A giraffes hunger level depends on the size of its last meal. What is the independent and dependent variable

Answers

Answer 1
the independent will be the the size of the meal and the dependent will be the hunger level.

Related Questions

a construction company charges $500 for the plans plus $600 per square foot to build a new home. Write an equation that shows this relationship

Answers

x = square feet

total cost = 500 + 600x


-3 1/2 * 0.5 help please

Answers

Convert -3 1/2 into an improper fraction.  That fraction is -7/2.  Mult. this by 1/2.
Result is -7/4 (answer)
Let -3 1/2 = -7/2.

Let 0.5 = 1/2.

(-7/2)(1/2) = -7/4

Done.

which is the smallest number? 3/4,1/5,10/23,2/31

Answers

A quick and easy way to do this particular question is to think all of these numbers are close to 1/2 except 2/31. So, the lowest is 2/31.

H O P E T H I S H E L P S!
3333333333333333333333

Which is the solution to the equation 2.6a + 18.4 = 28.8 round the nearest tenth if necessary. 1.4, 4, 18.2, 27

Answers

You would subtract 18.4 from 28.8 then divide that answer by 2.6. The answer would therefor be 4.

Answer:

Your answer is B=4

Step-by-step explanation:

hope it helps once again

please help me with this problem

Answers

129.95 * 0.55 = 71.4725

71.4725 * .06 = 4.28835

71.4725 + 4.28835 = $75.76

Answer = $75.76

Devin brought his snails collection to school. He has 10 snails. How could he put them into 2 tanks so two classes could see them?
Write equation for all the possible ways.
One of the ways is given.
Explain how you know you have found all the ways.

Answers

10 divided by 2 = 5 is one of the equations

What is the unit rate 3 for $5 4 for$6

Answers

The unit rate for 3 for $5 is around $1.70 or $1.60

The unit rate for 4 for $6 is $1.50
You have two separate problems here.  

a) 3 for $5 needs to be expressed as cost per unit.  Write $5/(3 units), and then simplify.  Here the unit rate is ($5/3) / unit, or $1.67 per unit.

b)  4 for $6:  Write $6/(4 units), and then reduce to lowest terms:  
(6/4) dollars per unit, or $1.50/unit

A scanner scanned 56 photos in 7 minutes. If it scans photos at a constant rate, it can scan _____ photos in 27 minutes. Numerical Answers Expected! PLEASE HELP

Answers

It can scan 216 photos in 27 minutes since the rate is 8 photos per minute.
Writing and solving an equation of two ratios would be one of the easier ways to solve this problem.

56 photos          x
-------------- = ------------
  7 min            27 min

x is found as follows:  (56 photos)(27 minutes) = (7 min)(x)

Divide both sides by (7 min) to get the answer, x, which is measured in "photos."

Approximate, to the nearest 0.1°, all angles θ in the interval [0°, 360°) that satisfy the equation. (Enter your answers as a comma-separated list.)
(a) sin θ = 0.9263 θ = °
(b) cos θ = −0.6909 θ = °
(c) tan θ = −1.5416 θ = °
(d) cot θ = 1.3952 θ = °
(e) sec θ = 1.4293 θ = °
(f) csc θ = −2.3174

Answers

(a) sin θ = 0.9263 θ = 67.9°, 112.1° (b) cos θ = â’0.6909 θ = 133.7°, 226.3° (c) tan θ = â’1.5416 θ = 123.0°, 303.0° (d) cot θ = 1.3952 θ = 35.6°, 215.6° (e) sec θ = 1.4293 θ = 45.6°, 225.6° (f) csc θ = â’2.3174 θ = 205.6°, 334.4° This is simply a matter of knowing how to use the trig identities and reflections. I am going to assume that you have access to an arctangent function (the ability to get the angle from the tangent of the angle) and that you have no other inverse trig functions available. The arctangent function is assumed to only work for positive tangents and returns a value between 0 and 90 degrees. (a) sin θ = 0.9263 θ = 67.9°, 112.1° The cos will be sqrt(1-0.9263^2) = 0.3768 The tan will be 0.9263/0.3768 = 2.4583 atan(2.4583) = 67.9° Since the sin is positive, there are 2 angles, one in quadrant 1 and another in quadrant 2. The angle for quadrant 2 will be 180° - 67.9° = 112.1° (b) cos θ = â’0.6909 θ = 133.7°, 226.3° The cos is negative, but we'll use the positive value for the basic angle calculations. sin = sqrt(1-0.6909^2) = 0.7230 tan = 0.7230/0.6909 = 1.0465 atan(1.0465) = 46.3° Since the cos is negative, the angles are in quadrants II and III. The angles will be 180° - 46.3° = 133.7° 180° + 46.3° = 226.3° (c) tan θ = â’1.5416 θ = 123.0°, 303.0° atan(1.5416) = 57.0° Since the tangent is negative, the angles are in quadrants II and IV. 180° - 57.0° = 123.0° 360° - 57.0° = 303.0° (d) cot θ = 1.3952 θ = 35.6°, 215.6° tan = 1/1.3952 = 0.7167 atan(0.7167) = 35.6° Since the cot is positive, the angles are in quadrants I and III 180° + 35.6° = 215.6° (e) sec θ = 1.4293 θ = 45.6°, 225.6° cos = 1/1.4293 = 0.6996 sin = sqrt(1-0.6996^2) = 0.7145 tan = 0.7145/0.6996 = 1.0213 atan(1.0213) = 45.6° Since the sec is positive, the angles are in quadrants I and III 180° + 45.6° = 225.6° (f) csc θ = â’2.3174 θ = 205.6°, 334.4° sin = 1/2.3174 = 0.4315 cos = sqrt(1-0.4315^2) = 0.9021 tan = 0.4315/0.9021 = 0.4783 atan(0.4783) = 25.6° Since the csc is negative, the angles are in quadrants III and IV 180° + 25.6° = 205.6° 360° - 25.6° = 334.4°

a) [tex]\[ \theta = 67.9^\circ, 112.1^\circ \][/tex], b) [tex]\[ \theta = 133.7^\circ, 226.3^\circ \][/tex], c) [tex]\[ \theta = 122.7^\circ, 302.7^\circ \][/tex], d) [tex]\[ \theta = 35.8^\circ, 215.8^\circ \][/tex], e) [tex]\[ \theta = 45.5^\circ, 314.5^\circ \][/tex] and f) [tex]\[ \theta = 154.4^\circ, 334.4^\circ[/tex].

Let's solve each part:

(a) [tex]\(\sin \theta = 0.9263\)[/tex]

1. Find the reference angle using [tex]\(\theta = \sin^{-1}(0.9263)\)[/tex]:

[tex]\[ \theta \approx 67.9^\circ \][/tex]

2. Since [tex]\(\sin \theta\)[/tex] is positive, the angles are in the first and second quadrants:

[tex]\[ \theta_1 \approx 67.9^\circ \][/tex]

[tex]\[ \theta_2 \approx 180^\circ - 67.9^\circ = 112.1^\circ \][/tex]

So, the solutions are:

[tex]\[ \theta = 67.9^\circ, 112.1^\circ \][/tex]

(b) [tex]\(\cos \theta = -0.6909\)[/tex]

1. Find the reference angle using [tex]\(\theta = \cos^{-1}(-0.6909)\)[/tex]:

[tex]\[ \theta \approx 133.7^\circ \][/tex]

2. Since [tex]\(\cos \theta\)[/tex] is negative, the angles are in the second and third quadrants:

[tex]\[ \theta_1 \approx 133.7^\circ \][/tex]

[tex]\[ \theta_2 \approx 360^\circ - 133.7^\circ = 226.3^\circ \][/tex]

So, the solutions are:

[tex]\[ \theta = 133.7^\circ, 226.3^\circ \][/tex]

(c) [tex]\(\tan \theta = -1.5416\)[/tex]

1. Find the reference angle using [tex]\(\theta = \tan^{-1}(-1.5416)\)[/tex]:

[tex]\[ \theta \approx -57.3^\circ \][/tex]

2. Adjust the reference angle to fall within the interval [tex]\([0^\circ, 360^\circ)\)[/tex]:

[tex]\[ \theta_1 = 360^\circ - 57.3^\circ = 302.7^\circ \][/tex]

3. Since [tex]\(\tan \theta\)[/tex] is negative, the angles are in the second and fourth quadrants:

[tex]\[ \theta_2 = 180^\circ + (-57.3^\circ) = 122.7^\circ \][/tex]

So, the solutions are:

[tex]\[ \theta = 122.7^\circ, 302.7^\circ \][/tex]

(d) [tex]\(\cot \theta = 1.3952\)[/tex]

1. Find the reference angle using [tex]\(\theta = \cot^{-1}(1.3952)\)[/tex]:

[tex]\[ \theta \approx 35.8^\circ \][/tex]

2. Since [tex]\(\cot \theta\)[/tex] is positive, the angles are in the first and third quadrants:

[tex]\[ \theta_1 \approx 35.8^\circ \][/tex]

[tex]\[ \theta_2 \approx 180^\circ + 35.8^\circ = 215.8^\circ \][/tex]

So, the solutions are:

[tex]\[ \theta = 35.8^\circ, 215.8^\circ \][/tex]

(e) [tex]\(\sec \theta = 1.4293\)[/tex]

1. Convert to [tex]\(\cos \theta\)[/tex]:

[tex]\[ \cos \theta = \frac{1}{1.4293} \approx 0.6996 \][/tex]

2. Find the reference angle using [tex]\(\theta = \cos^{-1}(0.6996)\)[/tex]:

[tex]\[ \theta \approx 45.5^\circ \][/tex]

3. Since [tex]\(\cos \theta\)[/tex] is positive, the angles are in the first and fourth quadrants:

[tex]\[ \theta_1 \approx 45.5^\circ \][/tex]

[tex]\[ \theta_2 \approx 360^\circ - 45.5^\circ = 314.5^\circ \][/tex]

So, the solutions are:

[tex]\[ \theta = 45.5^\circ, 314.5^\circ \][/tex]

(f) [tex]\(\csc \theta = -2.3174\)[/tex]

1. Convert to [tex]\(\sin \theta\)[/tex]:

[tex]\[ \sin \theta = \frac{1}{-2.3174} \approx -0.4316 \][/tex]

2. Find the reference angle using [tex]\(\theta = \sin^{-1}(-0.4316)\)[/tex]:

[tex]\[ \theta \approx -25.6^\circ \][/tex]

3. Adjust the reference angle to fall within the interval [tex]\([0^\circ, 360^\circ)\)[/tex]:

[tex]\[ \theta_1 = 360^\circ - 25.6^\circ = 334.4^\circ \][/tex]

4. Since [tex]\(\sin \theta\)[/tex] is negative, the angles are in the third and fourth quadrants:

[tex]\[ \theta_2 = 180^\circ + (-25.6^\circ) = 154.4^\circ \][/tex]

So, the solutions are:

[tex]\[ \theta = 154.4^\circ, 334.4^\circ[/tex]

The complete question is:

Approximate, to the nearest 0.1°, all angles θ in the interval [0°, 360°) that satisfy the equation. (Enter your answers as a comma-separated list.)

(a) sin θ = 0.9263

θ = °

(b) cos θ = −0.6909

θ = °

(c) tan θ = −1.5416

θ = °

(d) cot θ = 1.3952

θ = °

(e) sec θ = 1.4293

θ = °

(f) csc θ = −2.3174

θ = °

Given the equation D =m/v if D=2/3 and v=m+1., then m=
-3
2
1

Answers

D = m/v     D = 2/3   v = m + 1

2/3 = m/m + 1

2/3(m + 1) = m

2(m + 1)/ 3 = m

2(m + 1) = 3m

2m + 2 = 3m

2 = 3m - 2m

2 = m 

m = 2

hope that helps, God bless!

Write the equation of a vertical line containing (5,-8)

Answers

check the picture below.

Evaluate 4x-3 when x=_3

Answers

Final answer:

To evaluate the expression 4x-3 for x = -3, we substitute -3 into the expression and follow the order of operations, resulting in a value of -15.

Explanation:

To evaluate the expression 4x-3 when x is -3, we simply substitute -3 in place of x and calculate the result as follows:

Replace x with -3: 4(-3) - 3.Multiply 4 by -3: -12 - 3.Finally, subtract 3 from -12 to get: -15.

Therefore, evaluating 4x-3 when x is -3 gives us -15.

will award 40 points if you answer correctly

Bottles of water sell for 1.50$ each.
Graph the relationship between the number of bottles sold and the total cost.

Answers

see picture for the graph

equation: y = 1.50x

Answer:

Step-by-step explanation:

took the test (k12) and its halfway to 50 if you see in the picture

A 1950 kg car moves with a velocity of 11 m/s. What is its kinetic energy? Joules

Answers

The formula for Kinetic Energy is given by

KE = 0.5 × mv²

We have:
m, the mass = 1950 kg
v, the velocity = 11 m/s

KE = 0.5 × 1950 × 11²
KE = 117975 joules

The Red Sox have won 3 World Series titles in the last 11 years. At this rate, how long will it take them to win 20 World Series?

Answers

The answer is 74 years. do 11/3=3.67. Then 3.67x20 =73.4 and since that .4 is not a full year you would have to round up to 74
73  1/3 years
What I did was use a proportion:

11/3 and x/20
Then you cross multiply:

3x=220
Then solve. 

Write an explicit formula for the sequence (3,7,11,15,19,23,27,...)

Answers

Final answer:

The explicit formula for the given sequence is a_n = 3 + 4(n-1).

Explanation:

The given sequence is (3, 7, 11, 15, 19, 23, 27, ...).

To find the explicit formula for this sequence, we can observe that each term is obtained by adding 4 to the previous term. So, the formula can be written as:

an = 3 + 4(n-1)

where n represents the position of the term in the sequence.

Lucy deposits $7000 into an account that pays simple interest at a rate of 3% per year. How much interest will she be paid in the first 6 years?

Answers

7000*.03*6=??  Step 1. multiply 7000*.03=210 Step 2. multiply 210*6=1260. the answer is $1,260.00 
Final answer:

Lucy will be paid $1260 in interest in the first 6 years.

Explanation:

To calculate the interest Lucy will be paid in the first 6 years, we will use the simple interest formula:

Interest = Principal x Rate x Time

Given:

Principal (P) = $7000Rate (R) = 3% per yearTime (T) = 6 years

Plugging in the values, we get:

Interest = $7000 x 0.03 x 6 = $1260

Therefore, Lucy will be paid $1260 in interest over the first 6 years.

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If the circumference of a circle is 201 centimeters what is the radius of the circle (to the nearest whole number)? Use 3.14 for pi



A) 32 centimeters
B) 128 centimeters
C) none
D) 16 centimeters
E) 64 centimeters

Answers

Final answer:

The radius of a circle with a circumference of 201 centimeters is approximately 32 centimeters, found by dividing the circumference by 2 times pi (π), using 3.14 as the value of pi. The correct answer is A) 32 centimeters.

Explanation:

The question asks us to find the radius of a circle when its circumference is given to be 201 centimeters. We use the circumference formula of a circle, which is C = 2πr, where C stands for circumference, π (pi) is a constant approximately equal to 3.14, and r represents the radius of the circle.

To find the radius, we rearrange this formula to solve for r:

Divide both sides of the equation by 2π to isolate r.

Plug in the given circumference value, C = 201 cm, and the approximate value of pi, π = 3.14, into the rearranged formula.

So the calculation would be r = C / (2π) = 201 / (2 * 3.14) = 201 / 6.28. When we compute this, we get r ≈ 32 centimeters to the nearest whole number.

Therefore, the correct answer is A) 32 centimeters.

jamal has a box with some toy cars in it. he puts 3 more toy cars into the box now there are 22 toy cars in the box how many toy cars were in the box before

Answers

For short X + 3 = 22, so work it backwords 22 - 3 = X so 22 - 3 = 19 Your answer should be 19

Assume that the distance from Earth to the moon is exactly 238,855 miles and that it took astronauts 75 hours to reach the moon in 1969. How far did the astronauts travel each hour, on average, during their trip to the moon? 3,004.73 miles mc026-1.jpg miles 3,317.4305 miles mc026-2.jpg miles

Answers

you would do 238855 divided by 75 ===3184.73333 mph

On average during their trip, their speed was 3184.8 miles/hr.

What is a unitary method?

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

We know Distance = Speed×Time.

∴ Speed = Distance/Time.

Given, The distance from Earth to the moon is exactly 238,855 miles and it took astronauts 75 hours.

So, the average speed is (238855/75) miles/hr.

= 3184.8 miles/hr.

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Find the quotient 4/6÷4/12

Answers

Keep Change Flip is the way to think about dividing fractions.
First-  4/6 divided by 4/12
Next- Change the division sign to multiplecation   4/6 time 4/12
Then- Flip the second number    4/6 times 12/4
Now multiply

48/24   this simplifies down to 2

14.4% of what number is 10.44

Answers

im not sure but i rounded 1.50336 and i got 1.5 so i think that would be your answer. 

Kevin and randy Muise have a jar containing 41 coins all of which are either quarters or nickels . The total value of coins in the jar is 7.45 how many of each type of coin do they have

Answers

Final answer:

To find the number of quarters and nickels, we can set up a system of equations using the total number of coins and the total value of the coins. Solving this system of equations, we find that Kevin and Randy have 27 quarters and 14 nickels.

Explanation:

To solve this problem, we can set up a system of equations. Let's use the variables q (number of quarters) and n (number of nickels). We know that there are a total of 41 coins, so we can write the equation q + n = 41. We also know that the total value of the coins is $7.45, so we can write the equation 0.25q + 0.05n = 7.45.

Now we can solve this system of equations using substitution:

Isolate one variable in one of the equations. Let's isolate q in the first equation: q = 41 - n.Substitute this expression for q in the second equation: 0.25(41 - n) + 0.05n = 7.45.Simplify and solve for n: 10.25 - 0.25n + 0.05n = 7.45. Simplifying further, we get 0.20n = 2.80. Dividing by 0.20, we find that n = 14.Substitute this value of n back into the first equation to find q: q = 41 - 14 = 27.

Therefore, Kevin and Randy have 27 quarters and 14 nickels in their jar.

which of the following shows a strategy to use to find 4x275 (4x300)+(4x25)
(4x300)-(4x25) (4x275)-100 (4x200)+75

Answers

[tex]4*275 (4x^3^0^0)+(4x^2^5) (4x^3^0^0)-(4x^2^5) (4x^2^7^5)-100 (4x^2^0^0)+75[/tex] 


The correct strategy is (4x275) - 100. So option (3) is correct.

To find 4 multiplied by 275 using the given strategies, let's go through each one:

1. (4x300) + (4x25):

First, calculate (4x300) = 1200. Then, calculate (4x25) = 100. Finally, add these results together: 1200 + 100 = 1300.

2. (4x300) - (4x25):

Calculate (4x300) = 1200. Then, calculate (4x25) = 100. Now, subtract the second result from the first: 1200 - 100 = 1100.

3. (4x275) - 100:

Simply multiply 4 by 275 to get 1100. Then, subtract 100: 1100 - 100 = 1000.

4. (4x200) + 75:

Calculate (4x200) = 800. Then, add 75: 800 + 75 = 875.

The correct strategy is the third one: (4x275) - 100.

Detailed Calculation:

1. [tex]\(4 \times 275 = 1100\)[/tex]

2. [tex]\(1100 - 100 = 1000\)[/tex]

So, using the strategy of (4x275) - 100, the result is 1000.

On a town map, each unit of the coordinate plane represents 1 mile. Three branches of a bank are located at A(−3, 1), B(4, 3), and C(2, −1). A bank employee drives from Branch A to Branch B and then drives halfway to Branch C before getting stuck in traffic. What is the minimum total distance the employee may have driven before getting stuck in traffic? Round to the nearest tenth of a mile if necessary.

Answers

distance formula : sqrt ((x2 - x1)^2 + (y2 - y1)^2)
(-3,1)...x1 = -3 and y1 = 1
(4,3)...x2 = 4 and y2 = 3
now we sub
d = sqrt ((4 - (-3)^2 + (3 - 1)^2)
d = sqrt ((4 + 3)^2 + (2^2))
d = sqrt (7^2 + 2^2)
d = sqrt (49 + 4)
d = sqrt 53
d = 7.28 ...so its 7.28 miles from A to B

d = sqrt ((x2 - x1)^2 + (y2 - y1)^2)
(4,3)...x1 = 4 and y1 = 3
(2,-1)...x2 = 2 and y2 = -1
now we sub
d = sqrt ((2 - 4)^2 + (-1 - 3)^2)
d = sqrt (-2^2) + (-4^2)
d = sqrt (4 + 16)
d = sqrt 20
d = 4.47....but the employee only drives halfway....so this trip was 4.47/2 = 2.235

so the minimum total distance is : 7.28 + 2.235 = 9.515  rounds to 9.5 miles


The radius r of a circle is increasing at a rate of 8 centimeters per minute. find the rate of change of the area when r = 39 centimeters

Answers

dr/dt= 8cmM-¹
dA/dt = ?
but A= πr²
so dA/dr =2πr
but recall
dA/dt = dA/dr • dr/dt
dA/dt = 2πr • 8cmM-¹
dA/dt = 2×π×39 ×8 = 624cm²M-1
Final answer:

The rate of change of the area of the circle when the radius is 39 centimeters is 1976π cm²/min. This uses the concept of related rates in calculus and the area formula A = πr².

Explanation:

The problem deals with the concept of related rates in calculus. In this problem, we're looking at how the rate of change of the radius of a circle impacts the rate of change of the area of the circle. The formula for the area of a circle is A = πr².

Differentiating both sides with respect to time(t) gives dA/dt = 2πr(dr/dt). In this case, dr/dt (the rate of change of the radius) is given as 8 cm/min. To find dA/dt (the rate of change of the area) when r = 39 cm, we substitute these values into the differentiated equation: dA/dt = 2π(39cm)(8 cm/min) = 1976π cm²/min

So, the rate of change of the area when r = 39 centimeters is 1976π cm²/min. As the radius increases, the area of the circle increases at a rate directly proportional to the radius.

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The value V of a square glass varies directly as the square of its length X cm. If the value of a square glass with length 3 cm is $243, find the value of a glass with length 5 cm

Answers

Given that the value V of a square glass varies directly as the square of its length X cm.

Then, the variation equation is given by

[tex]V\propto X^2 \\ \\ \Rightarrow V=kX^2[/tex]

Given that value of a square glass with length 3 cm is $243, we have:

[tex]243=k(3)^2=9k \\ \\ \Rightarrow k= \frac{243}{9} =27 \\ \\ \Rightarrow V=27X^2[/tex]

Thus, the value of a glass with length 5 cm is

[tex]V=27(5)^2=27\times25=\bold{\$675} [/tex]

The value V of a square glass varies directly as the square of its length X cm. This means that V is proportional to [tex]X^2[/tex], which can be expressed as:

[tex]\[ V = kX^2 \][/tex]

where k is the constant of proportionality.

Given that the value of a square glass with length 3 cm is $243, we can use this information to find the constant k:

[tex]\[ 243 = k(3)^2 \][/tex]

[tex]\[ 243 = 9k \][/tex]

[tex]\[ k = \frac{243}{9} \][/tex]

[tex]\[ k = 27 \][/tex]

Now that we have the value of k, we can find the value of a glass with length 5 cm by substituting X = 5 into the original equation:

[tex]\[ V = 27(5)^2 \][/tex]

[tex]\[ V = 27 \times 25 \][/tex]

[tex]\[ V = 675 \][/tex]

Therefore, the value of a glass with length 5 cm is $675.

The answer is: 675.

Let c be the curve of intersection of the parabolic cylinder x2 = 2y, and the surface 3z = xy. find the exact length of c from the origin to the point 2, 2, 4 3 . step 1

Answers

Parameterize the curve [tex]C[/tex] by [tex]\mathbf r(t)=\left\langle t,\dfrac{t^2}2,\dfrac{t^3}6\right\rangle[/tex] (essentially replacing [tex]x=t[/tex] and finding equivalent expressions for [tex]y,z[/tex] in terms of [tex]t[/tex].

The length of [tex]C[/tex] is given by the line integral

[tex]\displaystyle\int_C\mathrm dS=\int_{t=0}^{t=2}\|\mathbf r'(t)\|\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2\left\|\left\langle1,t,\dfrac{t^2}2\right\rangle\right\|\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2\sqrt{1+t^2+\dfrac{t^4}4}\,\mathrm dt[/tex]
[tex]=\displaystyle\frac12\int_0^2\sqrt{4+4t^2+t^4}\,\mathrm dt[/tex]
[tex]=\displaystyle\frac12\int_0^2\sqrt{(t^2+2)^2}\,\mathrm dt[/tex]
[tex]=\displaystyle\frac12\int_0^2(t^2+2)\,\mathrm dt[/tex]
[tex]=\dfrac12\left(\dfrac{t^3}3+2t\right)\bigg|_{t=0}^{t=2}[/tex]
[tex]=\dfrac12\left(\dfrac83+4\right)[/tex]
[tex]=\dfrac{10}3[/tex]

The sum of the square of two consecutive whole number is 25. Find the numbers

Answers

Don't you mean "the sum of the squares ..."?
The sum of the squares of two consecutive whole numbers is 25.  Find the numbers.  Let the first be represented by x and the second by x+1.
Then x^2+(x+1)^2=25.  Expanding, x^2+x^2+2x+1=25.
Rewriting this as a quadratic equation in standard form,

2x^2+2x+1=25, or 2x^2+2x-24=0.  Simplifying, x^2+x-12=0.
Factoring, (x-3)(x+4)=0.  Solving for x:  x-3=0, so x=3; x+4=0, so x=-4.
Choose the positive x value:  x=3.  Then the next consecutive number is 2+1=3+1=4.

Check:  Does 3^2 + 4^2 = 5^2 = 25?  Yes.
The numbers are 3 and 4.

Find the volume of the solid whose base is the circle x^2+y^2=81 and the cross sections perpendicular to the x-axis are triangles whose height and base are equal.

Find the area of the vertical cross section A at the level x=6.

Answers

Sent a picture of the solution to the problem (s). Just rotate pic.

The volume of the cone will be 1526.8 cubic units. The area of the vertical cross-section A at level x = 6 will be 72 square units.

What is Geometry?

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The equation of the base circle is given below.

x² + y² = 81

x² + y² = 9²

Then the radius of the circle is 9 units. Then the height of the cone is the same as the diameter of the circle.

h = 2r

h = 2 x 9 = 18

The volume of the cone will be

V = (1/3)πr²h

V = (1/3) × π × 9² × 18

V = 1526.8 cubic units

The area of the vertical cross-section A at the level x = 6 will be

A = (1/2) x (18 - 6) x (18 - 6)

A = (1/2) x 12²

A = (1/2) x 144

A = 72 square units

More about the geometry link is given below.

https://brainly.com/question/7558603

#SPJ2

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