Answer:
(a)
i) [tex]V=12.6m/s[/tex]
ii) [tex]V=12.06m/s[/tex]
iii) [tex]V=12.006m/s[/tex]
(b)
[tex]V = 10m/s[/tex]
Step-by-step explanation:
Given
[tex]s = 6t^2 + 4[/tex]
Solving (a): Average velocity between t = 1 and t = 1 + h
When t = 1
[tex]t_1 = 1[/tex]
[tex]s_1 = 6t^2 + 4 = 6 * 1^2 + 4 = 6 + 4 =10[/tex]
i) h = 0.1
When t = 1 + h
[tex]t_2 = 1 + 0.1 = 1.1[/tex]
[tex]s_2= 6t^2 + 4 = 6 * (1.1)^2 + 4 = 11.26[/tex]
Average velocity is then calculated as:
[tex]V = \frac{s_2 - s_1}{t_2 - t_1}[/tex]
[tex]V = \frac{11.26 - 10}{1.1- 1} = \frac{1.26}{0.1} = 12.6[/tex]
[tex]V=12.6m/s[/tex]
ii) h = 0.01
When t = 1 + h
[tex]t_2 = 1 + 0.01 = 1.01[/tex]
[tex]s_2= 6t^2 + 4 = 6 * (1.01)^2 + 4 = 10.1206[/tex]
Average velocity is then calculated as:
[tex]V = \frac{s_2 - s_1}{t_2 - t_1}[/tex]
[tex]V = \frac{10.1206 - 10}{1.01- 1} = \frac{0.1206}{0.01} = 12.06[/tex]
[tex]V=12.06m/s[/tex]
ii) h = 0.001
When t = 1 + h
[tex]t_2 = 1 + 0.001 = 1.001[/tex]
[tex]s_2= 6t^2 + 4 = 6 * (1.001)^2 + 4 = 10.012006[/tex]
Average velocity is then calculated as:
[tex]V = \frac{s_2 - s_1}{t_2 - t_1}[/tex]
[tex]V = \frac{10.012006 - 10}{1.001- 1} = \frac{0.012006 }{0.001} = 12.006[/tex]
[tex]V=12.006m/s[/tex]
Solving (b): Instantaneous velocity at t = 1
When t = 1
[tex]t = 1[/tex]
[tex]s = 6t^2 + 4 = 6 * 1^2 + 4 = 6 + 4 =10[/tex]
Velocity is:
[tex]V = \frac{s}{t}[/tex]
[tex]V = \frac{10}{1}[/tex]
[tex]V = 10m/s[/tex]
A mathematician simplifies the expression mentally.
17.2 (20+45) - (4.75)
What is the best estimate of the value of the expression?
0 381
O 1,114
O 1,844
O 5,521
Answer:
1,114
Step-by-step explanation:
17.2(65)- (4.75)
1118 - 4.75
1113.25
Answer:
Step-by-step explanation:
1114
Which of the following equations has no solution?
3x + 1 = 2x + 1
3x + 1 = 3x + 1
3x + 1 = 3x + 2
Answer:
the last one
..
Which expression is equivalent to 1/4(2 – 5x + 6)?
Answer: the answer is CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C
A model rocket is launched directly upward at a speed of 28 meters per second from a height of 12 meters. The function f(t) = - 4.9t ^ 2 + 28t + 12, mo models the relationship between the height of the rocket and the time after launch. in seconds When seconds after launch will the rocket hit the ground? Do not round until the final answer. Then round your answer to two decimal places. Provide your answer below:
Answer:
6.11 seconds
Step-by-step explanation:
Given
[tex]f(t) = -4.9t^2 + 28t + 12[/tex]
Required
When will it hit the ground?
When it hits the ground, f(t) = 0.
So, we have:
[tex]0 = -4.9t^2 + 28t + 12[/tex]
Solve quadratic equation using formula
[tex]t = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]
[tex]t = \frac{-28 \± \sqrt{28^2 - 4*-4.9*12}}{2*-4.9}[/tex]
[tex]t = \frac{-28 \± \sqrt{1019.2}}{-9.8}[/tex]
[tex]t = \frac{-28 \± 31.92}{-9.8}[/tex]
Split
[tex]t = \frac{-28 + 31.92}{-9.8}[/tex] or [tex]t = \frac{-28 - 31.92}{-9.8}[/tex]
[tex]t = \frac{3.92}{-9.8}[/tex] or [tex]t = \frac{-59.92}{-9.8}[/tex]
[tex]t = -0.4[/tex] or [tex]t = 6.11[/tex]
Time can not be negative. So:
[tex]t = 6.11[/tex]
50 POINTS AND BRAINLIEST!
Determine if the graphed function is linear or nonlinear.
Select from the drop down menu to correctly complete the sentence.
The graphed function is
A. Linear
B. Non-linear
Answer:
its A linear
Step-by-step explanation:
its going upwards and that means its linear and when the end point is going downwards that means its non linear
Answer:
my answer was incorrect my mistake
HELPP! I"LL GIVE THE FIRST RIGHT ANSWER BRAINLIEST!!!
Answer:
61
Step-by-step explanation:
Heights of Smith's Adult grandchildren median: 339
Heights of Thompsons' Adult Grandchildren median: 400
400 - 339 = 61
SYSTEM OF EQUATIONS
The sum of three times Sophia's age and twice Nick's age is 73. Twice Sophia's age plus four times Nick's age is 86. How old is Sophia?
A local ice cream shop sells root beer floats for $2.75 and milkshakes for $6. One day the shop sold 10 more root beer floats than milkshakes and made $290. How many root beer floats were sold on this day? How many milkshakes?
Answer:
30 milkshakes and 40 root beer floats
Step-by-step explanation:
Set up a system of equation (r is root beer and m is milkshake)
2.75r+6m=290
m+10=r
Substitute
2.75(m+10)+6m=290
2.75m+27.5+6m=290
8.75m=262.5
m=30
Now plug in 30 and solve for r
30+10=40
Determine if the equation y = 15(1.35)* represents exponential growth or decay and justify. Hint: Think about the growth and decay equations.
Answer:sdfghgfdfghnhgfdfgh
Step-by-step explanatsdfghjhgfghjk
====================================================
Explanation:
The equation is in the form y = a*(b)^x
The 'a' is the initial or starting value. In this case, a = 15.
The b is the base of the exponent which is tied to growth or decay. If 0 < b < 1, then we have decay. If b > 1, then we have growth.
Since b = 1.35, and 1.35 > 1, this means b > 1 and the given equation represents exponential growth.
Solving 1+r = 1.35 leads to r = 0.35. This means the growth rate is 35%
Simplify: -6(x + 5) show work plz
Answer:
The answer is -6x - 30
Step-by-step explanation:
1) Expand by distributing terms.
[tex] - 6x - 6 \times 5[/tex]
2) Simplify 6 × 5 to 30.
[tex] - 6x - 30[/tex]
Thus, the answer is -6x - 30.
Answer:
-6x - 30
Step-by-step explanation:
Multiply using the distributive property.
-6x - 30
Hope this helps
Use the given area of the base and the height to find the volume of the right rectangular prism, in cubic units.
You dident give us a picture of it so we cant tell
Which equation is equivalent to 2-2(3x - 1)=2
Answer:
it should be C
Step-by-step explanation:
I hope this helps! I am sorry if I am wrong!
Answer:
c
Step-by-step explanation:
2-2(3x-1)=2 2-6x+2=2 . 2-6x+2=2 4-6x=2 . -6x+4=2 . -6x+4-4=2-4 -6x=-2 -6x=-2 -6x/-6=-2/-6 x=1/3 .
In a lab experiment, 5400 bacteria are placed in a petri dish. The conditions are such
that the number of bacteria is able to double every 4 hours. How many bacteria would
there be after 17 hours, to the nearest whole number?
Answer:
it’s 102747.494736, estimate is 102747
Step-by-step explanation:
can someone help me with this
Answer:
A
Step-by-step explanation:
Help I forgot how to do this
Answer:
number 5 is 11 and number 6 is 16
Step-by-step explanation:
you substitute a for 4 bc a equals 4 and than finish the equation 4+7=11
6. you substitute b for 2 and c for 8 and multiply which than is 16
Find the area of the triangle below.
6
18
A =
units squared
Answer:
hhhdddhhsuuwuwuww?w?w?
What is the value of k in the following equation?
2(4k + 5) + 3(3 – 3k) = 25
Answer:
K = - 6
Step-by-step explanation:
Let's solve your equation step-by-step.
2(4k+5)+3(3−3k)=25
Step 1: Simplify both sides of the equation.
2(4k+5)+3(3−3k)=25
(2)(4k)+(2)(5)+(3)(3)+(3)(−3k)=25(Distribute)
8k+10+9+−9k=25
(8k+−9k)+(10+9)=25(Combine Like Terms)
−k+19=25
−k+19=25
Step 2: Subtract 19 from both sides.
−k+19−19=25−19
−k=6
Step 3: Divide both sides by -1.
An item costs $410 before tax, and the sales tax is $24.60.
Find the sales tax rate. Write your answer as a percentage.
Answer:
$434.60
Step-by-step explanation:
$410.60 added to $24.60 equals $434.60
Solve triangle ABC if a = 19, b = 16, and the m∠A = 61°.
c =
∠B =
∠C =
Answer:
A≈132.94m²
Step-by-step explanation:
A=absinγ
2=19·16·sin(61°)
2≈132.9422m²
Hope this helps!!!
Celesta and Sam found that 14 marbles would fill each pouch. There were 12 pouches. How many marbles
did they need to fill all the pouches?
simplify the expression Please HELP
Can someone help me please
Answer:
the second one. (3,-4)(6,-4)
Step-by-step explanation:
Answer:
the answer is B
Step-by-step explanation:
because if you draw the points on a coordinate grid, you will see that there's 3 units between them
at the market Miss Winn bought 3/4 IB of grapes and 5/8 idea of cherries how many ounces of grapes did Miss win by
Answer:
12 oz of grapes
Step-by-step explanation:
1 lb = 16 oz so 16*3/4 = 12
Manuel and Peter are standing 12 ft. apart from each other and looking up at a kite that is flying between them. Manuel is flying the kite on a 65 ft. string at an angle of 70(degrees) with the ground. How far is Peter from the kite?
A. 61.9 ft.
B. 65.8 ft.
C. 68.1 ft.
D. 99.5 ft.
Answer:
C. 68.1 ft.
Step-by-step explanation:
Hope this helps
Answer:
Trigonometric Identities and Applications Test Part 1
1. a,c,e
2. B sinx
3.b,d
4. D sec thea
5. b,c
6. A. 0.67
7. A sqrt 6- sqrt2/4
8. A cos^2 47=....
9. B 2+sqrt3/4
10. c,e
11. C .63
12. A 8.9
13 D 8.0
14 D 86.2
15 61.9 ft
16 writen
17. a,d
18. b,c
19 a,d
20 writen
Step-by-step explanation:
took part one and I missed some but it's to help others in need :)
Nick is splitting 4 quarts of ice cream with 9 members of the team. If the ice cream is split evenly, how many will each person get? Explain.
Answer:
Each member will get 3 and 1/2 cups or 3.5 cups of ice cream.
A video game store is selling video games 3 for $37.50. How much would they earn if they sold 2?
Answer:
25
Step-by-step explanation:
ok so you need to find out how much each game is sold for
First 37.50 divided by 3 and that will equal 12.5
second, you need to find out how much 2 games cost so you eithermultiply
12.5 by 2 or add 12.5 two times and you will get 25
hope this helped;)
Mean = 25
Standard Deviation = 3.8
P(X
Find the value of k.
Round to 2 decimal values.
Answer:
The normal distribution is explained for the solution of this question.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Mean = 25, Standard Deviation = 3.8
This means that [tex]\mu = 25, \sigma = 3.8[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{X - 25}{3.8}[/tex]
If P(X > k) = a
We have to find [tex]X = k[/tex] when Z has a pvalue of 1 - a.
If P(X < k) = a
We have to find [tex]X = k[/tex] when Z has a pvalue of a.
Two angles are complementary. The measure of the first is (3x+14) and the measure of the second one is (5x-20). What are the measures of the two angles?
Answer:
x=17
Step-by-step explanation:Isolate the variable by dividing each side by factors that don't contain the variable. x=17. I hope this helps
Which expression is equivalent to f(x)=6x^2-13x+5
Answer:
(3x - 5)(2x - 1)
Step-by-step explanation:
6x² - 13x + 5
6x² - (10 + 3)x + 5
6x² - 10x - 3x + 5
2x(3x - 5) - (3x - 5)
(3x - 5)(2x - 1)
Which means, 6x² - 13x + 5 is equivalent to (3x - 5)(2x - 1) or vice versa
Tai has 1/2 gallon of milk left in his
refrigerator. He pours the milk into
glasses that can each hold a 5/64 gallon.
How many glasses can Tai fill
completely with milk?
Answer:
He can completely fill six glasses, and there will be one glass 2/5 of the way full.
Step-by-step explanation: