What are the values of x and y? Question options:
A) x = 18√3 y = 9√3
B) x = 9; y = 9√3
C) x = 9√2 ; y = 9
D) x = 9√3 ; y = 9

Answer: -7[tex]\leq[/tex]x[tex]\leq[/tex]6

The interval in which the function h(x) = 5x³ - 3x^5 is increasing is given as follows:

(−1,0)∪(0,1).

The function in this problem is defined as follows:

h(x) = 5x³ - 3x^5.

To obtain the intervals for increase of decrease, the critical points of the function need to be obtained, which are the values of x for which the derivative is of zero.

The derivative of the function in this problem is given as follows:

h'(x) = 15x² - 15x^4.

Hence the critical points of the function are given as follows:

15x² - 15x^4 = 0

15x²(1 - x²) = 0.

Hence:

Then the signals of the derivative in each interval is given as follows:

The function is increasing when the derivative is positive, hence the interval is given as follows:

(−1,0)∪(0,1).

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The length of the curve [tex]r(t) = 4t i + 8t^{3/2} j + 9t^{2}k, 0\leq t\leq 1[/tex] is 13.

The given curve is defined by the parametric equation [tex]r(t) = 4t i + 8t^{3/2} j + 9t^{2}k, 0\leq t\leq 1[/tex].

The length of a curve is given by the formula

⇒  [tex]|| r(t) || = \int\limits^a_b {\sqrt{{(x')^{2}} + (y')^{2} + (z')^{2} } } \, dt[/tex]

where the variables x', y', z' are defined as

[tex]x' = \frac{d(4t)}{dt} = 4 \\y' = \frac{d(8t^{3/2})}{dt} = 12t^{1/2} \\x' = \frac{d(9t^{2})}{dt} = 18t\\[/tex]

Hence, substituting the values in the formula for the length

⇒ [tex]|| r(t) || = \int\limits^0_1 {\sqrt{{(4)^{2}} + (12t^{1/2})^{2} + (18t)^{2} } } \, dt[/tex]

⇒ [tex]|| r(t) || = \int\limits^0_1 {\sqrt{{16 + 144t + 324t^{2}} } \, dt[/tex]

The given definite integral is in the form of

[tex]\int\limits^a_b {\sqrt{P(x)}} \, dx = \int\limits^a_b {\sqrt{{ax^{2} + bx + c}} } \, dx[/tex]

where P(x) is a polynomial of degree 2.

Writing the polynomial P(x) as

⇒ [tex]\sqrt{P(x)} = \sqrt{a}\sqrt{{(x + b_1)^{2} + c_1}} dx[/tex]

⇒ [tex]\int\limits^a_b {\sqrt{P(x)}} \, dx = \sqrt{a}\int\limits^a_b {\sqrt{{(x + b_1)^{2} + c_1}}} \, dx[/tex]

where [tex]b_1, c_1[/tex] are defined as

⇒ [tex]b_1= \frac{a}{2b} \\c1 = \frac{c}{a} - b_1^{2}[/tex]

Therefore, the solution will be

⇒ [tex]\int\limits^a_b {\sqrt{{(x + b_1)^{2} + c_1}}} \, dx = \frac{(b_1 + x)\sqrt{P(x)} + c_1log{(b_1 + x + \sqrt{P(x)}}}{2}[/tex]

Hence, solving the integral

⇒ [tex]|| r(t) || = \int\limits^0_1 {\sqrt{{16 + 144t + 324t^{2}} } \, dt[/tex]

we get the value as 13.

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Answer:

y = 2x-3

Step-by-step explanation:

Find slope from the two points (which is 2)

and then plug in one of the points (either (3,3) or (1,-1)) to find b in y=mx+b.

Combine everything, and there's your equation

Answer:

27cm

Step-by-step explanation:

[tex]s + s + s = p \\3x + x + x = 45 \\ 5x = 45 \\ \frac{5x}{5} = \frac{45}{5} \\ x = 9[/tex]

That's the length of one of its legs

The length of the base = 3x

= 3 x 9

= 45cm

Answer:

22.7551745473%

Step-by-step explanation:

I could be very wrong but to find the percentage of change you have to divide the increase by the original number, and then multiply it by 100.

20851820-16986510=3865310

3865310/16986510=0.22755174547

0.22755174547*100=22.755174547

This answer can then be rounded up to 23%

This problem can be solved using divide and conquer techniques. An method known as "divide and conquer" works by breaking down a large task into smaller ones.

An algorithmic pattern is known as Divide and Conquer. In algorithmic approaches, the idea is to take a dispute involving a large amount of input, divide the input into smaller pieces, solve the problem on each of the smaller pieces, and then combine the piecewise solutions into a comprehensive solution. The Divide and Conquer is the algorithmic  name of the approach that was used to solve the issue.

The three steps below are used in a dispute utilizing the Divide and Conquer method.

Create a group of subproblems from the main issue.

Conquer: Recursively and individually solve each subproblem.

Combine: Combine the solutions to the individual subproblems to arrive at the overall solution.

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There is no statistical support in the data for the claim that seeded clouds typically cover more than 300 acres per foot by average acrefeet.

Since the significance level is set at 0.10, the meteorologists can conclude that the data does not provide statistical evidence that the average acrefeet from seeded clouds is more than 300.

This is because the calculated p-value is greater than the significance level. This means that there is not sufficient evidence to reject the null hypothesis, which states that the average acrefeet from seeded clouds is no greater than 300.

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Answer:

25 kilometres West direction

The value of the double integral  ∫∫ (8x)/(1 + xy) dA ; R = [0, 8] x [0, 1] is  11.77

In this question we need to calculate the double integral. {8x}/{1 + xy} dA ; R = 0, 8 0, 1

i.e., to find ∫∫ (8x)/(1 + xy) dA ; R = [0, 8] x [0, 1]

First we integrate the function (8x)/(1 + xy)  as a function of y, treating the variable x as a constant.

G(x) = ∫_[0, 8] ((8x)/(1 + xy) ) dy

G(x) = 8 ln(8x + 1)

Now we calculate the integral of the previous result as a function of x.

i.e., ∫_[0, 1] G(x) dx

= ∫_[0, 1] [8 ln(8x + 1)] dx

= 9 ln(9) - 8

= 11.77

Therefore, the solution to the double integral (8x)/(1 + xy) dA ; R = [0, 8] x [0, 1] is 11.77

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Answer:

---------------------------

Given is an AP with:

Use the explicit rule to find the 26th term:

Correct choice is (2).

32 minutes and 2 seconds - 12 minutes and 15 seconds

 0 days 0 hours 32 minutes 2 seconds

- 0 days 0 hours 12 minutes 15 seconds

_________________________________

= 0 days 0 hours 19 minutes 47 seconds

[tex]=\fbox{19 minutes and 47 seconds or 19.783333 minutes}[/tex]

The simplified version of 8y = -2x + 4 is y = -1 / 4x + 1 / 2, so option A is correct.

Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

Given equation:

8y = -2x + 4

Divide both sides by 8,

8y / 8 = -2x / 8 + 4 / 8

Simplify the above expression,

y = -1 / 4x + 1 / 2

Therefore, the simplified version of 8y = -2x + 4 is y = -1 / 4x + 1 / 2.

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Answer: 2.1

Step-by-step explanation:

Calculator

Answer:

  replacement is 1/3 the volume of the original

Step-by-step explanation:

You want to compare the volumes of a cone with diameter 6 in and height 2 in to one with a diameter of 2 in and height of 6 in.

The volume of a cone is jointly proportional to the height and the square of the diameter:

  V ∝ d²h

The ratio of the volume of the replacement cone to the original is ...

  r = V2/V1 = ((2 in)²(6 in))/((6 in²)(2 in) = 2/6 = 1/3

The replacement cone has 1/3 the volume of the original.

The number must multiply each side of the equation to produce the equivalent equation is -5/3.

Algebraic equations with equivalent solutions or roots are called equivalent equations. An analogous equation is one that is created by adding or removing the identical quantity or expression from both sides of a given equation. An equation is equivalent if both sides are multiplied or divided by the same non-zero value.

The given equation is -3/5 x= 48

Multiply each side of the equation by -5/3, we get

[tex]\frac{-3x}{5} \times\frac{-5}{3} =48\times(\frac{-5}{3} )[/tex]

x=-80

Therefore, the number must multiply each side of the equation to produce the equivalent equation is -5/3.

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"Your question is incomplete, probably the complete question/missing part is:"

What number must multiply each side of the equation -3/5 x= 48 to produce the equivalent equation x= -80?

Step-by-step explanation:

the angle south-east of x is hard to read.

I assume this is 86 (but could be also 96).

remember, the sum of all angles in a triangle is always 180°.

and the intersection angles between 2 lines are the same in both sides of the lines. the only difference between above and below angles is that they are left-right mirrored.

so,

180 = x + 22 + 86

x = 180 - 22 - 86 = 72°

x and y are intersection angles of 2 lines and are therefore equal (due to the left-right mirroring).

y = x = 72°

180 = w + 33 + 72

w = 180 - 33 - 72 = 75°

remember also that the sum of all angles around a single point on one side of a line is always 180°, because the line can be seen as diameter of a circle with the point being the circle center. and the degrees of a half-circle are 180°.

180 = angle1 + unnamed angle = angle1 + 85

angle1 = 180 - 85 = 95°

180 = angle2 + angle3 + unnamed angle =

= 42 + angle3 + 85

angle3 = 180 - 42 - 85 = 53°

for the third question we don't see a picture of the situation. I assume this is a circle with O being the center of the circle, and Q, N, P are points on the circle arc.

it is not clear, if the angle QOP is part of the angle QON, or if they are separate segments of the circle.

if the angle QOP is part of the angle QON, then the angle PON = 142 - 46 = 96°

if the angle QOP is separate from the angle QON, then the angle PON = 360 - 142 - 46 = 172°

Answer:

9 * -8

____   =-72/6

2  * 3

The Probability that at least one trip will last less than one hour =7/8

It refers to the ratio of favorable outcome to the total possible outcome.

The possibility of happening an event is probability.

Probability of staying in the alternative time for more than an hour is 8

each trip is likely to last for more than one hour so probability of at least one trip will last more than an hour =1/8

Now, probability of at least one trip will last less than one hour = 1-1/8

                                                                                                    7/8

hence, the result is 7/8

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Answer:

b. 133 passengers

Step-by-step explanation:

The anount of weight taken by the passengers can be up to [tex]36600-7320=29280[/tex] lbs.

Dividing this by [tex]220[/tex] lb per passenger, we get there can be up to [tex]\lfloor 29280/220 \rfloor=133[/tex]

The maximum amount per month that Inez would spent on rent is $1170 knowing that he could spend no more than 30% of the take home pay.

Here Inez heard that a a general rule, he should pend no more than 30% of her take-home pay on rent. If Inez' take-home pay i $46. 800 per year.

The term Take-home pay is the net amount of income received after the deduction of taxes, benefits, and voluntary contributions from a paycheck. It is the difference resulting from the subtraction of all deductions from gross income.

Pay = $46,800

Total allowed = 46,800 x 0.30

Total allowed = $14,040

Now since we know that there are 12 months in a year, we need to divide the Total allowed by 12 to find how much Inez can pay in rent per month.

14,040 / 12 = $1,170

Following the rule that he could not spend more than certain of the take home pay he should rent $1170.

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The speed of the distance between the two planes is increasing at 325 mph as they approach JWD Airport.

The two planes form a right triangle, with the jet flying due east at 450 mph and the turboprop approaching from the south at 275 mph. The hypotenuse of the triangle is the distance between the planes, and the length of the hypotenuse is changing as the planes approach the airport. The rate of change of the length of the hypotenuse is equal to the sum of the rates of change of the two sides of the triangle, which are the speeds of the jet and the turboprop. As they are both 100 miles from the airport, the speed of the distance between the two planes is equal to the sum of the two speeds, or 450 mph + 275 mph = 325 mph. Therefore, the distance between the two planes is changing at a rate of 325 mph.

Rate of change of distance between the planes = Rate of change of jet + Rate of change of turboprop

= 450 mph + 275 mph

= 325 mph.

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The formula for the area A of a trapezoid [tex]A= \frac{1}{2} (b_{1} + b_{2})h[/tex], the formula for the height of the trapezoid is [tex]h= \frac{2A} {(b_{1} + b_{2})}[/tex] , and the height of the given trapezoid is 6cm.

(a) let us find the formula for the area A of a trapezoid as follows-

As b₁, b₂ being the lengths of the bases and 'h' is the height.

So, the formula for the area A of a trapezoid is given by-

[tex]A= \frac{1}{2} (b_{1} + b_{2})h[/tex]

(b) Let us solve for the formula for the height h of the trapezoid as follows-

As the formula for the area A of a trapezoid is [tex]A= \frac{1}{2} (b_{1} + b_{2})h[/tex]

So, the formula for height h of the trapezoid can be given by -

[tex]h= \frac{2A} {(b_{1} + b_{2})}[/tex]

(c) Let us find the new formula to find the height h of the trapezoid as follows-

Using, [tex]h= \frac{2A} {(b_{1} + b_{2})}[/tex] to find the height h of the trapezoid.

So,

[tex]h= \frac{2A} {(b_{1} + b_{2})}[/tex]  

[tex]h= \frac{2(72)} {16 +8}[/tex]   --------(substituting the values of b₁ = 16, b₂ = 8, A = 72cm²)

h = 144/24

h = 6 cm

Hence, the height of the trapezoid is 6cm.

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The complete question is -

a. Write the formula for the area A of a trapezoid. Use b1 and b2 for the length of the base, and use h for the height. A=

b. Solve the formula for h. H=

c. Use the new formula to find the height h of the trapezoid. The height of the trapezoid in centimeters.

Since the stages are simply whole values taken one after the other, they should be whole numbers or integers.

What in mathematics is a whole number?

Complete numbers those figures that contain zero and natural integers. not a decimal or fraction. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …} Integer. a negative number, zero, or a counting number. Whole numbers are made up of all the ordinal numbers and 0.

                       Natural numbers are the term used to describe counting numbers in mathematics. Therefore, the whole number can be described as a combination of all natural numbers and 0. Along with zero, all positive integers are also considered whole numbers.

He is currently on step 5, there are 15 steps total, therefore he is actually 10 steps away from the top of the ladder. If we walk down the ladder with N being negative, he is -5 steps from the ground.

{ N | N ∈ ℤ , -5 ⩽ N ⩽ 10 }

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The time taken to traveled the van and the tornado before they  meet as per the speed of the van and the tornado is equal to 2.6 minutes.

As given in the question,

Speed of the van along the straight road = 94 kilometers per hour

After travelling distance of 7 kilometers

Speed of the tornado along the same road = 69 km/hour

Total relative speed of van and tornado = 94 + 69

                                                                  = 163km/hour

Distance travelled between two different speed = 7km

Time used to traveled before they meet = distance / speed

                                                                   = 7 / 163

                                                                   = 0.043 hours

                                                                   = 2.58minutes

                                                                   = 2.6minutes

Therefore, the time required to traveled the van and the tornado before they   meet is equal to 2.6 minutes.

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Answer:                                                                                                                                                      

Step-by-step explanation:

In a series of transformations, dilation would make two figures similar as opposed to congruent.

Rotation, reflection and translation are known as rigid transformations.

This means they do not change the size or shape of a figure, they simply move it.

These rigid transformations preserve congruence.

Dilation, however, are not rigid transformation, since they change the size of  a shape.

Dilation would not change the shape, just the size: the angle measures would be the same, and the ratio of corresponding sides would be equal to the scale factor used in the dilation.

This would give us a similar, but not congruent.

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