid, four-sided, layers, pile
A climber is standing at the top of mount kazbek, approximately 3.1 miles above sea level. the radius of the earth is 3959 miles. what is the climber's distance to the horizon? enter your answer as a decimal in the box. round only your final answer to the nearest tenth. mi
Answers
AC=3959+3.1=3962.1 mi
To evaluate for x we use the Pythagorean theorem, this is given by:
c^2=a^2+b^2
c=AC is the hypotenuse
a and b are the legs
plugging in the values we shall have:
3962.1^2=x^2+3959^2
x^2=3961.1^2-3959^2
x^2=24555.41
hence
x=156.7 mi
Answer: 156.7 mi
The nearest tenth, the climber's distance to the horizon is approximately 156.6 miles.
The climber's distance to the horizon can be calculated using the Pythagorean theorem, where the Earth's radius and the climber's height above sea level form a right-angled triangle.
[tex]\[ d^2 + R^2 = (R + h)^2 \][/tex]
Expanding the right side of the equation gives us:
[tex]\[ d^2 + R^2 = R^2 + 2Rh + h^2 \][/tex]
Subtracting [tex]\( R^2 \)[/tex] from both sides, we get:
[tex]\[ d^2 = 2Rh + h^2 \][/tex]
Since [tex]\( h^2 \)[/tex] is very small compared to [tex]\( 2Rh \)[/tex] (because [tex]\( h \)[/tex] is much smaller than [tex]\( R \))[/tex], we can neglect [tex]\( R^2 \)[/tex] in our calculation for a more practical approximation. This leaves us with:
[tex]\[ d^2 \approx 2Rh \][/tex]
Taking the square root of both sides to solve for [tex]\( d \)[/tex], we have:
[tex]\[ d \approx \sqrt{2Rh} \][/tex]
Now, plugging in the values for [tex]\( R \) and \( h \):[/tex]
[tex]\[ d \approx \sqrt{2 \times 3959 \times 3.1} \][/tex]
[tex]\[ d \approx \sqrt{2 \times 3959 \times 3.1} \][/tex]
[tex]\[ d \approx \sqrt{24516.8} \][/tex]
[tex]\[ d \approx 156.6 \text{ miles} \][/tex]
Rounding to the nearest tenth, the climber's distance to the horizon is approximately 156.6 miles.
Can someone help me solve 2√x−4=10 I'm confused.
Answers
let's analyze two cases
case A) 2(√x)−4=10
2√x=10+4----> 2√x=14----> √x=14/2----> square---> x=7²----> x=49
case B)
2√(x-4)=10
√(x-4)=10/2-----> square---> x-4=5²----> x=25+4-----> x=29
Use a calculator to find the mean and standard deviation of the data. Round to the nearest tenth.
20, 16, 18, 9, 20, 16,14
A. mean=15.9 standard deviation= 3.6
B. mean= 16 standard deviation= 12.7
C. mean= 16.1 standard deviation= 3.6
D. mean= 16.1 standard deviation= 12.7
Answers
Please, see the attached file.
Thanks.
Find the fifth term of the arithmetic sequence in which
t1 = 3 and tn = tn-1 + 4.
A) 5
B) 7
C) 19
D) 23
Answers
. (06.02)
The table below shows data for a class's mid-term and final exams:
Mid-Term Final
96 100
95 85
92 85
90 83
87 83
86 82
82 81
81 78
80 78
78 78
73 75
Which data set has the smallest IQR? (1 point)
They have the same IQR
Mid-term exams
Final exams
There is not enough information
2. (06.02)
The box plots below show student grades on the most recent exam compared to overall grades in the class:
two box plots shown. The top one is labeled Class. Minimum at 74, Q1 at 78, median at 85, Q3 at 93, maximum at 98. The bottom b
Which of the following best describes the information about the medians? (1 point)
The exam median is only 1–2 points higher than the class median.
The exam median is much higher than the class median.
The additional scores in the second quartile for the exam data make the median higher.
The narrower range for the exam data causes the median to be higher.
3. (06.02)
The box plots below show attendance at a local movie theater and high school basketball games:
two box plots shown. The top one is labeled Movies. Minimum at 60, Q1 at 65, median at 95, Q3 at 125, maximum at 150. The botto
Which of the following best describes how to measure the spread of the data? (1 point)
The IQR is a better measure of spread for movies than it is for basketball games.
The standard deviation is a better measure of spread for movies than it is for basketball games.
The IQR is the best measurement of spread for games and movies.
The standard deviation is the best measurement of spread for games and movies.
4. (06.02)
The box plots below show the average daily temperatures in April and October for a U.S. city:
two box plots shown. The top one is labeled April. Minimum at 50, Q1 at 60, median at 67, Q3 at 71, maximum at 75. The bottom b
What can you tell about the means for these two months? (1 point)
The mean for April is higher than October's mean.
There is no way of telling what the means are.
The low median for October pulls its mean below April's mean.
The high range for October pulls its mean above April's mean.
5. (06.02)
The table below shows data from a survey about the amount of time high school students spent reading and the amount of time spent watching videos each week (without reading):
Reading Video
5 1
5 4
7 7
7 10
7 12
12 15
12 15
12 18
14 21
15 26
Which response best describes outliers in these data sets? (2 points)
Neither data set has suspected outliers.
The range of data is too small to identify outliers.
Video has a suspected outlier in the 26-hour value.
Due to the narrow range of reading compared to video, the video values of 18, 21, and 26 are all possible outliers.
6. (06.02)
Male and female high school students reported how many hours they worked each week in summer jobs. The data is represented in the following box plots:
two box plots shown. The top one is labeled Males. Minimum at 0, Q1 at 1, median at 20, Q3 at 25, maximum at 50. The bottom box
Identify any values of data that might affect the statistical measures of spread and center. (2 points)
The females worked less than the males, and the female median is close to Q1.
There is a high data value that causes the data set to be asymmetrical for the males.
There are significant outliers at the high ends of both the males and the females.
Both graphs have the required quartiles.
7. (06.02)
The table below shows data from a survey about the amount of time students spend doing homework each week. The students were either in college or in high school:
High Low Q1 Q3 IQR Median Mean σ
College 50 6 8.5 17 8.5 12 15.4 11.7
High School 28 3 4.5 15 10.5 11 10.5 5.8
Which of the choices below best describes how to measure the spread of this data? (2 points)
Both spreads are best described with the IQR.
Both spreads are best described with the standard deviation.
The college spread is best described by the IQR. The high school spread is best described by the standard deviation.
The college spread is best described by the standard deviation. The high school spread is best described by the IQR.
Answers
1. The dataset with the smallest IQR is the Mid-term exams. 2. The exam median is only 1–2 points higher than the class median. 3. The standard deviation is the best measurement of spread for games and movies.
Explanation:1. The dataset with the smallest IQR is the Mid-term exams. To find the IQR, first, calculate the first quartile (Q1) and the third quartile (Q3). Then, find the difference between Q3 and Q1. By comparing the IQR values for the Mid-term and Final exams, it can be determined that the Mid-term exams have the smallest IQR.
2. The exam median is only 1–2 points higher than the class median. The box plot's median represents the middle value of the dataset. By comparing the medians of the exam and class data, it can be determined that the exam median is only 1–2 points higher than the class median.
3. The standard deviation is the best measurement of spread for games and movies. While the IQR can measure spread, the standard deviation is a more precise measurement. Comparing the spread of the data, the standard deviation is the best measurement for both games and movies.
Learn more about Measuring Data Spread and Center here:https://brainly.com/question/32664364
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Various statistical measures such as IQR, Standard Deviation, Median and Mean were used to interpret the given data in numerous scenarios. Outliers were identified and impacts on datasets were evaluated.
Explanation:To answer these questions, we need to understand few key statistical terms: 'Mean' is the simple average of data, 'Median' is the middle score of data, 'IQR' (Inter Quartile Range) is the difference between the upper quartile (Q3) and the lower quartile (Q1), which helps in understanding the spread and '.'Standard Deviation' measures the absolute variability of a dataset.
Question 1: IQR for the mid-term exams is Q3 (92) - Q1 (82) = 10. IQR for the final exams is Q3 (85) - Q1 (78) = 7. So, the final exams have the smallest IQR.
Question 2: The boxes showing median indicates that the exam median is only 1–2 points higher than the class median.
Question 3: Since the spread of the data at basketball games and local movie theaters demonstrates varied distributions, both the IQR and the standard deviation should be used to evaluate the data spread.
Question 4: Box plots do not provide direct information on the mean. So, there is no way of telling what the means are.
Question 5: For the video hours, we see that values 18, 21, and 26 lie far from the main part of the data, thus they can be considered as possible outliers.
Question 6: The male data set shows a high data value, which causes the data set to be asymmetrical. This could affect statistical measures like the mean and standard deviation.
Question 7: The spread of the college data, having a large standard deviation and IQR, is best described by the standard deviation. The high school data, with smaller numbers, is best described by the IQR.
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There are 25 counters is a bag 6 red, 4 white, 7 blue, and 8 yellow. you choose one counter at random. which color you least likely to choose
Answers
By calculating the probability of choosing a counter at random, we find that we are least likely to choose a white counter as it has the least probability.
What is probability?Probability is simply how likely something is to happen.
Probability of choosing a red counter = 6/25 = 0.24
Probability of choosing a white counter = 4/25 = 0.16
Probability of choosing a blue counter = 7/25 = 0.28
Probability of choosing a yellow counter = 8/25 = 0.32
Learn more about Probability here
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What is the degree of the polynomial function f(x) = 2x3 + 7x5 − 4x − 12?
Answers
Need help with these 2 questions please and thanks
Answers
1) Problem # 15.
(i) [tex] \lim_{x \to \ 60^{-} } f(x) [/tex]
You have to approach the value of x by the left. That is the horizontal segment at y = 56 (with the open circle to the left and the solid circle to the right).
So, the value of the limit es 56.
(ii) [tex] \lim_{x \to \ 60^{+} } f(x)[/tex]
You have to approach the x value by the right. That is the horizontal segment at y = 68.
So the value of the limit is 68.
(iii) Since, the existence of the limit requires that both limits from the left and the right be equal, the conclusion is that the limit does not exist.
That is shown in the graph because the way the function is defined is different if the value of x is greater or less than 60.
(iv) What causes the graph to jump vertically by the same amount at discontinuites is that the rates are defined in intervals and not in a continuous way.
2) Problem 16. Mathematical induction.
Mathematical induction requires 3 steps: 1) Initial hypothesis, 2) assume the equation is valid for n = k, and 3) prove the equation is valid for n = k+1.
This is the solution step by step.
1) Initial hypothesis: first term ⇒ n = 1
left side: 8
rigth side: 4n(n+1) = 4(1+1) = 4(2) = 8
8 = 8 ⇒ check
2) Assume n = k
letf side: 8 + 16 + 24 + ... + 8k
right side: 4k(k + 1)
3) Proove for n = k + 1
left side: 8 + 16 + 24 + ... + 8k + 8(k+1)
right side: 4(k+1) (k + 1 + 1) = 4(k+1)(k+2)
Since 8 + 16 + 24 + ... 8k is assumed to be equal to 4k(k+1), then the left side ends as:
left side: 4k(k+1) + 8(k+1)
take common factor k + 1 → (k+1)(4k + 8)
take common factor 4 for the second parenthesis → (k+1) 4(k + 2) = 4(k+1)(k+2)
So, we have shown that the left side is equal fo the right side, which completes the proof by induction.
Which expressions are equivalent to the one below? Check all that apply.
16^x/4^x
A. 16^x
B. (16-4)^x
C. 4^x * 4^x/ 4^x
D. (16/4)^x
E. 4^x
F. 4
Answers
= 4^2x / 4^x
= 4^x so E is one choice.
also C and D
Factor this expression.
3x2 – 6x
A. 3(x – 2)
B. 3(x2 – 2)
C. 3x(x2 – 2)
D. 3x(x – 2)
Answers
Answer:
D.3x(x-2)
Step-by-step explanation:
i already did this
How do do a 3/4 as a fraction, decimal, and percent?
Answers
Answer:
3/40.7575%Step-by-step explanation:
How do do a 3/4 as a fraction, decimal, and percent?
1) 3/4 is just a fraction
2) 3:4 = 0.75 (0.75 = 75%)
3) 75%
The domain of f(x)=2logx+3 is x > 3.
true.
false.
Answers
x > 0
So, there is not other function for this problem. Thus, the answer is false. See the figure below that shows f(x)
A soccer league has 170 players. Of those players 60% are boys. How many boys are in the soccer league
Answers
170•0.6 = 102
There are 102 boys in the soccer league.
2. The height of one square pyramid is 24 m. A similar pyramid has a height of 8 m. The volume of the larger pyramid is 648 m3. The surface area of the smaller pyramid is 124 m^2. Determine each of the following, showing all your work and reasoning: find the surface area of the larger pyramid
Answers
Surface area of square pyramid = a² +2a √((a²/4) + h²)
a = base edge
h = height
for the large pyramid;
volume = 648 m³
height = 24 m
Volume = a²h / 3
648 m³ = a² x 24 m / 3
a² = 81 m²
a = 9 m
by applying surface area equation to the large pyramid,
surface area = a² +2a √((a²/4) + h²)
= 9² + 2 x 9 √((9² / 4 ) + 24²
= 520.53 m²
hence surface area of large pyramid = 520.53 m²
V = a²h / 3648 * 3 / 24= a² a² = 81 a = 9
Area of square is 9 sq.m.
Area of the lateral sides of the larger pyramid:
a = 1/2 b*h
b = 9
h = sqrt (24^2 + 4.5^2)
h = 24.42
a = 1/2 (9 * 24.42) = 109.88
SURFACE AREA = 4 lateral sides area + base area
SURFACE AREA = 4 * 109.88 + 9*9 = 520.53
please help will give brainiest!!!
Answers
How: Re-arrange formulae knowing tan(theta) = sin(theta)/cos(theta)
such that it become: cos(theta) -sin(theta)/cos(theta) x cos(theta) = 0.
From there; cos (theta) = sin(theta) (by re-arranging). Now, substitute figures of b), pie/4 = 45 degrees. At 45 degrees, sin(45) = cos(45) = 1/square root of 2. Also, 5pie/4 = 235 degrees. At 235 degrees, sin(235) = cos(235) = -1/square root of 2
b. [tex] \frac{ \pi }{4} or \frac{5 \pi }{4} [/tex]
Explanation:
Before we begin, remember that:
tan α = [tex] \frac{sin \alpha }{cos \alpha } [/tex]
Now for the given, we have:
cos θ - tan θ * cos θ = 0
cos θ - [tex] \frac{sin theta }{cos theta } [/tex] * cos θ = 0
cos θ - sin θ = 0
cos θ = sin θ
Now, divide both sides by cos θ, we get:
1 = tan θ
Following the ASTC rule, we know that the tan function is positive in the first and third quadrants.
This means that:
either θ = [tex] \frac{ \pi }{4} [/tex]
or θ = π + [tex] \frac{ \pi }{4} [/tex] = [tex] \frac{ 5 \pi }{4} [/tex]
Hope this helps :)