The function shaped like a U is in the form of a basic quadratic equation and is represented as a parabola.
The graph of a quadratic function is a U-shaped curve called a parabola. An important feature of graphs is that they have extreme points called vertices.
When the parabola opens upwards, the vertex represents the lowest point of the graph, or the minimum value of the quadratic function. When the parabola opens downwards, the vertex represents the highest point or maximum of the graph.
In both cases, the vertex is the inflection point of the graph. Graphs are also symmetrical about a vertical line through the vertices called the axis of symmetry.
The standard form or basic function for a parabola will be in the form of a quadratic function such as -
[tex]f(x)=a(x-h)^{2} +k[/tex]
where, [tex](h,k)[/tex] = vertex
Thus, the function shaped like a U is in the form of a basic quadratic equation and is represented as a parabola.
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y=x-8 how would I do it
to find two points that satisfy the function, you need to give one value and calculate the other one, for example.
I will use x=4 and x=8
when x=4
y=4-8=-4
so one point is (4,-4)
and when x=8
y=8-8=0
so the other point is (8,0)
so you need to graph these points and then plot the line, like this:
what is the area of the triangle formed from (0,-1) (0,4) and (4,-1)
The area of the triangle is 10 square units formed from (0,-1), (0,4), and (4,-1).
What is the Area of a Triangle?A triangle is a closed shape composed of three angles, three sides, and three vertices.
The triangle is formed from (0,-1), (0,4), and (4,-1) which are given in the question.
As per the attached graph,
The length of the base of the triangle = 4 units
The length of the height of the triangle = 5 units
The area of the triangle = 1/2 × 4 × 5
The area of the triangle = 10 square units
Therefore, the area of the triangle is 10 square units formed from (0,-1), (0,4), and (4,-1).
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whstbis the area in square inches of the shaded part of the retangle below
The shaded area is trapezium with parallel sides as a = 10, b = 5 and height of trapezium is h = 18 in.
The formula for the area of trapezium is,
[tex]A=\frac{1}{2}\cdot(a+b)\cdot h[/tex]Determine the area of the tapezium.
[tex]\begin{gathered} A=\frac{1}{2}\cdot(10+5)\cdot18 \\ =15\cdot9 \\ =135 \end{gathered}[/tex]So area of shaded region is 135 square inch.
b.InOut133171066co38Rule:
Suppose that the rule is of the form
[tex]y=mx+b[/tex]Where m is the slope and b is the intercept
The slope can be found using the formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]You can take any two consecutive x and y values from the given table.
[tex]\frac{17-3}{3-1}=\frac{14}{2}=7[/tex]Similarly,
[tex]\frac{66-17}{10-3}=\frac{49}{7}=7[/tex]As you can see, you will end up with the same slope.
Now let us find the intercept b.
Take any x, y coordinates from the table
[tex](x,y)=(1,3)[/tex]Now substitute them in the slope-intercept equation.
[tex]\begin{gathered} y=7x+b \\ 3=7(1)+b \\ 3=7+b \\ b=-7+3 \\ b=-4 \end{gathered}[/tex]So the rule is
[tex]y=7x-4[/tex]Verification:
Let us verify whether we got the correct rule or not
Substitute the input x coordinates into the rule and check the outputs y coordinates.
[tex]\begin{gathered} y=7(1)-4=7-4=3 \\ y=7(3)-4=21-4=17 \\ y=7(10)-4=70-4=66 \\ y=7(6)-4=42-4=38 \end{gathered}[/tex]As you can see, we have got the same results therefore, the rule is correct.
ine TrackerWhat additional piece of information is needed in order to say thatthese two triangles are congruent by AAS postulate?BO BC DEO AB DEO BC EFO AB DF
Answer
Option B is correct.
AB ≅ DE
Explanation
The key to two triangles being similar according to AAS is that they have two angles and an excluded side in common.
An excluded side does not reside between the two congruent angles.
So, for these two triangles to be congruent according to AAS,
Angle C = Angle F
Angle B = Angle E
And
Side AB ≅ Side DE
Hope this Helps!!!
Allison stated that 48/90 is a terminating decimal equal to 0.53. Why is she true or why is she wrong.
Answer:
She was Wrong, because it is not a terminating decimal
Explanation:
Given the fraction;
[tex]\frac{48}{90}[/tex]Let us reduce the fraction to its least form, then convert it to decimal.
[tex]\frac{48}{90}=\frac{8}{15}[/tex]converting to decimal we have;
The decimal form of the given fraction is;
[tex]\begin{gathered} 0.533\ldots \\ =0.53\ldots \end{gathered}[/tex]Which is not a terminating decimal, because it has an unending, repeatitive decimal.
Therefore, she was Wrong, because it is not a terminating decimal
Reason quantitatively. The two rectangles shown
are similar. What is the value of x
Two shapes are similar if the ratio of the lengths of their corresponding sides are equal.
Both shapes given in the question are rectangles, therefore, one pair of opposite sides is longer than the other.
We can find the ratio for the bigger rectangle since it has all the values complete and then compare this ratio to the smaller rectangle to find the value of the unknown side.
The ratio of the longer side to the shorter side for the bigger rectangle is
[tex]\begin{gathered} \frac{16}{2} \\ =8 \end{gathered}[/tex]Therefore, for the smaller rectangle, the ratio of the longer side to the shorter side is
[tex]\frac{4}{x}=8[/tex]Solving for x, we have
[tex]\begin{gathered} x=\frac{4}{8} \\ x=0.5 \end{gathered}[/tex]The value for x is 0.5.
In a video game, Connor scored 25% more points than Max. If c is the number of points that Connor scored and m is the number of points that Max scored. Write an equation that represents the situation.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Connor scored = c
Max scored = m
equation = ?
Step 02:
Connor scored =>>> + 25% Max scored
c = m + m * 0.25
c = m ( 1 + 0.25)
c = 1.25 m
The answer is:
c = 1.25 m
Mrs. Roberts bought 4 student movietickets and one adult ticket that cost $12.Write an expression to represent the totacost of the tickets. Let s represent eachstudent ticket
Total cost = 4s+12
student's ticket price = s
Number of students tickets= 4
Adult's tickets price = $12
Number of Adult's tickets = 1
Total cost = (number of students tickets x price of each student's ticket) + ( number of adult tickets x price of each adult ticket)
Total cost of the tickets (y)= 4s + 1(12)
y = 4s+12
On Thursday Tyler‘s math teacher helped him write the expression T equals -2 parentheses 3+ age parentheses to represent the temperature change for that day indicate all the expressions below the equivalent to T equals negative age parentheses 3+ H parentheses
t = - 2 (3 + h )
Step 1: Expand the parenthesis so that -2 multiplies all the terms in the bracket
t = -2 x 3 - 2 x h
t = - 6 - 2h
Comparing the answer to the options provided
Option C is the best option
solve for x. then find the missing piece(s) of the parallelogram for #6.
Solution
Recall
[tex]\begin{gathered} 50x+130x=180\text{ \lparen supplementary\rparen} \\ 180x=180 \\ divide\text{ both sides by 180} \\ \frac{180x}{180}=\frac{180}{180} \\ \\ x=1 \\ \end{gathered}[/tex]The final answer
[tex]x=1[/tex]At which angle is secant of theta equals negative radical 2 question mark
The equation is given to be:
[tex]\sec\theta=-\sqrt{2}[/tex]Recall that sec is the inverse of cos. Thus, we have:
[tex]\frac{1}{\cos\theta}=-\sqrt{2}[/tex]Rewriting the equation, we have:
[tex]\cos\theta=-\frac{1}{\sqrt{2}}[/tex]We can find the arccos of both sides:
[tex]\theta=\arccos(-\frac{1}{\sqrt{2}})[/tex]Since we know that:
[tex]\cos(-x)=\cos(x)[/tex]Then, we have:
[tex]\theta=\arccos(\frac{1}{\sqrt{2}})[/tex]Recall the identity:
[tex]\arccos(\frac{1}{\sqrt{2}})=\frac{3\pi}{4}+2\pi n,\:θ=\frac{5\pi}{4}+2\pi n[/tex]Therefore, the answer is the SECOND OPTION.
One of the roofers claims that the roof area of each pillar is the same as the area of a square with edges of 21.5 feet.The roofer is correct or incorrect?
SOLUTION
We have been given the height of each lateral triangular face of the roof h as 13.4 ft and the length of the square base of the pyramid as 21.5 feet
We want to know if the area of the square base is the same as the area of each triangular lateral face
Area of the square base is
[tex]21.5\times21.5=462.25\text{ ft}^2[/tex]Area of the four triangular lateral face becomes
[tex]\begin{gathered} 4(\frac{1}{2}\times b\times h) \\ =4\times\frac{1}{2}\times21.5\times13.4 \\ =2\times21.5\times13.4 \\ =576.2\text{ ft}^2 \end{gathered}[/tex]From our calculations, the area of the square base is 462.25 square-feet,
While the area of the four lateral face triangle of the roof is 576.2 square-feet
Hence the roofer is incorrect
PLEASE just give me the answers and not a whole defintion of every single word. I just want quick answers so I can check my work. *don't worry, this is just a math practice
7. m and n are parallel because both alternate interior angles are equal.
8.m and n are parallel because Alternate exterior angles are equal.
9.m and n are parallel Because corresponding angles are equal.
10. m and n are parallel because corresponding and consecutive angles are equal.
11. m and n are parallel because alternate exterior angles are equal.
12.m and n are parallel because vertical (opposite) angles are equal.
g(x)= 6/x find (g°g). and domain in set notation.
We have to find the expression for the composition
[tex]g\circ\text{ g\lparen x\rparen}[/tex]Where
[tex]g(x)=\frac{6}{x}[/tex]And express its domain in set notation. We will start by finding the expression for the composition
[tex]g\circ\text{ }g(x)=g(g(x))=g(\frac{6}{x})[/tex]that is we firsts evaluate the inner functions that in this case is g, now taking as argument y=6/x, we evaluate the outer function that in this case also is g, as follows:
[tex]g\text{ \lparen }\frac{6}{x})=\frac{6}{\frac{6}{x}}=\frac{6}{6}=x[/tex]That is, the composition g*g is equal to x, the identity.
Now we will find the domain of g*g:
Note that the domain of a composition is an interception, as follows:
[tex]Domain\text{ }g\circ\text{ g=\textbraceleft Domain of }g\text{ \textbraceright }\cap\text{ \textbraceleft Image of }g\text{ \textbraceright}[/tex]Therefore, we have to find the domain and image of g, and intercept both sets. We start with the domain of g_
[tex]Domain\text{ of }g\text{ }=\text{ }\mathbb{R}\text{ - \textbraceleft0\textbraceright}[/tex]That is all the real numbers except the 0. Now note that the image of g is
[tex]Image\text{ g= }\mathbb{R}\text{ - \textbraceleft0\textbraceright}[/tex]Finally, the domain of the composition g*g, can be obtained by the formula above:
[tex]Domain\text{ of }g\circ\text{ g=}\mathbb{R}\text{ -\textbraceleft0\textbraceright }\cap\text{ }\mathbb{R}\text{ - \textbraceleft0\textbraceright= }\mathbb{R}\text{ - \textbraceleft0\textbraceright=}(-\infty\text{ },0)\text{ }\cup\text{ }(0,\infty)\text{ }[/tex]Therefore, the domain of the composition are all the real numbers excluding the 0.
-
A gardener builds a rectangular fence around a garden using at most 56 feet of fencing. The length of the fence is four feet longer than the widthWhich inequality represents the perimeter of the fence, and what is the largest measure possible for the length?
We know that
• The gardener used at most 56 feet of fencing.
,• The length of the fence is four feet longer than the width.
Remember that the perimeter of a rectangle is defined by
[tex]P=2(w+l)[/tex]Now, let's use the given information to express as inequality.
[tex]2(w+l)\leq56[/tex]However, we have to use another expression that relates the width and length.
[tex]l=w+4[/tex]Since the length is 4 units longer than the width. We replace this last expression in the inequality.
[tex]\begin{gathered} 2(w+w+4)\leq56 \\ 2(2w+4)\leq56 \\ 2w+4\leq\frac{56}{2} \\ 2w+4\leq28 \\ 2w\leq28-4 \\ 2w\leq24 \\ w\leq\frac{24}{2} \\ w\leq12 \end{gathered}[/tex]The largest width possible is 12 feet.
Now, we look for the length.
[tex]\begin{gathered} 2(12+l)\leq56 \\ 24+2l\leq56 \\ 2l\leq56-24 \\ 2l\leq32 \\ l\leq\frac{32}{2} \\ l\leq16 \end{gathered}[/tex]Therefore, the largest measure possible for the length is 16 feet.#13 how many seconds will it take for a ball dropped from a window 144 feet high to hit the ground below?
Question 13.
Given:
Height = 144 feet.
Let's determine how many seconds it will take for a ball dropped from a window of the given height to hit the ground.
Here, we have the equation:
[tex]y=-16x^2+144[/tex]Where:
y represents the height of the ball after x seconds.
Now, when the ball hits the ground, the height will be 0 ft.
Thus, to find the time at 0 ft, substitute 0 for y and solve for x:
[tex]\begin{gathered} 0=-16x^2+144 \\ \\ 16x^2=144 \end{gathered}[/tex]Divide both sides by 16:
[tex]\begin{gathered} \frac{16x^2}{16}=\frac{144}{16} \\ \\ x^2=9 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} \sqrt{x^2}=\sqrt{9} \\ \\ x=3 \end{gathered}[/tex]Therefore, it will take the ball 3 seconds to hit the ground.
ANSWER:
• (a). y = -16t² + 144
• (b). 3 seconds
I don’t understand the question its asking for the depth at 4 weeks and 9 weeks
Answer
Lake depth after 4 weeks: 343.6 ft
Lake depth after 9 weeks: 340.6 ft
Step-by-step explanation
The relation between time and lake depth is linear. Using the x-variable to represent time and the y-variable to represent the lake depth, we can use the next equation to relate these variables:
[tex]y=mx+b[/tex]where m is the slope and (0, b) is the y-intercept of the line.
The slope of the line that passes through the points (x₁, y₁) and (x₂, y₂) is calculated as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]From the table, this line passes through (0, 346) and (2, 344.8), then its slope is:
[tex]m=\frac{344.8-346}{2-0}=\frac{-1.2}{2}=-0.6[/tex]From the table, this line passes through (0, 346), then parameter b is 346.
Substituting m = -0.6 and b = 346, the equation of the line is:
[tex]y=-0.6x+346[/tex]Evaluating this line at x = 4, that is, when time = 4 weeks, we get the next depth:
[tex]\begin{gathered} y=-0.6(4)+346 \\ y=-2.4+346 \\ y=343.6\text{ ft} \end{gathered}[/tex]Evaluating the equation of the line at x = 9, that is, when time = 9 weeks, we get the next depth:
[tex]\begin{gathered} y=-0.6(9)+346 \\ y=-5.4+346 \\ y=340.6\text{ ft} \end{gathered}[/tex]1. The graph shown represents the altitude of a hikerduring a period of time. Write a possible situationrepresented by the graph.Altitude (feet)Time (hours)2. Use the vertical line test to determine if the relation represented on the graph
The vertical line test consists in tracing various vertical lines throughout the function and checking wheter this lines will touch the function more than once.
As we can see none of the lines touch the graph more than once, therefore this graph is a function.
the minimum point on the graph of the equation y = f(x) is (-1,-3). what is the minimum point on the graph of the equation y=f(x)+5?
the minimum point on the graph of the equation y = f(x) is (-1,-3). what is the minimum point on the graph of the equation y=f(x)+5?
we have that
the rule of this transformation is equal to
(x,y) ------> (x, y+5)
so
(-1,3) -----> (-1,3+5)
(-1,8) is the minimum pointWhich of the following things is not contained at the plane B?
Related with the picture and your question, you should notice that an element is not contained in a set, that in your case is the plane B, when any of its points is outside of this one.
Then by the picture we could notice that the line q is not contained at the plane B, because the point G is inside q but it is not in B.
Let n =2. Evaluate the following (nn)n
We have the following:
[tex](nn)n[/tex]n=2
[tex]2\cdot2\cdot2=8[/tex]Convert the following unit areas as indicated. Choose the right answe Area Conversion Number Table English Area Conversion Number Metric Area Square Miles Square Miles Acres Acres Square Yards Square Feet Square Inches 2.59 259 4.05 x 10-3 4.05 x 10-1 8.36 x 10-1 9.29 x 10-2 6.45 Square Kilometers Hectares Square Kilometers Hectares Square Meters Square Meters Square Centimeters 50 in.2 to cm2
Answer:
322.5 square centimeters
Explanation:
To convert from square inches to square centimeters, we need to multiply the number by the conversion factor 6.45, so 50 in² are equivalent to:
50 in² x 6.45 = 322.5 cm²
Therefore, the answer is 322.5 square centimeters.
what's the probability of randomly meeting a four child family with either exactly one or exactly two boy children
1) Let the Probability of randomly meeting a four child family with exactly one child: P(A)
Let the Probability of randomly meeting a four child family with exactly 2 boy children : P(B)
Since the question is about how do we get to the Probability of meeting A or B
We can write:
P(A ∪ B) = P(A) + P(B) - P(A * B)
2) Knowing the subspace. We subtract to not count twice the Probability of A , and B.
If the events are mutually exclusives, i.e. there are no common elements so so we can write that
P(A ∪ B)= P(A) +P(B)
Hi I need help with these questions, if you can only answer 1 that’s okay. Thank you!
Each square in the block represents each block of size = 0.1*0.4 = 0.04.
1.
The factor 1.5 is divided into two number because in the figure it is shown that the 1 is up to orange line and 0.5 is up to black line and we want to find only area of divided parts.
That is
1*0.4 + 0.5 * 0.4
= 0.4+0.20
= 0.6
2.
Each square in the block represents each block of size = 0.1*0.4
= 1*4/10*10
= 4/100
= 0.04
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Precalc and i need help withb. Sec(18pie)c. Sin(7pie/6) tan(8pie/3)d. Tan(pie/12)
In b we need to find:
[tex]\sec 18\pi[/tex]It's important to recal that the secant is equal to:
[tex]\sec 18\pi=\frac{1}{\cos18\pi}[/tex]Another important property that will be useful is:
[tex]\cos x=\cos (x+2\pi m)[/tex]Where m is any integer. Let's see if we can write 18*pi using this. We can take x=0 so we have:
[tex]\begin{gathered} 18\pi=x+2\pi m=2\pi m \\ 18\pi=2\pi m \end{gathered}[/tex]If we divide both sides by 2*pi:
[tex]\begin{gathered} \frac{18\pi}{2\pi}=\frac{2\pi m}{2\pi} \\ 9=m \end{gathered}[/tex]Since m is an integer then we can assure that:
[tex]\cos 18\pi=\cos (0+2\pi\cdot9)=\cos 0=1[/tex]Then the secant is given by:
[tex]\sec 18\pi=\frac{1}{\cos18\pi}=\frac{1}{\cos 0}=1[/tex]So the answer to b is 1.
In c we need to find:
[tex]\sin (\frac{7\pi}{6})\tan (\frac{8\pi}{3})[/tex]Here we can use the following properties in order to write those angles as angles of the first quadrant:
[tex]\begin{gathered} \sin (x)=-\sin (x-\pi) \\ \tan (x)=\tan (x-m\pi)\text{ with }m\text{ being an integer} \end{gathered}[/tex]So we have:
[tex]\begin{gathered} \sin (\frac{7\pi}{6})=-\sin (\frac{7\pi}{6}-\pi)=-\sin (\frac{\pi}{6}) \\ \tan (\frac{8\pi}{3})=\tan (\frac{8\pi}{3}-3\pi)=\tan (-\frac{1}{3}\pi) \end{gathered}[/tex]If we convert these two angles from radians to degrees by multiplying 360° and dividing by 2*pi we have:
[tex]\begin{gathered} \frac{\pi}{6}\cdot\frac{360^{\circ}}{2\pi}=30^{\circ} \\ -\frac{1}{3}\pi\cdot\frac{360^{\circ}}{2\pi}=-60^{\circ} \end{gathered}[/tex]And remeber that:
[tex]\tan x=-\tan (-x)[/tex]So we get:
[tex]\begin{gathered} \sin (\frac{7\pi}{6})=-\sin (\frac{\pi}{6})=-\sin (30^{\circ}) \\ \tan (\frac{8\pi}{3})=\tan (-\frac{\pi}{3})=-\tan (\frac{\pi}{3})=-\tan (60^{\circ}) \end{gathered}[/tex]Then we can use a table of values:
Then:
[tex]\sin (\frac{7\pi}{6})\tan (\frac{8\pi}{3})=\sin (30^{\circ})\cdot\tan (60^{\circ})=\frac{1}{2}\cdot\sqrt[]{3}=\frac{\sqrt[]{3}}{2}[/tex]So the answer to c is (√3)/2.
In d we need to find:
[tex]\tan (\frac{\pi}{12})[/tex]In order to do this using the table we can use the following:
[tex]\begin{gathered} \tan x=\frac{\sin x}{\cos x} \\ \sin 2x=2\sin x\cos x \\ \cos 2x=\cos ^2x-\sin ^2x \\ \cos ^2x+\sin ^2x=1 \end{gathered}[/tex]So from the first one we have:
[tex]\tan (\frac{\pi}{12})=\frac{\sin (\frac{\pi}{12})}{\cos (\frac{\pi}{12})}[/tex]We convert pi/12 into degrees:
[tex]\frac{\pi}{12}\cdot\frac{360^{\circ}}{2\pi}=15^{\circ}[/tex]So we need to find the sine and cosine of 15°. We use the second equation:
[tex]\begin{gathered} \sin 30^{\circ}=\frac{1}{2}=\sin (2\cdot15^{\circ})=2\sin 15^{\circ}\cos 15^{\circ} \\ \sin 15^{\circ}\cos 15^{\circ}=\frac{1}{4} \end{gathered}[/tex]Then we use the third:
[tex]\begin{gathered} \cos (30^{\circ})=\frac{\sqrt[]{3}}{2}=\cos (2\cdot15^{\circ})=\cos ^215^{\circ}-\sin ^215^{\circ} \\ \frac{\sqrt[]{3}}{2}=\cos ^215^{\circ}-\sin ^215^{\circ} \end{gathered}[/tex]And from the fourth equation we get:
[tex]\begin{gathered} \cos ^215^{\circ}+\sin ^215^{\circ}=1 \\ \sin ^215^{\circ}=1-\cos ^215^{\circ} \end{gathered}[/tex]We can use this in the previous equation:
[tex]\begin{gathered} \frac{\sqrt[]{3}}{2}=\cos ^215^{\circ}-\sin ^215^{\circ}=\cos ^215^{\circ}-(1-\cos ^215^{\circ}) \\ \frac{\sqrt[]{3}}{2}=2\cos ^215^{\circ}-1 \\ \cos 15^{\circ}=\sqrt{\frac{1+\frac{\sqrt[]{3}}{2}}{2}} \\ \cos 15^{\circ}=\sqrt{\frac{1}{2}+\frac{\sqrt[]{3}}{4}} \end{gathered}[/tex]So we found the cosine. For the sine we use the expression with the sine and cosine multiplying:
[tex]\begin{gathered} \sin 15^{\circ}\cos 15^{\circ}=\frac{1}{4} \\ \sin 15^{\circ}\cdot\sqrt[]{\frac{1}{2}+\frac{\sqrt[]{3}}{4}}=\frac{1}{4} \\ \sin 15^{\circ}=\frac{1}{4\cdot\sqrt[]{\frac{1}{2}+\frac{\sqrt[]{3}}{4}}} \end{gathered}[/tex]Then the tangent is:
[tex]\tan (15^{\circ})=\frac{\sin(15^{\circ})}{\cos(15^{\circ})}=\frac{1}{4\cdot\sqrt[]{\frac{1}{2}+\frac{\sqrt[]{3}}{4}}}\cdot\frac{1}{\sqrt[]{\frac{1}{2}+\frac{\sqrt[]{3}}{4}}}=\frac{1}{4}\cdot\frac{1}{\frac{1}{2}+\frac{\sqrt[]{3}}{4}}[/tex][tex]\tan (15^{\circ})=\frac{1}{4}\cdot\frac{1}{\frac{1}{2}+\frac{\sqrt[]{3}}{4}}=\frac{1}{2+\sqrt[]{3}}[/tex]Then the answer to d is:
[tex]\frac{1}{2+\sqrt[]{3}}[/tex]calculate the difference quotient and use your results to find the slope of the tangent line
Approximate Slope of a Function
We are given the function:
[tex]H(x)=8\ln x+3[/tex]We will find the approximate value of the slope at (e,11).
It's required to use 3 possible values of the approximation differential h.
Let's use h=0.1 and evaluate the function at x = e + 0.1 = 2.8182818
Compute:
[tex]H(e+0.1)=8\ln 2.8182818+3=11.2890193[/tex]Compute the difference quotient:
[tex]H^{\prime}=\frac{11.2890193-11}{0.1}=2.890193[/tex]Now we use h=0.01:
[tex]H(e+0.01)=8\ln 2.728281828+3=11.02937635[/tex]The difference quotient is:
[tex]H^{\prime}=\frac{11.02937635-11}{0.01}=2.9376353[/tex]Finally, use h=0.001:
[tex]H(e+0.001)=8\ln 2.719281828+3=11.00294249[/tex][tex]H^{\prime}=\frac{11.00294249-11}{0.001}=2.9424943[/tex]The last result is the most accurate, thus the slope of the tangent line is 2.94
a single pump is filling a storage container with water at a rate of 60 gallons per minute. after 30 minutes, an additional pump turns on and the container begins to fill at a total rate of 130 gallons per minute for an additional 30 mins. the container already had 1500 gallons of water when it began to be filled a) create a graph showing the amount of water the tank contains for the first 60 minutes b) write a piecewise defined functions for the volume, V, as a function of time, t, measured in minutes
Now we graph the piecewise defined function:
car is coasting backwards downhill at a speed of 2.9 m/s when the driver gets the engine started. After 2.5 s, the car is moving uphill at 4.8 m/s. Assuming that the uphill is the positive direction, what is the car's average acceleration? m/s2
The average acceleration of the car is 3.08 m/s² .
The speed of the car down hill = - 2.9m/s
The speed of the car uphill = 4.8 m/s
An object's average acceleration over time is determined by dividing the change in velocity, Δv, by the duration of the period, Δt.
Average acceleration = Δv ÷ Δt
Now the change in velocity ΔV = 4.8 - (-2.9) = 7.7 m/s
Change is time Δt = 2.5 seconds
Average acceleration of the car = 7.7 / 2.5 m/s² = 3.08 m/s²
In mechanics, the acceleration is the change is speed that refers to the exact rate at which the object's velocity varies with respect to time varies. Acceleration is a vector quantity since it has both a magnitude and a direction. The direction of an object's acceleration is determined by the direction of the net force acting on it.
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Sara made an error in solve the one-step equation below.5x + 9 = 29-9 -9- 4x = 29/4. /4x = -7.25What is the error that Sara made?What should Sara had done to solve the one-step equation above insteadof what she did?What is the answer that Sara should have found for the above one-step equation?*
To solve this one-step equation you:
1. Substract 9 in both sides of the equation:
In this step is the mistake as Sara gets as result -4x=29 and the corret result of substract 9 in both sides of the equation is 5x=20.2. Divide both sides of the equation into 5:
Then, the answer that Sara should found for the equation is x=4