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3 years ago

Write this number in standard form. 5.46×105=

Mathematics

2 answers:

mixas84 [53]3 years ago

8 0

Answer:

573.3

Step-by-step explanation:

just multiply it out

Aleksandr [31]3 years ago

6 0

Answer:

5.733×10^2

Step-by-step explanation:

The question says you are to leave the answer in standard form not just only multiply which means you're to first multiply then you're supposed to bring a decimal point right after the first number and give the corresponding index which is 10^2 because you moved it twice to the left making it a positive index.

5.46×105

573.3

5.733×10^2

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A line crosses through the points (0,2) and (-10, -16) Which of the following is the slope of the line?

Elodia [21]

Answer:

9/5

Step-by-step explanation:

The slope between the two points can be found by ...

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

m = (-16-2)/(-10-0) = -18/-10

m = 9/5

The slope of the line is 9/5. Perhaps this is a match to choice A.

3 0

3 years ago

If the integral of the product of x squared and e raised to the negative 4 times x power, dx equals the product of negative 1 ov

Nataly_w [17]

Answer:

$A + B + E = 32$

Step-by-step explanation:

Given

$\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C$

Required

Find $A +B + E$

We have:

$\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C$

Using integration by parts

$\int {u} \, dv = uv - \int vdu$

Where

$u = x^2$ and $dv = e^{-4x}dx$

Solve for du (differentiate u)

$du = 2x\ dx$

Solve for v (integrate dv)

$v = -\frac{1}{4}e^{-4x}$

So, we have:

$\int {u} \, dv = uv - \int vdu$

$\int\limits {x^2\cdot e^{-4x}} \, dx = x^2 *-\frac{1}{4}e^{-4x} - \int -\frac{1}{4}e^{-4x} 2xdx$

$\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} - \int -\frac{1}{2}e^{-4x} xdx$

$\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} \int xe^{-4x} dx$

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

Solving

$\int xe^{-4x} dx$

Integration by parts

$u = x$ ---- $du = dx$

$dv = e^{-4x}dx$ ---------- $v = -\frac{1}{4}e^{-4x}$

So:

$\int xe^{-4x} dx = -\frac{x}{4}e^{-4x} - \int -\frac{1}{4}e^{-4x}\ dx$

$\int xe^{-4x} dx = -\frac{x}{4}e^{-4x} + \int e^{-4x}\ dx$

$\int xe^{-4x} dx = -\frac{x}{4}e^{-4x} -\frac{1}{4}e^{-4x}$

So, we have:

$\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} \int xe^{-4x} dx$

$\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} +\frac{1}{2} [ -\frac{x}{4}e^{-4x} -\frac{1}{4}e^{-4x}]$

Open bracket

$\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{x^2}{4}e^{-4x} -\frac{x}{8}e^{-4x} -\frac{1}{8}e^{-4x}$

Factor out $e^{-4x}$

$\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{x^2}{4} -\frac{x}{8} -\frac{1}{8}]e^{-4x}$

Rewrite as:

$\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{1}{4}x^2 -\frac{1}{8}x -\frac{1}{8}]e^{-4x}$

Recall that:

$\int\limits {x^2\cdot e^{-4x}} \, dx = -\frac{1}{64}e^{-4x}[Ax^2 + Bx + E]C$

$\int\limits {x^2\cdot e^{-4x}} \, dx = [-\frac{1}{64}Ax^2 -\frac{1}{64} Bx -\frac{1}{64} E]Ce^{-4x}$

By comparison:

$-\frac{1}{4}x^2 = -\frac{1}{64}Ax^2$

$-\frac{1}{8}x = -\frac{1}{64}Bx$

$-\frac{1}{8} = -\frac{1}{64}E$

Solve A, B and C

$-\frac{1}{4}x^2 = -\frac{1}{64}Ax^2$

Divide by $-x^2$

$\frac{1}{4} = \frac{1}{64}A$

Multiply by 64

$64 * \frac{1}{4} = A$

$A =16$

$-\frac{1}{8}x = -\frac{1}{64}Bx$

Divide by $-x$

$\frac{1}{8} = \frac{1}{64}B$

Multiply by 64

$64 * \frac{1}{8} = \frac{1}{64}B*64$

$B = 8$

$-\frac{1}{8} = -\frac{1}{64}E$

Multiply by -64

$-64 * -\frac{1}{8} = -\frac{1}{64}E * -64$

$E = 8$

So:

$A + B + E = 16 +8+8$

$A + B + E = 32$

4 0

3 years ago

hello loves!! I've been stuck on this question for like 2 hours lol! i need some help, ill give 100 points :)

lana66690 [7]

Answer:

61.12 units²

Step-by-step explanation:

(½ × pi × r²) + (½ × b × h)

½ [(3.14 × 4²) + (8 ×9)]

½(122.24)

61.12 units²

6 0

4 years ago

Read 2 more answers

Several different cheeses are for sale. The cheese comes in wedges

Tom [10]

Answer:

area = 39.25 cm²

Step-by-step explanation:

The top and bottom area of a cheese wedge is shaped like a sector of a circle so finding the area of the top surface of this wedge is same as applying the area of a sector.

Top surface area(sector) = ∅/360 × πr²

where

∅ = central angle

r = radius

Top surface area(sector) = ∅/360 × πr²

area = 45/360 × π × 10²

area = 1/8 × 100π

area = 100π/8

area = 100 × 3.14/8

area = 314 /8

area = 39.25 cm²

7 0

3 years ago

1. Determine P(green) and P(orange for the spinner. Write the probabilities as fractions, decimals and percents.

belka [17]

Answer:

A) P(Green) = 1/8, 0.125, 0r 12.5%

P(Orange) = 1/2, 0.5, or 50%

B) P(Not Yellow) = 3/4, 0.75, or 75%

Step-by-step explanation:

A) P(Green) = 1/8, 0.125, 0r 12.5%

P(Orange) = 1/2, 0.5, or 50%

B) P(Not Yellow) = 3/4, 0.75, or 75%

6 0

3 years ago