Help! I need help with these two questions (10 points each!)

The first equation is separable:

dy/dx = x/y   ⇒   y dy = x dx

(provided that y ≠ 0)

Integrating both sides yields

1/2 y² = 1/2 x² + C

Given that y(0) = -8, we find

1/2 • (-8)² = 1/2 • 0² + C   ⇒   C = 32

so that the particular solution is

1/2 y² = 1/2 x² + 32

Solving for y explicitly, we have

y² = x² + 64

y = ± √(x² + 64)

but since y(0) is negative, we take the negative solution:

y = - √(x² + 64)

The second equation is also separable:

du/dt = (2t + sec²(t)) / (2u)   ⇒   2u du = (2t + sec²(t)) dt

Integrate both sides:

u² = t² + tan(t) + C

Given u(0) = -6, we have

(-6)² = 0² + tan(0) + C   ⇒   C = 36

and so

u² = t² + tan(t) + 36

u = ± √(t² + tan(t) + 36)

but again we take the negative root here to agree with the initial condition, so

u = - √(t² + tan(t) + 36)

Answer:

6.67%

Step-by-step explanation:

5 / 75 = 0.066667

(0.066667)(100) = 6.67%

Answer:

4x+14 = 2(2x+7}

12x+6=6{2x+1}

Answer:

22. 30

23. 20

25. Thirty to twenty, or 30:20

Step-by-step explanation:

22.6*5

23.4*5

[tex]\text{Area of circle} = \pi r^2\\\\\implies 2 = \pi r^2\\\\\implies r^2 = \dfrac 2{\pi}\\\\\\\implies r = \sqrt{ \dfrac 2{\pi}} = 0.798~ \text{m.}[/tex]

Answer:

r≈.8m

Step-by-step explanation:

Formula used

A=πr2

r=√a/π =√2/π ≈.79788

rounded it is .8m

Answer:

You know that 1 mile = 5280 feet and 1 foot = 12 inches, so using these conversion factors you can go from one to the other.

I hope this answered you question!

Step-by-step explanation:

Answer:

126 inches = 10.5 feet = 3.5 yards

Step-by-step explanation:

42 in = 3.5 ft = 1.1667 yds

2.5 ft = 30 in = 0.8333 yds

1.5 yds = 54 in = 4.5 ft

42+30+54= 126 in

3.5+2.5+4.5= 10.5 ft

1.5+0.8333+1.1667= 3.5 yds

10.5/3= 3.5 yds

Answer: 4509

8,140-3,631

= 4509

Problem 1

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

Explanation:

a1 = 1.7 = amount of concrete for the first step

a4 = x = amount of concrete for the fourth step

Sn = sum of the first n terms of an arithmetic sequence

Sn = (n/2)*(a1 + an)

S4 = (4/2)*(a1 + a4)

S4 = 2(1.7+x)

S4 = 2x+3.4

S4 = 17

2x+3.4 = 17

2x = 17-3.4

2x = 13.6

x = (13.6)/2

x = 6.8

We need 6.8 cubic feet of concrete for the fourth step. We'll use this value to help us find the common difference d

an = nth term of an arithmetic sequence

an = a1 + d(n-1)

a4 = a1 + d(4-1)

a4 = a1 + 3d

6.8 = 1.7 + 3d

6.8-1.7 = 3d

5.1 = 3d

(5.1)/3 = d

1.7 = d

d = 1.7

Coincidentally, the common difference is the same as the first term. This won't always happen.

Now we can compute the 12th term

an = a1 + d(n-1)

a12 = 1.7 + 1.7(12-1)

a12 = 20.4

which is then used to find the sum of the first 12 terms

Sn = (n/2)*(a1 + an)

S12 = (12/2)*(a1 + a12)

S12 = 6(1.7 + 20.4)

S12 = 132.6

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Problem 2

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

Explanation:

The center is (h,k) = (0,10) which is where the nozzle is located.

The distance from (0,10) to (0,25) is 15 units, so r = 15.

Also, the distance from (0,10) to (0,-5) is also 15 units.

Plug those values into the equation below.

[tex](x-h)^2 + (y-k)^2 = r^2\\\\(x-0)^2 + (y-10)^2 = 15^2\\\\x^2 + (y-10)^2 = 225\\\\[/tex]

That equation represents the boundary of the circle, which is where the water can reach.

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Problem 3

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

Explanation:

Or note that,

a3 = 0.81*(a2) = 0.81*(0.81a1) = a1*(0.81)^2 = 6.7*(0.81)^2 =  4.39587

which must mean,

This is based off the idea that [tex]a_n = a(r)^{n-1}[/tex]

So,

a6 = a1*(0.81)^5

a6 = 6.7*(0.81)^5

a6 = 2.33614554867

a6 = 2.336

I’m not sure but I need points so please mark this as answer :)

Answer:

Percent change = 600 - 30 |30| × 100% = 570 30 × 100 = 1900% (increase). Where: 30 is the old value and 600 is the new value.

Step-by-step explanation:

The cost function of the rectangular yard is 114x + 57y = 1500

Let x represent the length of the rectangular yard and y represent the width of the rectangular yard.

Since you need to fence only 3 sides, hence:

2x + y = Perimeter

Each foot cost $57 per foot and there is $1500 to spend, hence:

2x(57) + y(57) = 1500

114x + 57y = 1500

y = (1500 - 114x) / 57

The area (A) of the rectangular yard is:

A = x * y

A = xy

A = x[(1500 - 114x) / 57)

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Answer:

Missing side = x+2

Step-by-step explanation:

The perimeter of the classroom, 6x+3, is equal to the 4 side lengths added up.

In their first line of work, the first plus sign should be an equal sign as follows:

6x+3 = 3x+1+x+x+?

simplify

6x+3 = 5x+1+?

subtract (5x+1) from both sides

x+2 = ?

There's the length of the missing side.

Answer:

impossible

Step-by-step explanation:

a cube with faces labeled 1-6 does not have an odd number greater than 5

Answer:

C or the third option.

Step-by-step explanation:

The equation is y = 4x - 4

Hope this helps! Pls give brainliest!

Answer:

100%

Step-by-step explanation:

Numbers on a die are 1,2,3,4,5,6 which are all greater than zero, so the probability is 6/6 or 100%.

Answer:

41

Step-by-step explanation:

In a direct proportion function, the constant of proportionality is the same as the slope of the graph.

Use points (0, 0) and (1, 41).

slope = (41 - 0)/(1 - 0) = 41/1 = 41

constant of proportionality = 41

The expression of sinU as a fraction is 12/13

Find the diagram attached.

To get the fraction represented by sinU, we will use the SOH CA TOA identity.

From the diagram;

Since sin theta = opp/hyp

SinU = ST/SU

SinU = 12/13

Hence the expression of sinU as a fraction is 12/13

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Explanation:

(I). 5/6 (4X+8) = (3/8) X - (1/4)

→ [{5(4X) + 5(8)}/6] = (3/8)X - (1/4)

→ [{20X + 40}/6] = (3/8)X - (1/4)

→ [{(20X/6) + (40/6) = (3/7)X - (1/4)

Now,

shift all variables fraction on LHS and constant fraction on RHS.

→ [(20X/6) - (3X/7)]= -(1/4) - (40/6)

Take the LCM of LHS denominator of 6&7 is 42.

→ [(140X - 18X)/42] = -(1/4)-(40/6)

→ [(122X)/42] = -(1/4)-(40/6)

Again take the LCM of the denominator in RHS i.e 4&6 is 12.

→ [(122X)/42] = (-12 - 80)/4

→ [(122X)/42] = (-92)/4

By doing Cross multiply the fraction, we get

→ 4(122X) = 42(-92)

→ 488X = -3 864

→ X = -3 864÷488

Therefore, X = -3864/488

Answer: Hence, the value of X for the given problem is -3864:488.

Explanation:

ii)Given algebraic equation is: 5(3p-5)+4p=5p-6(p+4)

→ 15p - 25 + 4p = 5p - 6p + 24

Shift all variables in LHS and constant on RHS.

→ 15p + 4p +6p = 25+24

→ 19p + 6p = 49

→ 25p = 49

Shift the number 25 from LHS to RHS.

Therefore, p = 49/25.

Answer: Hence, the value of P for the given algebraic equation is 49/25.

Answer: 12

Step-by-step explanation: there are 60 minutes in an hour. 60/5=12

Answer:

Freeze thaw cycle

Step-by-step explanation:

The force which produce avalanches and landslides is gravity.

The process by which the Earth's surface is worn down is called erosion. Erosion and weathering are two distinct but related processes. The decomposition of materials through chemical or physical processes is known as weathering. When weathered materials like soil and rock fragments are carried away by wind, water, or ice, erosion occurs.

The Earth's three substances—air, water, and ice—continue to flow in large quantities from one location to another, making erosion an essential component of human life. The energy in their flow is extremely high. All of the small and large substances in their path break and move in the flow's direction.

The most dramatic, unexpected, and hazardous examples of earth elements being pushed by gravity are landslides and avalanches. Avalanches are abrupt snowfalls, whereas landslides are sudden rockfalls.

Massive chunks of rock move swiftly and violently when they abruptly break free from a cliff or hillside. The falling rocks are kept from slowing down by air that is trapped beneath them. Avalanches and landslides can travel at speeds of 200 to 300 km/h.

Prevention's,

Be mindful of your surroundings and keep an eye out for changes in the environment.

When it rains heavily, keep an eye out for deck or patio tilting, cracks or bulges in slopes, and drooping posts or fences. As soil steadily presses against a house and shifts windows and doors out of place, sticking windows and doors can be an indication of earth movement.

Because landslides are more likely to occur where they have already happened, look for landslide scars.

Hence,  Earth materials are transported by gravity from higher elevations to lower heights. Examples of hazardous gravity-driven erosion include mudflows, avalanches, and landslides.

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Answer:

x =1 if understood it correctly

Step-by-step explanation:

Answer:

Given that they know the law I think 82.93% of drivers obey this law

Answer:

the answer is

Step-by-step explanation:

i took the test

Answer:

The rat population in a major metropolitan city is given by the formula n(t)=67e^0.035t where t is measured in years since 1994 and n(t)is measured in millions.

Answer:

27

Step-by-step explanation:

Answer:

27 feet

Step-by-step explanation:

One way to do this is: 15 * 0.8 = 12 and you can add the original 15 feet to get 27 feet in total. I converted the 80 percent to a decimal and added it back to the original number.

Another way to do this is: 15 * 1.8 and the result is also 27 feet.

Answer:

y-4=4(x-1)

Step-by-step explanation:

y=4x

The slope of the equation = m = 4

when x=1

y=4(1)

y=4

we get point from the equation which is (1,4)

point-slope formula = y-y₁=m(x-x₁)

*plot the the point we get and the slope in the formula above

= y-4=4(x-1)

An equation in point-slope form to find the perimeter y of a square with side length x is y-4=4(x-1).

Given that, the perimeter of a square is four times the length of one side.

The point slope form is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point.

The equation of the point slope form is: (y - y1) = m(x - x1)

where, (x, y) is a random point on the line and m is the slope of the line.

The equation is y=4x

If the side length of a square is 1 centimeter, then y=4

So, the coordinate point is (1, 4)

The slope of an equation y=4x is 4

Put (x1, y1)=(1, 4) and m=4 in slope intercept form

That is, slope intercept form is y-4=4(x-1)

Therefore, an equation in point-slope form to find the perimeter y of a square with side length x is y-4=4(x-1).

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