The 58 m/s initial velocity of the arrow with height, y = 58•t - 0.83•t², gives;
(1) 55.925 m/s
(2) 56.257 m/s
(3) 56.3317 m/s
(4) 56.33917 m/s
(b) 56.34 m/s
How can the average and instantaneous velocity be calculated?Initial velocity of the arrow = 58 m/s
Height of the arrow is; y = 58•t - 0.83•t²
The above kinematic equation can be analyzed as follows;
(1) The height at t = 1 is found as follows;
y = 58 × 1 - 0.83 × 1² = 57.17
Height at t = 1.5 s. is y = 58×1.5 - 0.83×1.5² = 85.1325
Average velocity = ∆y/∆tWhich gives;
Average velocity = (85.1325-57.17)/(1.5-1) = 55.925
The average velocity in the interval [1, 1.5] is therefore;
55.925 m/s(2) [1, 1.1]
Height at t = 1.1 s. is y = 58×1.1 - 0.83×1.1² = 62.7957
Which gives;
Average velocity = (62.7957-57.17)/(1.1-1) = 56.257
The average velocity is 56.257 m/s(3) [1, 1.01]
Height at t = 1.01 s. is y = 58×1.01 - 0.83×1.01² = 57.733317
Which gives;
Average velocity = (57.733317-57.17)/(1.01-1) = 56.3317
The average velocity is 56.33 m/s
(4) [1, 1.001]
Height at t = 1.01 s. is y = 58×1.001 - 0.83×1.001² = 57.22633917
Which gives;
Average velocity = (57.22633917-57.17)/(1.001-1) = 56.33917
The average velocity is 56.33917 m/s(b) The equation for the instantaneous velocity is found as follows;
v = dy/dt = 58 - 2×0.83•t
After 1 second, we have;
t = 1
v = 58 - 2×0.83 × 1 = 56.34
The instantaneous velocity at t = 1 seconds is 56.34 m/s
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the total of the square of a number n and the difference between seventeen and the square of the number
Answer:
Step-by-step explanation:
n²+(17-n²)=n²+17-n²=17
Answer: n²+(17-n²)=n²+17-n²=17
Step-by-step explanation:
Rewrite each fraction as a percent and each percent as a fraction.
List any five rational number between -5/6 and 5/6
The five rational number between -5/6 and 5/6 are [tex]\frac{-4}{6} ,\ \frac{-3}{6} ,\ \frac{-2}{6} , \ \frac{-1}{6} ,\ \frac{1}{6}[/tex]
A rational number, in arithmetic, a number that can be expressed as the quotient p/q of two integers such that q ≠ 0. In addition to all fractions, the set of rational numbers includes all integers, each with an integer as the numerator and 1 as the denominator.When dividing a rational number (that is, a fraction), the result is in decimal form, with either trailing decimals or repeating decimals.We have given two rational numbers [tex]\frac{-5}{6}[/tex] and [tex]\frac{5}{6}[/tex] .
For finding rational number make the denominator of given numbers same.
As the denominator of given numbers is already same so , we don't need to multiply .
Thus , five rational numbers are
[tex]\frac{-4}{6} ,\ \frac{-3}{6} ,\ \frac{-2}{6} , \ \frac{-1}{6} ,\ \frac{1}{6}[/tex]
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Maysa made an error in her work on the following problem. 3 .5 − 2 . 46 = 1 . 16 Describe Maysa's error. Explain how you would use a model or place-value concepts to help Maysa build understanding. Give the correct answer in your explanation.
The error in the subtraction process is that 0.1 is not added to the 0 in the hundredth place of the term 3.5, so as to enable 0.06 to be subtracted from it.
The correct equation is as follows;
3.5 - 2.46 = 1.04Which method can be used to find the correct value to the equation?The given equation that has an error is presented as follows;
3.5 - 2.46 = 1.16
The description of the error in the above equation is that during subtraction, the 0.06 value on the right of the subtraction mark is not subtracted from the zero to the right of .5, and carried down.
The correct process for the subtraction is presented as follows;
3.5¹0
- 2.46
1.04
Therefore;
3.5 - 2.46 = 1.04Learn more about number place values here:
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Which graph is a function of x?
Answer:
The first one is a function of x. The graph with a straight line up and down (vertical).
Step-by-step explanation:
1. Round each decimal to the nearest whole number.
b. 34.972
a. 0.948
Answer:
34.972 ≈ 35
0.948 ≈ 1
Hope this helps :)
Step-by-step explanation:
To round to the nearest whole number look at the tenths place (the place right after the decimal). If the number is 1,2,3,4 then round down or keep the number the same. If the number is 5,6,7,8,9 then round up.
Help me please with this! Thank you :)
Answer:
I'm pretty sure it's 5:4 or 5/4. I think this because there are 5 peaches and four oranges.
2. Create a sequence to fit the given criteria. Describe your
sequence using figures, words, or numbers. Provide the first
four terms of the sequence. Explain how you know that it is
a sequence.
a. Create a sequence that begins with a positive integer, is
decreasing by multiplication, and is finite.
Need help quick please
A geometric sequence with first term 16 and common ratio 0.5, with 10 terms, satisfies the requirements for this problem, and the first four terms are:
16, 8, 4, 2.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
For this problem, we have that:
Sequence begins with a positive integer, hence the first term is 16. (chosen value, any positive integer suffices).The sequence is decreasing by multiplication, hence q > 0 and q < 1, q = 0.5 is a possible value and the sequence is geometric.A finite number of terms, we chose 10.Each term is the previous term multiplied by 0.5, hence the first four terms are:
16, 8, 4, 2.
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Express each decimal as a fraction -0.4
Answer:
It will be. - 4/10 only that
2<3x-1 ≤ 5 solution to compound inequality
The solution of the inequality is 1<x<2.
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations.
According to the given statement;
2 < 3x - 1 < 5
or, 2 + 1 < 3x - 1 + 1 < 5 + 1
or, 3 < 3x < 6
Divide the whole by 3, we get
or, 3/3 < (3/3)x < 6/3
or, 1 < x < 2
hence, the solution of the inequality is 1<x<2.
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South Beach Middle School has 1,272 total students. The students are
Divided into equal classes of 24 students each. How many classes are
There in all?
There are 53 classes in South Beach middle school
How to calculate the number of classes in the school ?South beach middle school has 1,272 students
The students are divided into equal classes of 24 students each
Therefore the number of classes can be calculated by dividing the total population of the students in the school by 24
= 1272/24
= 58
Hence there are 58 classes in the school
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Calculate the average rate of change of the given function f over the intervals [a, a + h] where h = 1, 0.1, 0.01, 0.001, and 0.0001. (Technology is recommended for the cases h = 0.01, 0.001, and 0.0001.) (Round your answers to seven decimal places.) f(x)=x^2/8; a = 1
The average rate of change of the given function f over the intervals-
f(x) = x²/8 ; x=a=1
the average rate of change of f(x) over the time interval [a, a + h] is
rc= [f(a +h) - f(a) ] / [(a +h)-a] = [(a +h)²/8 - a²/8] /h = 1/h [ (a²/8 +a*h/4+ h²/8) - a²/8]
= a /4+ h/8
then
rc= a/4+ h/8
for x=a=1 and h=1
rc= 1/4 + 1/8 = 0.375
for a=1 and h=0.1
rc= 1/4 + 0.1/8 = 0.2625
for a=1 and h=0.01
rc= 1 /4+ 0.01/8 = 0.25125
for a=1 and h=0.001
rc= 1/4 + 0.001/8 = 0.250125
for a=1 and h=0.0001
rc= 1 /4+ 0.0001/8 = 0.2500125
when h goes smaller , the average rate of change gets closer to the instantaneous rate of change of f(x) in x=a=1 (the derivative of f in a=1) , that is
f'(x) = x
then
f'(a) = a
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Is 21.337 greater or less than 21.31
Answer: greater than
Step-by-step explanation:because 21.337 [tex]\leq[/tex] 21.310 or 21.31Answer:
Yes, because 21.337 rounded down is 21.34, and that is larger than 21.31
Step-by-step explanation:
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day :)
given g(x) = -x - 4, find g(-2)
Answer: -2
Step-by-step explanation:
[tex]g(x) = g(-2) = -(-2)-4=2-4=-2[/tex]
89% means 89 out of?
Answer:
100
Step-by-step explanation:
Find exact value of 6 trigonometric functions of angle 11pi/3
Answer:
sin 11pi/3 = - root3/2
cos 11pi/3 = 1/2
tan 11pi/3 = - root3
csc11pi/3 =-2root3/3
sec11pi/3= 2
cot11pi/3 = -root3/3
see image
Step-by-step explanation:
This is a question that you should use the Unit Circle to find the answers. Unit Circle looks like a horrible math nightmare pizza, but it is really a great big giant Answer Key. It has all the trig answers on it.
First, change 11pi/3 to an angle that IS on the Unit Circle. See image for three ways to change 11pi/3 to an equivalent (on the UnitCircle) angle 5pi/3.
Then, since the Unit circle is the Answer Key. Use the x and y given, in the form (x, y) to find all 6 trig values.
Memorize for this type of question:
sin = y (they both have that long i sound)
cos = x
tan = y/x
csc (flip over sin) = 1/y
sec = 1/x (flip cos)
cot = x/y (flip tan)
Also, to make things hairier, you have to know how to rationalize the denominator. This just means you canNOT leave a sqrt symbol on the bottom of a fraction.
And unfortunately, if you never learned how to manipulate a fraction over a fraction, you will have to do that too. Use Keep-Change-Flip. That makes it super do-able. See image.
7x7=7X (5+____________)
=( __________ × 5) + (7 ×______ )
=______ + ______
=______
What is the vertex and minimum and maximum of
y= -2/3|x-1|
The vertex of the function is (1, 0), the maximum is y = 0 and it has no minimum
How to determine the vertex and minimum and maximum of the function?The function is given as:
y = -2/3|x - 1|
The above function is an absolute value function
An absolute value function is represented as:
y = a|x - h| + k
Where the vertex is
Vertex = (h, k)
By comparing y = a|x - h| + k and y = -2/3|x - 1|, we have
(h, k) = (1, 0) --- vertex
a = -2/3
Because a = -2/3 is negative, then the vertex is a maximum
Hence, the vertex of the function is (1, 0), the maximum is y = 0 and it has no minimum
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First, translate triangle FDE down 5 units. Second, reflect it over the y axis. Label the image F'D'E'.? what do I do
Answer:
Step-by-step explanation:
Answer:
first translate triangle FDE down 5 units
second reflect it over the y axis
The image
Step-by-step explanation:
a(1)=−2 a(n)=a(n−1)−5
Answer:
What do I solve for?
Step-by-step explanation:
What is the coefficient of the third term in this expression?
8-3n+ 10m + 4k
SOLVE PROBLEMS WITH RATIOS AND PROPORTIONS
. A recipe uses a 2:5 ratio of baking soda to brown sugar Write an equation and find the missing quantity for
each situation.
a. How much brown sugar do you need if you want to use 6 tablespoons of baking soda?
b. How much baking soda do you need if you want to use 20 teaspoons of brown sugar?
c. How much brown sugar do you need if you want to use 4 cups of baking soda?
d. How much baking soda do you need if you want to use 60 grams of brown sugar?
Using proportions, it is found that:
a) You need 15 tablespoons of brown sugar.
b) You need 8 tablespoons of baking soda.
c) You need 10 cups of brown sugar.
d) You need 24 cups of baking soda.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, that can be either direct(cross multiplication) or inverse(line multiplication), deriving from proportional relationships. One example of application of proportions is for ratio problems.
For this problem, the recipe uses a 2:5 ratio of baking soda to brown sugar, hence:
2/7 of the recipe is of soda.5/7 of the recipe is of sugar.The amount of sugar is 5/2 of the amount of soda.The amount of soda is 2/5 of the amount of sugar.Hence, for item a, the amount is:
5/2 x 6 = 30/2 = 15.
You need 15 tablespoons of brown sugar.
For item b, the amount is:
2/5 x 20 = 40/5 = 8.
You need 8 tablespoons of baking soda.
For item c, the amount is:
5/2 x 4 = 20/2 = 10.
You need 10 cups of brown sugar.
For item d, the amount is:
2/5 x 60 = 120/5 = 24.
You need 24 cups of baking soda.
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can someone help me with this
We get that the value of (f + g)(x) is 11 x - 1.
Function: a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
We are given the two functions:
f(x) = 4 x + 3
g(x) = 7 x - 4
We need to find:
(f + g)(x)
We know that this is equal to
= f(x) +g(x)
Substituting the values, we get that:
= 4 x + 3 + 7x - 4
Combining the like terms, we get that:
= 11 x - 1
Therefore, we get that the value of (f + g)(x) is 11 x - 1.
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The diagram shows three vertical poles X, Y and Z. Calculate the distance between Pole X Pole Z.
Using the Pythagorean Theorem, the distance between Pole X and Pole Z is of 15.3 m.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
The first part of the distance is the hypotenuse of a right triangle of sides 0.5 and 2.5, tracing a right triangle at the top of pole X and tracing it to segment Y, hence:
df² = 0.5² + 2.5²
df = sqrt(0.5² + 2.5²)
df = 2.55m.
For the second part, we apply equivalent triangles, as we can also trace a right triangle at the top of segment Y to segment Z, hence:
0.5/2.5 = df/ds
1/5 = 2.55/ds
ds = 2.55 x 5 = 12.75m
Then the total distance is:
2.55 + 12.75 = 15.3 m.
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Please help !! I don’t know what x is !
Answer:
x = √65
Step-by-step explanation:
You are given a right triangle with leg lengths 4 and 7, and you are asked for the length of the hypotenuse, x.
Pythagorean theoremThe Pythagorean theorem relates the lengths of the sides of a right triangle. It tells you the square of the hypotenuse (x²) is the sum of the squares of the other two sides.
x² = 4² +7² . . . . . . . . . Pythagorean relation
x² = 16 +49 = 65 . . . evaluate the expression
x = √65 . . . . . . . . . . take the square root
1. Name three acute angles.
a. NOK, JOK, KOL
b. NOM, JOK, KOL
c. NOM, JOK, KON
please show me what is 11.54(-2.6)
Determine if the statement is true or false. If it is false, explain what must be changed in the statement to make it true. If it is true, explain why you believe it to be true.
The common difference for the geometric sequence given by 1, -1, -3, -5, -7… is 2.
The statement is false and the changes to make the statement true are:
Change the sequence type to arithmetic sequenceChange the common difference to -2How to determine if the statement is true or false?The statement is given as:
The common difference for the geometric sequence given by 1, -1, -3, -5, -7… is 2.
The above statement is false because of the following reasons:
The sequence is an arithmetic sequence (not a geometric sequence)The common difference for the sequence is -2 not 2 i.e.. -1 - 1 = -2Hence, the statement is false and the changes to make the statement true are:
Change the sequence type to arithmetic sequenceChange the common difference to -2Read more about sequence at:
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Five subtracted from a number equals 10. Find the number.
Answer:the number is 15
if i am correct give me brainliest
Step-by-step explanation:because 5-15=10 the number is 15
please help need asap
Answer: X = 21/6
Step-by-step explanation:
The angle is a 90 degree angle.
that means we know 21x+6=90
21x = 90-6
21x=84
x = 84/24
x = 21/6
x = 21/6