Find the area under the curve y = 1.5 x − 2.5 from x = 5 to x = t and evaluate it for t = 10 , t = 100 . Then find the total area under this curve for x ≥ 5 .

Answer:

send the complete question . there are some missing signs .

The formula for the velocity, v is √2E/m

Kinetic energy is half the mass multiplied by the square of the speed of the object

It is written thus;

Kinetic energy = 1/ 2 × m × v²

To solve for 'v' mean that we should make 'v' the subject of formula

E = 1/ 2 mv²

E = \(\frac{mv^2}{2}\)

cross multiply

\(2E = mv^2\)

To make 'v' the subject, we have

\(v = \sqrt{\frac{2E}{m} }\)

Thus, the formula for the velocity, v is √2E/m

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Answer:

z = 47.2°

w = 42.8°

y = 42.8°

x = 47.2°

Step-by-step explanation:

found altitude ('h') first:  6/h = h/7;  h = \(\sqrt{42}\)

found base by using Pythagorean Theorem:

7² + (\(\sqrt{42}\))² = c²

c = \(\sqrt{91}\)

found angle z using Rule of Sines:

sin 90 / \(\sqrt{91}\) = sin z / 7

arcsin z = 7 / \(\sqrt{91}\) = 47.2°

found angle w by adding 90 and 47.2, then subtracting from 180 to get 42.8°

found angle y by subtracting m∡z from 90° to get 42.8°

found angle x by adding 90 and 42.8°, then subtracting from 180

If r is < 0, then lambda must be:  Less than 0, Less than 1, Greater than 1  and Greater than 0. The correct answers are: A), B), C), and D).

Recall that the exponential growth or decay model is given by the function:

\(y = y0 * e^(rt)\)

where y0 is the initial value of the function, r is the rate of change (growth or decay), t is the time, and e is the mathematical constant approximately equal to 2.71828.

If r < 0, then the function represents exponential decay, and we have:

\(y = y0 * e^(rt)\)

y/y0 = e^(rt)

Taking the natural logarithm of both sides, we get:

ln(y/y0) = rt

r = (1/t) * ln(y/y0)

Since ln(y/y0) is the natural logarithm of a ratio, it can take any real value. Therefore, r can take any negative value, and there is no restriction on the value of lambda (which is\(e^r\)).

So, the correct answers are: A), B), C), and D).

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Answer:

Option (A)

Step-by-step explanation:

Two bases of the the given cylinder are circular in shape in the given picture.

When we take a cross-section of the cylinder parallel to the bases or perpendicular to the height, we get a circle exactly same as the bases (As shown on the rectangular slide).

Cross-section will have the same radius as the bases of the cylinder.

Therefore, Option (A) will be the answer.

Answer:

2^10 ÷ d

Step-by-step explanation:

raise 2 to the 10th power = 2^10

quotient of the result and d

= 2^10 ÷ d

At most, they can wash 96 cars and mow 96 lawns.

To determine the maximum number of cars they can wash and lawns they can mow, we need to consider the work rates of each person and the total number of hours they work.

Huey can wash 6 cars or mow 3 lawns in one hour, so in 8 hours, he can wash 6 \(\times\) 8 = 48 cars or mow 3 \(\times\) 8 = 24 lawns.

Dewey can wash 3 cars or mow 3 lawns in one hour, so in 8 hours, he can wash 3 \(\times\) 8 = 24 cars or mow 3 \(\times\) 8 = 24 lawns.

Louie can wash 3 cars or mow 6 lawns in one hour, so in 8 hours, he can wash 3 \(\times\) 8 = 24 cars or mow 6 \(\times\) 8 = 48 lawns.

Since two of them wash cars and one mows lawns, the maximum number of cars they can wash is the sum of the maximum cars each person can wash, which is 48 + 24 + 24 = 96 cars.

The maximum number of lawns they can mow is the sum of the maximum lawns each person can mow, which is 24 + 24 + 48 = 96 lawns.

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Answer:

To determine the x-intercept, we set y equal to zero and solve for x. Similarly, to determine the y-intercept, we set x equal to zero and solve for y. ...

To find the x-intercept, set y = 0 \displaystyle y=0 y=0.

To find the y-intercept, set x = 0 \displaystyle x=0 x=0.

Step-by-step explanation:

Answer: c

Step-by-step explanation:

Because the total should be at the end plus how much pounds it is so c

Answer:

64 km/1 h

Step-by-step explanation:

the set of points at which the function G(x, y) = ln(1+x−y) is continuous is the set of all (x, y) such that y < x+1.

To determine the set of points at which the function G(x, y) = ln(1+x−y) is continuous, we need to check for continuity in both x and y directions.

First, we consider the x-direction. The function ln(1+x−y) is continuous for all x and y such that 1+x−y > 0, i.e., x−y > −1. Therefore, the set of points at which the function is continuous in the x-direction is the set of all (x, y) such that x−y > −1.

Next, we consider the y-direction. The function ln(1+x−y) is continuous for all x and y such that 1+x−y > 0, i.e., x > y−1. Therefore, the set of points at which the function is continuous in the y-direction is the set of all (x, y) such that x > y−1.

To determine the overall set of points at which the function is continuous, we need to find the intersection of the sets of points where the function is continuous in the x and y directions.

The set of all (x, y) such that x−y > −1 is equivalent to the set of all (x, y) such that y < x+1.

The set of all (x, y) such that x > y−1 is equivalent to the set of all (x, y) such that y < x+1.

Therefore, the set of points at which the function G(x, y) = ln(1+x−y) is continuous is the set of all (x, y) such that y < x+1.

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So, the maximum value of the function || Bx|| subject to the constraint is e. 9

The function we want to maximize is ||Bx||, where B is the given matrix and x is a vector with \(||x||^2 = 1\). We can rewrite this as:

\(||Bx||^2 = (Bx)^(T) (Bx) = x^{(T)} B^{(T)} B x\)

Since B is a 2x2 matrix, \(B^{(T)}B\) is also a 2x2 matrix:

\(B^{(T)} B = [4 0]\)

[0 9]

Thus, we can write:

\(||Bx||^2 = x^{(T)} B^{(T)} B x = [x1 x2] [4 0; 0 9] [x1; x2] = 4x1^2 + 9x2^2\)

So, we need to maximize the function\(4x1^2 + 9x2^2\) subject to the constraint \(x1^2 + x2^2 = 1.\)

We can use Lagrange multipliers to solve this problem. The Lagrangian function is:

\(L(x1, x2, \lambda) = 4x1^2 + 9x2^2 - \lambda(x1^2 + x2^2 - 1)\)

The partial derivatives are:

∂L/∂x1 = 8x1 - 2λx1 = 0

∂L/∂x2 = 18x2 - 2λx2 = 0

\(\partial L/\partial \lambda = -(x1^2 + x2^2 - 1) = 0\)

From the first two equations, we can see that x1 = 4λ and x2 = 9λ. Substituting these into the third equation, we get:

\(x1^2 + x2^2 = (4\lambda)^2 + (9\lambda)^2 = 1\)

Solving for λ, we get:

λ = ±1/√(97)

We can plug these values of λ into x1 and x2 to get two possible vectors:

x1 = 4λ = ±4/√(97)

x2 = 9λ = ±9/√(97)

We need to find the maximum value of ||Bx||, which is:

||Bx|| = ||[2 0; 0 -3] [x1; x2]|| = ||[2x1; -3x2]|| = 2|x1| + 3|x2|

Plugging in the values of x1 and x2, we get:

||Bx|| = 2|4/√(97)| + 3|9/√(97)| = 38/√(97)

Therefore, the answer is not one of the options given.

However, the closest option is e. 9, which is approximately equal to 38/4.12. So, the closest answer is e. 9.

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Answer: 1⅓ batch of cookies

Step-by-step explanation:

From the question, we are given the information that a cook has 4 cups of raisins to make oatmeal cookies and that the recipe requires 3 cup of raisins for each batch of cookies.

Therefore, the number of batches of cookies that the cook can make will be the number of cups of rasins that the cook has divided by the number of reasons needed for each cookie. This will then be:

= 4/3

= 1⅓ batch of cookies

To answer these questions, we need to determine the fuel consumption rate and use it to calculate the fuel left and total distance.

a) Find the fuel consumption rate:
The airplane used 40,000 - 13,000 = 27,000 gallons of fuel in 8 hours.
Fuel consumption rate = 27,000 gallons / 8 hours = 3,375 gallons/hour.

b) Calculate the fuel left after 2.5 more hours:
Fuel used in 2.5 hours = 3,375 gallons/hour × 2.5 hours = 8,437.5 gallons.
Fuel left when the plane lands = 13,000 gallons - 8,437.5 gallons = 4,562.5 gallons.

c) Find the total distance of the flight:
Total flight time = 8 hours + 2.5 hours = 10.5 hours.
Total distance = average speed × total flight time = 550 miles/hour × 10.5 hours = 5,775 miles.

So, (a) there will be 4,562.5 gallons of fuel left in the tank when the plane lands, and (b) the total distance of the flight is 5,775 miles.

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(C.) reflection and (D.) rotation produce congruent images.

What three transformations are congruent?

We can generate congruent shapes by combining the three types of transformations: rotations, reflections, and translations. Actually, using a combination of one or more of these three transformations, any pairs of congruent shapes can be matched to one another.

(A) Dilation, (B) horizontal stretch, and (E) translation do not produce congruent images because they change the size, shape, and/or orientation of the original object.

(C) Reflection produces congruent images because the resulting image is a mirror image of the original object, and therefore has the same size and shape.

(D) Rotation produces congruent images because the resulting image is the same shape and size as the original object, just rotated to a different orientation.

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Answer:

All angles in a triangle sum up to 180 degrees. The value of x is 45 degrees.

Step-by-step explanation:

Answer:

9 pieces

Step-by-step explanation:

first convert 40cm to m by dividing by 100cm

then divide 3.6m by 0.4 then the ans will come.

A) There are 9 strings each of length of 40 cm.
B) 0.20, 5/12, 75% is already in the ascending order.
C) The bearing of Klayton from Lakeshore is also 196°.

In mathematics, it deals with numbers of operations according to the statements.

A) A 3.6 m long string is to be cut into pieces, each of length 40 cm.
3.6 m = 3.6 * 100cm
3.6 m = 360 cm
Let the number of stings be x
x * 40 = 360
x = 360 / 40
x = 9
there are 9 strings each of length of 40 cm.

Arranging the following in ascending order of magnitude: 0.20, 5/12, 75%
0.20, 5/12, 75% is already in the ascending order.

The bearing of Lakeshore from Klayton is 196°. The bearing of Klayton from Lakeshore is also 196°.

Thus, the answers to the given problem are calculated above.

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Answer:

c) 21

Step-by-step explanation:

\( \sqrt{169} + \sqrt{64} \)

13+8

answer is 21

Answer:

w=8

Step-by-step explanation:

1(8)+12=2(8)+4

8+12=16+4

20=20

Answer:0.6

Step-by-step explanati

Answer:0.5, -1, -2.5, -4 onward

Step-by-step explanation: subtract 1.5 every time 1000 times.

Answer:

Step-by-step explanation:

Median mean middle number when listed from smallest to biggies

1    6    6    9    12    16    84                    

                  |                                             >Then 9 is the median

Answer:

The median is 1

Step-by-step explanation:

Median means middle value in a set of data.

"Listen carefully to your teacher."

When the line of slope of 3 passes through two points, the value of y is -8.

The slope or gradient of a line in mathematics is a number that describes both the direction and the steepness of the line. The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope is a numerical value that describes the steepness of a line and is typically calculated by dividing the vertical distance by the horizontal distance (rise over run) between two points.

Here,

m=3

m=(y2-y1)/(x2-x1)

3=(y+5)/(-3+(2))

-3=y+5

y=-8

The value of y is -8 when the line of slope of 3 is passing through 2 points as given.

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Alex's statement that it is more likely to roll an even number on the second number cube if he rolls an odd number on the first number cube is not correct.

The probability of rolling an even number on the second number cube is the same regardless of whether an odd or even number is rolled on the first number cube.

Each number cube has 6 faces, and 3 of those faces are even numbers (2, 4, and 6).

So the probability of rolling an even number on a single number cube is 3/6 or 1/2.

This probability does not change based on the result of the roll on the other number cube.

Hence, No, Alex is not correct.

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9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The sides marked on the triangle are adjacent to and opposite the given angle. The mnemonic SOH CAH TOA is intended to remind you which trig functions relate which sides. The one applicable here is TOA:

  Tan = Opposite/Adjacent

Using the values on the diagram, we have ...

  tan(65°) = 18/y

Multiplying by y/tan(65°) gives ...

  y = 18/tan(65°)

  y ≈ 8.3935 ≈ 8.4

Answer:

To calculate the surface area of a square pyramid, we need to find the area of the base and the area of each triangular face, then add them together.

First, let's find the area of the base:

Area of square base = (side length)^2 = (15m)^2 = 225m²

Next, let's find the area of each triangular face:

Area of triangular face = (1/2) x (base length) x (height)

The base length of each triangular face is equal to the side length of the square base, which is 15m. We need to find the height of the pyramid to calculate the area of each triangular face.

To do this, we can use the Pythagorean theorem. Since the pyramid is a right pyramid (meaning the apex is directly above the center of the square base), the height is the hypotenuse of a right triangle with legs equal to half the length of one side of the base. Thus, the height can be found as follows:

height = sqrt((side length/2)^2 + height^2)

We can simplify this to:

height^2 = side length^2 - (side length/2)^2

height^2 = 225 - 56.25

height^2 = 168.75

height = sqrt(168.75)

height ≈ 12.99m

Now we can calculate the area of each triangular face:

Area of triangular face = (1/2) x (base length) x (height)

Area of triangular face = (1/2) x 15m x 12.99m

Area of triangular face ≈ 97.43m²

Finally, we can add the area of the base and the area of the four triangular faces together to get the total surface area:

Total surface area = area of base + 4 x area of triangular face

Total surface area = 225m² + 4 x 97.43m²

Total surface area ≈ 620.72m²

Therefore, the answer is A. 620.72 m².

Step-by-step explanation:

Answer:

$7.03

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

y> -23+2 is everything about the line the -21. So yes,