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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Which graph represents a reflection across the x-axis of g(x) = Three-fourths(3)x?
See attached images for the graph.
Which function is represented in the
graph below?
Answer:
Option 2
Step-by-step explanation:
There is an amplitude of 1/2, a period of pi, and a non-zero y-intercept.
The sum of 2 numbers is 73, and their difference is 11.
Find the numbers.
Answer: 42 and 31
Step-by-step explanation:
Let x be one number and y be the other.
We will write mathematical equations for these two numbers.
The sum of 2 numbers is 73.
x + y = 73
Their difference is 11.
x - y = 11
See attached for the graph.
The point of intersection is our solution.
Consider a binomial experiment. if the number of trials is increased, what happens to the expected value? To the standard deviation? Explain
The expected value or mean of binomial distribution is also increased by increasing the number of trials.
The standard deviation of binomial distribution is also increased by increasing the number of trials.
According to the question
There is binomial experiment.
The condition given in the question is 'if the number of trials is increased, what happens to the expected value and to the standard deviation'.
We all know,
In binomial distribution, The mean or expected value is given by np whereas the variance is given by np(1 - p) where (1 - p) taken as q is the probability of failure and p is the probability of success.
The standard deviation of binomial distribution is [tex]\sqrt{npq}[/tex].
From the expected value formula we can see that number number of trials is directly proportional to mean or expected value.
Thus we can say that
If the number of trials is increasing, then the expected value is also increasing.
From the standard deviation of binomial distribution we can see that if the number of trials increasing then the standard deviation also increasing because standard deviation is directly proportional to number of trials.
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Pick the correct answer
Please help thanks :)
Answer:
B
Step-by-step explanation:
First create the equation that has slope of -1 in the form of y=mx+b. Because the slope is -1, m=-1, so the equation is y=-x+b. Now we see that we are given the point (-3, 8) as an intersection point. Substitute x and y for -3 and 8 in our equation. With this information, our equation becomes 8=3+b. Solving, b=5. Our equation is now y=-x+5.
Simplifying all of the answer choices, we have
A. y=-x-5
B. y=-x+5
C. y=-x-5
D. and E. as what they already show
The only answer that matches is B.
pls help i don’t know how to do this
Answer: [tex]\displaystyle\\\frac{2\pi }{3},\ \frac{5\pi }{3} .[/tex]
Step-by-step explanation:
[tex]\displaystyle\\tan\theta=-\sqrt{3}\ \ \ \ 0\leq \theta\leq 2\pi \\\theta =\frac{2\pi }{3}+\pi N\ \ \ (N=0,\ 1,\ 2,\ 3\ ...)\\ N=0\\\theta=\frac{2\pi }{3} +\pi *0\\\theta=\frac{2\pi }{3}\ \ \ \ ( 0\leq \theta\leq 2\pi)\\ N=1\\\theta=\frac{2\pi }{3}+\pi *1 \\\theta=\frac{2\pi }{3} +\pi \\\theta=\frac{2\pi +3\pi }{3} \\\theta=\frac{5\pi }{3} \ \ \ ( 0\leq \theta\leq 2\pi)\\[/tex]
[tex]N=2\\\theta=\frac{2\pi }{3}+2\pi \\ \theta=\frac{2\pi +3*2\pi }{3}\\ \theta=\frac{2\pi +6\pi }{3} \\\theta=\frac{8\pi }{3} \\\theta=2\frac{2}{3} \pi \ \ \ \ (\notin0\leq \theta\leq 2\pi).\\[/tex]
what is the correct solution to the original inequality?
-4(5/2 + 3/2x) > 8
pls help LP 69 credits
Answer:
x < - 3 or x ∈ (-∞, -3)==============================
GivenInequality:
[tex]-4(\cfrac{5}{2} +\cfrac{3}{2}x) > 8[/tex]SolutionSteps1. Distribute:
[tex]-4(\cfrac{5}{2}) -4(\cfrac{3}{2}x) > 8[/tex]2. Multiply:
[tex]-10-6x > 8[/tex]3. Collect like terms:
[tex]-10-8 > 6x[/tex]4. Addition:
[tex]-18 > 6x[/tex]5. Divide both sides by 6:
[tex]-3 > x[/tex] or [tex]x < -3[/tex]Interval notation for this solution is:
x ∈ (-∞, -3)Answer:
[tex]x < -3[/tex]
Interval notation: (-∞, 3)
Step-by-step explanation:
Given inequality:
[tex]-4 \left(\dfrac{5}{2}+\dfrac{3}{2}x\right) > 8[/tex]
Divide both sides by -4 (remembering to change the direction of the inequality sign, since we are dividing by a negative):
[tex]\implies \dfrac{ -4 \left(\dfrac{5}{2}+\dfrac{3}{2}x\right)}{-4} > \dfrac{8}{-4}[/tex]
[tex]\implies \dfrac{5}{2}+\dfrac{3}{2}x < -2[/tex]
Subtract ⁵/₂ from both sides:
[tex]\implies \dfrac{5}{2}+\dfrac{3}{2}x-\dfrac{5}{2} < -2-\dfrac{5}{2}[/tex]
[tex]\implies \dfrac{3}{2}x < -\dfrac{9}{2}[/tex]
Multiply both sides by 2:
[tex]\implies \dfrac{2 \cdot 3}{2}x < -\dfrac{2 \cdot 9}{2}[/tex]
[tex]\implies \dfrac{\diagup\!\!\!\!2 \cdot 3}{\diagup\!\!\!\!2}x < -\dfrac{\diagup\!\!\!\!2 \cdot 9}{\diagup\!\!\!\!2}[/tex]
[tex]\implies 3x < -9[/tex]
Divide both sides by 3:
[tex]\implies \dfrac{3x}{3} < \dfrac{-9}{3}[/tex]
[tex]\implies x < -3[/tex]
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Find the producer surplus at the equilibrium point. 3) s(x) = x 3, 0 k x k 3; x = 3
The producer surplus at the equilibrium point is 1.0146
An equilibrium (or equilibrium point) of a dynamical machine-generated via an autonomous machine of everyday differential equations (ODEs) is a solution that doesn't change with time.
Equilibrium is the country in which the marketplace delivers and calls for stability each different, and as a result, expenses turn out to be solid. usually, an over-deliver of products or services reasons charges to head down, which leads to higher demand—at the same time as a below-supply or scarcity reasons costs to head up resulting in fewer calls.
The equilibrium equations (balance of linear momentum) are given in index form as(1.4)σji,j+bi=ρu¨i, I,j=1,2,3where σij are additives of (Cauchy) stress, ρ is mass density, and bi is body force additives.
Producer Surplus = area of shadestportion
Area of shaded portion = free of rect minus area of OneD
Aves of OABO=Now serving from
"[3√74-3/5]
= √(x+3)" de
=2 (2√6-√5)
(Jon= √46 = Fure=456-255
(x+3)+1
Area of rectangle OA BC =316
= 3√6
producer surplus = 3√6 - (ure -2√5)
= 2√3-66
= 1.0146
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find the size of each of the angles marked with letter
Answer: ||||||| n=41° |||||| m=59° IIIII p=260° IIII
Step-by-step explanation:
Alternate angle:
<m=<59°
m=59°
<n=<41°
n=41°
______________
p+41°+59°= 360°
p+100°=360°
p=360°-100°
p=260°
Answer:
n = 49
m= 31
p= 280
Step-by-step explanation:
41 + n = 90
n= 90 -41 = 49
59 + m = 90
m = 90 - 59 = 31
Hope this helps!
p + n + m = 360
p = 360 - 49 - 31 = 280
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]\displaystyle{f(x) = -2(x-3)^2 + 2}[/tex]
Step-by-step explanation:
To find y-intercept of a graph, we have to substitute x = 0 to find it - consider each functions:
First Choice
[tex]\displaystyle{f(x) = 2x(x+14)-64}\\\\\displaystyle{f(0) = 2\cdot 0(0+14)-64}\\\\\displaystyle{f(0) = 0\cdot 14-64}\\\\\displaystyle{f(0) = -64}[/tex]
Second Choice
[tex]\displaystyle{f(x) = (x+4)^2+2x}\\\\\displaystyle{f(0) = (0+4)^2 + 2(0)}\\\\\displaystyle{f(0) = 4^2}\\\\\displaystyle{f(0) = 16}[/tex]
Third Choice
[tex]\displaystyle{f(x) = (x-16)^2 + 4}\\\\\displaystyle{f(0) = (0-16)^2 + 4}\\\\\displaystyle{f(0) = (-16)^2 + 4}\\\\\displaystyle{f(0) = 256 + 4}\\\\\displaystyle{f(0) = 260}[/tex]
Fourth Choice
[tex]\displaystyle{f(x) = -2(x-3)^2 + 2}\\\\\displaystyle{f(0) = -2(0-3)^2 + 2}\\\\\displaystyle{f(0) = -2(-3)^2 + 2}\\\\\displaystyle{f(0) = -2\cdot 9 + 2}\\\\\displaystyle{f(0) = -18+2}\\\\\displaystyle{f(0) = -16}\\[/tex]
Therefore, fourth choice is correct.
Rounding off 6 400mm
The rounding off a given number implies approximating the number to the required value. Thus the answer to the given question is 6 000 mm.
Rounding off a given number implies approximating the number to the required value. This can be done in two major ways: rounding up or rounding down.
Rounding up implies considering the required digit if it is up to or greater than 5, which turns to 1. Rounding down requires no consideration of digits less than 5 which turns to 0.
Thus considering the given question, Since the second digit is 4 which is lesser than 5, then it turns to a zero. So that;
rounding off 6 400 mm would give 6 000 mm.
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Which test point holds true for the inequality 3/2y-2x>=1? Where does the shaded area lie for this inequality? The test point holds true for this inequality. The shaded area for the inequality lies the boundary line.
The test That holds true for this inequality is given as 1/4 and 1
How to solve for the inequality3/2 y - 2x > 1
The goal is to make y the subject
then
3/2 y > 2x + 1
We have to divide through the equation by 3/2
Such that y > 4/3 x + 2/3
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Pls help …. Need it immediately ….
The answer is 10.73 years.
Here, the formula we can use is :
[tex]\boxed {Children = \frac{Boys+Girls}{2}}[/tex] (for the average)
Substitute the values mentioned in the question.
10.54 = (10.35 + Girls)/2
21.08 = 10.35 + Girls
Girls = 10.73 years
The slope-intercept form given (6,-5) & perpendicular to -5x - 7y = -17.
Answer:
[tex]y=\dfrac{7}{5}x-\dfrac{67}{5}[/tex]
Step-by-step explanation:
Slope-intercept form of a linear equation:
[tex]y=mx+b[/tex]
where:
m is the slope.b is the y-intercept.Rearrange the given equation so that it is in slope-intercept form:
[tex]\implies -5x-7y=-17[/tex]
[tex]\implies -7y=5x-17[/tex]
[tex]\implies y=-\dfrac{5}{7}x+\dfrac{17}{7}[/tex]
Therefore, the slope of the given equation is -⁵/₇.
If two lines are perpendicular to each other (at right angles), the product of their slopes will be -1. Therefore, their slopes will be negative reciprocals of each other.
Therefore, the slope of the line perpendicular to the given equation is:
[tex]\sf m=\dfrac{7}{5}[/tex]
Substitute the found slope and the given point (6, -5) into the slope-intercept formula and solve for b:
[tex]\implies -5=\dfrac{7}{5}(6)+b[/tex]
[tex]\implies -5=\dfrac{42}{5}+b[/tex]
[tex]\implies b=-\dfrac{67}{5}[/tex]
Substitute the found slope and the found value of b into the slope-intercept formula to create the equation for the perpendicular line:
[tex]\implies y=\dfrac{7}{5}x-\dfrac{67}{5}[/tex]
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The volume of a cylindrical can of beans is 45 π cubic centimeters. if the diameter is 6 centimeters, what is the height of the can in centimeters?
Answer:
h = 5 cm
Step-by-step explanation:
Givens
d = 6cm
V = 45cubic cm
Formula
V = pi * r^2 h substitute values into the formula
Solution
d = 2*r
6 = 2*r Divide both sides by 2
6/2 = 2r / 2
3 = r
45 pi cm^3 = pi * (3)^2 * h Divide both sides by pi
45 pi/pi = pi * 9 * h / pi
45 = 9h Divide both sides by 4
45/4 = 9h/9
5 cm
The hollenbecks own a square lot with area 3600 square meters. they plan to fence just three sides of this lot. how many meters of fence must they purchase?
Answer: 180 meters
Step-by-step explanation: To solve this we need to find the square root of 3600. 6x6 = 36 so we know the square root is 60. That means that each side of the square lot is 60 meters. If they fence 3 sides they will need to purchase 60x3= 180 meters of fence.
A bag contains 3 red marbles, 7 blue marbles, and 2 green marbles. what is the probability of choosing a blue marble when one marble is drawn?
Answer: 7/12
Step-by-step explanation: There is a total of 3+7+2 = 12 marbles in the bag. 7 are blue marbles so there is a 7/12 chance of getting a blue marble when one marble is drawn.
Answer:
7/12
or an 84%
Step-by-step explanation:
AArea of a circle Take a rope, tie it at one corner of a door knob and then. find out how much area can be covered if you cart move around. Also mention the name of 2D figure obtained. Tie a stone on one end of the rope and then rotate it. . Find the area of obtained figure take the length of rope as a radius.
Answer:
A=113 cm²
Step-by-step explanation:
If the length of the rope is 6 cm
then the radius of the circle we draw is 6 cm.
Area of the circle is A = π·r²
A = π·6² ≈ 3.14· 36 ≈ 113cm²
Find two positive numbers whose product is 81 and whose sum is a minimum. (enter your answers as a comma-separated list. )
Answer: 18
Step-by-step explanation: the smallest two positive numbers whose product is 81 are 9 and 9. 9+9 is equal to 18.
PLS SOLVE ASAP. I will mark brainlest.
Answer:
• [tex](w \cdot u) (7)[/tex] = [tex]\bf 8[/tex]
• [tex](u \cdot w) (7)[/tex] = [tex]\bf 22[/tex]
Step-by-step explanation:
We are given:
[tex]u(x) = x^2 + 6[/tex]
[tex]w(x) = \sqrt{x + 9}[/tex].
• [tex](w \cdot u) (7)[/tex]. read as "w of u of 7", means we have to input 7 into the function [tex]u(x)[/tex], and use the output we get as input for the function [tex]w(x)[/tex] :
[tex](w \cdot u) (7)[/tex]
⇒ [tex]w(u(7))[/tex]
⇒ [tex]w(7^2 + 6)[/tex]
⇒ [tex]w(55)[/tex]
⇒ [tex]\sqrt{55 + 9}[/tex]
⇒ [tex]\sqrt{64}[/tex]
⇒ [tex]\bf 8[/tex]
• Similarly, we can evaluate [tex](u \cdot w) (7)[/tex] :
[tex](u \cdot w) (7)[/tex]
⇒ [tex]u(w(7))[/tex]
⇒ [tex]u(\sqrt{7 + 9})[/tex]
⇒ [tex]u(\sqrt{16})[/tex]
⇒ [tex]u(4)[/tex]
⇒ [tex]4^2 + 6[/tex]
⇒ [tex]\bf 22[/tex]
The answers are :
(w o u)(7) = 8
(u o w)(7) = 22
To find the first answer, substitute u(x) in w(x), and set x = 7.
u(7) = 7² + 6 u(7) = 49 + 6u(7) = 55w(u(7)) = √(55 + 9)w(u(7)) = √64w(u(7)) = 8(w o u)(7) = 8To find the second answer, substitute w(x) in u(x), and set x = 7.
w(7) = √(7 + 9)w(7) = √16w(7) = 4u(w(7)) = 4² + 6u(w(7)) = 16 + 6u(w(7)) = 22(u o w)(7) = 22Find the polar equation of an ellipse with its focus at the pole and vertices at (−1,0) and (3,0).
The polar equation of an ellipse is [tex]r=-\frac{3}{1+2cos\theta}[/tex].
The vertices of ellipse are (−1,0) and (3,0).
The polar equation of an ellipse can be represented as
[tex]r=\frac{ep}{1+ecos\theta}[/tex]
where e is the eccentricity.
Eccentricity, e = [tex]\frac{c}{a}[/tex]
c is the distance from the center to the focus and a is the distance from the center to the vertex
[tex]c=\frac{3-(-1)}{2}[/tex]
⇒ [tex]c=\frac{4}{2}[/tex]
⇒ c = 2
[tex]a=\frac{3+(-1)}{2}[/tex]
⇒ [tex]a=\frac{2}{2}[/tex]
⇒ a = 1
Then, e = [tex]\frac{2}{1}[/tex]
⇒ e = 2
Now, the polar equation of an ellipse becomes as,
⇒ [tex]r=\frac{2p}{1+2cos\theta}[/tex] ------- (1)
Now plug in a vertex point such as (-1,0) and solve for p,
⇒ [tex]-1=\frac{2p}{1+2cos0}[/tex]
⇒ [tex]-1=\frac{2p}{1+2(1)}[/tex] [∵ cos 0 = 1]
⇒ [tex]-1=\frac{2p}{3}[/tex]
⇒ [tex]-3=2p[/tex]
⇒ [tex]p=-\frac{3}{2}[/tex]
Thus the polar equation of an ellipse (1) becomes as,
⇒ [tex]r=\frac{2(-\frac{3}{2} )}{1+2cos\theta}[/tex]
⇒ [tex]r=-\frac{3}{1+2cos\theta}[/tex]
Hence we can conclude that the polar equation of an ellipse is [tex]r=-\frac{3}{1+2cos\theta}[/tex].
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the sum of two numbers is 123. when the larger number is added to 5 times the smaller, the sum is 343. find the numbers.
The two numbers are 68 and 55.
Given that the sum of two numbers is 123. when the larger number is added to 5 times the smaller, the sum is 343.
We need to find the numbers,
Let's call the two numbers x and y. According to the given information, we have the following two equations:
x + y = 123 (The sum of the two numbers is 123)
x + 5y = 343 (When the larger number is added to 5 times the smaller, the sum is 343)
Now, we can solve these two equations simultaneously to find the values of x and y.
Let's rearrange equation 1 to express x in terms of y:
x = 123 - y
Substitute this value of x into equation 2:
(123 - y) + 5y = 343
Now, solve for y:
123 + 4y = 343
4y = 343 - 123
4y = 220
y = 220 / 4
y = 55
Now that we have the value of y, we can find the value of x using equation 1:
x = 123 - y
x = 123 - 55
x = 68
So, the two numbers are 68 and 55.
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Find how many matches Peter won. plss answwer (ಥ _ ಥ)
Answer:
10 is the right answer...
Step-by-step explanation:
thanks
mark me as brainlist....
A soap company started a promotion in which each packet of detergent powder will have 20% extra powder at the
same price, Jenna buys a 2 kg packet of the detergent powder. How much total detergent powder will be in the packet?
2.4kg.,
..
hope it helps
particular company's net sales, in billions, from 2008 to 2018 can be modeled by the expression t2 + 14t + 85, where t is the number of years since the end of 2008. What does the constant term of the expression represent in terms of the context?
The constant in the expression represents that the company earned 85 billion dollars in 2008.
What does the constant represent?The expression given in the question is known as a quadratic function. A quadratic function is a function that usually has a single variable and it is raised to the power of 2. The graph of a quadratic function is a curve called a parabola. Parabolas may curve upward or downward
An example of a quadratic function is ax² + bx + c
Where: a,b, c are real numbers not equal to zero
c = constant.
The constant in this question is 85. It is the amount earned in 2008
Here are the options:
The company earned 85 billion dollars from 2008 to 2018
The company earned 85 billion dollars in 2008
The company earned 14 billion dollars from 2008 to 2018.
The company earned 14 billion dollars in 2008.
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NEED HELP SOLVING
has to be simplified
Alexa is a basketball player at East High. At a recent game, she made some three point shots and some two point shots. Alexa scored a total of 18 points and made 3 times as many two point shots as three point shots. Determine the number of three point shots Alexa made and the number of two point shots she made.
Answer:
6 2 point shots 2 3 points
Step-by-step explanation:
3 two point shot 1 3 point shot = 9
6 two point shot 2 3 point shot =18
Austin keeps a right conical basin for the birds in his garden as represented in the diagram. The basin is 40 centimeters deep, and the angle between the sloping sides is 77°. What is the shortest distance between the tip of the cone and its rim?
177.8 centimeters.
What is the formula for cos θ?The symbol for it is Cosθ, and it has the following form: adjacent/hypotenuse = cosθ. In other words, it divides the length of the hypotenuse by the length of the neighboring side, which is the side next to the angle (the longest side of a right triangle).When working with right-angled triangles, the Cos Theta Formula is particularly helpful. The Cosine of an angle in a right triangle is always equal to the hypotenuse's length divided by the length of the neighboring side. This makes it an excellent tool for resolving Cosine-related issues.The shortest distance between the tip of the cone and its rim:
cos θ= base/Hypotenuse
cos 77°=[tex]\frac{40}{H}[/tex]
[tex]0.22495=\frac{40}{H}[/tex]
[tex]H=177.8[/tex]
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The shortest distance between the tip of the cone and its rim exits 51.11cm.
What is the shortest distance between the tip of the cone and its rim?If you draw a line along the middle of the cone, you'd finish up with two right triangles and the line even bisects the angle between the sloping sides. The shortest distance between the tip of the cone and its rim exists in the hypotenuse of a right triangle with one angle calculating 38.5°. So, utilizing trigonometry and allowing x as the measurement of the shortest distance between the tip of the cone and its rim.
Cos 38.5 = 40 / x
Solving the value of x, we get
Multiply both sides by x
[tex]$\cos \left(38.5^{\circ}\right) x=\frac{40}{x} x[/tex]
[tex]$\cos \left(38.5^{\circ}\right) x=40[/tex]
Divide both sides by [tex]$\cos \left(38.5^{\circ}\right)$[/tex]
[tex]$\frac{\cos \left(38.5^{\circ}\right) x}{\cos \left(38.5^{\circ}\right)}=\frac{40}{\cos \left(38.5^{\circ}\right)}[/tex]
simplifying the above equation, we get
[tex]$x=\frac{40}{\cos \left(38.5^{\circ}\right)}[/tex]
x = 51.11cm
The shortest distance between the tip of the cone and its rim exits 51.11cm.
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Use special right triangles to find the value of the variables no decimal answers
Step-by-step explanation:
This is trigonometry. Focusing on Y initially, we can see that Y is the opposite, and 32 is the hypotenuse. Therefore, we must use sin:
[tex] \sin(60) = \frac{y}{32} [/tex]
[tex]y = \sin(60) \times 32[/tex]
[tex]y \approx28[/tex]
Next X. We can see that X is the adjacent, and 32 is the hypotenuse, so we must use cos:
[tex] \cos(60) = \frac{x}{32} [/tex]
[tex]x = \cos(60) \times 32[/tex]
[tex]x = 16[/tex]
Now let's look at A. We can see that a is the adjacent, and 12 is the opposite, so we must use tan:
[tex] \tan(60) = \frac{12}{a} [/tex]
[tex]a = \frac{12}{ \tan(60) } [/tex]
[tex]a \approx7[/tex]
Now, B. We can see that B is the hypotenuse, and 12 is the opposite, so we must use sin:
[tex] \sin(60) = \frac{12}{b} [/tex]
[tex]b = \frac{12}{ \sin(60) } [/tex]
[tex]b \approx14[/tex]
Answer:
Below in bold.
Step-by-step explanation:
The first triangle is a 30-60-90 triangle,
so the sides are in the ratio 2 : 1 : √3, where 2 is the hypotenuse, the 1 is adjacent to 60 degree angle and the √3 is opposite the 60 degree angle.
So x = 1/2 * 32 = 16
and y = 16√3 or 27.71 to nearest hundredth.
The second one is the same special triangle, so
√3/2 = 12/b
b = 24/√3
= 8√3 or 13.86 to nearest hundredth.
a = 1/2 b = 4√3 or 6.93 to nearest hundredth.
Select the correct answer. What is the value of the limit ? lim x 5 square x^2 +4
By direct evaluation, we will see that the limit is equal to 29.
How to find the limit?Here we want to find the limit of the given expression when x tends to 5.
[tex]\lim_{x \to \ 5} x^2 + 4[/tex]
We can directly evaluate the expression in x = 5 and see if we get a real value different than zero.
By direct evaluation, we get:
[tex]\lim_{x \to \ 5} x^2 + 4 = 5^2+ 4 = 29[/tex]
Notice that the limit does give a whole number, then in this way, we conclude that the limit of the given expression when x tends to 5 is equal to 29.
If you want to learn more about limits:
https://brainly.com/question/26123730
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Answer:
square 29
Step-by-step explanation: