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2 years ago

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This year Albert and his grandfather's ages total to 64 years. In 3 years, Albert's grandfather will be 6 times as old. How many

years older than Albert is his grandfather this year?

1 answer:

Keith_Richards [23]2 years ago

6 0

Answer: Albert's grand father is 50 years older that Albert this year.

Step-by-step explanation:

Let x represent Albert's age this year.

Let x represent Albert's grandfather age this year.

This year Albert and his grandfather's ages total to 64 years. This means that

x + y = 64- - - -- - - - - -1

In 3 years, Albert's grandfather will be 6 times as old. This means that

y + 3 = 6(x + 3)

y + 3 = 6x + 18

y = 6x + 18 - 3

y = 6x + 15

Substituting y = 6x + 15 into equation 1, it becomes

x + 6x + 15 = 64

7x = 64 - 15 = 49

x = 49/7

x = 7

y = 6x + 15 = 6 × 7 + 15

y = 57

The difference between their ages is 57 - 7 = 50 years

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Calculate cos(480°) and sin(480°).

hram777 [196]

Answer:

$\cos(480^\circ)=-\dfrac{1}{2}$

$\sin(480^\circ)=\dfrac{\sqrt{3}}{2}$

Step-by-step explanation:

Calculate the value of trigonometry function.

$\cos(480^\circ)$ and $\sin(480^\circ)$

Split the angle between 0 to 90° using trigonometry formula.

$\Rightarrow \cos(360^\circ+120^\circ)$

$\Rightarrow \cos(120^\circ)$ $\because \cos(360+\theta)=\cos\theta$

$\Rightarrow \cos(180^\circ-60^\circ)$ $\because 120=180-60$

$\Rightarrow -\cos(60^\circ)$ $\because \cos(180-\theta)=-\cos\theta$

$\Rightarrow -\dfrac{1}{2}$

Therefore, cos(480°) = -0.5

$\Rightarrow \sin(360^\circ+120^\circ)$

$\Rightarrow \sin(120^\circ)$ $\because \sin(360+\theta)=\sin\theta$

$\Rightarrow \sin(180^\circ-60^\circ)$ $\because 120=180-60$

$\Rightarrow \sin(60^\circ)$ $\because \sin(180-\theta)=\sin\theta$

$\Rightarrow \dfrac{\sqrt{3}}{2}$

Therefore, sin(480°) = 0.866

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3 years ago

, list the first five terms of each sequence.<br> f(n + 1) = −2f(n) + 8 and f(1) = 1 for n ≥ 1

svet-max [94.6K]

Answer: 1, 7, 1, 7, 1.

Step-by-step explanation:

The given function : $f(n+1)=-2f(n)+8$ and f(1) = 1 for n ≥ 1

We put value of n=1,2,3,4 , we get

For n=1 , $f(2)=f(1+1)=-2f(1)+8=-1(1)+8=-1+8=7$

For n=2 , $f(3)=f(2+1)=-2f(2)+8=-1(7)+8=1$

For n=3 , $f(4)=f(3+1)=-2f(3)+8=-1(1)+8=7$

For n=4 , $f(5)=f(4+1)=-2f(4)+8=-1(7)+8=1$

Hence, the first five terms of the given sequence are 1, 7, 1, 7, 1.

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3 years ago

What numbers have an absolute value of -3

lisov135 [29]

Answer: ? Maybe 3???

Step-by-step explanation:

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2 years ago

Read 2 more answers

Subtract 12h+1 from 34h+4 . what is the answer? a.−1/4h+5 b.1/4h+5 c.−1/4h d.1/4h+3

Lemur [1.5K]

Answer:

D

Step-by-step explanation:

We would like to solve:

(3/4h + 4) - (1/2h + 1)

This is equivalent to:

3/4h + 4 - 1/2h - 1

First, combine like terms; that is, combine the terms with h in them and combine the terms without h in them:

3/4h - 1/2h + 4 - 1

The common denominator for 3/4 and 1/2 is 4, so:

3/4h - 1/2h = 3/4h - 2/4h = 1/4h

Put this back in:

1/4h + 4 - 1

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The answer is thus D.

<em>~ an aesthetics love</em>

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3 years ago

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