The direction of the parabola is determined by the leading coefficient of the polynomial (a > 0 - Upwards, a < 0 - Downwards). The y-intercept of the polynomial is c and the two zeros of the polynomial are x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c).
What are the characteristics of quadratic equations?
Herein we have a quadratic equation of the form f(x) = a · x² + b · x + c. To determine the direction of the parabola, we must transform this expression into its vertex form and looking for the sign of the vertex constant:
f(x) = a · x² + b · x + c
f(x) = a · [x² + (b / a) · x + (c / a)]
f(x) + b² / (4 · a) - c = a · [x² + (b / a) · x + b² / (4 · a²)]
f(x) + b² / (4 · a) - c = a · [x + b / (2 · a)]²
If a > 0, then the direction of the parabola is upwards, but if a < 0, then the direction of the parabola is downwards.
The y-intercept is found by evaluating the quadratic equation at x = 0:
f(0) = a · 0² + b · 0 + c
f(0) = c
And the zeros are determined by the quadratic formula:
x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c)
The direction of the parabola is determined by the leading coefficient of the polynomial (a > 0 - Upwards, a < 0 - Downwards). The y-intercept of the polynomial is c and the two zeros of the polynomial are x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c).
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Find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x + 1, y = 0, x = 0, x = 2; about the x-axis
The volume of a solid is [tex]\frac{26}{3} \pi[/tex].
Given
The given curves about the specified line. y = x + 1, y = 0, x = 0, x = 2; about the x-axis
Curve is y = x + 1
Line is y = 0
We have to find out the volume v of the solid obtained by rotating the region bounded by these curves.
If the region bounded above by the graph of f, below by the x-axis, and on the sides by x=a and x=b is revolved about the x-axis, the volume V of the generated solid is given by [tex]V = \pi \int\limits^b_a {(f(x))^{2} } \, dx[/tex]. We can also obtain solids by revolving curves about the y-axis.
Volume of a solid:
According to washer method:
[tex]V = \pi \int\limits^b_a {(f(x))^{2} } \, dx[/tex]
Using washer method, where a=0 and b=2, we get
V = [tex]\pi \int\limits^2_0 {(x+1)^{2} } \, dx[/tex]
= [tex]\pi[ \frac{(x+1)^{3} }{3} ]0 \ to \ 2[/tex]
= [tex]\pi [\frac{(3+1)^{3} }{3} -\frac{(0+1)^{3} }{3}][/tex]
= [tex]\pi [\frac{27}{3} -\frac{1}{3} ][/tex]
= [tex]\pi [\frac{26}{3}][/tex]
= [tex]\frac{26}{3} \pi[/tex]
Therefore the volume of a solid is [tex]\frac{26}{3} \pi[/tex].
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BRAINLIEST!
On a number line, the coordinates of P and Q are 8 and 48, respectively. The midpoint of PQ is B, the midpoint of BQ is C, and the midpoint of PC is D. What is the coordinate of D?
Answer:
23 is the answer
Identify sinJ as a fraction and as a decimal rounded to the nearest hundredth.
The figure shows right triangle J K L with right angle L. The length of leg L J is equal to 7 point 2 units. The length of leg K L is equal to 3 units. The length of hypotenuse J K is equal to 7 point 8 units.
In the given right triangle, the trigonometric ratio, sin J has a fractional value of 5/13 and a decimal value of 0.39.
In trigonometry, for a right triangle, the sine (sin) of any angle θ is given as the ratio of its opposite side to the hypotenuse of the triangle, that is, sin θ = (opposite side)/(hypotenuse).
In the question, we are asked to find the trigonometric ratio, sin J, for the given right triangle JKL.
The side opposite to angle J is KL, which has a value of 3 units.
The hypotenuse of the given right triangle is JK, which has a value of 7.8 units.
Thus, sin J can be calculated as:
sin J = KL/JK = 3/7.8 = 5/13 = 0.39.
Thus, in the given right triangle, the trigonometric ratio, sin J has a fractional value of 5/13 and a decimal value of 0.39.
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Consider the following set of equations:
Equation A: y = -x + 5
Equation B: y = 6x - 2
Which of the following is a step that can be used to find the solution to the set of equations?
O-x=6x + 2
O-x-2= 6x + 5
O-x+5= 6x-2
dations:
O-x+ 5 = 5x
The correct option is the thrid one, the first step is
-x+5= 6x-2
Which of the following is a step that can be used to find the solution to the set of equations?Here we have the system of equations:
y = -x + 5
y = 6x - 2
Now, the variable "y" should represent the same thing in both equations, then we can write:
-x + 5 = y = 6x - 2
If we remove the middle part, we get the equation that only depends on x:
-x + 5 = 6x - 2
This is the first step that we should use to solve the system of equations, which is the one in option 3.
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URGENT!!! What happens to the graph of y=−x6−6x5+50x3+45x2−108x−108 as x heads toward ∞ and −∞?
A. as x→∞, y→−∞ as x→−∞, y→−∞
B. as x→∞, y→∞ as x→−∞, y→∞
C. as x→∞, y→∞ as x→−∞, y→−∞
D. as x→∞, y→−∞ as x→−∞, y→∞
Using limits, the correct option regarding the end behavior of the function is given by:
A. as x→∞, y→−∞ as x→−∞, y→−∞.
How to find the end behavior of a function f(x)?The end behavior is found calculating the limit of f(x) as x goes to infinity.
For this problem, the equation is given by:
[tex]f(x) = -x^6 - 6x^5 + 50x^3 + 45x^2 - 108x - 108[/tex]
Since x goes to infinity, we consider only the term with the highest exponent, hence the limits are given as follows:
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} -x^6 - 6x^5 + 50x^3 + 45x^2 - 108x - 108 = \lim_{x \rightarrow -\infty} -x^6 = -(-\infty)^6 = -\infty[/tex]
[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} -x^6 - 6x^5 + 50x^3 + 45x^2 - 108x - 108 = \lim_{x \rightarrow \infty} -x^6 = -(\infty)^6 = -\infty[/tex]
Hence the correct option is:
A. as x→∞, y→−∞ as x→−∞, y→−∞.
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If amy cuddy and her research team originally established a sample size of n=200 (100 in each group) and then discovered that 86% of the high-power group (86 of 100) took a gambling risk while 60% of the low-power group (60 of 100) took the risk, then the p-value would have been much lower than that originally found in question 1. this p-value would have been less sensitive and would have provided stronger evidence for the researcher's hypothesis. state the p-value, rounding to 5 decimal places.
The p-value that would be given as the evidence would be given as p-value = 0.00002 and also P value = 0.00003
How to solve for the p valueThe sample size of the first sample = 100
x1 = success 0f 86%
We have to find the proportion of this = 0.86
The sample size of the second sample n2 = 100
x12 = success 0f 60%
We have to find the proportion of this = 60/100
= 0.6
The difference = 0.86-0.6= 0.26
Next we have to find the pooled proportion. This is taken given as p = (x1+x2)/(n1+n2) this gives us 0.73
Next we have to find the standard error
= √(p*(1-p)*(1/n1+ 1/n2)= 0.06279
Z stat = (0.26-0)/0.0628= 4.1411
From here the p value would have to be
p-value = 0.00002 and also
P value = 0.00003
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help if u can ty! pls do not answer if u cannot help
Based on the logarithms given, the requirement to use one digit, and the figures to be produced, the right numbers are:
log₈2 · 4log₇ 6/5log₉3¹What log produces an integer?The log of a number gives 1 which is an integer so we can find numbers that when multiplied, produce a number that can be taken a log of. Those numbers are 2 and 4:
= 2 x 4
= 8
Log₈ = 1
What log produces an irrational number?Taking the log of a number to a decimal form leads to an irrational number. So, find numbers that when divided, will give a decimal:
= 6/5
= 1.2
Take a log of 7:
log₇ (1.2) will give an irrational number.
The remaining numbers ae 9, 3, and 1.
What log produces a rational number?With the numbers 9,3 and 1, the log to produce a rational number is:
log₉3¹ = log₉9¹/² = 1/2
1/2 is a rational number.
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Alan's bamboo plant adds some flair to his apartment. In four weeks, Alan has trimmed a total of inches off the top of the plant. What is the rate of change in the plant's height in terms of inches per week? Ignore the growth rate of the plant.
The rate of change in the plant's height in terms of inches per week will be 1 2/3 inches.
How to calculate the rate?Rate of change is used to mathematically describe the percentage change in value over a defined period of time, and it represents the momentum of a variable.
The calculation for the rate of change is simple in that it takes the current value of a stock or index and divides it by the value from an earlier period.
The change in y (y being the height of the plant) over 4 weeks was 6 2/3 inches and there are four weeks. Therefore, the average height will be:
= 6 2/3 ÷ 4
= 1 2/3 inches
The average rate of change of the plant growth per week was 1 2/3 inches.
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Complete question:
Alan's bamboo plant adds some flair to his apartment. In four weeks, Alan has trimmed a total of 6 2/3 inches off the top of the plant. What is the rate of change in the plant's height in terms of inches per week? Ignore the growth rate of the plant.
a.+1 2/3B)-1 2/3C)+3/5D)-5/2
The average of three numbers, p, q and 27 is 28.The average of five numbers p, q, r, s and 27 is 31.Find the average of r and s.
Using the given information, the average of r and s is 35.5
Calculating AverageFrom the question, we are to determine the average of r and s
From the give information,
The average of p, q and 27 is 28.
That is,
(p + q + 27)/3 = 28
p + q + 27 = 3×28
p + q + 27 = 84
p + q = 84 - 27
p + q = 57
Also,
The average of p, q, r, s and 27 is 31
That is,
(p + q + r + s + 27)/5 = 31
p + q + r + s + 27 = 5 × 31
p + q + r + s + 27 = 155
Thus,
57 + r + s + 27 = 155
r + s = 155 - 57 - 27
r + s = 71
The average of r and s is (r + s)/2
(r + s)/2 = 71/2
(r + s)/2 = 35.5
Hence, the average of r and s is 35.5
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I dont know this, please can someone help
The table of values for y=1/2x-1 is completed as follows:
x y
-2 -2
-1 -3/2
0 -1
1 -1/2
2 0
3 1/2
Exactly one value from the set of second components of the ordered pair is connected with each value from the set of first components of the ordered pairs in a relation known as a function.
Given function: y=1/2x-1
For x = -2
Value of y = -2
For x = -1
Value of y = 1/2(-1)-1 = -3/2
For x = 0
Value of y = 1/2(0)-1 =-1
For x = 1
Value of y = 1/2(1)-1 = -1/2
For x = 2
Value of y = 0
For x = 3
Value of y = 1/2(3)-1 = 1/2
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_______ 2. Find the length of PQ
A. 4.5π units
B. 9π units
C. 54π units
D. 12π units
Answer:
D
Step-by-step explanation:
Pq=opp/hyp
(135+12)=180
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
[tex]y = mx + n[/tex]
[tex]m = \frac{y - y}{x - x} = \frac{5 - ( - 1)}{ - 5 - ( - 3)} = \frac{6}{ - 2} = - 3[/tex]
[tex]y = - 3x + n \\ [/tex]
Since both ( -3 , -1 ) and ( -5 , 5 ) pass through the line, they both satisfy its equation. Substitute any point in the new equation, I will choose ( -5 , 5 )[tex]5 = - 3( - 5) + n \\ n = 5 - 15 = - 10[/tex]
[tex]y = - 3x - 10[/tex]
PLS HALP ASAP
A vertical slice through a three-dimensional solid produces a two-dimensional shape.
tall rectangle
Which one of the following solids can produce this two-dimensional shape when sliced vertically?
Answer:
the answer is B
a 3d rectangle slided vertically can produce a 2d rectangle
The difference of the means is found and then compared to each of the mean absolute deviations. which is true?
The difference between the mean times is about 2 times the absolute deviation of the data sets.
Given that the difference of the means is found.
The difference in the means is basically the absolute difference between the mean of two groups. It explains the mean of two groups. It explains how much difference that exists between the average between two groups.Calculating mean difference is significant during clinical trials where we have the experimental group and the control group. The mean absolute deviations is basically the variation of each data value from the mean. It tells us how much the values in a set of data differ from the mean value. It explains the reach of values in a data set. There is a relationship that exists between the difference of the mean absolute deviations.
Hence the difference between the mean times is about 2 times the absolute deviation of the data sets.
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The
is the z-score right at the edge of the rejection region.
A. Critical value
B.crucial value
C. Critical region
D.vital statistics
The critical value is the z-score right at the edge of the rejection region option (A) is correct.
What is a normal distribution?It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.
It is given that:
The z-score is right at the edge of the rejection region.
As we know, the rejection zone is the area in which we have sufficient data to reject the null hypothesis if our test statistic falls within it.
Thus, the critical value is the z-score right at the edge of the rejection region option (A) is correct.
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Which term is not possible in the domain of a sequence?
The term that is not possible in the domain of a sequence is:
-5
What is the domain of a function?The domain of a function is the set that contains all possible input values for the function. For a sequence, the domain is the set that contains all the indexed of the terms, starting at 0 and going until the nth term.
For example, suppose we have the following sequence: 3, 5, 7, ...
The term with index 0 is 3.The term with index 1 is 5.The term with index 2 is 7.From what was explained above, which also can be visualized with the example, an index term of a sequence cannot be negative, hence the term that is not possible in the domain of a sequence is:
-5.
Which is the only negative number of the options.
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Which equation is represented by the graph below?
The equation of the graph, in slope-intercept form, is: C. y = 2/3x + 6.
How to Write a Linear Equation in Slope-Intercept Form?The linear equation of a graph in slope-intercept form is expressed as y = mx + b. Where the variable in the equation are as follows:
b = y-intercept (this is the point on the y-axis where the line intercepts).m = slope (this is the rise/run along the line = change in y / change in x).Considering the graph given, to write the linear equation it represents, find the slope (m) and the y-intercept (b) of the line.
Slope (m) = rise/run = 2 units/3 units
Slope (m) = 2/3.
The line intercepts the y-axis at y = 6, thus, the y-intercept (b) would be 6. b = 6.
Substitute m = 2/3 and b = 6 into the slope-intercept form equation, y = mx + b:
y = 2/3x + 6
Thus, the equation, in slope-intercept form, that represents the linear graph as shown in the image given is: C. y = 2/3x + 6.
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how do you solve this?
we are given x here, so we already know that our first coordinate is equal to -2.
in order to find the next coordinate, we have to substitute x for -2 in the y=mx+b equation.
the equation is
[tex]y = \frac{2}{3} x + 23[/tex]
so in substituting x for -2 we get
[tex]y = \frac{2}{3} ( - 2) + 23[/tex]
all we need to do is multiply ⅔ by -2, which gives us -1,3333.
we now have
[tex]y = - 1.3333 + 3[/tex]
so we add them together and get :
[tex]y = 1.666666[/tex]
hope this helps!!<3
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
[tex]\textsf{A. } y=3x^2+10x-8[/tex]
Step-by-step explanation:
We are given the information that a function has zeros at x = ⅔ and x = -4. In order to find the function that has those zeros, we can substitute the value of the zeros into each function. If the value of a function equates to zero with both values, then that is the function we are looking for.
..................................................................................................................................................
Standard Form of a Quadratic: ax² + bx + c = 0.
..................................................................................................................................................
[tex]\large \text{$y = 3x^2+10x-8 \implies 0=3x^2+10x-8$}[/tex]
[tex]\boxed{\begin{minipage}{15 em}{\text{$x=\dfrac{2}{3}$}} \\ \\\implies 0=3\left(\dfrac{2}{3}\right)^2+10\left(\dfrac{2}{3}\right)-8\\\\\implies 0=3\left(\dfrac{4}{9}\right)+10\left(\dfrac{2}{3}\right)-8\\\\\implies 0=\not{3}\left(\dfrac{4}{\not{9}\ 3}\right)+\dfrac{20}{3}-8\\\\\implies 0=\dfrac{4}{3}+\dfrac{20}{3}-8\\\\\implies 0=\dfrac{24}{3}-8\\\\\implies 0=0\ \checkmark\end{minipage}}[/tex] [tex]\boxed{\begin{minipage}{15 em}{\text{$x=-4$}} \\ \\\implies 0=3(-4)^2+10(-4)-8\\\\\implies 0=3(16)-40-8\\\\\implies 0=48-48\\\\\implies 0=0\ \checkmark\end{minipage}}[/tex]
..................................................................................................................................................
[tex]\large \text{$y = 2x^2-5x-12 \implies 0=2x^2-5x-12$}[/tex]
[tex]\boxed{\begin{minipage}{15 em}{\text{$x=\dfrac{2}{3}$}} \\ \\\implies 0=2\left(\dfrac{2}{3}\right)^2-5\left(\dfrac{2}{3}\right)-12\\\\\implies 0=2\left(\dfrac{4}{9}\right)-\dfrac{10}{3}-12\\\\\implies 0=\dfrac{8}{9}-\dfrac{10}{3}-12\\\\\implies 0=\dfrac{8}{9}-\dfrac{10\times3}{3\times3}-\dfrac{12\times9}{9}\\\\\implies 0=\dfrac{8}{9}-\dfrac{30}{9}-\dfrac{108}{9}\\\\\implies0=-\dfrac{22}{9}-\dfrac{108}{9}\\\\\implies 0=-\dfrac{130}{9}\ \textsf{X}\end {minipage}}[/tex] [tex]\boxed{\begin{minipage}{15 em}{\text{$x=-4$}} \\ \\\implies 0=2(-4)^2-5(-4)-12\\\\\implies 0=2(16)+20-12\\\\\implies 0=32+20-12\\\\\implies 0=40\ \textsf{X}\end{minipage}}[/tex]
..................................................................................................................................................
[tex]\large \text{$y = 2x^2+5x-12 \implies 0=2x^2+5x-12$}[/tex]
[tex]\boxed{\begin{minipage}{15 em}{\text{$x=\dfrac{2}{3}$}} \\ \\\implies 0=2\left(\dfrac{2}{3}\right)^2+5\left(\dfrac{2}{3}\right)-12\\\\\implies 0=\dfrac{8}{9}\right)+\dfrac{10}{3}-12\\\\\implies 0=\dfrac{8}{9}\right)+\dfrac{10\times3}{3\times3}-\dfrac{12\times9}{9}\\\\\implies 0=\dfrac{8}{9}+\dfrac{30}{9}-\dfrac{108}{9}\\\\\implies0=\dfrac{38}{9}-\dfrac{108}{9}\\\\\implies 0=-\dfrac{70}{9}\ \textsf{X}\end{minipage}}[/tex] [tex]\boxed{\begin{minipage}{15 em}{\text{$x=-4$}} \\ \\\implies 0=2(-4)^2+5(-4)-12\\\\\implies 0=2(16)-20-12\\\\\implies 0=32-32\\\\\implies 0=0\ \checkmark\end{minipage}}[/tex]
..................................................................................................................................................
[tex]\large \text{$y = 3x^2-10x-8 \implies 0=3x^2-10x-8$}[/tex]
[tex]\boxed{\begin{minipage}{15 em}{\text{$x=\dfrac{2}{3}$}} \\ \\\implies 0=3\left(\dfrac{2}{3}\right)^2-10\left(\dfrac{2}{3}\right)-8\\\\\implies 0=3\left(\dfrac{4}{9}\right)-\dfrac{20}{3}-8\\\\\implies 0=\not{3}\left(\dfrac{4}{\not{9}\ 3}\right)-\dfrac{20}{3}-8\\\\\implies 0=\dfrac{4}{3}-\dfrac{20}{3}-\dfrac{8\times3}{3}\\\\\implies 0=-\dfrac{16}{3}-\dfrac{24}{3}\\\\\implies 0=-\dfrac{40}{3}\ \textsf{X}\end{minipage}}[/tex] [tex]\boxed{\begin{minipage}{15 em}{\text{$x=-4$}} \\ \\\implies 0=3(-4)^2-10(-4)-8\\\\\implies 0=3(16)+40-8\\\\\implies 0=48+40-8\\\\\implies 0=80\ \textsf{X}\end{minipage}}[/tex]
..................................................................................................................................................
Therefore, the function whose zeros are ⅔ and -4 is [tex]y=3x^2+10x-8[/tex].
I need to find the Value of x
Answer:
x = 4
Step-by-step explanation:
These triangles are similar by the AA Similarity Postulate.
12 + 4 = 16
(5x - 2)/12 = 6x/16 (3x/8)
Cross multiply: 8(5x - 2) = 12(3x)
40x - 16 = 36x
4x - 16 = 0
4x = 16
x = 4
Which linear function represents the line given by the point-slope equation y – 8 = y minus 8 equals startfraction one-half endfraction left-parenthesis x minus 4 right-parenthesis.(x – 4)?
The linear function which represents the line given by the point-slope equation is (B) [tex]f(x)=\frac{1}{2} x+6[/tex].
What is a linear function?The word linear function in mathematics refers to two distinct but related concepts. A linear function in calculus and related fields is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.To find the linear function which represents the line given by the point-slope equation:
Given: [tex]y-8=\frac{1}{2} (x-4)[/tex]
Distribute the right side:
[tex]y-8=\frac{1}{2} (x)-\frac{1}{2} 4\\y-8=\frac{1}{2} x-2[/tex]
Adds 8 on both sides:
[tex]y=\frac{1}{2}x-2+8\\y=\frac{1}{2}x+6[/tex]
Convert to function notation:
[tex]f(x)=y\\f(x)=\frac{1}{2} x+6[/tex]
Therefore, the linear function which represents the line given by the point-slope equation is (B) [tex]f(x)=\frac{1}{2} x+6[/tex].
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The complete question is given below:
Which linear function represents the line given by the point-slope equation y – 8 = y minus 8 equals start fraction one-half end fraction left-parenthesis x minus 4 right-parenthesis. (x – 4)?
A) F(x) = f(x) equals StartFraction one-half EndFraction x plus 4.X + 4
B) f(x) = f(x) equals StartFraction one-half EndFraction x plus 6.
C) X + 6 f(x) = f(x) equals StartFraction one-half EndFraction x minus 10.X –10
D) f(x) = f(x) equals StartFraction one-half EndFraction x minus 12.X – 12
The speed of sound is approximately 1,225 kilometers
per hour. When an object travels faster than the speed of
sound, it creates a sonic boom.
Write an inequality that describes s, the speeds at
which a moving object creates a sonic boom.
Enter your inequality without a thousands separator.
s > 1225 km/hr is the inequality that describes s, the speeds at which a moving object creates a sonic boom given that when an object travels faster than the speed of sound, it creates a sonic boom. This can be obtained the same way of finding algebraic equation using variables ad constants.
Find the required inequality:From the question it is given that:
speed of sound is approximately 1225 km/hra moving object creates a sonic boom given that when an object travels faster than the speed of sound, it creates a sonic boomFrom the given statements we can say that sonic booms are created ONLY WHEN the speed of object (s) is greater than the speed of the sound.
This clearly means that sonic booms are produced when s is greater that s
There are three possible situations in the given scenario:
Speed of light can be less than 1225 km/hr ⇒ s < 1225 km/hr ⇒ no sonic boom is created (assumption is wrong)s = 1225 km/hr ⇒ no sonic boom is created (assumption is wrong)s > 1225 km/hr ⇒ sonic boom is created (assumption is correct)Since we are looking for the true equation of creation of sonic waves,
it would be only the last one (s > 1225 km/hr).
Hence s > 1225 km/hr is the inequality that describes s, the speeds at which a moving object creates a sonic boom given that when an object travels faster than the speed of sound, it creates a sonic boom.
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s > 1225 km/hr is the inequality that describes s, the speeds at which a moving object creates a sonic boom given that when an object travels faster than the speed of sound, it creates a sonic boom. This can be obtained the same way of finding algebraic equation using variables ad constants.
Find the required inequality:
From the question it is given that:
speed of sound is approximately 1225 km/hr
a moving object creates a sonic boom given that when an object travels faster than the speed of sound, it creates a sonic boom
From the given statements we can say that sonic booms are created ONLY WHEN the speed of object (s) is greater than the speed of the sound.
This clearly means that sonic booms are produced when s is greater that s
There are three possible situations in the given scenario:
Speed of light can be less than 1225 km/hr ⇒ s < 1225 km/hr ⇒ no sonic boom is created (assumption is wrong)
s = 1225 km/hr ⇒ no sonic boom is created (assumption is wrong)
s > 1225 km/hr ⇒ sonic boom is created (assumption is correct)
Since we are looking for the true equation of creation of sonic waves,
it would be only the last one (s > 1225 km/hr).
Hence s > 1225 km/hr is the inequality that describes s, the speeds at which a moving object creates a sonic boom given that when an object travels faster than the speed of sound, it creates a sonic boom.
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hi i was just wondering how to do this question (attached below) - ive been trying to figure it out for ages but have had no luck - could use some help! thanks
Answer: 88°
Step-by-step explanation:
We know that the ratio of ∠DCB : ∠ACD is 3:1. In other words, ∠DCB is [tex]\frac{3}{3+1}[/tex], or [tex]\frac{3}{4}[/tex] of the whole angle (i.e., ∠ACB), while ∠ACD is [tex]\frac{1}{4}[/tex] of the whole angle.
To easily find ∠ACB, which is the sum of both angles, we can add up all the angles of [tex]\triangle ABC[/tex] and set it equal to 180°.
[tex]m\angle A + m\angle B + m\angle ACB = 180\\75+53+m\angle ACB=180\\128+m\angle ACB=180\\m\angle ACB=52[/tex]
From here, we can calculate ∠BCD by multiplying the value of ∠ACB by three-fourths.
[tex]m\angle BCD = \frac{3}{4}(m\angle ACB)\\m\angle BCD = \frac{3}{4}(52)\\m\angle BCD = 39[/tex]
Similar to what we did to get the measure of ∠ACB, we can add up all the angles measures of [tex]\triangle DBC[/tex] to get the measure of ∠BDC.
[tex]m\angle B + m\angle BDC + m\angle BCD = 180\\53+m\angle BDC + 39= 180\\92+ m\angle BDC=180\\m\angle BDC = 88[/tex]
The measure of ∠BDC is 88°.
math help please right now!!!!
Answer:
The second answer is correct.
Step-by-step explanation:
In a charity triathlon, Mark ran half the distance and swag a quarter of the distance. When he took a quick break to get a drink of Gatorade, he was just starting to bike the remaining 17 miles. What was the total distance of the race?
Answer:
68 miles
Step-by-step explanation:
The total distance can be determined from the fractions.
SolutionLet d represent the total distance of the race.
The distance running is 1/2d. The distance swimming is 1/4d. The remaining distance is 17 miles.
Remaining = total distance - distance running - distance swimming
17 mi = d -1/2d -1/4d = 1/4d . . . . . . . . use known fractions
68 mi = d . . . . . . . multiply by 4
The total distance of the race is 68 miles.
__
Additional comment
This would be a very difficult race. A typical "iron man" race has a swimming distance under 2.5 miles, less than 1/10 of the distance running. The biking distance is typically about 4 times the running distance of "only" 26 miles. An iron man race can take about 17 hours to complete.
This race has a 17-mile swimming segment, which would take a fast swimmer on the order of 8 hours, by itself. (This is 2.7 times the length of a "marathon" swim.) Here, the running distance is 34 miles, about 30% longer than a marathon.
The lifeguards at the beach post information of surfers by placing 3 flags, one above the other, on a flag pole. If there are 8 different flags available, how many possible signals can be flown?
Answer:
336
Step-by-step explanation:
They can place 1 of 8 frags on the bottom.
Now they have 7 flags left.
They can place 1 of 7 flags in the middle.
Now they have 6 flags left.
The can place 1 of 6 flags on top.
8 × 7 × 6 = 336
Jamie is 6 years older than tyrion now. in 2 years, jamie will be one year less than twice tyrion's current age. what is jamie's current age?
Answer:
Jamie is currently 15.
Step-by-step explanation:
A fair coin is flipped seven times. what is the probability of the coin landing tails up at least two times?
The required probability of the coin landing tails up at least two times is 15/16.
Given that,
A fair coin is flipped seven times. what is the probability of the coin landing tails up at least two times is to be determined.
What is probability?
Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
In the given question,
let's approach inverse operation,
The probability of all tails = 1 / 2^7 because there is only one way to flip these coins and get no heads.
The probability of getting 1 head = 7 /2^7
Adding both the probability = 8 / 2^7
Probability of the coin landing tails up at least two times = 1 - 8/2^7
= 1 - 8 / 128
= 120 / 128
= 15 / 16
Thus, the required probability of the coin landing tails up at least two times is 15/16.
Learn more about probability here:
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Pretest: Unit 3
Question 12 of 28
A ladder leans against a 15-foot-tall building to form a right triangle. The
ladder is placed so it is 8 feet from the base of the building. What is the
length of the ladder?
A. 289 ft
OB. 17 ft
O C. 13 ft
D. 161 ft
←BREMQU
Building
15 ft
Ladder
8 ft
42
XA
18
A point having a negative abscissa and negative ordinate is in quadrant ____.
Answer:
III
Step-by-step explanation:
This is a fact - A point having a negative abscissa and negative ordinate is in quadrant III.