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3 years ago

Which are equivalent to 3^2 x 3^4? check all that apply.

Mathematics

1 answer:

Gemiola [76]3 years ago

4 0

Equivalent to what 729 is the answer

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What is 7.5 as a fraction ?

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75/10 is 7.5 as a fraction

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2 years ago

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The sum of a number and 6% of itself is 42.4. find the number

kvasek [131]

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Step-by-step explanation:

6% of number = 6/100 × x = 6x/100 = 3x/50

Sum of the number and 6% of itself = 42.4

x + (3x/50) = 42.4

(50x+3x)/50 = 42.4

53x = 42.4 × 50

53x = 2120

x = 2120/53

x = 40

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2 years ago

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3 years ago

Find the solution r(t)r(t) of the differential equation with the given initial condition: r′(t)=⟨sin4t,sin7t,9t⟩,r(0)=⟨9,8,3⟩

Makovka662 [10]

$\mathbf r'(t)=\langle\sin4t,\sin7t,9t\rangle$
$\implies\mathbf r(t)=\displaystyle\int\mathbf r'(t)\,\mathrm dt$
$\mathbf r(t)=\displaystyle\left\langle\int\sin4t\,\mathrm dt,\int\sin7t\,\mathrm dt,\int9t\,\mathrm dt\right\rangle$
$\mathbf r(t)=\left\langle-\dfrac14\cos4t+C_1,-\dfrac17\cos7t+C_2,-\dfrac92t^2+C_3\right\rangle$

With $\mathbf r(0)=\langle9,8,3\rangle$ , we have

$\langle9,8,3\rangle=\left\langle-\dfrac14+C_1,-\dfrac17+C_2,C_3\right\rangle$
$\implies C_1=\dfrac{37}4,C_2=\dfrac{57}7,C_3=8$
$\implies\mathbf r(t)=\left\langle-\dfrac14\cos4t+\dfrac{37}4,-\dfrac17\cos7t+\dfrac{57}7,-\dfrac92t^2+8\right\rangle$

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3 years ago