solve it and show full calculus.
thank you!

The sprinter will complete the race in approximately 17.07 seconds.

To calculate the time for the race, we need to consider two parts: the acceleration phase and the constant velocity phase.

Acceleration Phase:

The acceleration of the sprinter is 1.64 m/s², and the distance covered during this phase is 25 m. We can use the equation of motion to calculate the time taken during acceleration:

v = u + at

Here:

v = final velocity (which is the velocity at the end of the acceleration phase)

u = initial velocity (which is 0 since the sprinter starts from rest)

a = acceleration

t = time

Rearranging the equation, we have:

t = (v - u) / a

Since the sprinter starts from rest, the initial velocity (u) is 0. Therefore:

t = v / a

Plugging in the values, we get:

t = 25 m / 1.64 m/s²

Constant Velocity Phase:

Once the sprinter reaches the end of the acceleration phase, the velocity remains constant. The remaining distance to be covered is 100 m - 25 m = 75 m. We can calculate the time taken during this phase using the formula:

t = d / v

Here:

d = distance

v = velocity

Plugging in the values, we get:

t = 75 m / (v)

Since the velocity remains constant, we can use the final velocity from the acceleration phase.

Now, let's calculate the time for each phase and sum them up to get the total race time:

Acceleration Phase:

t1 = 25 m / 1.64 m/s²

Constant Velocity Phase:

t2 = 75 m / v

Total race time:

Total time = t1 + t2

Let's calculate the values:

t1 = 25 m / 1.64 m/s² = 15.24 s (rounded to two decimal places)

Now, we need to calculate the final velocity (v) at the end of the acceleration phase. We can use the formula:

v = u + at

Here:

u = initial velocity (0 m/s)

a = acceleration (1.64 m/s²)

t = time (25 m)

Plugging in the values, we get:

v = 0 m/s + (1.64 m/s²)(25 m) = 41 m/s

Now, let's calculate the time for the constant velocity phase:

t2 = 75 m / 41 m/s ≈ 1.83 s (rounded to two decimal places)

Finally, let's calculate the total race time:

Total time = t1 + t2 = 15.24 s + 1.83 s ≈ 17.07 s (rounded to two decimal places)

Therefore, the sprinter will complete the race in approximately 17.07 seconds.

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Answer:

10.8333 miles per minute

Step-by-step explanation:

Answer:

what we have to find or to prove.

The function represented by the graph with the given transformations is |–x| + 2.

The function represented by the given transformations is |–x| + 2.

Let's analyze the transformations step by step:

Reflection across the x-axis:

Reflecting the parent absolute value function across the x-axis changes the sign of the function. The positive slopes become negative, and the negative slopes become positive. This transformation is denoted by a negative sign in front of the function.

Translation right 2 units:

Translating the function right 2 units shifts the entire graph horizontally to the right. This transformation is denoted by subtracting the value being translated from the input of the function.

Combining these transformations, the function |–x| + 2 results. The negative sign reflects the function across the x-axis, and the subtraction of 2 units translates it right. The absolute value is applied to the negated x, ensuring that the function always returns a positive value.

Thus, the function represented by the graph with the given transformations is |–x| + 2.

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Answer: -lx-2l

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

Distance is the same as difference.

9 - (-8) = 17

Answer:

17

Step-by-step explanation:

9 - (-8) = 17

Pls mark as branlist

Answer:D is wrong, Its C: 12.2 ft

Step-by-step explanation:

Answer:

= bruv

Step-by-step explanation:

you spelt power wrong too

Answer:

126.9° and 323.°1

Step-by-step explanation:

I'll use x instead of theta and you can replace it by theta

5 sin x + 3 = 0

5 sin x = - 3

Sin x = - 3/5

Key angle = sin¯¹ 3/5 = 36.8698

Sin negative, so we use the third and fourth quadrants

X = 90+36.8698, 360-36.8698

X = 126.8698, 323.1302

Theta = 126.9°, 323.°1

The weight of the male that has a body surface area of 2.3 would be = 108kg

The body surface area (BSA) is defined as the parameter that can be used to estimate the surface area of a person's body based on body weight and height.

The formula for BSA = √w×h/3600

The weight of the male = X

The height of the male = 176cm

The BSA = 2.3

From the formula, make w the subject of formula;

w = BSA²× 3600/h

w = 2.3²× 3600/176

w= 5.29×3600 /176

w = 19044/176

w = 108kg

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Answer:

\(\boxed{\boxed{\sf x=42\°}}\)

Step-by-step explanation:

Given the diagram, we can see that ∠PQR and ∠RQS are complementary angles.

*Two angles with measures that add up to 90° are known as Complementary angles.*

Therefore, m∠PQR+m∠RQS=90°

\(\sf \angle PQR+\angle RQS=90\°\)

\(\sf 48+x=90\°\)

Subtract 48 from both sides:

\(\sf 48+x-48=90-48\)

\(\sf x=42\°\)

_______________________________

Answer:

The measurement of x is 42⁰.

Step-by-step explanation:

SOLUTION :

Here, we can see that the given figure is complementary angle.

As we know that two angles are said to be complementary angles if they add up to 90 degrees.

Now, according to the question :

\(\longmapsto{\sf{Sum \: of \: two \: angles = {90}^{ \circ}}}\)

\(\longmapsto{\sf{Angle_1 + Angle_2 = {90}^{ \circ}}}\)

\(\longmapsto{\sf{{48}^{ \circ} + {x}^{\circ} = {90}^{ \circ}}}\)

\(\longmapsto{\sf{{x}^{\circ} = {90}^{ \circ} - {48}^{\circ} }}\)

\(\longmapsto{\sf{{x}^{\circ} = {42}^{\circ} }}\)

\(\star{\underline{\boxed{\sf{\pink{{x}^{\circ} = {42}^{\circ}}}}}}\)

Hence, the measurement of x is 42⁰.

\(\rule{300}{2.5}\)

According to the problem, Abby wrote a sentence about multiples of 5. Remember that a multiple is a number that can be divide by 5, in other words, we can express a multiple of 5 every number with form 5k.

Additionally, Abby noticed that multiples more than 5 and one less than five are also valid.

So, Abby's statement is conjecture. She has not shown that her statement is true for all values of n. The pattern she noticed for the first 20 values of n may not extend to all other values of n.

It's important to say that Abby made a conjecture, which means she didn't prove in a general case for all natural numbers.

Answer:

third option

Step-by-step explanation:

under a counterclockwise rotation of 90° about the origin

a point (x, y ) → (y, - x )

Then

A (- 1, - 2 ) → (- 2, - (- 1) ) → (- 2, 1 )

B (2, - 2 ) → (- 2, - 2 )

C (1, - 4 ) → (- 4, - 1 )

The new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)

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

The figure,

Where, we have

A = (-1, -2)

B = (2, -2)

C = (1, -4)

The rule of 90 degrees counterclockwise is

(x, y) = (-y, x)

Using the above as a guide, we have the following:

A = (2, -1)

B = (2, 2)

C = (4, 1)

Hence, the new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)

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Answer:

LETS

GO

BRANDON

Step-by-step explanation:

Answer:

10/6

Step-by-step explanation:

5:3

20:12 (get this by multplying 4)

10/6 (get this by multiplying 2)

Answer:

SAS

Step-by-step explanation:

Hope this helps :)

Using the combination formula, it is found that there are 193 selections that contain at least 3 Jacks.

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula, involving factorials.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In the context of this problem, we have that the possibilities with at least 3 Jacks are given as follows:

Hence the number of selections with at least four jacks is calculated as follows:

\(T = C_{4,3}C_{48,1} + C_{4,4}\)

T = 4 x 48 + 1

T = 193.

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Answer:

x =28

Step-by-step explanation:

Divide the numbers

Combine multiplied terms into a single fraction

Eliminate fraction denominators

Simplify

Divide both sides of the equation by the same term

The probability that a sample of size n = 62 is randomly selected with a mean between 189.7 and 213 is approximately 0.9702.

To find the probability that a single randomly selected value is between 189.7 and 213, we can use the standard normal distribution.

Step 1: Calculate the z-scores for the given values using the formula:

  z = (x - μ) / σ

  For 189.7:

  z1 = (189.7 - 189.7) / 96.7 = 0

  For 213:

  z2 = (213 - 189.7) / 96.7 ≈ 0.2417

Step 2: Utilize a standard typical conveyance table or number cruncher to find the probabilities comparing to the z-scores.

  P(189.7 < X < 213) = P(0 < Z < 0.2417) ≈ 0.0939

Therefore, the probability that a single randomly selected value is between 189.7 and 213 is approximately 0.0939.

To find the probability that a sample of size n = 62 is randomly selected with a mean between 189.7 and 213, we use the central limit theorem. Under specific circumstances, the testing dispersion of the example mean methodologies a typical conveyance

Step 1: Calculate the standard error of the mean (σ_m) using the formula:

  σ_m = σ / sqrt(n)

  σ_m = 96.7 / sqrt(62) ≈ 12.2878

Step 2: Convert the given qualities to z-scores utilizing the equation:

  z = (x - μ) / σ_m

  For 189.7:

  z1 = (189.7 - 189.7) / 12.2878 = 0

  For 213:

  z2 = (213 - 189.7) / 12.2878 ≈ 1.8967

Step 3: Utilize a standard typical conveyance table or mini-computer to find the probabilities relating to the z-scores.

  P(189.7 < M < 213) = P(0 < Z < 1.8967) ≈ 0.9702

Therefore, the probability that a sample of size n = 62 is randomly selected with a mean between 189.7 and 213 is approximately 0.9702.

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Answer:

Angle(b)= 79°

Step-by-step explanation:

Because M and N are parallel so the answer is 79°

Also see the angle is less than 90°

9514 1404 393

Answer:

  D and E are each 62 cm

Step-by-step explanation:

Apparently, you want the total width of the bookcases to match the width of the wall.

  132 +92 +108 +w +w = 456

  332 +2w = 456

  2w = 124 . . . . . . . subtract 332

  w = 62 . . . . . . . . . divide by 2

The width of bookcases D and E is 62 cm.

On solving the provided question, we can say that triangle BIG and triangle FUN are similar to each other and are congruent, so angle N is congruent to angle G.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here,

we have been provided with that

triangle BIG and triangle FUN are similar to each other and are congruent.

Angle N is congruent to angle G.

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Answer:

1/2

Step-by-step explanation:

the circle has 8 pieces so that's how you get the denominator

you count how many A's there are and that is your numerator

so now 4/8 and reduce to get a half

8

In this pattern, we have 4 12 then 20.

We can see that the difference 4 and 12 is 8.

Since the difference between 12 and 20 is also 8, the common difference of the sequence is 8.

The distance between the tops of the buildings is 28.5 meters.

To find the distance between the top of the buildings, we can use the concept of similar triangles.

Let's denote the height of the shorter building as "a" (12 m) and the height of the taller building as "b" (19 m). The distance between the buildings can be denoted as "c" (18 m), and the distance between the top of the buildings as "x" (which we need to find).

We can set up a proportion based on the similar triangles formed by the buildings:

a/c = b/x

Substituting the known values:

12/18 = 19/x

To find "x," we can cross-multiply and solve for "x":

12x = 18 * 19

12x = 342

x = 342/12

x = 28.5 m

Therefore, the distance between the tops of the buildings is 28.5 meters.

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Answer:

5, 6

Step-by-step explanation:

Answer:

Los números son:

6 y 5

Step-by-step explanation:

Planteamiento:

a * b = 30

a + b = 11

Desarrollo:

De la segunda ecuación del planteamiento:

a = 11-b    

Sustituyendo esta última ecuación en la primer ecuación del planteamiento:

(11-b)*b = 30

11*b + b*-b = 30

11b - b² - 30 = 0

-b² + 11b - 30 = 0

b = {-11±√((11²)-(4*-1*-30))} / (2*-1)

b = {-11±√(121-120)} /-2

b = {-11±√1} / -2

b = {-11±1} / -2

b₁ = {-11-1} / -2 = -12/-2 = 6

b₂ = {-11+1} / -2 = -10/-2 = 5

Comprobación:

6*5 = 30

6+5 = 11

Answer:

The jumping dolphin is approx. 6 meters under sea level

The flying seagull is approx. 8 meters under sea level

The mobula ray is approx. 2 meters under sea level

The clownfish is approx.t 4 meters under sea level

The octopus is approx.  8 meters under sea level

The jumping dolphin: The mobula ray is 9 meters lower than the jumping dolphin.

The flying seagull: The mobula ray is 11 meters lower than the flying seagull.

The octopus: The mobula ray is 11 meters higher than the octopus.

The jumping dolphin: The albatross is 1 meter lower than the jumping dolphin.

The flying seagull: The albatross is 3 meters lower than the flying seagull.

The octopus: The albatross is 13 meters higher than the octopus.

The jumping dolphin: The clownfish is 8 meters lower than the jumping dolphin.

The flying seagull: The clownfish is 10 meters lower than the flying seagull.

The octopus: The clownfish is 6 meters higher than the octopus.

If the new dolphin is above the dolphin in the picture, then its distance from the surface of the ocean is 6 - 3 = 3 meters.

If the new dolphin is below the dolphin in the picture, then its distance from the surface of the ocean is 6 + 3 = 9 meters.

✧☆*: .｡. Hope this helps, happy learning! (✧×✧) .｡.:*☆✧

Answer:

\( - 3(x + 4) {}^{2} - 4\)

Step-by-step explanation:

Vertex form is

\(a(x - h) {}^{2} + k = f(x)\)

We know that h and k are both -4. Let x be -2 and y be -16.

\(a( - 2 + 4) {}^{2} - 4 = - 16\)

\(a(2) {}^{2} - 4 = - 16\)

\(4a - 4 = - 16\)

\(4a = - 12\)

\(a = - 3\)

So the equation in vertex form is

\( - 3(x + 4) {}^{2} - 4\)

Answer:

rewrite 0,26 as a proper fraction (in the format of a over b) show all steps

Answer:

(a) 0
(b) 0
(c) 1
The function is not continous at x = 9

Step-by-step explanation:

To the left and right of the point x = 9, the graph would seem to continue at  f(x) = 0, however on the exact point x = 9 there is a hole in the graph allowing it to be equal to 1. Due to the hole in the graph, it is not continuous

Apologies if this is wrong its been a bit since I did calculus

Answer:

Step-by-step explanation:

When naming lines, you can use the label of the line, in this case, m, and can also name the points in either direction, since the line goes on forever in both directions (it's different with rays). The leaves only line B as an answer.

The vertex of XYZ would be Y, since the vertex is always the middle number.