Ayudenme a resolver esos 2 problemas, son inecuaciones, ya tengo la respuesta, falta solucion

The rate (in km/h) at which the distance from the plane to the radar station is increasing a minute later is 0 km/h (rounded to the nearest whole number).

To solve this problem, we can use the concepts of trigonometry and related rates.

Let's denote the distance from the plane to the radar station as D(t), where t represents time. We want to find the rate at which D is changing with respect to time (dD/dt) one minute later.

Given:

The plane is flying with a constant speed of 360 km/h.

The plane passes over the radar station at an altitude of 1 km.

The plane is climbing at an angle of 30°.

We can visualize the situation as a right triangle, with the ground radar station at one vertex, the plane at another vertex, and the distance between them (D) as the hypotenuse. The altitude of the plane forms a vertical side, and the horizontal distance between the plane and the radar station forms the other side.

We can use the trigonometric relationship of sine to relate the altitude, angle, and hypotenuse:

sin(30°) = 1/D.

To find dD/dt, we can differentiate both sides of this equation with respect to time:

cos(30°) * d(30°)/dt = -1/D^2 * dD/dt.

Since the plane is flying with a constant speed, the rate of change of the angle (d(30°)/dt) is zero. Thus, the equation simplifies to:

cos(30°) * 0 = -1/D^2 * dD/dt.

We can substitute the known values:

cos(30°) = √3/2,

D = 1 km.

Therefore, we have:

√3/2 * 0 = -1/(1^2) * dD/dt.

Simplifying further:

0 = -1 * dD/dt.

This implies that the rate at which the distance from the plane to the radar station is changing is zero. In other words, the distance remains constant.

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Answer:

0.0119047619

Step-by-step explanation:

Answer:

21/4

Step-by-step explanation:

1/4 ÷ (17 + 4)

1/4 ÷ (21)

21 × 1/4 = 21/4

-TheUnknownScientist

The height of Ara now is 55 inches.

Ara and Shea were once the same height. Since then Shea has grown 20% while Aria has grown half as much inches as Shea. Sheila is now 60 inches tall.  Therefore, let's find the height of Ara now.

Hence,

Let Shea initial height = x

Shea has grown 20%. Hence,

0.2x + x = 60

1.2x = 60

x = 60 / 1.2

x = 50

Hence, Shea grew 60 - 50 = 10 inches

Aria has grown half as much inches as Sheila.

Hence,

Aria height = 50 +  1 / 2 (10)

Aria height = 50 + 5

Aria height = 55 inches

Therefore,

Aria's height now = 55 inches

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Answer:

4x+3(3x-4)=1

4x+9x-12=1

13x=13

x=1

The graph of the function y = 1/3x - 2 is added as an attachment

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

So, the equation is

y = 1/3x - 2

The above function is a linear function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking note of the above transformations rules

The graph of the function is added as an attachment

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Answer:

shorter piece = 6. longer piece = 12

Step-by-step explanation:

short piece = s

long piece = l

l+s= 18

l= 6+s , substitute

6+s+s = 18

6+2s= 18

2s= 18-6

2s= 12

s=12/2

s= 6= shorter piece

l= 6+s

l= 6+6= 12 = longer piece

Out of the 400 surveyed students, 327 were either seniors or commuters.

To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.

According to the information given:

There were 262 seniors.

There were 215 commuters.

150 of the seniors were also commuters.

To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.

Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters

= 262 + 215 - 150

= 327

Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.

It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.

This ensures an accurate count of the students who fall into either category.

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Answer:

The correct answer is - 900

Step-by-step explanation:

A palindrome is a positive integer that is same whether read from left to right or from right to left. For example, 123321 palindromes.

An n-digit palindrome is determined from the first  n/2  digits if n is even, and from the first n+1/2 digits if n is odd.

Therefore, if  n  is even, there are  9×10⁽n⁻²/²⁾  palindromes; and if n is odd, there are  9×10⁽n₋²/²⁾ palindromes.  where n is number of digits.

For  n=5 , there are  9×10²=900 palindromes

The function f(x) = x + 10√(9 - x) is increasing on the interval (-∞, 9) and decreasing on the interval (9, ∞).

To determine the intervals on which the function is increasing or decreasing, we need to find the derivative of the function and analyze its sign.

Let's find the derivative of the function f(x) = x + 10√(9 - x) with respect to x.

f'(x) = 1 + 10 * (1/2) * (9 - x)^(-1/2) * (-1)

= 1 - 5√(9 - x) / √(9 - x)

= 1 - 5 / √(9 - x).

To analyze the sign of the derivative, we need to find the critical points where the derivative is equal to zero or undefined.

Setting f'(x) = 0:

1 - 5 / √(9 - x) = 0

5 / √(9 - x) = 1

(√(9 - x))^2 = 5^2

9 - x = 25

x = 9 - 25

x = -16.

The critical point is x = -16.

We can see that the derivative f'(x) is defined for all x values except x = 9, where the function is not differentiable due to the square root term.

Now, let's analyze the sign of the derivative f'(x) in the intervals (-∞, -16), (-16, 9), and (9, ∞).

For x < -16:

Plugging in a test value, let's say x = -17, into the derivative:

f'(-17) = 1 - 5 / √(9 - (-17))

= 1 - 5 / √(9 + 17)

= 1 - 5 / √26

≈ 1 - 0.97

≈ 0.03.

Since f'(-17) is positive, the function is increasing in the interval (-∞, -16).

For -16 < x < 9:

Plugging in a test value, let's say x = 0, into the derivative:

f'(0) = 1 - 5 / √(9 - 0)

= 1 - 5 / √9

= 1 - 5 / 3

≈ 1 - 1.67

≈ -0.67.

Since f'(0) is negative, the function is decreasing in the interval (-16, 9).

For x > 9:

Plugging in a test value, let's say x = 10, into the derivative:

f'(10) = 1 - 5 / √(9 - 10)

= 1 - 5 / √(-1)

= 1 - 5i,

where i is the imaginary unit.

Since the derivative is not a real number for x > 9, we cannot determine the sign.

Combining the information, we conclude that the function f(x) = x + 10√(9 - x) is increasing on the interval (-∞, 9) and decreasing on the interval (9, ∞).

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Answer: x-100 < 115

Step-by-step explanation: X is less then 215

The required amount of the space available is 0.045 cubic meter.

We need to determine Space inside the steps.

The Volume is defined as the mass of object per unit density.

The required space = 0.3*0.4*0.5 - 0.15*0.5*0.2

                                 =  0.06 - 0.015

                                 =    0.045 cubic meter

Hence, the required amount of the space available will be 0.045 cubic meter.

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Remove parenthesis, rearrange, and combine like terms.

7+i-6+4i

1i+4i+7-6

5i+1

---

hope it helps

Answer:

h(0) = -2

x = 3

Step-by-step explanation:

Line is intersecting x and y axes at points (1, 0) & (0, -2)

Slope of line (m) = (-2 - 0)/(0 - 1) = -2/(-1) = 2

y - intercept (b) = -2

Equation of line in slope-intercept form is given as:

y = mx + b

plugging the values of m and b in the above equation, we find:

y = 2x + (-2)

y = 2x - 2

Replacing y by h(x), we find:

h(x) = 2x - 2 (This is the required function)

Plug x = 0 in the function, this gives:

h(0) = 2(0) - 2

h(0) = 0 - 2

h(0) = -2

Plug h(x) = 4

4 = 2x - 2

4 + 2 = 2x

6 = 2x

x = 6/2

x = 3

The equation that is quadratic in all the equations is 6(2x+4)²=(2x+4)+2

A quadratic equations defined as any equation that can be rearranged in standard form as ax²+bx+c=0 or -b±\(\frac{\sqrt{} b^{2}-4ac }{2a}\)

From the list of equations the one that carries the standard form for a quadratic equation is

6(2x+4)²=(2x+4+)+2

Expand the brackets to have

6[(2x+4)(2x+4)=(2x+4)+2

6[4x²+8x+8x+16]=(2x+4)+2

Collecting like terms and opening the brackets further;

6[4x²+16x+16]=2x+4+2

=24x²+96x+96=2x+6

Collecting like terms we have

24x²+96x-2x+96-6=0

⇒24x²94x+90=0

In conclusion, the equation carries 2 as its highest power therefore, it is a quadratic equation.

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Answer:

See explanations below

Step-by-step explanation:

What the step for answer

Given the nth terms of as sequence expressed as

Sins a ≥ 3, we can find the third term of the sequence

an  = 2an-1 + an-2 - 2an-3

If a1 = 6 and a2 = 0 and a0 = 3

a3 = 2a2 + a1 - 2a0

a3 = 2(0) + 6 - 2(3)

a3 = 0 + 6 - 6

a3  = 0

If n = 4

a4 = 2a3 + a2 - 2a1

a4 = 2(0) + 0 - 2(6)

a4 = 0 + 0 - 12

a4  = -12

1) The expression 2⁻ˣ⁺³ = 3 is matched with graph B.

2 The expression  3ˣ⁺¹=3 is matched with graph C.

3) The expression 4ˣ = 3 is matched with graph

4 ) The expression 1ˣ/4 = 3 is matched with graph

1) The graph of the expression 2⁻ˣ⁺³ = 3  represents an exponential function where the y-coordinate is 3 when the base 2 raised to the power of (-x+3).

2) The graph of the expression 3ˣ⁺¹=3represents an exponential function where the y-coordinate is 3 when the base 3 raised to the power of (x+1). This graph is a straight line with a slope of 1.

3)  The graph of the equation 4ˣ = 3 represents an exponential function where the base 4 raised to the power of x is equal to 3. This equation has a single solution, which can be determined using logarithms.

4) The graph of the expression 1ˣ/4 = 3 represents an exponential function where the base 1 raised to the power of (x/4) is equal to 3.

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Answer:

The answer is 7

Step-by-step explanation:

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

for our purposes we must rearrange this problem to find one of the sides, not the hypotenuse

\( {a}^{2} = {c}^{2} - {b}^{2} \)

plugging in our numbers we get

\( {25}^{2} - {24}^{2} = 49\)

\( \sqrt{49} = 7\)

Answer:

Vertex N corresponds to Vertex S

Side QR corresponds to Side LM

Answer:

A) \(x=-1\pm\sqrt{\frac{13}{6}}\)

Step-by-step explanation:

\(\displaystyle x=\frac{-12\pm\sqrt{12^2-4(6)(-7)}}{2(6)}\\\\x=\frac{-12\pm\sqrt{144+168}}{12}\\\\x=\frac{-12\pm\sqrt{312}}{12}\\\\x=\frac{-12\pm2\sqrt{78}}{12}\\\\x=-1\pm\frac{\sqrt{78}}{6}\\\\x=-1\pm\sqrt{\frac{78}{36}}\\\\x=-1\pm\sqrt{\frac{13}{6}}\)

Answer:

-9.57

Step-by-step explanation:

\(\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=15\pi \end{cases}\implies 15\pi =2\pi r\implies \cfrac{15\pi }{2\pi }=r\implies \cfrac{15}{2}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{15}{2} \end{cases}\implies A=\pi \left( \cfrac{15}{2} \right)^2\implies A=\cfrac{225\pi }{4}\implies A=56.25\pi\)

Answer:

B

Step-by-step explanation:

2^2 x 5^2 = 100

Answer:

It would be 7 miles away.

Step-by-step explanation:

I think.

Jack's home is 5 miles away from the school.

Important information:

According to the Pythagoras Theorem:

\(\text{Hypotenuse}^2=\text{Perpendicular}^2+\text{Base}^2\)

Jack goes 4 miles north and 3 miles east. It forms a right triangle with legs 4 miles and 3 miles, and we have to find the hypotenuse to get the distance between his school and home.

Using the Pythagoras Theorem, we get

\(\text{Hypotenuse}^2=(3)^2+(4)^2\)

\(\text{Hypotenuse}^2=9+16\)

\(\text{Hypotenuse}=\sqrt{25}\)

\(\text{Hypotenuse}=5\)

Therefore, Jack's home is 5 miles away from the school.

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Answer:

95% = Within two standard deviations from the mean

99.7% = Within three standard deviations from the mean

68% = Within one standard deviation from the mean

Step-by-step explanation:

I hope this helped! If it did, please click "Thanks" to help me out!

Answer:

y=-5x-1

Step-by-step explanation:

If parallel lines, then the slope is the same.

y=-5x+b

To solve for b, plug in (-1,4)

(4)=-5(-1)+b

4=5+b

-1=b **Subtract 5 from both sides**

y=-5x-1

iN linear equations, store 1 jeans is cheaper than store 2.

What are instances of linear equations?

one store the jeans are selling for 1/5 off the original price of $70

              $70 * 1/5  = 14

second store the same jeans are selling for 1/3 off the original price $81

                 $81 * 1/3  = 27

So, store 1 jeans is cheaper than store 2.

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Answer:

The answer is -81.

Step-by-step explanation:

Let me know if I got it wrong.

Answer:

-1.5,0,1

Step-by-step explanation:

Answer:

Christmas lights are price based shopping products

Step-by-step explanation:

From the question we understand that, Beth bought as many cheapest lights as possible. This means that she places value over quantity than quality.

The above is an illustration of price based shopping products where customers (in this case, Beth) see all products (in this case, Christmas lights) as similar products, irrespective of their different qualities (after all, they all light Christmas trees).

Because of this, the customer will opt for least expensive items, leaving the more expensive items.