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3 years ago

The net of a prism is shown.

Mathematics

1 answer:

Novosadov [1.4K]3 years ago

8 0

Answer:

Step-by-step explanation:

surface area=4×5+2×1/2×3×4+5×5+3×6

=20+12+25+18

=75

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How do you calculate percentage? Is there an easier way?

san4es73 [151]

Divide the numerator of the fraction by the denominator. the first two digits of the decimal is the percentage

6 0

3 years ago

Find the amplitude of y = -4 sin x.

lyudmila [28]

Answer:
4
Explanation:
The amplitude of a sine function is the absolute value of the coefficient of sin(in other words, the absolute value of the number multiplying the sin)
In this case, that is |-4|=4

6 0

2 years ago

Because of their connection with secant lines, tangents, and instantaneous rates, limits of the form ModifyingBelow lim With h

Gre4nikov [31]

Answer:

$\dfrac{1}{2\sqrt{x}}$

Step-by-step explanation:

$f(x) = \sqrt{x} = x^{\frac{1}{2}}$

$f(x+h) = \sqrt{x+h} = (x+h)^{\frac{1}{2}}$

We use binomial expansion for $(x+h)^{\frac{1}{2}}$

This can be rewritten as

$[x(1+\dfrac{h}{x})]^{\frac{1}{2}}$

$x^{\frac{1}{2}}(1+\dfrac{h}{x})^{\frac{1}{2}}$

From the expansion

$(1+x)^n=1+nx+\dfrac{n(n-1)}{2!}+\ldots$

Setting $x=\dfrac{h}{x}$ and $n=\frac{1}{2}$ ,

$(1+\dfrac{h}{x})^{\frac{1}{2}}=1+(\dfrac{h}{x})(\dfrac{1}{2})+\dfrac{\frac{1}{2}(1-\frac{1}{2})}{2!}(\dfrac{h}{x})^2+\tldots$

$=1+\dfrac{h}{2x}-\dfrac{h^2}{8x^2}+\ldots$

Multiplying by $x^{\frac{1}{2}}$ ,

$x^{\frac{1}{2}}(1+\dfrac{h}{x})^{\frac{1}{2}}=x^{\frac{1}{2}}+\dfrac{h}{2x^{\frac{1}{2}}}-\dfrac{h^2}{8x^{\frac{3}{2}}}+\ldots$

$x^{\frac{1}{2}}(1+\dfrac{h}{x})^{\frac{1}{2}}-x^{\frac{1}{2}}=\dfrac{h}{2x^{\frac{1}{2}}}-\dfrac{h^2}{8x^{\frac{3}{2}}}+\ldots$

$\dfrac{x^{\frac{1}{2}}(1+\dfrac{h}{x})^{\frac{1}{2}}-x^{\frac{1}{2}}}{h}=\dfrac{1}{2x^{\frac{1}{2}}}-\dfrac{h}{8x^{\frac{3}{2}}}+\ldots$

The limit of this as $h\to 0$ is

$\lim_{h\to0} \dfrac{f(x+h)-f(x)}{h}=\dfrac{1}{2x^{\frac{1}{2}}}=\dfrac{1}{2\sqrt{x}}$ (since all the other terms involve $h$ and vanish to 0.)

8 0

3 years ago

Find the values of x and y

icang [17]

Answer:

$x=15\\y=38$

Step-by-step explanation:

By definition, the sum of the interior angles of a triangle is 180 degrees.

You can observe that the given triangle has an angle that measures 90 degrees and it also has two equal sides.This means that the other two angles are equal.

Knowing this, you can conclude that the triangle is an Isosceles Right Triangle and the other angles measure 45 degrees each.

Therefore, now you know that:

$3x=45$

Solving for "x", you get that its value is:

$x=\frac{45}{3}\\\\x=15$

And for the other angle:

$y+7=45$

Solving for "y", you get that its value is the following:

$y=45-7\\\\y=38$

8 0

3 years ago

Jo eats 2,200 calories per day. She eats 450 calories at breakfast and twice as many at lunch. If she eats three meals with no s

tiny-mole [99]

Jo's lunch contains the most calories because if its twice breakfast and breakfast is 450 multiply that X2 you get 950. Then add 950 plus 450 you get 1400 then subtract 1400 from 2200 then you get the remaining 800 calories which shows that the most calories she eats is in her lunch meal.

7 0

3 years ago

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