Consider the function f(x)= 1−3x^2, −5≤x≤2. a. The absolute maximum value is _____ and occurs at x= _____.
b. The absolute maximum value is _____ and occurs at x= _____.

The interval containing the values of k for which the curves to not cross nor touch is given as follows:

0 < k < 3.

The two functions in the context of this problem are defined as follows:

The functions will not cross neither touch if the following quadratic equation has no solutions, that is:

x² + 2x + 1 = 2kx - k.

x² + (2 - 2k)x + 1 + k = 0.

The coefficients of the quadratic equation are given as follows:

a = 1, b = 2 - 2k, c = 1 + k.

The discriminant is calculated as follows:

Δ = b² - 4ac

Δ = (2 - 2k)² - 4(1)(1 + k)

Δ = 4k² - 8k + 4 - 4 - 4k

Δ = 4k² - 12k

The roots of the discriminant are as follows:

4k² - 12k = 0

4k(k - 3) = 0

k = 0, k = 3.

The equation has no solution if the discriminant is negative. A concave up quadratic equation is negative between it's roots, hence the interval is:

0 < k < 3.

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The equation x² + 4x + 9 = 0 are complex numbers: x = -2 + i√5 and x = -2 - i√5.

To find the solutions for the equation x² + 4x + 9 = 0, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Comparing this equation with the given equation x² + 4x + 9 = 0, we can see that a = 1, b = 4, and c = 9.

Plugging in these values into the quadratic formula, we have:

x = (-4 ± √(4² - 4(1)(9))) / (2(1))

x = (-4 ± √(16 - 36)) / 2

x = (-4 ± √(-20)) / 2

Since the value inside the square root is negative, we know that the solutions will involve complex numbers. Simplifying further, we have:

x = (-4 ± i√20) / 2

x = (-4 ± 2i√5) / 2

Simplifying the expression by dividing both the numerator and denominator by 2, we get:

x = -2 ± i√5

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The population mean and  population standard deviation for the given sample data from a normal population is  10 and 3.46 respectively.

Sample data is equal to,

10, 8, 12, 15, 13, 11, 6, 5

The point estimate of the population mean can be calculated by finding the sample mean,

sample mean 'x' = (10 + 8 + 12 + 15 + 13 + 11 + 6 + 5) / 8

                           = 10

The point estimate of the population mean is 10.

The point estimate of the population standard deviation can be calculated by finding the sample standard deviation,

Sample variance

= [ Σ ( xi - x )^2 / ( n - 1 ) ]

= [(10 - 10)^2 + (8 - 10)^2 + (12 - 10)^2 + (15 - 10)^2 + (13 - 10)^2 + (11 - 10)^2 + (6 - 10)^2 + (5 - 10)^2] / (8 - 1)

= 0 + 4 + 4 + 25 + 9+ 1 + 16 + 25 / 7

= 84/7

=12

⇒Sample standard deviation = √(sample variance)

⇒Sample standard deviation= √(12)

⇒Sample standard deviation≈ 3.46

The point estimate of the population standard deviation is approximately 3.46.

Therefore, the population mean and the population standard deviation is equals to 10 and 3.46 respectively.

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Answer:

24/48 is the wer

Step-by-step explanation:

Answer:

the answer is

Step-by-step explanation:

\( \frac{6 }{ 12} = \frac{24}{n} \)

6*n=24*12

\(n = \frac{24 \times 12}{6} \)

n=48

Answer: a very straight forward b 2 4 and 6 c 9

Step-by-step explanation:

Answer:

b= sin(43°) * 8 / sin(55°) ≈ 6.7

Step-by-step explanation:

Regarding the law of sines, each angle corresponds to the side opposite of it. Here, that means that the 82 degree angle is opposite of side c (so they correspond) and that the 55 degree angle corresponds to the side with 8cm. However, we are trying to find the length of side b. Therefore, assuming that the side with 8cm is side A, if we know that

sin A / a = sinB/b = sin C / C

= sin(55°)/8 = sinB/b = sin(82°) / c, we can take c out of the equation to get

sin(55°)/8 = sinB/b

If we know sinB, we can multiply both sides by 8 to remove a denominator to get

sin(55°) * b / 8 = sinB

multiply both sides by 8 to remove the other denominator to get

sin(55°) * b = sinB * 8

divide both sides by sin(55°) to isolate the b

b = sinB * 8/sin(55°).

Therefore, if we know sinB, we can figure out the length of b.

Because the angles of a triangle add up to 180 degrees, we can say that

180 = 82 + 55 + angle B

180 = 137 + B

subtract both sides by 137 to isolate B

43 = B

b= sin(43°) * 8 / sin(55°) ≈ 6.7

The dimensions of the rectangle has a width = 12cm and length = 5cm.

In calculating the area of a rectangle, we multiply its length and width.

Let us use the letter x to represent the width, so that the length = x - 7

hence we calculate for the unknown x as follows;

x(x - 7) = 60

expand and equate to zero to derive a quadratic equation

x² + 7x - 60 = 0

by factorisation;

x² - 12x + 5x - 60 = 0

x(x - 12) +5(x -12) = 0

(x + 5)(x - 12) = 0

thus for x + 5 = 0

x = -5

and for x - 12 = 0

x = 12

Therefore, x = 12 is true for the quadratic equation and also for the width = 12 and length = 5cm for the rectangle.

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Amelia was at camp for 6 days. The equation used to determine how many days(D) she was at camp is C x D = 6D and S - (C x D) = E

Given data:

S = initial amount = $54

D = the number of days

C = the cost per day = $6

E: the ending amount = $18

Amelia started with S=$54 and spent C=$6 each day at camp.

Therefore, the total amount she spent at camp is given in an algebraic expression that states the product of two variables:

C x D = 6D

Next, she ended with E=$18. So, the equation can be written in algebraic expression that states the difference between the variable:

S - (C x D) = E

Substituting the values in the equation we get:

54 - 6D = 18

54 - 18 = 6D

36 = 6D

D = 6

Therefore, Amelia was at camp for 6 days.

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The integral of (42³ - 2r + 7) dz is equal to (42³ - 2r + 7)z + C.

To integrate the function (42³ - 2r + 7) dz, we treat r as a constant and integrate with respect to z. The integral of a constant with respect to z is simply the constant multiplied by z:

∫ (42³ - 2r + 7) dz = (42³ - 2r + 7)z + C

where C is the constant of integration.

Note: The integral of a constant term (such as 7) with respect to any variable is simply the constant multiplied by the variable. In this case, the variable is z.

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Answer:

x=87/8

Step-by-step explanation:

2/3x=8-3/4

2/3x=32/4-3/4

2/3x=29/4

x=29/4*3/2

x=87/8

Answer:

2.4°F a minute.

Step-by-step explanation:

54 / 22.5 = 2.4°F a minute.

Answer:

$358.2

Step-by-step explanation:

• We have to first find the hourly wage for the week in which he worked 24 hours:

hourly wage = \(\frac{\$ 477.60}{24 \space\ h}\)

                     = $19.9 /h

• Now we can use this hourly wage to calculate how much he would make next week if he worked 18 hours:

he would make = 18 h × $19.9 /h

                          = $358.2

Answer:

The prime factorization of 32 in exponential form is

\(2^5\)

Step-by-step explanation:

The prime factorization of 32 is,

32/2 = 16,

16/2 = 8,

8/2 = 4,

4/2 = 2,

2/2 = 1,

So, we get, 2*2*2*2*2

In exponential form, we get, 2*2*2*2*2 = 2^5

\(2^5\)

The probability of the car encountering it's first red light on the third day, i.e., P(Y = 3) will be 0.1479

According to the question,

we have to calculate the probability of the car encountering it's first red light on the third day, i.e., P(Y = 3)

Here,

Probability of encountering a Red light = 0.35, since traffic light at the intersection is red 35% of the time.

And Y is the number of days that pass up to and including the first time the car encounters a red light, i.e.,

The distribution here is a geometric one, where

P(Y = 3)

= P(Not red light in initial 2 lights) x P(red light in third light)

= [(1 - 0.35)² X 0.35]

= 0.1479

so, the probability of the car encountering it's first red light on the third day, i.e., P(Y = 3) will be 0.1479.

Note:

mean and variance of this question is not possible to find out.

the complete question ends till the probability to find the first red light on the third day.

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Answer:

-2c^13

hopefully i helped :)

Answer: x+y+1=0

Step-by-step explanation:

m=y2-y1/x2-x1

 = 4-(-2) /-5-1

 =6/-6

 =-1

equation of line

y-y1=m(x-x1)

y-(-2) =-1(x-1)

y+2=-x+1

x-1+y+2=0

x+y+11=0

Answer:

n

Step-by-step explanation:

Any regular polygon has a sum of 180(n-2), where n is the number of sides. You can place n as the number of sides to figure out the total amount of degrees.

Answer:

the answer is 5.1 killograms

Step-by-step explanation:

hope this helps

Answer:

See below

Step-by-step explanation:

b) 200 ft = -16 (t-2)^2  + 400

      200 / 16 = (t-2)^2

           sqrt (12.5 ) = t-2

              2 + sqrt (12.5)  = t  

Answer:

I'm a little confused by this question:

Lines and things that are linear are relatively boring in mathematics. What if my function f(x) = g'(x). I’m going to ask the same question in a different way.

What is an approximate value of g'(1.1)?

So I know L(x)=f(a)+f′(a)(x−a)

If I substitute items in, I get g′(x)+g′′(x)(x−x).

Since x−x=0 I always am going to end up with L(x)=g′(x)

I don't think this can be the right answer since I know the whole point is to use the 2nd derivative, but if you get 0 for (x−a), then the whole part ends up being 0. What am I missing here?

I'm completely lost here because these are the followup question after the one above:

Now things are interesting. Suppose g(1) = 0 and g'(1) = 1.

Use linear approximation to approximate the value of g(1.1). The answer to #2 and #3 gives us a slope of a tangent line and a value of a function, which we can use.

Use your previous answers to approximate the value of g(1.2). Somehow, this second derivative has caused an adjustment to our approximation.

What did using the second derivative do to the approximation?

Do you believe the approximation is better or worse than our original?

Step-by-step explanation:

Answer:

11.4 gallons

Step-by-step explanation:

Divide 28.5 by 5 then multiply by 2:

(28.5 ÷ 5) x 2 = 5.7 x 2 = 11.4

Answer:

1 monkey because it ate one of the cats

Step-by-step explanation:

Answer:

3 cats in 3corners

Step-by-step explanation:

the question is incorrect the correct question is  IN A SQUARE ROOM THERE ARE 4 CATS IN EVERY CORNER?

Hey there !!!!

If you read that there are 4 cats in the room and in front of each cat is another 3 cats, then it might lead you to the answer of 16. This is not correct.

You will have reached this answer if you assumed that there was 3 cats in front of every cat in the corner. That would mean 4 cats in every coner.

You can reach this answer by dissecting each statement in the riddle. The first statement, “In a square room there are 4 cats in every corner of the room,” then we know that the room is square with 4 corners and that there are 4 cats to begin with.

The second statement of the riddle reads “In front of each cat there are 3 cats.” As we already know from the first statement that there are 4 cats in the room, each cat will see the other 3 cats in the other 3 corners of the room.

hope it helped

Answer:

picking a prime number

Step-by-step explanation:

from 1 - 20 : 20

>6 : 15

<12 : 11

even number: 10

Prime: (2,3,5,7,11,13,17,19) 8

The ratio of a : b : c in the linear equation is 2 : -1 : -1

From the question, we have the following equation that can be used in our computation:

ax + by + c = 0

The points on the line are given as

(2 ,3) and (8 , 15)

A linear equation is represented as

y = mx + c

Where

Slope = m

y-intercept = c

This means that

3 = 2m + c

15 = 8m + c

Subtract the equations

So, we have the following representation

6m = 12

Divide by 6

m = 2

Substitute m = 2 in 3 = 2m + c

3 = 2 * 2 + c

So, we have

c = -1

Substitute m = 2 and c = -1 in y = mx + c

y = 2x - 1

So, we have

2x - y - 1 = 0

Recall that

ax + by + c = 0

This means that

a : b : c = 2 : -1 : -1

Hence, the ratio is 2 : -1 : -1

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Answer:

37

Step-by-step explanation:

Good Luck! I double checked my answer!

Answer:

37

Step-by-step explanation:

Hey There!

They want us to find the hypotenuse using the Pythagorean Theorem

The Pythagorean Theorem says

\(a^2+b^2=c^2\)

or that the two legs ( shorter side) square, added together equal the hypotenuse square

Note: This only works with right triangles

so basically

\(hypotenuse^2=35^2+12^2\\35^2=1225\\1262=144\\144+1225=1369\\\sqrt{1369} =37\)

Therefore the missing side length equals 37

hope this helps!

Answer:

11:45

Step-by-step explanation:

Let \(n=0\). Then \(0^3 = 0\) but 0 > 0 is a false statement.

The statement that proves that angle XWY is equal to angle ZYW is

A. If two parallels are cut by a transverse, then alternate interior angles are congruent

Alternate interior angles are a pair of angles that are formed on opposite sides of a transversal line when two parallel lines are intersected by the transversal.

When a transversal intersects two parallel lines, it creates eight angles. Among these angles, the alternate interior angles are located on the inside of the parallel lines and on opposite sides of the transversal.

In a parallelogram, the two opposite sides are parallel to each other hence the line crossing them will lead to formation of alternate interior angles

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