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3 years ago

Remember to line up the partial products carefully. 1. 75 X5

Mathematics

2 answers:

svetoff [14.1K]3 years ago

6 0

Answer:

8.75

Step-by-step explanation:

i multiplied 5×5 and got 25 7×5+2 and got 37 then multiplied 5×1+3

1.75

Anon25 [30]3 years ago

3 0

Answer: 8.75

3 2

1.75

× 5

---------

8 .75

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If I average a speed of 60 miles per hour while driving, how many hours of driving time will it take me to reach Arizona?

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Answer:

Well where do you start

Step-by-step explanation:

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3 years ago

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The current population of Smyrna, Maine, is 380 and grows at a rate of 3% per year. Which equation could be used to determine ho

Lena [83]

The number of people after n years is calculated through the equation,
An = (Ao)(1 + r)^n
where An is the population after n years, Ao is the initial population and r is the rate. Substituting the known values,
420 = (380)(1 + 0.03)^n
The answer is letter A.

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3 years ago

If PQRS is a rectangle, find the length of QT

MAVERICK [17]

Step-by-step explanation:

Since, opposite sides of a rectangle are equal and each angle is of 90°.

$\therefore$ QP = RS = 14 cm

$In \:\triangle QPS, \: \angle QPS = 90\degree$

$\therefore \: QS= \sqrt{QP^2+ PS^2} \\ \therefore \: QS= \sqrt{(14)^2+ (20)^2 } \\ \therefore \: QS= \sqrt{196 + 400} \\ \therefore \: QS= \sqrt{596} \\ \therefore \: QS= 24.41 \: m$

$\because$ Diagonals of a rectangle bisects each other.

$\therefore\: QT = \frac{1}{2} QS\\\therefore\: QT = \frac{1}{2} \times 24.41\\\therefore\: QT =12.205\\\huge\orange {\boxed {\therefore\: QT =12.21\:m}}$

4 0

3 years ago

Help me with these please

olchik [2.2K]

Step-by-step explanation:

(1) y = x e^(x²)

Take derivative with respect to x:

dy/dx = x (e^(x²) 2x) + e^(x²)

dy/dx = 2x² e^(x²) + e^(x²)

dy/dx = (2x² + 1) e^(x²)

Take derivative with respect to x again:

d²y/dx² = (2x² + 1) (e^(x²) 2x) + (4x) e^(x²)

d²y/dx² = (4x³ + 2x) e^(x²) + 4x e^(x²)

d²y/dx² = (4x³ + 6x) e^(x²)

Substitute:

d²y/dx² − 2x dy/dx − 4y

= (4x³ + 6x) e^(x²) − 2x (2x² + 1) e^(x²) − 4x e^(x²)

= 4x³ + 6x − 2x (2x² + 1) − 4x

= 4x³ + 6x − 4x³ − 2x − 4x

= 0

(2) y = sin⁻¹(√x)

sin y = √x

sin²y = x

Take derivative with respect to x:

2 sin y cos y dy/dx = 1

sin(2y) dy/dx = 1

dy/dx = csc(2y)

Take derivative with respect to x again:

d²y/dx² = -csc(2y) cot(2y) 2 dy/dx

d²y/dx² = -2 csc²(2y) cot(2y)

Substitute:

2x (1 − x) d²y/dx² + (1 − 2x) dy/dx

= 2 sin²y (1 − sin²y) (-2 csc²(2y) cot(2y)) + (1 − 2 sin²y) csc(2y)

Use power reduction formula:

= (1 − cos(2y)) (1 − ½ (1 − cos(2y))) (-2 csc²(2y) cot(2y)) + (1 − (1 − cos(2y))) csc(2y)

= (1 − cos(2y)) (1 − ½ + ½ cos(2y)) (-2 csc²(2y) cot(2y)) + cos(2y) csc(2y)

= (1 − cos(2y)) (½ + ½ cos(2y)) (-2 csc²(2y) cot(2y)) + cot(2y)

= (cos(2y) − 1) (1 + cos(2y)) csc²(2y) cot(2y) + cot(2y)

= (cos²(2y) − 1) csc²(2y) cot(2y) + cot(2y)

= -sin²(2y) csc²(2y) cot(2y) + cot(2y)

= -cot(2y) + cot(2y)

= 0

8 0

3 years ago

Find an equation of the line passing through the pair of points. Write the equation in the form Ax +By = C.

Alexxandr [17]

9514 1404 393

Answer:

5x -y = -37

Step-by-step explanation:

One way to find the coefficients A and B is to use the differences of the x- and y-coordinates:

A = Δy = y2 -y1 = 2 -(-3) = 5

B = -Δx = -(x2 -x1) = -(-7 -(-8)) = -1

Then the constant C can be found using either point.

5x -y = 5(-7) -2 = -37

The equation of the line is ...

5x -y = -37

_____

<em>Additional comment</em>

This approach comes from the fact that the slope of a line is the same everywhere.

$\dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{\Delta y}{\Delta x}\\\\\Delta x(y-y_1)=\Delta y(x-x_1)\qquad\text{cross multiply}\\\\\Delta y(x-x_1)-\Delta x(y-y_1)=0\qquad\text{subtract y term}\\\\\Delta y(x) -\Delta x(y) = \Delta y(x_1)-\Delta x(y_1)\qquad\text{Ax+By=C form}$

The "standard form" requires that A be positive, so we chose point 1 and point 2 to make sure that was the case.

5 0

3 years ago