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ValentinkaMS [17]
3 years ago
14

Jackson’s age was 2/5 of the age he will be 20 years from now 7 years ago. How old is Jackson now?

Mathematics
1 answer:
bonufazy [111]3 years ago
4 0
<h3>The present age of Jackson is 25 years old</h3>

<em><u>Solution:</u></em>

Let the present age of Jackson be "x"

Therefore

Jackson's age 7 years ago = x - 7

And, Jackson's age after 20 years = x + 20

From given question,

Jackson’s age was 2/5 of the age he will be 20 years from now 7 years ago

\frac{2}{5} \times (x + 20) = x - 7\\\\2(x + 20) = 5(x - 7)\\\\2x + 40 = 5x - 35\\\\5x - 2x = 40 +35\\\\3x = 75\\\\Divide\ both\ sides\ by\ 3\\\\x = 25

Thus present age of Jackson is 25 years old

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Prove :<br>sin²θ + cos²θ = 1<br><br><br>thankyou ~​
Gnom [1K]

Answer:

See below

Step-by-step explanation:

Here we need to prove that ,

\sf\longrightarrow sin^2\theta + cos^2\theta = 1

Imagine a right angled triangle with one of its acute angle as \theta .

  • The side opposite to this angle will be perpendicular .
  • Also we know that ,

\sf\longrightarrow sin\theta =\dfrac{p}{h} \\

\sf\longrightarrow cos\theta =\dfrac{b}{h}

And by Pythagoras theorem ,

\sf\longrightarrow h^2 = p^2+b^2 \dots (i)

Where the symbols have their usual meaning.

Now , taking LHS ,

\sf\longrightarrow sin^2\theta +cos^2\theta

  • Substituting the respective values,

\sf\longrightarrow \bigg(\dfrac{p}{h}\bigg)^2+\bigg(\dfrac{b}{h}\bigg)^2\\

\sf\longrightarrow \dfrac{p^2}{h^2}+\dfrac{b^2}{h^2}\\

\sf\longrightarrow \dfrac{p^2+b^2}{h^2}

  • From equation (i) ,

\sf\longrightarrow\cancel{ \dfrac{h^2}{h^2}}\\

\sf\longrightarrow \bf 1 = RHS

Since LHS = RHS ,

Hence Proved !

I hope this helps.

5 0
2 years ago
ASAP HELP ME plz wit this
Lina20 [59]

Answer:

Step-by-step explanation:What??

5 0
2 years ago
The mean age of a student book club is 14.2 years. A 27-year-old teacher is invited to join the club. How does the teacher’s age
MAXImum [283]
The new mean age will be greater than 14.2 years because the teacher is older than the previous mean.
3 0
3 years ago
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A. Evaluate ∫20 tan 2x sec^2 2x dx using the substitution u = tan 2x.
irakobra [83]

Answer:

The integral is equal to 5\sec^2(2x)+C for an arbitrary constant C.

Step-by-step explanation:

a) If u=\tan(2x) then du=2\sec^2(2x)dx so the integral becomes \int 20\tan(2x)\sec^2(2x)dx=\int 10\tan(2x) (2\sec^2(2x))dx=\int 10udu=\frac{u^2}{2}+C=10(\int udu)=10(\frac{u^2}{2}+C)=5\tan^2(2x)+C. (the constant of integration is actually 5C, but this doesn't affect the result when taking derivatives, so we still denote it by C)

b) In this case u=\sec(2x) hence du=2\tan(2x)\sec(2x)dx. We rewrite the integral as \int 20\tan(2x)\sec^2(2x)dx=\int 10\sec(2x) (2\tan(2x)\sec(2x))dx=\int 10udu=5\frac{u^2}{2}+C=5\sec^2(2x)+C.

c) We use the trigonometric identity \tan(2x)^2+1=\sec(2x)^2 is part b). The value of the integral is 5\sec^2(2x)+C=5(\tan^2(2x)+1)+C=5\tan^2(2x)+5+C=5\tan^2(2x)+C. which coincides with part a)

Note that we just replaced 5+C by C. This is because we are asked for an indefinite integral. Each value of C defines a unique antiderivative, but we are not interested in specific values of C as this integral is the family of all antiderivatives. Part a) and b) don't coincide for specific values of C (they would if we were working with a definite integral), but they do represent the same family of functions.  

3 0
3 years ago
2+17+8 rewritten correctly using the commutative property and then simplified correctly
zheka24 [161]

Answer:

Step-by-step explanation:

I am sorry this is to confusing for me

7 0
3 years ago
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