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3 years ago

Simplify x + 4 + 3x

2 answers:

4 0

4x + 4 because you combine the variables and x = 1 when it's by itself so 3x + x = 4x then you're left with 4 because there is no x beside it

Ostrovityanka [42]3 years ago

3 0

X+4+3x =
4x+4 (you sum the like terms )

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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

In direct variation, the variables change by a constant _______________.

jolli1 [7]

Direct variation is of the form y=kx (inverse variation is of the form y=k/x)

5 0

3 years ago

TIMED URGENT HELP PLS

balu736 [363]

Answer:

Step-by-step explanation:

8 0

3 years ago

One car traveled 220 miles and drove 10 mph hour slower than a second car which drove 260 miles. If the cars were traveling for

Colt1911 [192]

55 mph...if the 1st one drove 260 miles, that's 65mph for 4 hours...1st car has to be 55mph for 4 hours to get 220 miles.

3 0

3 years ago

Determine the number of terms n in each geometric series.<br> 13) a1 = 0.75, r = 4, Sn =1023.75

Gnom [1K]

Answer:

Number of terms: n=6

Step-by-step explanation:

We are given:

a₁ = 0.75

r = 4

Sₙ = 1023.75

We need to find number of terms i.e n

The formula used will be: $S_n=\frac{a(r^n-1)}{r-1}$

Putting values and fining n

$S_n=\frac{a(r^n-1)}{r-1}\\1023.75=\frac{0.75(4^n-1)}{4-1}\\ 1023.75=\frac{0.75(4^n-1)}{3}\\3\times 1023.75=0.75(4^n-1)\\3071.25=0.75(4^n-1)\\4^n-1=\frac{3071.25}{0.75}\\4^n-1=4095\\4^n=4095+1\\4^n=4096$

We know that $4^6= 4096$

$4^n=4^6$

Using Exponent rule: $a^n=a^b => n=b$

$n=6$

So, Number of terms: n=6

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3 years ago