The depth of the water on the shore of a beach varies as the tide moves in and out. The equation
D(t) = 0.75 cos (t) + 1.5 models the depth of the water, D(t), in feet and t as time in hours.
1. When will the tide be at its lowest for the first time when t > 0?
A) 3
B) 6
C) 9
D) 12
Answers
Answer:
C) 9 hours
Step-by-step explanation:
as per your picture the equation is
D(t) = 0.75×cos(pi/6 × t) + 1.5
the function cosine continuously "waves" from +1 to -1 and back.
the lowest value of this function for the first time after t>0 is when the cosine part reaches -1 the first time.
that is at 270° or 3pi/2.
so,
pi/6 × t = 3pi/2
1/6 × t = 3/2
t = 3×6/2 = 3×3 = 9
Related Questions
rewrite 16r^2s^2 as a power of a product
Answers
Answer: 16r²s²=(4rs)²
Step-by-step explanation:
[tex]16r^2s^2=\\\\4^2r^2s^2=\\\\(4rs)^2[/tex]
Find x
80°
x+51
X =
OK
60°
ALGEBRA
Answers
For the given triangle and the measures of the given angle the value of x is equal to -11° .
As given in the question,
For the given triangle,
Let us consider the triangle name ABC,
Where, m ∠A = x + 51° ,
m ∠ABC = 80° ( vertically opposite angle of given 80° angle.)
m ∠ACB = 60° ( vertically opposite angle of given 60° angle.)
To get the value of x we have,
Sum of all the interior angles of a triangle is equal to 180°
m ∠A + m ∠B + m ∠C = 180°
⇒ x + 51° + 80° + 60° = 180°
⇒ x + 191° = 180°
⇒ x = 180° - 191°
⇒ x = - 11°
Therefore, for the given triangle and the measures of the given angle the value of x is equal to -11° .
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passes through T(0, -2), perpendicular to CX with C (0, 3) and X (2, -1)
Answers
Answer:
it would be honestly idj
Step-by-step explanation:
im tryin to get point
A number is 2 times another number. If the larger number is increased by 14, the result is 4 less than 4 times the smaller number.
Answers
The smaller number is 9 and the larger number is 18.
According to the question,
We have the following information:
A number is 2 times another number. If the larger number is increased by 14, the result is 4 less than 4 times the smaller number.
Now, let's take the larger number to be x and the smaller number to be y.
So, we have the following expressions:
x = 2y ...(1)
x+14 = 4y-4
Putting the values of x from the equation 1:
2y+14 = 4y-4
Adding 4 to both sides of the equation:
2y+14+4 = 4y
2y+18 = 4y
Subtracting 2y from both sides of the equation:
18 = 4y-2y
18 = 2y
Dividing by 2 on both sides:
y = 18/2
y = 9
Now, putting this value in equation 1:
x = 2y
x = 2*9
x = 18
Hence, the smaller number is 9 and the larger number is 18.
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A triangle has vertices A(−1,2)
, B(2,5)
, and C(3,−4)
. If the image resulting from a rotation has vertices A'(−2,−1)
, B'(−5,2)
, and C'(4,3)
, write the rule that describes the rotation:
Answers
Answer: [tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)[/tex]
90 degree counter-clockwise rotation around the origin.
===================================================
Explanation:
Focus on A(-1,2) and A'(-2,-1)
The coordinates of point A have swapped to go from "-1,2" to "2,-1". Then we stick a negative in front of the new x coordinate to get "-2,-1"
In other words, we've gone from (x,y) to (y,x) to (-y,x)
Representing this with arrows looks like:
[tex]\left(\text{x}, \text{y}\right) \to \left(\text{y}, \text{x}\right) \to\left(-\text{y}, \text{x}\right)[/tex]
or in short
[tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)[/tex]
which represents a 90 degree counter-clockwise rotation around the origin.
-----------------------------------
Let's see if this rule works with point B(2,5). We should rotate to B'(-5,2)
[tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)\\\\\left(2,5\right) \to \left(-5, 2\right)[/tex]
Sure enough, it works for point B.
Lastly, let's check if it works for point C.
We should go from C(3,-4) to C'(4,3).
[tex]\left(\text{x}, \text{y}\right) \to \left(-\text{y}, \text{x}\right)\\\\\left(3,-4\right) \to \left(-(-4), 3\right)\\\\\left(3,-4\right) \to \left(4, 3\right)\\\\[/tex]
All points have been confirmed.
Huey lost 80 marbles. He was to find 45% of them. How many marbles did Huey find
Answers
Answer:
OK, so we know that 50% of the 80 marbles is 40, but we are supposed to find 45% of it, so basically it is 36 marbles he has found, I hope this is right!
Love from Ella
Which number is greatest? 24/100 0.3 16%
Answers
.3
16% = .16
.3 is the greatest number
The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $22.25 for 25 pounds of laundry and $36.49 for 41 pounds of laundry. In words, describe the graph of the proportional relationship.
Answers
The required expression for the laundry service is y = 0.89x.
Given that,
The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $22.25 for 25 pounds of laundry and $36.49 for 41 pounds of laundry.
proportionality is defined as between two or more sets of values, and how these values are related to each other in a sense are they directly proportional or inversely proportional to each other.
here
Let the pound of laundry be x and the charge corresponding to the pound of the laundry be y.
According to the question,
y ∝ x
y = kx
Put x = 25 and y = 22.25
22.25 = k 25
k = 0.89
Put back k in the proportional equation,
y = 0.89x
Thus, the required expression for the laundry service is y = 0.89x.
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Answer:
Step-by-step explanation:
The required expression for the laundry service is y = 0.89x.
Given that,
The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $22.25 for 25 pounds of laundry and $36.49 for 41 pounds of laundry.
What is proportionality?
proportionality is defined as between two or more sets of values, and how these values are related to each other in a sense are they directly proportional or inversely proportional to each other.
here
Let the pound of laundry be x and the charge corresponding to the pound of the laundry be y.
According to the question,
y ∝ x
y = kx
Put x = 25 and y = 22.25
22.25 = k 25
k = 0.89
Put back k in the proportional equation,
y = 0.89x
Thus, the required expression for the laundry service is y = 0.89x.
cómo se saca el porcentaje
Answers
Answer:
Step-by-step explanation:
Para determinar el porcentaje, tenemos que dividir el valor por el valor total y luego multiplicar el resultado por 100.
Extra Credit
Where does this function cross the x-axis?
y = 25x² - 49
Answers
Answer:
Step-by-step explanation:
45
help meeeeeeeeeeeeeeeeee please
Answers
Answer:
x= 3.4
x+2= 5.4
x+3= 6.4
Step-by-step explanation:
Just figured it out :)
Serena just started working at the local salon. She is paid $9.85 per hour and earns, on
average, $58.50 in tips each day. Roseline just started working at a bank. Since she
does not receive tips, she earns $16.35 an hour. The system of equations
{y=9.85x+58.50 y=16.35x can be used to represent the amount of money earned, y,
each day for working x hours.
Determine the number of hours Serena and Roseline have to work to earn the same
amount of money.
Answers
The number of hours Serena and Roseline have to work to earn the same amount of money will be 9 hours.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Serena recently began working at the nearby salon. By and large, $58.50 in tips every day. Roseline recently began working at a bank. Since she doesn't get tips, she procures $16.35 60 minutes. The arrangement of conditions {y = 9.85x + 58.50 and y = 16.35x} can be utilized to address how much cash is procured, y, every day for working x hours.
The number of hours Serena and Roseline have to work to earn the same amount of money will be given as,
16.35x = 9.85x + 58.5
6.5x = 58.5
x = 9 hours
The number of hours Serena and Roseline have to work to earn the same amount of money will be 9 hours.
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Kendrick needed 10 gallons of gas last week. This week, Kendrick ended up needing 40%
less. How much gas is that?
Answers
Answer:
6 gallons
Step-by-step explanation:
40% of 10 is 4 gallons less
10 - 4 = 6 gallons
Divide £72 into.
Ratio 4:5
Answers
Thus, 72 is divided into 32 and 40 in a 4:5 ratio. A ratio expresses the number of times one number contains another.
What is meant by Ratio?A ratio is the number of times one number contains another. For example, if a bowl of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six.Similarly, the lemon to orange ratio is 6:8, and the orange to total fruit ratio is 8:14. A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero.A proportion exists as a equation that sets two ratios equal to each other. For example, if there is one boy and three girls, the ratio could be written as 1: 3. (for every one boy there are 3 girls)Given:
The given ratio is 4:5.
To find: We have to divide 72 in this ratio.
To divide 72 in the 4:5 ratio, we must perform the following steps:
The ratio is 4:5.
We can write the number of the ratio as 4x and 5x by multiplying a constant x.
The total ratio is 4x+5x=9x.
So, 9x is equal to 72.
We can write-
9x=72
x=8.
So, putting the value of x we get-
4×8 and 5×8
So, the numbers are 32 and 40.
Thus 72 divides itself as 32 and 40 in 4:5 ratio.
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in october 2012, apple introduced a much smaller version of the apple ipad, known as the ipad mini. weighing less than 11 ounces, it was 50% lighter than the standard ipad. battery tests for the mini ipad showed that battery life is uniformly distributed between 8.5 and 12 hours. what is the value of 'a'? answer to one decimal.
Answers
a) The Probability density function of given uniform distribution example is
F(x) = 1/3.5 for 8.5 < x< 12
Uniform distribution in Statistics is a type of probability distribution in which all possible outcomes have equally likely chance to occur. It is generally represented by U(x,y) where
x ---> minimum value and y---> maximum value
Probability density function is a probability function which defines the density of continuous random variable lying between specified range
values. It is denoted by f( a<X<b)
Probability density function for uniform distribution is F(x) = 1/(b-a) for a<x<b where a and b are parameters of uniform distribution.
We have following informations,
weigh of mini iPad = 11 ounces or 50% lighter than standard iPad.
Assume that the battery of iPad is uniformly distributed between 8.5 hours to 12 hours.
this implies a = 8.5 , b = 12
F(x) = 1/(12 - 8.5) = 1/3.5 for 8.5<x<12
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#Complete Qestion :
In October 2012, Apple introduced a much smaller variant of the Apple iPad, known as the iPad Mini. Weighing less than 11 ounces, it was about 50% lighter than the standard iPad. Battery tests for the mini ipad showed that battery life is uniformly distributed between 8.5 and 12 hours. what is the value of 'a'? answer to one decimal. Assume that the battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours.
a) What is the probability that the battery life for an iPad Mini will be 10 hours or less?
simplify 8^15 ÷8^-3 math is hard for me
Answers
Answer:
8^18
Step-by-step explanation:
8^15
8^−3
=
8^15
8−3
= 8^15− (−3)
= 8^18
What is the simplest positive form of
-35(mod 6)?
Answers
in november's math meet, the little monsters of beast academy solved $\frac{1}{5}$ of the problems. in march's math meet, they solved $\frac 23$ of the problems. (there might be different numbers of problems asked in november and march.) in total, the little monsters solved $13$ of $30$ problems over both math meets. how many problems were asked at march's math meet?
Answers
The little monsters solved 15 problems in March's Math meet
Given, that in November's math meet, the little monsters of beast academy solved 1/5 of the problems.
In March's math meet, they solved 2/3 of the problems.
In total, the little monsters solved 13 of 30 problems over both math meets.
Let, the number of problems in November be n,
and the number of problems in March be m
According to the question,
n + m = 30 as, the total problems be 30
Now, (1/5)n + (2/3)m = 13 as, they solved total 13 problems
n + m = 30 ... (1)
n/5 + 2m/3 = 13 ... (2)
On simplifying Eq (2) becomes
3n + 10m = 195 ... (2)
On multiplying Eq (1) by 3, we get
3n + 3m = 90
3n + 10m = 195
On subtracting, we get
- 7m = - 105
m = 105/7
m = 15
So, the problems asked in March's Math meet be 15.
Hence, 15 problems were asked at March's Math meet.
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along a river is to be fenced. suppose that no fence is needed along the river, the fence on the side opposite the river costs $40 per foot, and the fence on the other sides costs $10 per foot. if the field must contain 64,800 square feet, what dimensions will minimize costs?
Answers
The dimensions required to minimize the cost of fencing is 180ft and 360 ft.
According to question
The cost of fence on opposite side of river is $40.
The cost of fence on other sides of river is $10.
Total yield = 64800 sq. feet
Let the length of fence on the opposite side of fence be x and width of fence on the other side be y.
Area of fence = xy = 64800 sq feet
⇒ [tex]y = \frac{64800}{x}[/tex]
Let C be the cost of making fence.
For cost to be minimum, dC/dx should be equal to zero.
C = 40x + 10y * 2
⇒ C = [tex]40x + 10(\frac{64800}{x})*2[/tex]
⇒ [tex]\frac{dC}{dx} = 40 + 20 * 64800 * \frac{-1}{x^{2} } = 0[/tex]
⇒ [tex]40x^{2} = 20 * 64800[/tex]
⇒ [tex]x^{2} = 32400[/tex]
⇒ [tex]x = 180[/tex]
⇒ [tex]y = \frac{64800}{180} = 360[/tex]
So, the dimensions needed will be 180 ft and 360 ft.
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Shelley is searching online for airline tickets. Two weeks ago, the cost to fly from Boston to Hartford was $220. Now the cost is $355. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
Answers
The percentage increase is 61.36%. If the airline charges an additional $50 baggage fee, the new percentage increase will be 45.68%.
What is the percent increase?A percentage increase denotes how much a percentage has risen over time. To get at this figure, discover the difference between the original and final values, then deduct it to get the actual sum of the decrease.
The idea of Percentage increase is simply the amount of increase from the original(initial) to the final figure expressed in terms of 100 parts of the original. E.g. A 10% increase implies that if the original value is divided into 100 parts, the value has increased by an extra 10 parts. So, if the initial value rose by 16%, the value would rise by 16 for every 100 units, and so on.
The formula for calculating the percentage increase can be expressed as:
[tex]\%\ increase= \frac{new \ value - original \ value}{original \ value}\times 100[/tex]
[tex]\%\ increase= \frac{355- 220}{220}\times 100[/tex]
[tex]\%\ increase= \frac{135}{220}\times 100[/tex]
[tex]\mathbf{=61.36\%}[/tex]
[tex]New \ \%\ increase= \frac{new \ value - original \ value}{original \ value}\times 100[/tex]
[tex]New \ \%\ increase= \frac{405- 220}{405}\times 100[/tex]
[tex]New \ \%\ increase= \frac{185}{405}\times 100[/tex]
[tex]New \ \%\ increase=\mathbf{45.68\%}[/tex]
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It take Jada 20 minute to walk to chool. It take Andre 80% a long to walk to chool. How long doe it take Andre to walk to chool?
Answers
Andre takes 36 minutes to walk to the school.
Given, It take Jada 20 minutes to walks to school.
It takes Andre 80% a long to walk to school.
As, Andre takes 80% more to walk to school
So, the time Andre takes = 20×180/100
the time Andre takes = 2×18
the time Andre takes = 36 minutes
Hence, Andre takes 36 minutes to walk to the school.
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The 1st term of a certain sequence is -10, and the 2nd term is 1. Each subsequent term is obtained by adding the 2 immediately preceding terms. What Is the 5th term of this sequence?
Answers
In a sequence of first term-10 and the 2nd term is 1. the 5th term of this sequence is -17
How to find the fifth term of the sequenceinformation given in the question
The 1st term of a certain sequence is -10
the 2nd term is 1
Each subsequent term is obtained by adding the 2 immediately preceding terms
the 5th term of this sequence = ?
Each subsequent term is obtained by adding the 2 immediately preceding terms. This statement means is applied as below
Therefore:
third term
3rd term
= first term + 2nd term
= -10 + 1
= -9
4th term
= 3rd term + 2nd term
= -9 + 1
= -8
5th term
= 4th term + 3rd term
= -9 + -8
= -9 - 8
= - 17
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Select the correct answer. Cole’s age is 3 years less than his sister Tina’s age, t. If Cole is 18, which equation represents this situation, and how old is Tina? A. The equation that represents this situation is t − 3 = 18. Tina is 21. B. The equation that represents this situation is t + 3 = 18. Tina is 15. C. The equation that represents this situation is 3 − t = 18. Tina is 21. D. The equation that represents this situation is -3 − t = 18. Tina is 15.
Answers
The equation that represents this situation is t − 3 = 18. Tina is 21. The correct option is A.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Cole’s age is 3 years less than his sister Tina’s age, t. If Cole is 18.
The equation will be written as,
C = T - 3
18 = T-3
T = 18 + 3
T = 21 years
Therefore, the equation that represents this situation is t − 3 = 18. Tina is 21. The correct option is A.
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In a recent student government election the ratio of students who voted for the winner to all the students who was 0.70 to the number of students who wrote it was 75 how many votes did the winner get?
Answers
The winner received 53 of the 75 votes in the student gov. election according to provided ratio.
What is ratio?
In arithmetic, a magnitude relation shows range times one number contains another.
Main body:
Because the ratio of students who voted for the winner compared to all students who voted is 0.70
we can rewrite this as:
0.70 = 70/100
And, because we know the total number of students who voted is 75 and if we call the number of students who voted for the winner s , we can then write this relationship and solve for s :
[tex]\frac{70}{100} = \frac{s}{75}[/tex]
Multiplying both sides by 75.
75*[tex]\frac{70}{100} = \frac{s}{75}[/tex]*75
s= 75*70/100
s = 5250/100
s = 52.5
s ≈ 53.
Hence ,The winner received 53 of the 75 votes.
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A helicopter leaves A and flies 40 miles due east. Then the helicopter flies
10 miles due south and arrives at B. Work out the bearing of B from A.
Answers
The bearing of the helicopter from B to A is 75.96 degrees
How to determine the bearing of the helicopter from B to AInformation from the question
A helicopter leaves A and flies 40 miles due east
the helicopter flies
10 miles due south
Work out the bearing of B from A = ?
The bearing from B to A is worked using SOH CAH TOA
The direction of movements describes a right angle triangle of
opposite = 40 miles
adjacent = 10 miles
The bearing is calculated using tan, TOA let the angle be x
tan x = Opposite / Adjacent
tan x = 40 / 10
tan x = 4
x = arc tan 4
x = 75.96 degrees
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Dad fills the car's gas tank when it is about 1/2 empty. Later, he fills the tank when it is about 3/4 empty. He bought a total of 18 1/2 gallons of gas on those two days. How many gallons does the tank hold?
Answers
Dad's car's gas tank holds 14.8 gallons of the gas.
Define the term mixed fraction?A mixed fraction is one generated by integrating a whole number as well as a fraction.
When the car's gas tank is nearly half full, Dad fills it up. Later, when the tank is about 3/4 full, he fills it. Total gas purchased = 18 1/2 gallons of gas.Changed the mixed fraction in decimal.
Total gas purchased = 37/2 = 18.5 gallons of gas.
Let x be the gallons of gas tank contains.
Then,
(1/2)x + (3/4)x = 18.5
Multiply both sides by 4,
2x + 3x = 74
5x = 74
x = 14.8 gallons
Thus, Dad's car's gas tank holds 14.8 gallons of the gas.
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A number is being multiplied by a power of 10. Find the number.
Enter your answers in the boxes.
___________ × 102 = 700
___________ × 103 = 36,000
___________ × 105 = 400,000
Answers
Answer:
When you have the base of 10 and an exponential index of “n”, the powers of 10 says that the resulting number will be 1 followed by “n” number of zeros. So for example, 10 to the 7th represents the same thing as 1 followed by 7 zeros. The result is 10,000,000 (10 million). Multiplying whole numbers by a power of ten would mean that you ...
Which is the order from least to greatest of the following
4/3, 0.8, 1/5, 30%?
A. 4/3, 0.8, 1/5, 30%
B. 30%, 4/3, 0.8, 1/5
C. 1/5, 4/3, 30%, 0.8
D. 1/5, 30%, 0.8, 4/3
Answers
Which is the order from least to greatest of the following
A. 4/3, 0.8, 1/5, 30%
1.33 , 0.8 , 0.2 , 0.3
B. 30%, 4/3, 0.8, 1/5
0.3 , 1.33 , 0.8 , 0.2
C. 1/5, 4/3, 30%, 0.8
0.2 , 1.33 , 0.3 , 0.8
D. 1/5, 30%, 0.8, 4/3
0.2 , 0.3 , 0.8 , 1.33 these are listed smallest to largest
In Exercises 1-4, graph the equation. Ider
1. y - 2 = 2(x - 2)
Answers
What is the distance between (-5,-6),(-9,-4)
Answers
Answer:
The distance between [tex](-5,-6),(-9,-4)[/tex] is [tex]6 units[/tex].
Step-by-step explanation:
Distance Formula :
[tex]\sqrt{(x_{2}^{2} -x_{1}^{2}) +( y_{2}^{2} -y_{1}^{2})}[/tex]
Given,
The two points are
[tex](-5,-6),(-9,-4)[/tex]
To calculate the distance between two points, use the distance formula.
[tex]\sqrt{(x_{2}^{2} -x_{1}^{2}) +( y_{2}^{2} -y_{1}^{2})}[/tex]
Substitute the actual values of the points into the distance formula.
Distance[tex]=\sqrt{((-9)^{2} -(-5)^{2}) +( (-4)^{2} -(-6)^{2})}[/tex]
[tex]=\sqrt{(81-25)+(16-36)}[/tex]
[tex]=\sqrt{36}[/tex]
[tex]=6[/tex]