ANSWER:
6 gallons regular gas with 10% ethanol and 4 gallons E85 fuel with 85% ethanol
STEP-BY-STEP EXPLANATION:
In this case, we must test with values for each fuel class to arrive at the correct answer.
For example, 6 gallons of 10% ethanol and 4 gallons of 85% ethanol:
[tex]\begin{gathered} 10\text{\% of 6 =}\frac{10}{100}\cdot6=0.6\text{ gallons of ethanol in it} \\ 85\text{\% of 4 =}\frac{85}{100}\cdot4=3.4\text{ gallons of ethanol in it} \\ \text{ Total ethanol in 10 gallons is 0.6 + 3.4 = 4 gallons }\rightarrow\text{ 4 gallons is 40\% of 10} \\ \text{Therefore, we have 10 gallons of fuel containing 40\% ethanol } \end{gathered}[/tex]What is the effect on the graph of f(x) = x2 when it is transformed toh(x) = 3x2 + 12?A. The graph of f(x) is horizontally compressed by a factor of 5 andshifted 12 units up.O B. The graph of f(x) is vertically compressed by a factor of 5 andshifted 12 units to the left.O C. The graph of f(x) is horizontally stretched by a factor of 5 andshifted 12 units to the left.O D. The graph of f(x) is vertically compressed by a factor of 5 andshifted 12 units up.SUBMIT
the fraction 1/5 horizontally expands the graph and the constant 12 move up the graph because is a sum
so the right option is the last
D. The graph of f(x) is vertically compressed by a factor of 5 and
shifted 12 units up
Use the Distributive Property to find each missing factor.6 x 8 = ( 4 x ____) + ( 2 x 8 )10 x 3 = (___ x 3 ) + ( 2 x 3 )(___ X 7 ) = ( 3 x 7 ) + ( 2 x ___)( 8 X ___) = (___ x 8 ) + ( 4 X 8 )3rd grade subject Distributive property
The question is given below as
[tex]6\times8=(4\times\ldots)+(2\times8)[/tex]The distributive property of multiplication states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately, then adding the two products together for the same result as multiplying the first number by the sum.
[tex]a(b+c)=a\times b+a\times c[/tex]Let the missing factor in the question be x
[tex]\begin{gathered} 6\times8=(4\times\ldots)+(2\times8) \\ 6\times8=(4\times x)+(2\times8) \end{gathered}[/tex]By multiplying,
We will have
[tex]\begin{gathered} 6\times8=(4\times x)+(2\times8) \\ 48=4x+16 \end{gathered}[/tex]Collect like terms,by subtracting 16 from both sides
[tex]\begin{gathered} 48=4x+16 \\ 48-16=4x+16-16 \\ 32=4x \end{gathered}[/tex]Divide both sides by 4
[tex]\begin{gathered} 4x=32 \\ \frac{4x}{4}=\frac{32}{4} \\ x=8 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} 6\times8=(4\times8)+(2\times8) \\ 6\times8=8(4+2) \\ 6\times8=6\times8 \end{gathered}[/tex]Therefore,
The missing factor = 8
It takes 3/4 of an hour for an automated sprinkler to cover 2/7 of a lawn after an hour has passed what fraction of the lawn has been covered
Answer:
x=8/21
Step-by-step explanation:
(3/4)/(2/7) = 1/x
(3/4)x = (2/7)
x = (2/7) / (3/4)
x = (2/7) * (4/3)
x = 8/21
Which of the following are true about a one-to-one function? Select all that apply.1. It graph will pass the horizontal line test2. It will always have an inverse 3. It’s graph is symmetric about the y-axis 4. It will always have either a local or maximum but not both 5. The graph will pass through point (1,1).
SOLUTION
Recall the definition of a one-to-one function
one to one function or one to one mapping states that each element of one set, say Set (A) is mapped with a unique element of another set, say, Set (B), where A and B are two different sets
There, the correct answers are
1. It graph will pass the horizontal line test
2. It will always have an inverse
Can someone please help me with this I really need help
Please
The complete table is as follows:
x = 0, p(x) = 0x = 1, p(x) = 4x = 2, p(x) = 8x = 3, p(x) = 12x = 4, p(x) = 16x = 5, p(x) = 20x = 6, p(x) = 24The equation that represent the function is p(x) = 4x.
How to represent equation of a table?Function p represents the perimeter in inches of a square with side length x inches.
Therefore,
perimeter of a square = 4l
where
l = side lengthHence, x represent the side length and p(x) is the perimeter of the square.
Therefore, the equation that represent the situation is as follows;
p(x) = 4x
Let's fill the table as follows:
x = 0, p(x) = 0x = 1, p(x) = 4(1) = 4x = 2, p(x) = 4(2) = 8x = 3, p(x) = 4(3) = 12x = 4, p(x) = 4(4) = 16x = 5, p(x) = 4(5) = 20x = 6, p(x) = 4(6) = 24learn more on equation here: https://brainly.com/question/29326385
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The scores of individual students on the American College Testing (ACT) composite college entrance examination have a normal distribution with mean 18.6 and standard deviation 5.9. What is the probability that the mean score of an SRS of 40 students chosen from all those taking the test is 21 or higher? Round your percentage to 2 decimals.
Given data
*The given mean is
[tex]\mu=18.6[/tex]*The given standard deviation is
[tex]\sigma=5.9[/tex]The value of the z score is calculated as
[tex]z=\frac{x-\mu}{\sigma}[/tex]Substitute the values in the above expression as
[tex]\begin{gathered} z=\frac{21-18.6}{5.9} \\ =0.41 \end{gathered}[/tex]The probability that the mean score of an SRS of 40 students chosen from all those taking the test is 21 or higher is given as
[tex]\begin{gathered} P(Z\ge21)=P(X\ge0.41) \\ =1-P(X<0.41) \end{gathered}[/tex]The corresponding probability is evaluated by the table.
Substitute the values in the above expression as
[tex]\begin{gathered} P(Z\ge21)=1-0.6591 \\ =0.34 \end{gathered}[/tex]what digit is in the
Given:
[tex]\frac{13}{7}+\frac{9}{14}[/tex]Find LCM of the denominators.
LCM (7, 14)=14.
Multiply the numerator of each fraction by the LCM 14 and divide by 14.
[tex]\begin{gathered} \frac{1}{14}(\frac{14\times13}{7}+\frac{9\times14}{14}) \\ =\frac{1}{14}(2\times13+9) \\ =\frac{1}{14}(26+9) \\ =\frac{35}{14} \\ =\frac{5}{2} \end{gathered}[/tex]Therefore, the result of the sum is 5/2.
2^4c^-10 to a fraction
The given expression is
[tex]2^4c^{-10}[/tex]We have to solve the power of 2.
[tex](2\cdot2\cdot2\cdot2)c^{-10}=16c^{-10}[/tex]Then, we use the property for negative exponents.
[tex]a^{-b}=\frac{1}{a^b}[/tex]This means we have to move the power to the denominator.
[tex]\frac{16^{}}{c^{10}}[/tex]Therefore, the fraction is[tex]\frac{16}{c^{10}}[/tex]Write T for true or F for false. 6. The number 14 is a multiple of 4. 7. The Identity Property says that any number times 1 equals the number itself. 8. A bar diagram can be used to show 3 X 6.
In the number 6, it says the number 14 is a multiple of 4. It means there would be an integer number X which when multiplied by 4 would result in the number 14. To check it, we can perform the following calculation.
[tex]14=X\times4\to X=\frac{14}{4}=3.5[/tex]Because the value of X found is not an integer, 6. is FALSE
In the number 7, it says the Identity Property rays that any number times 1 equals the number itself. This property says that there is a number that, when multiplied by any number will always equal the number itself, and this is the number 1. From this, 7 is TRUE
Number 8 says a bar diagram can be used to show 3X6. This technique can be used to show any multiplication by an integer number. Because both. 3 and 6, are integer, 8 is TRUE
A=16xx-6use the given area to find the missing sides of the rectangle
The area of the rectangle is given as 16 units squared
The length = x
The width = x-6
The area of a rectangle is given by the formula;
A= l * w
A= x {x-6}
16 = x^2 -6x -----------form a quadratic equation as;
[tex]x^2-6x-16\text{ =0}[/tex]Find the factors of -16 that can add or subtract to give -6
The factors will be -8 and 2
Factorize the equation as ;
[tex]x^2+2x-8x-16=0[/tex][tex]x(x+2)-8(x+2)=0[/tex][tex](x+2)(x-8)=0[/tex]Finding the real values of x , take that which will result to a positive length
( x-8) = 0
x-8 = 0
x= 8 units
So ; Length = x = 8 units
Width = x- 6 = 8-6 = 2 units
Answers
Length = 8 units
Width = 2 units
4-Which turkey is the better deal? * Sarah Lee Turkey $6.58 per lb O Butterball Turkey $11.16 for 2 lbs 4b-What is the Unit Price for the better deal? Round to the nearest hundredth) Put your answer in the form 0.00 or .00, so if answer is 43 cents, its 0.43 or.43, if there is a dollar amount like 1.50, do not add zeros in front).
We will determine the best deal as follows:
We divide 11.16 by 2 to obtain the value per Lb, and we get that for each Lb the price is $ 5.58.
So, the best deal is Butterball Turkey at a price of $5.58 per Lb.
please help me with this question and explain it so I can understand. thank you!
We can solve this question using trigonometric functions. Here, we use the tangent of the angle of elevation to find the height of the tree.
[tex]\begin{gathered} \tan 40^o=\frac{h}{35} \\ 0.839=\frac{h}{35} \\ 0.839\times35=h \\ 29.36=h \end{gathered}[/tex]Thus, the height of the tree is 29 feet (to the nearest foot).
a regular square pyramid has base whose area is 250 cm^2. a section parallel to the base and 31.8 cm above it has an area of 40 cm^2 . find the ratio of the volume of the frustum to the volume of the pyramid.
We are given that the area of the base of a pyramid is 250 cm^2. We are asked to determine the ratio of the volumes of the frustum and the volume of the pyramid. To do that, let's remember that the volume of a pyramid is given by:
[tex]V=\frac{1}{3}A_bh[/tex]Where:
[tex]\begin{gathered} A_b=\text{ area of the base} \\ h=\text{ height} \end{gathered}[/tex]Now, the volume of the frustum is given by:
[tex]V_f=\frac{1}{3}h_f(A_b+A_f+\sqrt[]{A_bA_f})[/tex]Where:
[tex]\begin{gathered} h_f=\text{ height of the frustum} \\ A_f=\text{ area of the base of the frustum} \end{gathered}[/tex]Now, the ratio of between the volume of the frustum and the volume of the pyramid is:
[tex]\frac{V_f}{V_{}}=\frac{\frac{1}{3}h_f(A_b+A_f+\sqrt[]{A_bA_f})}{\frac{1}{3}A_bh_{}}[/tex]We can cancel out the 1/3 and we get:
[tex]\frac{V_f}{V_{}}=\frac{h_f(A_b+A_f+\sqrt[]{A_bA_f})}{A_bh}[/tex]Now, we need to determine the heights. To do that we will use the fact that the ratio of the squares of the height of the pyramid and the height to the top of the pyramid is equivalent to the ratio of the areas, therefore, we have:
[tex](\frac{h}{h_t})^2=\frac{A_b}{A_f}[/tex]Now we substitute the areas:
[tex](\frac{h}{h_t})^2=\frac{250}{40}[/tex]Taking square root we get:
[tex]\frac{h}{h_t}=\sqrt[]{\frac{250}{40}}[/tex]Solving the operations:
[tex]\frac{h}{h_f}=2.5[/tex]Now we multiply by the height of the frustum on both sides:
[tex]h=2.5h_t[/tex]Now, let's look at the following diagram:
This shows us that the height of the frustum plus the height to the top must be equal to the height of the pyramid, therefore:
[tex]h=h_t+31.8[/tex]Substituting the relationship we determined for the height to the top we get:
[tex]h=\frac{h}{2.5}+31.8[/tex]Now we solve form the height "h" first by subtracting h/2.5 from both sides:
[tex]\begin{gathered} h-\frac{h}{2.5}=31.8 \\ \end{gathered}[/tex]Solving the operations:
[tex]\frac{1.5h}{2.5}=31.8[/tex]Now we multiply both sides by 2.5:
[tex]\begin{gathered} 1.5h=31.8\times2.5 \\ 1.5h=79.5 \end{gathered}[/tex]Now we divide by 1.5:
[tex]h=\frac{79.5}{1.5}=53[/tex]Therefore, the height of the pyramid is 53 cm. Now we substitute in the ratio of the volumes and we get:
[tex]\frac{V_f}{V_{}}=\frac{h_f(A_b+A_f+\sqrt[]{A_bA_f})}{A_bh}[/tex]Substituting the values:
[tex]\frac{V_f}{V_{}}=\frac{(31.8)(250+40+\sqrt[]{(250)(40)})}{(250)(53)}[/tex]Solving the operations:
[tex]\frac{V_f}{V}=0.936_{}[/tex]Therefore, the ratio is 0.936
your dinner bill was $21.00 if you leave a 20% tip, how much will the tip be?
As given by the question,
There are given that the total bill was $21.00
Now,
If leave a 20% tip,
Then,
[tex]\begin{gathered} 21\times\frac{20}{100}=21\times\frac{1}{5} \\ =4.2 \end{gathered}[/tex]Hence, the tip
there are 7 Red 3 blue and 5 green marbles in a bag what is the probability that the first three chosen will not be red?
Determine the total number of marble in the bag.
[tex]\begin{gathered} n(T)=7+3+5 \\ =15 \end{gathered}[/tex]Determine the probability for first three marbles be red.
[tex]\begin{gathered} P(R=3)=\frac{^7C_3^{}}{^{15}C_3} \\ =\frac{35}{455} \\ =\frac{7}{91} \end{gathered}[/tex]The probability for first three marble is not to be red is equal to one minus the probability for the first three marble be red.
[tex]\begin{gathered} P(R\ne3)=1-P(R=3) \\ =1-\frac{7}{91} \\ =\frac{91-7}{91} \\ =\frac{84}{91} \\ =\frac{12}{13} \end{gathered}[/tex]So answer is 12/13.
in ABC, G is the centroid. If BF=48 find BG
Recall that the centroid of the triangle is the intersection point of its medians, which are the lines that are formed by joining the midpoint of one side with the remainding vertex of the triangle. This point has the property that for each median it splits it in two smaller segments, one of which has the double of the length of the other.
We are given the following picture
Let us call the lenght of GF x. Since G is the centroid, then the length of BG is 2x. Note that the sum of the length of BG plus the length of GF should be BF. So we have the following equation
[tex]x+2x=48[/tex]Now, we should solve this equation for x. First we add the x terms on the left. So we get
[tex]3x=48[/tex]Finally, we divide by 3 on both sides, so we get
[tex]x=\frac{48}{3}=16[/tex]so the lenght of GF is 16. Now, si BG has the double length of FG, then the length of BG is 16*2 = 32.
The measures of the angles of a triangle are shown in the figure below. Find the
measure of the smallest angle.
The smallest measure of the angle in the given triangle is 3x - 15 which is 33°.
What are triangles?A triangle is a polygon with three edges and three vertices. It belongs to the basic geometric shapes. A triangle having vertices A, B, and C is known as triangle ABC. Any three locations in Euclidean geometry that are not collinear result in a distinct triangle and a distinct plane.So, the measure of the smallest angle in the triangle is:
90 + 4x - 7 + 3x - 15 = 1807x + 68 = 1807x = 180 - 68x = 112/7x = 16Now,
4x - 7 = 4(16) - 7 = 57°3x - 15 = 3(16) - 15 = 33°Therefore, the smallest measure of the angle in the given triangle is 3x - 15 which is 33°.
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Which of these describes the function graphed below? 6 2 8 6 2 8 -2 -6 -8 There is a nonlinear relationship between x and y when x is less than 1 and a linear relationship when x is greater than 1 O There is a linear relationship between x and y when x is less than 1 and a nonlinear relationship when x is greater than 1 There is a linear relationship between x and y when x is less than 0 and a nonlinear relationship when x is greater than 0. There is a nonlinear relationship between x and y when x is less than 0 and a linear relationship when x is greater than 0
Answer
Option C is correct.
There is a linear relationship between x and y when x is less than 0 and a nonlinear relationship when x is greater than 0.
Explanation
From the graph, we can see that at values of x less than 0, the graph indicates a very straight line that translates to a linear relationship.
But at values of x greater than 0, the graph begins to curve showing that the relationship is no longer linear.
So, option C is correct.
Hope this Helps!!!
The answer is 139 ft provided by my teacher, I need help with the work
Answer:
139 ft
Explanation:
Given below is the diagram of the situation
the tangent ratio fo 24 degrees gives
[tex]\tan 24=\frac{h}{300}[/tex]multiplying both sides by 300 gives
[tex]300\cdot\tan 24=h[/tex][tex]h=133.57ft[/tex]We have to remember here that the measuring device was 5 ft above the ground; therefore,
[tex]\text{height}=133.57+5[/tex][tex]\text{height}=138.57ft[/tex]rounding to the nearest integer gives
[tex]\text{height}=139ft[/tex]which is our answer!
10. The graph of y=f(x) is given below.y!24168848 xWhat is the possible degree of f?A. 4IB. -3C. 2D. 3E. -1
Answer:
The degree of the function is;
[tex]3[/tex]Explanation:
From the given graph, we can observe that the function has two extremum (one minima and one maxima).
The degree of the function will be the number of extremum plus 1;
[tex]\text{degree}=n+1[/tex]Since there are two extremum on the graph then;
[tex]\begin{gathered} \text{degree}=2+1 \\ \text{degree}=3 \end{gathered}[/tex]Therefore, the degree of the function is;
[tex]3[/tex]Unit 5 Project 1. A projectile is fired upward from the ground with an initial velocity of 300 feet per second. Neglecting air resistance, the height of the projectile at any time I can be described by the polynomial function P(t) = -16ť + 3000 a. Find the height of the projectile when t = 1 second. b. Find the height of the projectile when t = 5 seconds. c. How long will it be until the object hits the ground? 2. A board has length (3x + 6x - 18) meters and width of 2x + 1 meters. The board is cut into three pieces of the same length a. Find the length of each piece. b. Find the area of each piece. c. Find the area of the board before it is cut. d. How is the area of each piece of the board related to the area of the board before it is cut? 3. A cubic equation has zeros at -2, 1, and 3. a. Write an equation for a polynomial function that meets the given conditions. b. Draw the graph of a polynomial function that meets the given conditions. 4. Alice was having a conversation with her friend Trina, who had a discovery to share: 10
1)
The polynomial modelling this scenario is expressed as
P(t) = - 16t^2 + 300t
where
P(t) represents the height at time t
a) To find the height of the projectile when t = 1 second, we would substitute
t = 1 into the equation. Thus,
P(1) = - 16(1)^2 + 300(1)
P(1) = - 16 + 300 = 284
Height of projectile when t = 1 second is 284 feet
b) To find the height of the projectile when t = 5 second, we would substitute
t = 5 into the equation. Thus,
P(1) = - 16(5)^2 + 300(5)
P(1) = - 400 + 1500
Height of projectile when t = 5 second is 1100 feet
c) At the time when the object hits the ground, the height would be zero. This means that p(t) = 0
Thus, the equation would be
0 = - 16t^2 + 300t
Factoring out 4t from the right, we have
0 = - 4t(4t - 75)
- 4t = 0 or 4t - 75 = 0
t = 0/-4 or 4t = 75
t = 0 or t = 75/4
t = 0 or t = 18.75
It will take 18.75 seconds until the object hits the ground
I don't even get like what a mean and a median is can you explain?
The mean is an average of a set of numbers, where in order to calculate it, we sum all the numbers and divide by the amount of numbers.
For example, in the set {2, 5, 7, 10}, the mean is:
[tex]\frac{2+5+7+10}{4}=\frac{24}{4}=6[/tex]The median is the middle term of the set when it's put in the crescent order.
For example, in the set {4, 7, 2, 10, 5}, the median is:
[tex]\begin{gathered} \text{crescent order}\to\mleft\lbrace2,4,5,7,10\mright\rbrace \\ \text{middle term}\to5 \end{gathered}[/tex]If the number of elements in the set is even, the median will be the average of the two middle terms. For example, in the set {4, 7, 2, 10, 5, 3}, the median is:
[tex]\begin{gathered} \text{crescent order}\to\mleft\lbrace2,3,4,5,7,10\mright\rbrace \\ \text{middle terms}\to4\text{ and 5} \\ \operatorname{median}\to\frac{4+5}{2}=4.5 \end{gathered}[/tex]Peyton go shopping she finds two shirts one cost $24.97 the other cost $13.75 she needs to know if she has enough money to buy both shirt using mental math she rounds $24.97 to $25 and add that to $13.75 to get $38.75 how does Peyton need to say to find the exact a total of 2 shirts
We know that Peyton wants to buy two shirts.
• First shirt cost $24.97.
,• Second shirt cost $13.75.
To do the mental math is ok to round $24.97 to $25, and them sum with $13.75.
However, to get the exact number, Peyton needs to subtract 3 pennies from the last amount $38.75, becuase she rounded before.
Therefore, to find the exact amount she needs to subtract 3 pennies.
Let F(x) = f(f(x)) and G(x) = (F(x)) ^ 2 . You also know that f(3) = 2 , f(2)=3, f^ prime (2)=7 , f^ prime (3)=11
From the information given,
F(x) = f(f(x)
G(x) = (F(x))^2
F'(x) = f'(f(x)) * f'(x)
F'(3) = f'(f(3)) * f'(3)
f'(f(3)) = f'(2) = 7
f'(3) = 11
F'(3) = 7 * 11
F'(3) = 77
G'(x) = 2F(x) * F'(x) = 2f(f(x) * F'(x)
G'(3) = 2F(3) * F'(3) = 2f(f(3) * F'(3)
Given,
f(f(3) = f(2) = 3
G'(3) = 2 * 3 * 77
G'(3) = 462
please help i dont know to do it please help
Given:
0.5
Let's write the decimal in form of a fraction a/b using integers.
To write the number in fractional form, we have:
[tex]0.5=5\times10^{-1}[/tex]Since the exponent is the negative of 1, using the definition of negative exponent, we have:
[tex]5\times10^{-1}=\frac{5}{10^1}=\frac{5}{10}[/tex]Therefore, the correct fraction is:
[tex]\frac{5}{10}[/tex]ANSWER:
[tex]\frac{5}{10}[/tex]What is (a+b) (a+b) =?What is (a+1) (a+1) = ?What is (a+3) (a+3)=?What is (x+5) ^2=?
SOLUTION:
Case: Expansion
Method:
[tex]\begin{gathered} a^2+b^2=(a+b)^2 \\ R.H.S\text{ }expansion \\ (a+b)^2 \\ (a+b)(a+b) \\ a(a+b)+b(a+b) \\ a^2+ab+ab+b^2 \\ a^2+2ab+b^2 \end{gathered}[/tex]Final answer:
FALSE
[tex]a^2+b^2\ne(a+b)^2[/tex]how do I find the value of x so f(x)=7
We have a function for which we only have the chart.
We need to find the value of x so that f(x)=7.
NOTE: As we are lookin for the value of x that makes the value of f(x) = 7, we are able to see it in the graph directly:
If we start at y=7, we can draw a line until we intersect the line for f(x). When this happens we draw a vertical line towards the x-axis until we intersect it.
The value of x at that point is the one that makes f(x)=7.
If we can not find the solution by graph, we have to find the equation of the line and clear x for f(x)=7.
SOLUTION WITH EQUATION:
With the information from the chart we have to find the equation.
We can identify two points in the function: (2,0) and (5,7).
Using the 2 known points, we calculate the slope of the line as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{7-0}{5-2}=\frac{7}{3}[/tex]Then, we can write the slope-point equation as:
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-0=\frac{7}{3}(x-2) \\ y=\frac{7}{3}x-\frac{14}{3} \end{gathered}[/tex]Then, if we know that y=7, we can replace y with this value and calculate x as:
[tex]\begin{gathered} y=7=\frac{7}{3}x-\frac{14}{3} \\ 7\cdot3=7x-14 \\ 21=7x-14 \\ 7x=21+14 \\ 7x=35 \\ x=\frac{35}{7} \\ x=5 \end{gathered}[/tex]Answer: the value of x so that f(x)=7 is x=5.
The question is in the image. Answer question 20 only.
To convert radians to degrees we use the formula:
[tex]\theta\cdot\frac{180}{\pi}[/tex]In this case the angle is 12 radians, then we have:
[tex]12\cdot\frac{180\degree}{\pi}=687.55[/tex]Therefore, the angle in degrees is 687.55°
Every day the ocean has two low tides and two high tides. Function g represents the height, in feet, of the water level in a cove relative to theaverage sea level. Let t represent the number of hours elapsed since the water height was equal to the average sea level after a low tide.s(e) = ssin(}t)Plot the points where s(4) is equal to the average sea level.
We can see from the question that we have the sine function, which is modeling the water level in a cove relative to the average sea level, and this function is given by:
[tex]g(t)=4sin(\frac{\pi}{6}t)[/tex]And we need to find the points where g(t) is equal to the average sea level.
1. To find it, we need to analyze the given function as follows:
2. Then we can say that the function has:
• An amplitude (the value from the ,midline of the function, in this case, x = 0,).
,• The period of the function is given by:
[tex]\begin{gathered} \text{ Period=}\frac{2\pi}{B} \\ \\ \text{ Period=}\frac{2\pi}{\frac{\pi}{6}}=2\pi(\frac{6}{\pi})=12 \\ \\ \text{ Period=}12 \end{gathered}[/tex]3. These values can be seen as follows:
4. To find the points where g(t) is equal to the average sea level, we can see that the average sea level is represented by the midline, x = 0, and from the graph, we can see that these points are points on the x-axis, and they are (6, 0), and (12, 0) for the given graph:
26. Find the area of the figure to the nearest tenth,165°7 inA. 13.5 in.B. 7.1 in 2C. 84.8 in 2D. 42.4 in?
To find the area of the segment of the circle, use the following formula:
[tex]A=\frac{a}{360}\pi r^2[/tex]Where a is the angle of the segment and r is the radius of it. Replace for the given values and find the area of the segment:
[tex]\begin{gathered} A=\frac{165}{360}\pi\cdot(7)^2 \\ A=70.55 \end{gathered}[/tex]