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Rina8888 [55]
3 years ago
8

The radius of the aluminum (Al) atom is 143 pm. The radius of the aluminum ion (Al3+) is 54 pm. By what percentage did the radiu

s change as the ion formed?

Mathematics
1 answer:
Romashka [77]3 years ago
6 0

Answer:

There was 62.23% change in radius as the ion formed.

Step-by-step explanation:

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Luis skates 2/3 mile from his home to school. Isabella skates 2/4 mile to get to school. Who skates father?
iogann1982 [59]
In order to figure out whether Luis or Isabella skates farther to get to school, we have to create a common denominator between the two fractions that represent the distance that each person walks.

The least common denominator of 3 and 4 is 12.  This means that we have to change both fractions into equal fractions with denominators of 12.

To figure this out, we must set up a proportion.
2/3 = x/12
To solve this proportion, we must cross-multiply the fractions.  We get:
24 = 3x
If we divide both sides by the coefficient of x which is 3, to get the variable x alone, we get:
x = 8

Therefore, 2/3 = 8/12, so Luis skates 8/12 mile from his home to school.

If we do the same process for the 2/4 mile to get to school for Isabella, we get 6/12, because both fractions are equal to 1/2.

Therefore, we know that Luis skates 8/12 mile to school and Isabella skates 6/12 mile to get to school.  Because they have the same denominator, we can just compare the numerators.  We know that 8 is greater than 6, thus Luis skates farther to get to school.

3 0
3 years ago
-3x^2-6x solve using the gcf
Vladimir [108]

Answer:

x = - 2, x = 0

Step-by-step explanation:

- 3x² - 6x ← factor out - 3x from each term

= - 3x(x + 2)

To solve equate to zero

- 3x(x + 2) = 0

Equate each factor to zero and solve for x

- 3x = 0 ⇒ x = 0

x + 2 = 0 ⇒ x = - 2

6 0
2 years ago
Read 2 more answers
A manufacturer is planning to sell a new product at the price of 210 dollars per unit and estimates that if x thousand dollars i
sattari [20]

Answer:

Development costs: $2757

Promotion costs: $3155

Step-by-step explanation:

This might seem like a two-variable problem, but in actuality it's not - because the demand function is a sum of two components, each being independent and using only one variable, we can solve for the two separately.

Moreover, the price per unit and cost per unit is constant, so each product yields exactly $80 ($210 - $130).

Let's solve separately.

We need to maximize:

$80 * 160y/(y+4) - 1000y = $12800 * y/(y+4) - $1000*y

$80 * 170x/(x+7) - 1000x = $13600 * x/(x+7) - $1000*x

Let's go:

$12800 * y/(y+4) - $1000*y = $12800 * (1 - 4/(y+4)) - $1000y = $12800 - $51200/(y+4) - $1000*y

we analyze the derivative. $12800 is a constant, so we can skip it. Derivative of 1/(y+4) is -(y+4)^-2, derivative of $1000y is $1000.

deriv = $51200/(y+4)/(y+4) - $1000

We find the changepoints by analyzing $51200/(y+4)/(y+4) - $1000 = $0. We don't need to worry about y+4 = 0 because we cannot spend negative money on development/advertisement.

(y+4)^2 = $51.2

y+4 ~= 7.155417528 (or -y-4 = 7.1554... but it doesn't make sense because negative budget so we don't analyze).

y ~= 3.155417528

lastly, we should check that it's actually a maximum there - but it is, the original function goes to negative infinity.

rounding $1000y to the nearest dollar gives us $3155

Let's do the same for x:

$13600 * x/(x+7) - $1000*x = $13600 * (1 - 7/(x+7)) - $1000x = $13600 - $95200/(x+7) - $1000*x

deriv = $95200/(x+7)/(x+7) - $1000

$95200/(x+7)/(x+7) - $1000 = $0

(x+7)^2 = 95.2

(x+7) ~= 9.75704873412

x ~= 2.75704...

rounding $1000x to the nearest dollar yields $2757

3 0
3 years ago
Solve the equation: sin(2x)= sin x
Anna [14]

Answer:

Below

Step-by-step explanation:

sin(2x) = 2 ×cos(x)× sin(x)

● sin(x) = 2 × cos(x) × sin(x)

● 2 × cos(x) = 1

● cos (x) = 1/2

So we can deduce that:

● x = Pi/3 + 2*k*Pi

● or x = -Pi/3 + 2*k*Pi

K is an integer

3 0
3 years ago
i am doing integers and the question is Michael withdrew$60 from his checking account name the integer that represent the situat
Slav-nsk [51]
X-60 WITH X BEING THE BANK ACCOUNT TOTAL - THE WITHDRAWAL DO U HAVE ANY ANSWER CHOICES?

5 0
3 years ago
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