Find the area of the region enclosed by f(x) and the x-axis for the given function over the specified interval. x2 + 2x + 2 x2 The area is 54 (Type an integer or a simplified fraction.)
Answers
To find this area, it is necessary to solve an integral, actually the sum of 2 integrals
[tex]\int (x^2+2x+2)dx+\int (3x+4)dx[/tex]The first one must be evaluated from -3 to 2 and the second one from 2 to 3
[tex]\begin{gathered} \int (x^2+2x+2)dx+\int (3x+4)dx \\ (\frac{x^3}{3}+x^2+2x)+(\frac{3x^2}{2}+4x) \\ \end{gathered}[/tex]Evaluate the first integral
[tex]\begin{gathered} \frac{x^3}{3}+x^2+2x\text{ (From -3 to 2)} \\ (\frac{2^3}{3}+2^2+2\cdot2)-(\frac{(-3)^3}{3}+(-3)^2+(2\cdot-3)) \\ \frac{8}{3}+4+4-(-\frac{27}{3}+9-6) \\ \frac{35}{3}+5=\frac{50}{3} \end{gathered}[/tex]Evaluate the second integral
[tex]\begin{gathered} \frac{3x^2}{2}+4x\text{ (From 2 to 3)} \\ (\frac{3\cdot(3^2)}{2}+4\cdot3)-(\frac{3\cdot(2^2)}{2}+4\cdot2) \\ (\frac{27}{2}+12)-(\frac{12}{2}+8) \\ \frac{15}{2}+4=\frac{23}{2} \end{gathered}[/tex]Now, solve the sum
[tex]\begin{gathered} \frac{50}{3}+\frac{23}{2} \\ \frac{100+69}{6}=\frac{169}{6} \end{gathered}[/tex]The area is 169/6
Related Questions
Ron bought two comic books on sale. Each comic book was discounted $1 off the regular price r. Write an expression to find what Ron paid before taxes. If each comic book was regularly $2.50, what was the total cost before taxes?
Answers
Step 1
Given;
[tex]\begin{gathered} A\text{ regular price of r for a comic book on sale} \\ A\text{ discount of \$1 before tax} \end{gathered}[/tex]Required; To
1) write an expression to find what was paid by Ron before taxes
2)Find the total cost before taxes of the comic books, if each one costs $2.50
Step 2
Write the expression of what Ron paid before taxes
[tex]\begin{gathered} \text{\$}2(r-1) \\ \text{Note; One book costs \$(r-1)} \\ \text{\$}(2r-2) \end{gathered}[/tex]Step 3
If each book was regularly $2.50, find the total cost before taxes
[tex]\begin{gathered} r=\text{\$}2.50 \\ \text{Total cost=\$(2(2.50)-2)} \\ \text{Total cost=\$(5-2)=\$}3 \end{gathered}[/tex]Interpret the remainder Solve each problem. Write A, B, C, D, or E to Indicate how you interpreted the remainder. A Use only the whole number. B Round up to the next whole number. C Use a mixed number. D Use a decimal. E Use only the remainder. 1. A group of 347 people have signed up for a bus trip to a baseball game. Each bus holds a maximum of 42 passengers. How many buses will be needed to take all the people to the game? 2. Andre and his sisters picked 105 pounds of grapes for their family's farm stand. They put the same amount of grapes into each of 30 bags. How many pounds of grapes were in each bag? 3. Paula charges an hourly rate for babysitting. Last month she worked 12 hours babysitting and earned $81. What does Paula earn per hour? 4. Mr. Parker owns The Glass Store. He received a shipment of 144 glass animals. He put an equal number of glass animals on each of 11 display shelves. How many glass animals were on each shelf? 5. Create Your Own Which letter did you not use in your answer? Make up a word problem of your own that uses this interpretation of the remainder.
Answers
question number 1
number of people = 347
number of buses = 42
number of buses that'll be required to take all passenger =
[tex]\frac{347}{42}=8.26[/tex]the reminder is a decimal hence the answer is option D.
if R200 is musted at 6% simple interests per year detemine the interest if earch after 4years
Answers
The interest calculated after 4 years for a principal amount of 200 at 6% rate of interest , is 48 and the total amount is 248.
Given,
P = 200
rate of interest (r) = 6%
time (t) = 4 years.
we know the simple interest formula as:
S.I = P×r×t/100
substitute the above values.
Interest = 200 × 4 × 0.06/100
= 800 × 0.06/100
= 8 × 0.06
= 0.48 × 100
= 48
Total amount = 200+48
= 248
Hence we get the total amount as 248 at the end of 4 years.
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Please help will mark Brainly
Answers
Answer:
Below
Step-by-step explanation:
A yes all values of y
B yes slope is undefined for a vertical line
C no there is no y axis intercept for this line
D yes the line intercepts the x-axis at x = -2
E no the domain is only x = -2
DIoll Solve the equation x³ + 2x² - 5x-6=0 given that 2 is a zero of f(x)= x³ + 2x² - 5x-6.The solution set is(Use a comma to separate answers as needed.)
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
f(x) = x³ + 2x² - 5x - 6
zero:
x = 2
Step 02:
roots:
solution set:
2 | 1 2 -5 -6
| 2 8 6
________________
1 4 3 0
x² + 4x + 3 = 0
(x + 3)(x + 1) = 0
x = - 3
x = - 1
The answer is:
solution set:
{-3 , -1 , 2}
I need help describing the sequence of transformations for 12 and 13.
Answers
12. For the first part we rotate 90° and reflect on the y-axis
Then we reflect on the x-axis
13. First we reflect on the y-axis, then we rotate 90° and finally we reflect on the x-axis
determine the domain of each function y=2x^4-3x^4+7x^2-1
Answers
Given:
[tex]y=2x^4-3x^4+7x^2-1[/tex]Simplify the function,
[tex]\begin{gathered} y=2x^4-3x^4+7x^2-1 \\ y=-x^4+7x^2-1 \end{gathered}[/tex]Domain: The domain of the function is the set of all possible input values for which the function is real or defined.
So, the domain of the given function is,
[tex]-\infty14. Imagine a particle starting at (1,0) and making one counterclockwise revolution on the unitcircle. Let t be the angle in standard position that corresponds to the particle's position. At howmany points along the path of the particle are the x and y coordinates equal?
Answers
Let's make a graph to better understand the question:
a.) A particle starting at (1,0) and making one counterclockwise revolution on the unit
circle.
In the given description, we can assume that the center of the circle when the particle makes a revolution is at the origin (0,0). Thus, the equation of the circle that the particle will make is:
[tex](x-h)^2+(y-k)^2\text{ = }r^2[/tex]At (h,k) = (0,0) and r = distance between (0,0) to (1,0).
We get,
[tex](x-0)^2+(y-k)^2=(\sqrt[]{(1-0)^2+(0-0)^2})^2[/tex][tex]x^2+y^2\text{ = }1[/tex]Plotting the graph,
In conclusion, there will be two points along the path of the particle that the x and y coordinate equal.
At, x = y, let's substitute this to the formula of the graph of the circle to get the coordinates.
[tex]x^2+y^2\text{ = }1[/tex][tex]x^2+x^2\text{ = }1[/tex][tex]2x^2\text{ = 1 }\rightarrow\text{ }\frac{2x^2}{2}=\text{ }\frac{1}{2}[/tex][tex]x\text{ = }\sqrt[]{\frac{1}{2}}[/tex][tex]x\text{ = y = }\pm\frac{1}{\sqrt[]{2}}[/tex]Therefore, the two points where the x and y will be equal is at:
[tex]\text{ x = y = +}\frac{1}{\sqrt{2}}\text{ and }-\frac{1}{\sqrt[]{2}}[/tex]How many ounces of water must be added to 85oz of a 40% salt solution to make a solution that is 17% salt?
Answers
Okay, here we have this:
Considering the provided information, we are going to calculate the requested value, so we obtain the following:
Accordingly, since the amount of salt remains the same, then we have the following equality, where x represents the amount of water that must be added:
0.4(85)=0.17(x+85)
Let's solve for x:
34=0.17x+14.45
0.17x=34-14.45
0.17x=19.55
x=19.55/0.17
x=115
Finally we obtain that must be added 115 ounces of water to make a solution that is 17% salt.
2. Select ALL coordinate pairs that are solutions to the inequality 5x + 9y<45. *
Answers
From the problem we have the inequality 5x + 9y < 45
Substitute the options and check if it satisfies the inequality.
(0, 0)
5(0) + 9(0) < 45
0 + 0 < 45
0 < 45
TRUE!
(5, 0)
5(5) + 9(0) < 45
25 < 45
TRUE!
(9, 0)
5(9) + 9(0) < 45
45 < 45
FALSE!
(0, 5)
5(0) + 9(5) < 45
45 < 45
FALSE!
(0, 9)
5(0) + 9(9) < 45
81 < 45
FALSE!
(-5, -9)
5(-5) + 9(-9) < 45
-25 - 81 < 45
-106 < 45
TRUE!
ANSWERS :
(0, 0), (5, 0) and (-5, -9)
Which coordinate plane contains the points (4 1/2,1) and (–2 1/2, –2)?
Answers
option C
Explanation:
To determine the graph with the coordinates given, let's check and state some of the coordinates of each graph in the option:
[tex]\begin{gathered} \text{Given coordinates:} \\ (4\frac{1}{2},1)\text{ : x = 4}\frac{1}{2},\text{ y = 1} \\ (-2\text{ }\frac{1}{2},\text{ -2) : x = }-2\text{ }\frac{1}{2},\text{ y = -2} \end{gathered}[/tex]a) Coordinates: (-2, -3), (4, 4)
There is no point at -4 1/2 or -2 1/2 on this graph
b) coordinates: (-2, -3), (3, 1/2)
Tere is no x value at -4 1/2 or -2 1/2 on this graph
c) when x = -2 1/2, y = -2
when x = 4 1/2, y = 1
d) There is no x value at 4 1/2 on this graph. There is also no x value at -2 1/2 on this graph
Hence, the coordinate plane that contains points (4 1/2, 1) and (-2 1/2, -2) is option C
solve the quadratic equation by the square root method. show all steps.
Answers
We have to solve the equation with the square root method:
[tex]\begin{gathered} 2(x-4)^2-6=18 \\ 2(x-4)^2=18+6 \\ 2(x-4)^2=24 \\ (x-4)^2=\frac{24}{2} \\ (x-4)^2=12 \\ \sqrt[]{(x-4)^2}=\sqrt[]{12} \\ x-4=\pm\sqrt[]{12} \\ x=4\pm\sqrt[]{12} \\ x=4\pm2\sqrt[]{3} \end{gathered}[/tex]Answer: The solutions are:
[tex]\begin{gathered} x_1=4-2\sqrt[]{3} \\ x_2=4+2\sqrt[]{3} \end{gathered}[/tex]Solve the equation for c: 52 = 4(c + 5)
Answers
Given:
[tex]52\text{ = 4(c + 5)}[/tex]Solution
We are required to solve the equation for c.
First, we open the bracket:
[tex]52\text{ = 4c + 20}[/tex]Next, we make c the subject of formular:
[tex]\begin{gathered} 4c\text{ = 52 - 20} \\ 4c\text{ = 32} \\ \text{Divide both sides of the equation by 4} \\ c\text{ = 8} \end{gathered}[/tex]Answer: c = 8
Write the probability of getting 2 heads when flipping a coin 2 times. (Write as a reduced fraction)
Answers
we have that
The probability of getting 1 head when flipping a coin one time is
P=1/2
so
the probability of getting 2 heads when flipping a coin 2 times is
P=(1/2)*(1/2)=1/4
therefore
the answer is
P=1/4hello this is a plane trigonometry question hopefully you can help I did every thing else it's just the last one I can't get the reference angle for five in this question
Answers
If the line joining the points (a,4) and (2,-5) is parallel to the line with given equation 2x-3y=12 find the value of a
Answers
Parallel lines have the same slope, thus, using the equation of the parallel line, we can find out the slope of the line that passes through the given points.
To find the slope of a line given its equation, we have to put the equation into the slope-intercept form, whcih we can do by solving the equation for y:
[tex]\begin{gathered} 2x-3y=12 \\ -3y=-2x+12 \\ y=\frac{-2}{-3}x+\frac{12}{-3} \\ y=\frac{2}{3}x-4 \end{gathered}[/tex]The slope of the line is the coefficient multiplying x, which is 2/3 in this case.
So, let's name the slope m:
[tex]m=\frac{2}{3}[/tex]Since the lines are parallel, both have the same slope m.
Also, if we want to find the slope given two numbers on the line, we can use the following equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So, we have the points (a, 4) and (2, -5) and we have the slope m = 2/3. Substituting these, we have:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1}_{} \\ \frac{2}{3}=\frac{-5-4}{2-a} \\ \frac{2}{3}=\frac{-9}{2-a} \\ 2(2-a)=3\cdot(-9) \\ 4-2a=-27 \\ -2a=-27-4 \\ -2a=-31 \\ a=\frac{31}{2} \end{gathered}[/tex]Thus, the value of a is 31/2.
Which pair of expressions are equivalent?
Answers
The pair of equivalent expression are 6(8f) and 48f
What is equivalent expression?Equivalent expressions are expressions that have similar value or worth but do not look the same.
Two expressions are said to be equivalent if they have the same value
irrespective of the value of the variable(s) in them.
Therefore, let's check the pair of expression and find which are equivalent.
6(8f) and 48f are equivalent expression.
If we simplify 6(8f), it will be as follows:
6(8f) = 6 × 8f = 48f
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A hemisphere bowl of radius 7ft has water in it to a depth of 2 ft. At what angle must it be tipped for the water to begin to flow out?
Answers
We have an hemisphere (a shape that is half a sphere) of radius r = 7 ft, that is a bowl filled with water up to a depth of 2 ft.
We have to find at what angle must it be tipped for the water begind to flow. We have to take into account that the level of the water will remain horizontal when we tip the bowl.
This will happen when the water level reaches the edge of the hemisphere.
This can be represented as:
The bowl have to be tipped so the edge descends 2 ft.
We can represent that in mathematical terms as:
Then, we can relate the angle with the depth using a trigonometric ratio:
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{\text{depth}}{\text{radius}}=\frac{2}{7} \\ \theta=\arcsin (\frac{2}{7}) \\ \theta\approx16.6\degree \end{gathered}[/tex]Answer: the angle is 16.6°
Daig 20. Sample Problem using Daum Equation Editor 4 - [3 :) and B - [: 6 51 Determine -3A + 2B Show all work using the Daum Equation Editor. Insert your image here:
Answers
The question is given as : -3A +2 B
[2 5] + { 6 5 }
[7 0 } { 1 1 }
For the first matrix , multiply by -3 and the second matrix multiply by 2
To multiply a matrix, every value in the bracket is multiplied by the scalar.
For -3A multiply the values in the bracket with -3 as;
[tex]\begin{bmatrix}{2} & {5} & \\ {7} & {0} & {} \\ {} & {} & \end{bmatrix}\times-3\text{ = }\begin{bmatrix}{-6} & {-15} & \\ {-21} & {0} & {} \\ {} & {} & {}\end{bmatrix}=-3A[/tex]For 2B
[tex]\begin{bmatrix}{6} & {5} & {} \\ {1} & {1} & {} \\ {} & {} & {}\end{bmatrix}\times2=\begin{bmatrix}{12} & {10} & \\ {2} & {2} & {} \\ {} & {} & {}\end{bmatrix}=2B[/tex]Now perform the addition as; -3A + 2B
[tex]\begin{bmatrix}{-6} & {-15} & \\ {-21} & {0} & {} \\ {} & {} & {}\end{bmatrix}+\begin{bmatrix}{12} & {10} & \\ {2} & {2} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{-6+12} & {-15+10} & \\ {-21+2} & {0+2} & {} \\ {} & {} & {}\end{bmatrix}[/tex]This will give the following;
[tex]\begin{bmatrix}{6} & {-5} & {} \\ {-19} & {2} & {} \\ {} & {} & {}\end{bmatrix}[/tex]Find the area of the triangle with the given measurements. Round the solution to thenearest hundredth if necessary.B = 74º, a = 14 cm, c = 20 cm (5 points)
Answers
Let's begin by listing out the given information:
[tex]\begin{gathered} \angle B=74^{\circ} \\ a=14\operatorname{cm} \\ c=20\operatorname{cm} \end{gathered}[/tex]We will calculate the area as shown below:
[tex]\begin{gathered} \text{We will obtain the third side using the Cosine Rule:} \\ b^2=a^2+c^2-2ac\cdot cosB \\ b=\sqrt[]{a^2+c^2-2ac\cdot cosB} \\ b=\sqrt[]{14^2+20^2-2(14)(20)\cdot cos74^{\circ}} \\ b=21.02cm \end{gathered}[/tex]The formula for area is given by Heron's formula:
[tex]\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ s=\frac{a+b+c}{2}=\frac{14+21.02+20}{2}=\frac{55.02}{2}=27.51 \\ s=27.51 \\ \Rightarrow A=\sqrt[]{27.51(27.51-14)(27.51-21.02)(27.51-20)} \\ A=134.58cm^2 \end{gathered}[/tex]Therefore, the area f
7a) The roots of the equation 4x^2 - 7x - 1 = 0 are G and H. Evaluate G^2+ H^2B) Write the equation of a quadratic with integer coefficients whose solutions are G^2 and H^2.Pls see the pic for more detail.
Answers
Given:
[tex]4x^2-7x-1=0[/tex]Solve:
Quadratic formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Where,
[tex]ax^2+bx+c=0[/tex]Compaire the equation then:
[tex]\begin{gathered} ax^2+bx+c=0 \\ 4x^2-7x-1=0 \\ a=4,b=-7,c=-1 \end{gathered}[/tex]So roots of equation is:
[tex]\begin{gathered} x=\frac{-(-7)\pm\sqrt[]{(-7)^2-4(4)(-1)}}{2(4)} \\ x=\frac{7\pm\sqrt[]{49+16}}{8} \\ x=\frac{7\pm\sqrt[]{65}}{8} \end{gathered}[/tex]So value of G and H is:
[tex]\begin{gathered} G=\frac{7+\sqrt[]{65}}{8};H=\frac{7-\sqrt[]{65}}{8} \\ G=\frac{7}{8}+\frac{\sqrt[]{65}}{8};H=\frac{7}{8}-\frac{\sqrt[]{65}}{8} \end{gathered}[/tex]So:
[tex]\begin{gathered} =G^2+H^2 \\ =(\frac{7}{8}+\frac{\sqrt[]{65}}{8})^2+(\frac{7}{8}-\frac{\sqrt[]{65}}{8})^2 \\ =(\frac{7}{8})^2+(\frac{\sqrt[]{65}}{8})^2+2(\frac{7}{8})(\frac{\sqrt[]{65}}{8})+(\frac{7}{8})^2+(\frac{\sqrt[]{65}}{8})^2-2(\frac{7}{8})(\frac{\sqrt[]{65}}{8}) \\ =2(\frac{49}{64}+\frac{65}{64}) \\ =2(\frac{114}{64}) \\ =\frac{114}{32} \\ =3.5625 \end{gathered}[/tex](B)
If roots is a and b the equation is:
[tex]x^2-(a+b)x+ab=0[/tex]Then equation is:
[tex]G^2+H^2=3.5625[/tex][tex]\begin{gathered} G^2H^2=(\frac{7}{8}+\frac{\sqrt[]{65}}{8})^2(\frac{7}{8}-\frac{\sqrt[]{65}}{8})^2 \\ =(0.875+1.00778)^2(0.875-1.00778)^2 \\ =(3.54486)(0.01763) \\ =0.0624 \end{gathered}[/tex]So equation is:
[tex]x^2-3.5625x+0.0624[/tex]The table represents the cost to eat at a buffet-style restaurant.Number ofPeople (p)2Cost (C)(including tax)27.5441.3155.0868.85345682.62Which equation could be used to calculate the cost. C, for any number of people, p, to eat at the restaurant?
Answers
We need to take the values of the table and check which of the options fit with the results.
In the first line of the table we have p=2 and C=27.54.
Using the equation in option A, for p=2 we would get:
[tex]\begin{gathered} C=p+27.54 \\ C=2+27.54 \\ C=29.54 \end{gathered}[/tex]Which is not value for C in the table. Thus we discard option A.
Using the equation for option B, for the value of p=2, we would get:
[tex]\begin{gathered} C=13.77p \\ C=13.77(2) \\ C=27.54 \end{gathered}[/tex]Which is indeed the value of the table.
To confirm, we try now with the next value of p, p=3, and check if we get the same result with equation B as with the table:
[tex]\begin{gathered} C=13.77p \\ C=13.77(3) \\ C=41.31 \end{gathered}[/tex]Which is also the value for C in the table.
Thus we confirm that option B is the correct equation
Find the values of x and y in the parallelogram.A46x+2211 BO x= 11, y = 24O x = 24, y = 11Ox=-11, y = 46O x=46, Y =-11
Answers
Since the opposite sides of a parallelogram are congruents, we can write the following equations:
[tex]\begin{cases}DA=BC \\ AB=CD\end{cases}[/tex]From the first one, we have:
[tex]y=11[/tex]From the second one, we have:
[tex]\begin{gathered} x+22=46 \\ x=46-22 \\ x=24 \end{gathered}[/tex]So we have x = 24 and y = 11, therefore the correct option is the second one.
Determine the domain and range Express your answer in interval notation
Answers
The domain of a function is the set of all values that the x-variable can take.
On the other hand, the range of the function is the set of all values that the function takes when it is evaluated at elements of the domain.
For the given expression:
[tex]p(x)=-\frac{1}{(x-1)^2}[/tex]The denominator is (x-1)^2. Since the denominator must be different from 0, then:
[tex]\begin{gathered} (x-1)^2\ne0 \\ \Rightarrow x-1\ne0 \\ \Rightarrow x\ne1 \end{gathered}[/tex]Then, the only restriction for the variable x is not to be equal to 1. Then, the domain of p(x) is the set of all real numbers except 1, which can be written using interval notation as:
[tex](-\infty,1)\cup(1,\infty)[/tex]Since the exponent of the denominator is 2, then the denominator is always positive. Since the coefficient of the term 1/(x-1)^2 is -1, then the whole expression must always be negative. Additionally, there is no way in which the expression can be equal to 0.
Then, the range of the function is the set of all negative numbers, which can be expressed using interval notation as:
[tex](-\infty,0)[/tex]Therefore, the answers are:
[tex]\begin{gathered} \text{ Domain: }(-\infty,1)\cup(1,\infty) \\ \\ \text{ Range: }(-\infty,0) \end{gathered}[/tex]rs + 2r210rs5s2Find the binomial factors
Answers
Rs+2r^2-10rs-5s^2
Combine like terms
2r^2-9rs-5s^2
Find the solution of the system of equations. 3x + 3y = 6 9x - 5y = -24
Answers
3x + 3y = 6 (eq. 1)
9x - 5y = -24 (eq. 2)
Multiplying equation 1 by 3,
3(3x + 3y) = 3*6
3(3x) + 3(3y) = 18
9x + 9y = 18 (eq. 3)
Subtracting equation 2 to equation 3,
9x + 9y = 18
-
9x - 5y = -24
---------------------
14y = 42
y = 42/14
y = 3
Replacing this result into equation 1,
3x + 3(3) = 6
3x + 9 = 6
3x = 6 - 9
3x = -3
x = -3/3
x = -1
How wide is the space betweeneach number on this clock?
Answers
Solution:
Given:
We have the angle between each hands of the clock to be
[tex][/tex]An ellipse has vertices (0,-5) and (0,5) and a minor axis of length 8.Part I: In what direction is this ellipse oriented? Part II: What are the coordinates of the center of this ellipse? Part III: What are the values of a and b for this ellipse? Part IV: Write the equation of this ellipse.
Answers
we know that
vertices (0,-5) and (0,5) --------> is a vertical ellipse
the minor axis of length 8 ------> 2b=8 -------> b=4
so
Part I: In what direction is this ellipse oriented?
Is a vertical ellipse
Part II: What are the coordinates of the center of this ellipse?
The center of the ellipse is the midpoint between the vertices
The midpoint between (0,-5) and (0,5) is the origin (0,0)
The center is the point (0,0)
Part III: What are the values of a and b for this ellipse?
b=4
2a=10 ---------> a=5
Part IV: Write the equation of this ellipse.
[tex]\begin{gathered} \frac{y^2}{a^2}+\frac{x^2}{b^2}=1 \\ substitute\text{ given values} \\ \frac{y^2}{5^2}+\frac{x^2}{4^2}=1 \\ therefore \\ \frac{y^2}{25}+\frac{x^2}{16}=1 \end{gathered}[/tex]solve: 10+7-4y=-5+6y+22 and decide whether it has infinite solutions or no solutions or one solution
Answers
answer is one solution
A giant panda gave birth to her baby at a zoo. The baby panda weighed 100 grams. At its health exam 51 days later the baby weighed 2.17 kilograms. How much weight did the panda cub gain after 51 days?
Answers
Day 1 Weight of Baby Panda = 100 grams
Day 52 (after 51 days) Weight of Baby Panda = 2.17 kg
To determine the weight increase of our baby panda, we have to convert first the units from kg to grams.
[tex]1kg=1000grams[/tex]Please know that 1kg = 1000 grams. Therefore, 2.17 kg is equal to:
[tex]2.17kg\times1000grams=2170grams[/tex]So now, the weight of our baby panda after 51 days is 2170 grams. To determine weight increase, we will subtract 100 grams from 2170 grams.
[tex]2,170grams-100grams=2,070grams[/tex]Therefore, the panda cub gained 2,070 grams after 51 days or 2.07kg.