Answer:
The dolphin will be above the surface of the water for 2 seconds.
Step-by-step explanation:
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
The height of the dolphin after t seconds is given by:
[tex]h(t) = -16t^2 + 96t - 128[/tex]
According to Micha's model, how long will the dolphin be above the surface of the water?
It stays above the surface of the water between the first and the second root. Initially, it is below water, when the first time for which [tex]h(t) = 0[/tex] it crosses the surface upwards, and then the second time for which [tex]h(t) = 0[/tex] it crosses the surface downwards.
We have to find these roots. So
[tex]h(t) = -16t^2 + 96t - 128[/tex]
[tex]-16t^2 + 96t - 128 = 0[/tex]
Multiplying by -16
[tex]t^2 - 6t + 8 = 0[/tex]
[tex]\Delta = (-6)^{2} - 4*1*8 = 36 - 32 = 4[/tex]
[tex]t_{1} = \frac{-(-6) + \sqrt{4}}{2} = 4[/tex]
[tex]t_{2} = \frac{-(-6) - \sqrt{4}}{2} = 2[/tex]
4 - 2 = 2
The dolphin will be above the surface of the water for 2 seconds.
A 20 ft. beam leans against a wall. The beam
reaches the wall 13.9 ft. above the ground.
What is the measure of the angle formed by the
beam and the ground?
Answer:
a 44°
Step-by-step explanation:
Think of the right triangle formed by the beam, the ground, and the wall.
The beam is the hypotenuse. For the angle between the ground and the beam, call it angle A, the 13.9 ft side is the opposite leg. The trig ratio that relates the opposite leg and the hypotenuse is the sine.
sin A = opp/hyp
sin A = 13.9/20
sin A = 0.695
A = sin^-1 0.695
A = 44°
What is the value of the expression below when x equals 4? 13 + 13x
Answer:
the answer is 50
Step-by-step explanation:
Six less than two times a number is 20
Answer:
2x - 6 = 20
2x - 6 + 6 = 20 + 6
2x = 26
x = 13
The number should be 13
Step-by-step explanation:
A movie theater has a seating capacity of 329. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 2388, How many children, students, and adults attended?
___ children attended.
___students attended.
____adults attended.
Answer:
170 children
74 students
85 adults
Step-by-step explanation:
Given
Let:
[tex]C = Children; S = Students; A = Adults[/tex]
For the capacity, we have:
[tex]C + S + A = 329[/tex]
For the tickets sold, we have:
[tex]5C + 7S + 12A = 2388[/tex]
Half as many as adults are children implies that:
[tex]A = \frac{C}{2}[/tex]
Required
Solve for A, C and S
The equations to solve are:
[tex]C + S + A = 329[/tex] -- (1)
[tex]5C + 7S + 12A = 2388[/tex] -- (2)
[tex]A = \frac{C}{2}[/tex] -- (3)
Make C the subject in (3)
[tex]C = 2A[/tex]
Substitute [tex]C = 2A[/tex] in (1) and (2)
[tex]C + S + A = 329[/tex] -- (1)
[tex]2A + S + A = 329[/tex]
[tex]3A + S = 329[/tex]
Make S the subject
[tex]S = 329 - 3A[/tex]
[tex]5C + 7S + 12A = 2388[/tex] -- (2)
[tex]5*2A + 7S + 12A = 2388[/tex]
[tex]10A + 7S + 12A = 2388[/tex]
[tex]7S + 22A = 2388[/tex]
Substitute [tex]S = 329 - 3A[/tex]
[tex]7(329 - 3A) + 22A = 2388[/tex]
[tex]2303 - 21A + 22A = 2388[/tex]
[tex]2303 +A = 2388[/tex]
Solve for A
[tex]A = 2388 - 2303[/tex]
[tex]A = 85[/tex]
Recall that: [tex]C = 2A[/tex]
[tex]C = 2 * 85[/tex]
[tex]C = 170[/tex]
Recall that: [tex]S = 329 - 3A[/tex]
[tex]S = 329 - 3 * 85[/tex]
[tex]S = 329 - 255[/tex]
[tex]S = 74[/tex]
Hence, the result is:
[tex]C = 170[/tex]
[tex]S = 74[/tex]
[tex]A = 85[/tex]
Answer:
Down Below
Step-by-step explanation:
The answer is actually
162 children
86 students
81 adults
162x5=810
86x7=602
81x12=972
I found the original problem and the total ticket sale was $2384.
So I wrote the answers for the original problem just in case!
Ty for your time!
I really need help please help
Answer: tan^-1(5/8) = 32 degrees from horizontal line
Step-by-step explanation: tan (Alfa) = 2000 / 3200 because
Angle from horizontal line. 2000/3200 = 20/32 = 5/8
if 70kg is 20% of peter's weight, then what is peter's total weight?
Answer:
14
Step-by-step explanation:
20\100×70=14........
A bear weighs 4,521 grams. How much does the bear weigh in kilograms
Answer:
A bear weighing 4,521 grams would weight 4.521 kilograms
Find the mean of the data in the dot plot below.
Answer:
the mean is 83.6
Step-by-step explanation:
Answer:
The mean is 83.6 cm
Step-by-step explanation:
81 + 83 +84 + 85 + 85 = 416
416 divided by 5 = 83.6
Find the limit when X approaches zero
2xsinx/1-cosx
Answer:
4
Step-by-step explanation:
[tex] Lim_{x \to 0}\frac{2 x\sin x}{1-\cos x} [/tex]
[tex] =Lim_{x \to 0}\frac{2 x\sin x}{1-\cos x}\times \frac{1+\cos x}{1+\cos x} [/tex]
[tex] =Lim_{x \to 0}\frac{2 x\sin x(1+\cos x) }{1^2 -\cos^2 x} [/tex]
[tex] =Lim_{x \to 0}\frac{2 x\sin x(1+\cos x) }{1 -\cos^2 x} [/tex]
[tex] =Lim_{x \to 0}\frac{2 x\sin x(1+\cos x) }{sin^2 x} [/tex]
[tex] =Lim_{x \to 0}\frac{2x(1+\cos x) }{sin x} [/tex]
[tex] =Lim_{x \to 0} 2(1+\cos x) \times \frac{1}{Lim_{x \to 0}\frac{sin x}{x}} [/tex]
[tex] =2(1+\cos 0) \times 1 [/tex]
[tex] = 2(1+1) [/tex]
[tex] = 2(2) [/tex]
[tex] \therefore Lim_{x \to 0}\frac{2 x\sin x}{1-\cos x}= 4 [/tex]
What is the solution to the equation shown on the number line?
Answer:
B
Step-by-step explanation:
x-4=18
+4 +4
x=22
Answer:
22
Step-by-step explanation:
X-4 =18
So now we have to find a number on the line which 4 is deducted from you can get 18 as the answer
So 22-4 = 18
someone please help me answer this!!
Helpppppppppppp me please
Answer:
C) x² = a/b
Step-by-step explanation:
You and your friend are selling magazine subscriptions. You sell 8 fewer magazine subscriptions than your friend. Together you sell 42 magazine subscriptions. a. Write a system of linear equations that represent the situation.
b. How many magazine subscriptions did you sell?
c. How many magazine subscriptions did your friend sell.
Answer:
b. you sold 17
c. your friend sold 25
Step-by-step explanation:
you=y your friend=x
y=x-8
42=x +y
42=x+(x-8)
42=x+x-8
42=2x-8
50=2x
25=x
Use x to solve for y...
y=25-8
y=17
What is the angle of A and B?
Answer:
a=90
b=30
Step-by-step explanation:
ZA and B are complementary angles. If m_A = (x – 15)° and m ZB = (x + 3)º, then find the measure of ZB.
Answer:
ZB = 54
Step-by-step explanation:
Complementary angles add to 90 degrees
ZA + ZB = 90
x-15 + x+3 = 90
Combine like terms
2x-12 =90
Add 12 to each side
2x-12+12 = 90+12
2x = 102
Divide by 2
2x/2 = 102/2
x = 51
We want to find the measure of ZB
ZB = x+3
ZB = 51+3
ZB = 54
The following set of data represents the age in years of newly married ladies in Desai. 15,25,17,20,22,24,19,16./ This data was collected after Deborah made an allegation that ladies in Desai get married at an age other than 18 years as is required by law. Does this data provide enough evidence at 5% level of significance to believe that the mean ages of ladies getting married in Desai is actually different from 18 years as claimed by Deborah?
Answer:
There is no significant evidence to conclude that the mean ages of ladies getting married in Desai is different from 18.
Step-by-step explanation:
Given the data:
15,25,17,20,22,24,19,16
Using calculator :
Mean value, xbar = 19.75
Standard deviation, s = 3.69
Samoke size, n
H0 : μ = 18
H1 : μ > 18
The test statistic :
Tstatistic = (xbar - μ) ÷ (s / sqrt(n))
Test statistic = (19.75 - 18) ÷ 3.69/ sqrt(8))
Test statistic = 1.75 ÷ 1.3046
Test statistic = 1.34
The Pvalue from test statistic ; df = n - 1 = 8 - 1 = 7
Pvalue = 0.111054
Decision :
If Pvalue < α ; reject H0
0.111053 > 0.05 ` Hence, we fail to reject H0
We can conclude that, There is no significant evidence to conclude that the mean ages of ladies getting married in Desai is different from 18.
Multiply 15 by 9 then divide by 2 fraction
Answer:
15x9 is 130 but, what u mean by divided by 2 fraction?
Step-by-step explanation:
135/ 2 this is correct unless you want a mixed fraction which is 67 and 1/2
Zoe supplies customs to a number of theatre companies she recently provided 20 different hats including 44 doors considering this data how many of the 15 has requested from Zoes inventory should you expect to be fedoras
Answer:
I was searching for the same answer but no one has it smh
Step-by-step explanation:
HURRY
Which function does this graph represent?
Answer:
B
Step-by-step explanation:
Hope this helps!
Answer:
the answer is B
Step-by-step explanation:
the answer is B
16. Garrett can complete four laps around the
track in 7 minutes and 45 seconds. How
many full laps can he complete in 1 hour
Answer:
Step-by-step explanation:
45 seconds = 45/60 = 0.75 minutes
7 minutes 45 seconds = 7.75 minutes
One hour = 60 minutes
Number of full laps = 60/ 7.75 = 6000/775 = 7.74
He can make 7 full laps in one hour
It’s in the picture ☝.
Answer:
120
Step-by-step explanation:
The whiskers you see on the sides, are known as the minimum(Left) and the maximum (right).
PLEASE HELP ME ON THIS!
the height of a rectangular prism is 8 meters, and the volume is 308 cubic meters. what is the area of the prisms base in square meters?
Answer:
The area of the prism's base in square meters is [tex]38.5m^2[/tex].
Step-by-step explanation:
The volume of a rectangular prism is found by multiplying the base of the prism by the height. Since you know that the volume is [tex]308m^3[/tex] and the height is [tex]8m[/tex], you just need to divide the volume by the height to get the area of the base, which would be [tex]\frac{308}{8}[/tex] or [tex]38.5m^2[/tex].
What is the diameter of a hemisphere with a volume of 69292 in?, to the
nearest tenth of an inch?
Answer:
64.2 in
Step-by-step explanation:
From deltamath
Yeah
use the laws of sine and cosine to find the missing Dimension part 3
Find the f to the nearest whole number
9514 1404 393
Answer:
12 or 103
Step-by-step explanation:
The given angle is opposite the shorter side, so there will be two solutions.
In order to find f, we need to know angle F. We can find that by first finding angle E.
E = arcsin(e/d·sin(D)) = arcsin(71/62·sin(36°)) = 42.307° or 137.693°
F = 180° -D -E = 180° -36° -{42.307°, 137.693°} = {101.693°, 6.307°}
Then the measure of f is ...
f = sin(F)/sin(D)×d = 62/sin(36°)×sin({101.693°, 6.307°})
f = {103.29, 11.59}
Side f is either 12 or 103.
Answer:
103Step-by-step explanation:
Find ∠E
sin E / 71 = sin 36° / 62sin E = 71 (sin 36°) / 62sin E = 0.673m∠E = arcsin (0.673)m∠E = 42° (rounded)Find m∠F
m∠F = 180° - (36° + 42°) = 102Find f
sin 102° / f = sin 36° / 62f = (62 sin 102°) / (sin 36°) f = 103 (rounded)A recipe for a pie calls for 2/4
cup of blackberries and 1/5 cup of raspberries.
What is the total amount of berries needed for the recipe?
Answer here
SUBMIT
Answer: 14/20=7/10 cup
Step-by-step explanation:
2/4 is equal to 10/20
1/5 is equal to 4/20
10/20+4/20= 14/20
Find the slope of a line that passes through the points (-7, 3) and (5, 6).
Answer:
the formula to find slope is m=∆y/∆y
this means m=y2-y1/x2-x1
using this formula
m=5-3/6-(-7)
m=2/13
Answer:
The slope is 0.25
Step-by-step explanation:
Which of the functiors below could have created this graph
Answer:
bces
Step-by-step explanation:
Solve and explain please
Answer:
x = 14Step-by-step explanation:
7x + 9 = 9x - 19. [Corresponding Angles]
=> 9x - 19 = 7x + 9
=> 9x - 7x = 19 + 9
=> 2x = 28
[tex] = > x = \frac{28}{2} [/tex]
=> x = 14 (Ans)
Solve for variable.
3k = 36
Answer:
k = 12
Step-by-step explanation:
Given 3k = 36 we want to isolate the variable (k) using inverse operations
So we want to get rid of the 3
3k = 3 times k (multiplication)
The inverse of multiplication is division so to get rid of the * 3 we want to divide by 3. Remember whatever we do to one side we have to do to the other side so we are going to divide each side by 3
3k/3=k
36/3=12
we're left with k = 12
x2+4x+3 solve for x.
Answer:
(x+1)(x+3)
Step-by-step explanation:
Let's factor x^2+4x+3
x^2+4x+3
The middle number is 4 and the last number is 3.
Factoring means we want something like
(x+_)(x+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get 4
Multiply together to get 3
Can you think of the two numbers?
Try 1 and 3:
1+3 = 4
1*3 = 3
Fill in the blanks in
(x+_)(x+_)
with 1 and 3 to get...
(x+1)(x+3)
