Answers
Answer:
see my photo bro. hope it can help.
Answer:
[tex]\textsf{(a)} \quad \overline{v}=-8t-4h-2[/tex]
[tex]\textsf{(b)} \quad v(t)=-8t-2[/tex]
[tex]\textsf{(c)} \quad L(t)=-26t+41[/tex]
(d) See attachment.
Step-by-step explanation:
Given equation for displacement:
[tex]s(t)=-4t^2-2t+5[/tex]
Part (a)Average velocity formula:
[tex]\boxed{\overline{v}=\dfrac{s(t_2)-s(t_1)}{t_2-t_1}}[/tex]
where:
[tex]\overline{v}[/tex] = average velocitys(t₁) = position function at t₁s(t₂) = position function at t₂t₁ = initial timet₂ = final timeTo find the average velocity of s(t) between the inputs t and t+h:
[tex]\textsf{Let}\;t_1 = t[/tex][tex]\textsf{Let}\; t_2 = t+h[/tex]Find expressions for s(t) at t₁ and t₂:
[tex]\implies s(t_1)=s(t)=-4t^2-2t+5[/tex]
[tex]\begin{aligned}\implies s(t_2)=s(t+h)&=-4(t+h)^2-2(t+h)+5\\&=-4(t^2+2th+h^2)-2t-2h+5\\&=-4t^2-8th-4h^2-2t-2h+5\end{aligned}[/tex]
Substitute the found values into the average velocity formula:
[tex]\begin{aligned}\implies \overline{v} =\dfrac{s(t_2)-s(t_1)}{t_2-t_1}}&=\dfrac{(-4t^2-8th-4h^2-2t-2h+5)-(-4t^2-2t+5)}{(t+h)-t}}\\\\&=\dfrac{-4t^2-8th-4h^2-2t-2h+5+4t^2+2t-5}{t+h-t}\\\\&=\dfrac{-8th-4h^2-2h}{h}\\\\ &=-8t-4h-2\\\\ \end{aligned}[/tex]
Therefore, the average velocity between the inputs t and t+h is:
[tex]\boxed{\overline{v}=-8t-4h-2}[/tex]
Part (b)To find the equation for instantaneous velocity v(t), differentiate the equation for displacement:
[tex]\begin{aligned}\implies v(t)&=s'(t)\\&=2 \cdot -4t^{(2-1)}-1 \cdot 2t^{(1-1)}+0\\&=-8t-2\end{aligned}[/tex]
Part (c)Find the value of s when t = 3:
[tex]\begin{aligned}\implies s(3)&=-4(3)^2-2(3)+5\\&=-4(9)-6+5\\&=-36-6+5\\&=-42+5\\&=-37\end{aligned}[/tex]
To find the gradient of s(t) at t = 3, substitute t = 3 into the differentiated function:
[tex]\begin{aligned}\implies s'(3)=v(3)&=-8(3)-2\\&=-24-2\\&=-26\end{aligned}[/tex]
Substitute the found gradient and found point (3, -37) into the point-slope form of a linear equation to find the equation of the tangent line L(t):
[tex]\begin{aligned}\implies s-s_1&=m(t-t_1)\\s-(-37)&=-26(t-3)\\s+37&=-26t+78\\s&=-26t+41\\\implies L(t)&=-26t+41\end{aligned}[/tex]
Part (d)See attachment.
Related Questions
Write the correct expression for the following statement:
x six times
Answers
x^6
Step-by-step explanation:
I don't know how to explain but I think this is what you mean
The measure of two complementary angles are in ratio 2:3. What is the measure of the smaller angle
Answers
ANSWER
36°
EXPLANATION
Let a and b be the measures of the two angles. We know that they are complementary, so their measures add up to 90°. Also, we know that the quotient between their measures is 2/3,
[tex]\begin{gathered} a+b=90 \\ \frac{a}{b}=\frac{2}{3} \end{gathered}[/tex]Solve the second equation for a,
[tex]a=\frac{2}{3}b[/tex]Replace a with this expression in the first equation,
[tex]\frac{2}{3}b+b=90[/tex]Add like terms,
[tex]\frac{5}{3}b=90[/tex]Solving for b,
[tex]b=90\cdot\frac{3}{5}=54[/tex]So the other angle is,
[tex]a=\frac{2}{3}b=\frac{2}{3}\cdot54=36[/tex]Hence, the measure of the smaller angle is 36°.
For the function f(x), = 10 (√x + 9), find f-¹(x).
Answers
The inverse of the function f(x) = 10 (√x + 9) is f⁻¹(x) = (x - 90)² / 100
Given,
The function, f(x) = 10 (√x + 9)
We have to find the inverse of the function, f⁻¹(x)
Here,
f(x) = 10 (√x + 9)
f(x) = 10√x + 90
Replace f(x) with y.
y = 10√x + 90
Swap x with y;
x = 10√y + 90
Solve for y
That is,
x = 10√y + 90
x - 90 = 10√y
(x - 90) / 10 = √y
Square both sides
((x - 90) / 10)² = √y²
(x - 90)² / 100 = y
Replace y with f⁻¹(x)
That is,
f⁻¹(x) = (x - 90)² / 100
Therefore,
The inverse for the function f(x) = 10 (√x + 9) is f⁻¹(x) = (x - 90)² / 100
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find 10-3. write the subtraction fact tow ways?
Answers
Answer:
10 - 3 = 7
10 - 7 = 3
Step-by-step explanation:
In order to earn extra money during the summer, Trevor is working as a house painter. The
amount of money he earns depends on the number of houses he paints.
m = the amount of money Trevor earns
h = the number of houses Trevor paints
Which of the variables is independent and which is dependent?
h is the independent variable and m is the
dependent variable
m is the independent variable and h is the
dependent variable
Submit
Answers
The correct answer to this question is that m is the dependent variable and h is the independent variable.
The amount of money Trevor earns can be formulated in the form of linear equation. A Linear equation is the one which can be expressed in the form of y = ax + b where y is dependent, and x is independent variable whereas a, b are coefficients. According to question amount of money Trevor earns will depend on the number of houses he paints. If m is the amount of money Trevor earns and h is the number of houses Trevor paints. This can be formulated as
m = hx + b and in this expression, m is dependent variable and h is independent variable as his earning will depend on the number of houses he paints.
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Solve this inequality
Answers
[tex]\boxed{ \large\displaystyle\text{$\begin{gathered}\sf \bf{-8\leq 10-2x < 28 } \end{gathered}$} }[/tex]
Separate the inequality compound in the inequality system.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{{\left\{ \begin{array}{r}10-2x\geq -8 \\ 10-2x < 28 \ \end{array} \right.} } \end{gathered}$} }[/tex]
We solve to: 10 - 2x < 28Order the unknown terms to the left side of the equation.[tex]\boxed{\bf{-2x < 28-10 }}[/tex]
Calculate the sum or difference.
[tex]\boxed{\bf{-2x < 18 }}[/tex]
Divide both sides of the equation by the coefficient of the invariable.[tex]\boxed{\bf{x > -\frac{18}{2} }}[/tex]
Clear the common factor
[tex]\boxed{\bf{x > -9} }}[/tex]
We solve to: 10 - 2x ≥ -8Order the unknown terms to the left side of the equation.
[tex]\boxed{\bf{-2x\geq -8-10 }}[/tex]
Calculate the sum or difference.
[tex]\boxed{\bf{-2x\geq -18 }}[/tex]
Divide both sides of the equation by the coefficient of the invariable.
[tex]\boxed{\bf{x\leq \frac{-18}{-2} }}[/tex]
Determine the sign of multiplication and division.
[tex]\boxed{\bf{x\leq \frac{18}{2} }}[/tex]
Clear the common factor
[tex]\boxed{\bf{x\leq 9}}[/tex]
[tex]\boxed{ \large\displaystyle\text{$\begin{gathered}\sf \bf{x > -9 \ and \ x\leq 9 } \end{gathered}$} }[/tex]
We find the intersection.
Answer = [tex]\boxed{ \large\displaystyle\text{$\begin{gathered}\sf \bf{-9 < x\leq 9 } \end{gathered}$} }[/tex]
Alternative forms: x ∈ (-9, 9]The field inside a running track is made up of a rectangle 84.39 m long and 73 m wide, together with a half-circle at each end. The running lanes are 9.76 m Wide all the way around.What is the area of the running track that goes around the field? Round to the nearest square meter.
Answers
To find the area of the running track that goes around the field, we need to follow the formula:
area of running track = outside area - inside area
1. Outside Area:
outside area = area of rectangle + 2× area of the semi- circle
= 92.52× 84.39 + π × 46.26² = 14527.32m²
2. Inside Area:
inside area = area of rectangle + 2× area of the semi- circle
= 73 × 84.39 + π × 36.5² = 10343.74m²
So, area of running track = 14527.32 m² - 10343.74m² = 4183.58m² ≈ 4184m²
Calculate the distance between the points L=(1, -8) and C=(9, -3) in the coordinate plane.
Round your answer to the nearest hundredth.
kintett. 41
Distance:
Answers
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ L(\stackrel{x_1}{1}~,~\stackrel{y_1}{-8})\qquad C(\stackrel{x_2}{9}~,~\stackrel{y_2}{-3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ LC=\sqrt{(~~9 - 1~~)^2 + (~~-3 - (-8)~~)^2} \implies LC=\sqrt{(9 -1)^2 + (-3 +8)^2} \\\\\\ LC=\sqrt{( 8 )^2 + ( 5 )^2} \implies LC=\sqrt{ 64 + 25 } \implies LC=\sqrt{ 89 }\implies LC\approx 9.43[/tex]
David has a coin collection. He keeps 9 of the coins in his box, which is 2% of the collection. How many total coins are in his collection?
Answers
Work Shown:
x = total number of coins
2% of x = 0.02x = 9 coins in the box
0.02x = 9
x = 9/0.02
x = 450 coins total
which of the following equations would not contain the point (4,12)?
A. y=1/2x+8 B. y= -2x+20
Answers
Answer:
A is the answer :))))))))))))))))))
A flower garden is shaped like a circle. Its diameter is . A ring-shaped path goes around the garden. The width of the path is .The gardener is going to cover the path with sand. If one bag of sand can cover , how many bags of sand does the gardener need? Note that sand comes only by the bag, so the number of bags must be a whole number. (Use the value for .)
Answers
The number sand bags required are 84 approximately.
Given, we have:
Diameter of garden = 38 yd
Width of path = 5 yd
Diameter of garden with path = 38 + 2 x 5 = 48 yd
We need to find area of path.
Area of path = Area of garden with path - area of garden
Area of path = π × 48²/4 - π × 38²/4
Area of path = 7234.56/4 - 4534.16/4
Area of path = 1808.64 - 1133.54
Area of path = 675.1 yd²
Area covered by one sand bag = 8 yd²
Number of sand bags required = Area of path/Area covered by one sand bag
=675.1/8
= 84.38 ≈ 84
Number of sand bags needed = 84
Therefore, number of sand bags required are 84.
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Triangle HIJ is similar to triangle KLM. Find the measure of side LM. Round your answer to the nearest tenth if necessary. Figures are not drawn to scale.
Answers
Given the following question:
We know the two triangles are similar
We also have the bases of the two triangles which means we can find how bigger the second triangle is, compared to the first triangle.
[tex]\begin{gathered} 5\times3.6=18 \\ 7\times3.6=25.2 \\ 25.2\text{ is already rounded to the nearest tenth} \\ LM=25.2 \end{gathered}[/tex]Question Solve for d. d³ = 27
Answers
Answer:
d = 3
Step-by-step explanation:
I took different numbers, like 1 and 2, and multiplied them to themselves 3 times, for example, 2 x 2 x 2, but since that answer was wrong, I decided to try a different number, which was 3 and that was correct.
Which value makes the equation 5b + 15 = 30 true?
A b=3
B b=9
C b= 10
D b=75
Answers
Answer:
Hello! The answer is A) B=3
Step-by-step explanation:
Hope I helped! Please mark brainiest if get chance.
(Ps: Are you an army?)
Then subtract 15 on both sides
5b=15
Divide 5 by 15
B=3
So , (5 x 3)+ 15= 30, would make this equation true.
I hope this helps :)
What is the area of the shaded triangle?The area of the shaded triangle is in. 2
Answers
The area of the shaded triangle is equal to:
[tex]A=\frac{1}{2}bh[/tex]the base of the shaded triangle is 4 in and the height is 5 in, then:
[tex]\begin{gathered} A=\frac{1}{2}(4)(5) \\ =\frac{1}{2}\cdot20 \\ =10 \end{gathered}[/tex]Therefore the shaded area is 10 squared inches.
Bob's Golf Palace had a set of 10 golf clubs that were marked on sale for $840. This was a discount of 10% off the original selling price.Step 2 of 4: If the golf clubs cost Bob's Golf Palace $390, what was their profit? Follow the problem-solving process and round youranswer to the nearest cent, if necessary.
Answers
Consider that the Bob's Golf Palace bought the set of golf clubs by $390.
Moreover, take into account that the golf clubs were markes on sale for $840.
The profit is only the difference between the marked on sale and the money Bob's Golf Palace payed:
$840 - $390 = $450
Hence, the profit was $450
Use four rectangles to estimate the area between the graph of the function f(x) = V3x + 5 and the x-axis on the interval[0, 4] using the left endpoints of the subintervals as the sample points. Round any intermediate calculations, if needed, to noless than six decimal places, and round your final answer to three decimal places.
Answers
Answer:
12.123
Step-by-step explanation:
You want the area under the curve f(x) = √(3x+5) on the interval [0, 4] estimated using the left sum and four subintervals.
Riemann sumWhen the interval [0, 4] is divided into four equal parts, each has unit width. That means the area of the rectangle defined by the curve and the interval width will be equal to the value of the curve at the left end of the interval.
The area we want is the sum ...
f(0) +f(1) +f(2) +f(3)
As the attachment shows, that sum is ...
area ≈ 12.123 . . . square units
__
Additional comment
The table values in the attachment are rounded to 7 decimal places. Trailing zeros are not shown. Actual values used have 12 significant digits, as the total shows.
Such a sum is called a Riemann sum, named for a German mathematician. Four such sums are commonly used, and further refinements are possible. Those are the left sum (as here), the right sum, the midpoint sum, and a sum using a trapezoidal approximation of the rectangle area.
For left, right, and midpoint sums, n function values are required for n subintervals. When the trapezoidal approximation is used, n+1 function values are required.
Need help please with this
Answers
Answer: It would be Answer D
Step-by-step explanation: He Subtracted from both sides in an incorrect order
What does the fundamental theorem of algebra state about the equation 2x2−x+2 = 0?Question 5 options:The fundamental theorem of algebra tells you that the equation will have two complex roots since the leading coefficient of the equation is 2. The roots arex = 1 ± i7.−−√The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are x = 1 ± i7.−−√The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots arex = 1±i15√4.The fundamental theorem of algebra tells you that the equation will have two complex roots since the leading coefficient of the equation is 2. The roots arex = 1±i15√4.
Answers
Given
Equation
[tex]2x^2-x+2=0[/tex]Procedure
The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are
[tex]x=\frac{1}{4}\pm\frac{\sqrt[]{15}}{4}[/tex]The discriminant b^2 - 4ac < 0
so, there are two complex roots.
Assume that AGHI ALMN. Which of the following congruence statements
are correct? Check all that apply.
A. ZN=21
B. ZL 41
C. ME ZH
☐ D. GH = LM
E. IG= LM
F. IH NM
Answers
The following congruence statements a, b, e, f are correct.
What is congruence in a triangle?
Triangle congruence: If all three corresponding sides and all three corresponding angles seem to be equal in size, two triangles are said to be congruent.
When two triangles are congruent, their sides and corresponding angles are identical.
Therefore, if GHI is congruent to LMN, then GH =LM, HI=MN and GI=LN, and also angle G=angle L, Angle H=angle M, while angle I = angle N, therefore the correct answers is f) ∠M= ∠H, (a) GH = LM b) ∠L=∠G. and e)IH=NM.
Therefore, option a, b, e, f are correct.
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The quotient of 134 and z is the same as 374
Answers
We will ahve the following:
[tex]\frac{134}{z}=374[/tex]Can you please help? I think it is ODD. Do you agree?
Answers
Given,
The function is:
[tex]f(x)=x+\frac{12}{x}[/tex]Taking x = -x then,
[tex]\begin{gathered} f(-x)=-x+\frac{12}{-x} \\ =-x-\frac{12}{x} \\ =-(x+\frac{12}{x}) \\ =-f(x) \end{gathered}[/tex]The function is odd.
Converting between fractions, decimals, and percentsUse the definition of the word percent to write each percent as a fraction and then as a decimal.
Answers
Answer:
See below for the completed table
Explanation:
A percentage is a number or ratio written as a fraction of 100. It is usually denoted using the symbol %.
To convert from percentage to fraction, divide the percentage by 100.
[tex]25\%=\frac{25}{100}[/tex]You can then convert the fraction to a decimal where:
[tex]\frac{25}{100}=0.25\text{ (In decimal form)}[/tex]Using the method described above, we calculate for the other values on the table:
[tex]\begin{gathered} 50\%=\frac{50}{100}=0.5 \\ 100\%=\frac{100}{100}=1 \\ 1\%=\frac{1}{100}=0.01 \\ 37.5\%=\frac{37.5}{100}=0.375 \\ 110\%=\frac{110}{100}=1.1 \\ \frac{1}{2}\%=\frac{0.5}{100}=0.005 \end{gathered}[/tex]The completed table is attached below.
What does the leading term of −5x^4+4x^3−6x^2+8 tell you?
Answers
Step-by-step explanation:
The leading term is -5x^4, which tells us the highest degree of the polynomial.
The leading term in the equation tells us about the degree and whether the curve opens outwards on inwards
What is an equation in one variable?
An equation is a polynomial in one variable with a finite degree
We are given an equation
[tex]-5x^4+4x^3-6x^2+8[/tex]
In this the leading term is -5x^4
Here the coefficient is negative this tells us that the curve opens downwards. if the coefficient has been positive then the curve would open outwards.
Also from the leading term we can find out the degree of the highest variable. the degree of highest variable in this case is 4
Hence, The leading term in the equation tells us about the degree of the variable and whether the curve opens outwards on inwards
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A population doubles every 27 years. Assuming exponential growth find the following:help find continuous growth rate (a) The annual growth rate: 2.6(b) The continuous growth rate is____% per year help (numbers)
Answers
Given,
A population doubles every 27 years.
a. Let initial population be 1 and after 27 years it becomes 2.
Considering r as the rate of annuall growth we have,
[tex]\begin{gathered} 1(1+r)^{27}=2 \\ \Rightarrow27\ln (1+r)=\ln 2 \\ \Rightarrow\ln (1+r_{})=\frac{0.693}{27} \\ \Rightarrow1+r=1.0257 \\ \Rightarrow r=0.026 \end{gathered}[/tex]Thus annual growth rate is 2.6%
b. For continuous growth,
[tex]\begin{gathered} 1(e^{27x})=2 \\ \Rightarrow27x=0.693 \\ \Rightarrow x=0.025 \end{gathered}[/tex]The continuous growth rate is _2.5___% per year
1/2 ^1/2 please show the steps
Answers
The value of [tex](\frac{1}{2} )^{\frac{1}{2} }[/tex] is 0.707.
1÷2 = 0.5
Given, [tex](\frac{1}{2} )^{\frac{1}{2} }[/tex]
Could be written like, [tex](0.5)^{0.5}[/tex] or √(1 ÷ 2) or √(0.5)
So the value of √(0.5) is 0.707.
Another way is to factorize each integer as the product of its primes using the square root prime factorization method. Follow these methods to find the square root of a certain number using prime factorization:
Step 1: Divide the supplied integer by its decimal equivalent.
Step 2: If the connected components are identical, a pair is generated.
Step 3: Choose one of the pair members for her.
Step 4: Multiply the prime numbers you got by picking one from each pair.
Step 5: This product is the square root of the specified number.
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n
4 Which expression is equivalent to 8.508 ÷ 70.9?
A 8.508 709
B 85.08 709
C 850.8 709
D 8,508 709
5 What is the value of 0.5 ÷ 0.8? Show your work.
Answers
Answer:
a because 8.508
Step-by-step explanation:
0.625 so it easy 0.5:0.8
2(3x+6)-96=6(2x-4)-56Which value of x makes the equation true?A. X=-2B. x=-2/3C. x=2D. x=3
Answers
Given equation:
[tex]2(3x+6)-96=6(2x-4)-56[/tex]Solve the equation to find the value of x,
[tex]\begin{gathered} 2(3x+6)-96=6(2x-4)-56 \\ 2(3x)+2(6)-96=6(2x)-6(4)-56 \\ 6x+12-96=12x-24-56 \\ 6x-84=12x-80 \\ -84+80=12x-6x \\ -4=6x \\ x=\frac{-4}{6} \\ x=-\frac{2}{3} \end{gathered}[/tex]Hence, x=-2/3
Answer: option B) is correct
Answer:
2(3×+6) is 96 _6 by (2×4=5) with A.X
From a group of 6 people, you randomly select 5 of them.
What is the probability that they are the 5 oldest people in the group?
Give your answer as a fraction
Answers
The probability that they are the 5 oldest people in the group is 1/6.
Given that we have a group of 6 people, and we randomly select 5 of them.
We need to find the probability that they are the 5 oldest people in the group.
The total number of ways to select 5 people from a group of 6 people is given by 6C5 which is equal to 6.
This means that there are only 6 possible outcomes when we randomly select 5 people from a group of 6 people.
We know that the 5 oldest people in the group can be selected only in one way.
So, the number of favorable outcomes is 1.
Hence, the probability of selecting the 5 oldest people from the group when 5 people are randomly selected is: Probability = favorable outcomes/total outcomes Probability = 1/6
Therefore, the probability that they are the 5 oldest people in the group is 1/6.
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How many 1/4 pound hamburgers could be made from 5 1/2 pounds of hamburger meat?
Answers
Given:
Total amount of hamburger meat = 5½ pounds
Let's find how many ¼ pound hamburgers could be made from 5½ pounds of hamburger meat.
To find how many pound hamburger could be made divide 5½ by ¼.
Thus, we have:
[tex]5\frac{1}{2}\div\frac{1}{4}[/tex]To perform the division, take the following steps:
Step 1:
Convert the mixed fraction to improper fraction
[tex]\frac{11}{2}\div\frac{1}{4}[/tex]Step 2:
Flip the fraction on the right and change the division symbol to multiplication
[tex]\begin{gathered} \frac{11}{2}\ast\frac{4}{1} \\ \\ =\frac{11\ast4}{2\ast1} \\ \\ =\frac{44}{2} \\ \\ =22 \end{gathered}[/tex]Therefore, 22 of ¼ pound of hamburger could be made from 5½ pounds of hamburger meat.
ANSWER:
22