1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
OLEGan [10]
3 years ago
6

If y varies directly as x^2 and y=12 when x=2, find y when x=5

Mathematics
1 answer:
Shkiper50 [21]3 years ago
7 0
y=ax^2\\\\y=12\ \ \ and\ \ \ x=2\ \ \ \Rightarrow\ \ \ 12=a\cdot 2^2\ \ \ \Rightarrow\ \ \ a= \frac{4}{12}= \frac{1}{3}  \\\\y=\frac{1}{3} x^2\\\\x=5\ \ \ \Rightarrow\ \ \ y=\frac{1}{3} \cdot5^2=\frac{25}{3} =8\frac{1}{3}
You might be interested in
The vertices of a triangle are A (-2, 2), B (4,10), and C (0, -2). Find the equation of the line that contains
Tpy6a [65]

Answer:

y = 1/2 x + 3

Step-by-step explanation:

mid point of line BC = (2, 4)

slope of the line containing median (m) = 1/2

y intercept (b)= 3

since y = mx + b

y = 1/2x + 3

4 0
3 years ago
after 3 weeks a corn plant is 2 ft tall after 9 weeks the plant is 8 ft tall write an equation that represents the height Y in f
spayn [35]

Answer:

The equation would be y = x - 1

Step-by-step explanation:

In order to find the equation of the line, we first can express the two sets of data as an ordered pair. The two ordered pairs would be (3, 2) and (9, 8). Now that we have these, we can use the slope formula to find the slope.

m (slope) = (y2 - y1)/(x2 - x1)

m = (8 - 2)/(9 - 3)

m = 6/6

m = 1

Now that we have the slope, we can use either point and point slope form to get the equation.

y - y1 = m(x - x1)

y - 2 = 1(x - 3)

y - 2 = x - 3

y = x - 1

3 0
4 years ago
Integral of ln times cube root x dx
zvonat [6]
If u = ln(x^(1/3))
then by the chain rule
du = [1/x^(1/3)] * (1/3)x^(-2/3) dx = (1/3)(1/x) dx. 
You could get there faster by noting that
 ln(x^(1/3)) = (1/3) ln(x), so du = (1/3) dx/x
3 0
3 years ago
60 out of 300 is what percent?
ch4aika [34]

100%/x%=300/60(100/x)*x=(300/60)*x       - we multiply both sides of the equation by x100=5*x       - we divide both sides of the equation by (5) to get x100/5=x 20=x x=20
now we have: 60 is 20% of 300

Hope I helped!
~ Zoe
5 0
3 years ago
Read 2 more answers
(1 point) An insurance company offers its policyholders a number of different premium payment options. For a randomly selected p
Olegator [25]

Answer:

a)

X    |  1        3      5       7

f(X) | 0.4   0.2   0.2    0.2

b) P(4

Step-by-step explanation:

For this case we have defined the cumulative distribution function like this:

F(X) = 0, x

F(X) = 0.4, 1 \leq x

F(X) = 0.6, 3 \leq x

F(X) = 0.8, 5 \leq x

F(X) = 1, x \geq 7

And we know that the general definition for the distribution function is given by:

F(x) = P(X \leq x) = \sum_{i\leq k} f(i)

Where f represent the density function.

Part a

For this case we need to find the density function, so we can find the values for the density for each value of X = 1,2,3,4,5,6,7,... since X is a discrete random variable.

f(1) = P(X=1) = P(X \leq 1) - P(X=0) = F(1) -F(0) = 0.4-0=0.4

f(2) = P(X=2) = P(X \leq 2) - P(X=0)- P(X=1) = F(2) -F(1) = 0.4-0.4=0

f(3) = P(X=3) = P(X \leq 3) - P(X=0)- P(X=1) -P(X=2) = F(3) -F(2) = 0.6-0.4=0.2

f(4) = P(X=4) = P(X \leq 4) - P(X=0)- P(X=1) -P(X=2)-P(X=3) = F(4) -F(3) = 0.6-0.6=0

f(5) = P(X=5) = P(X \leq 5) - P(X=0)- P(X=1) -P(X=2)-P(X=3)-P(X=4) = F(5) -F(4) = 0.8-0.6=0.2

f(6) = P(X=6) = P(X \leq 6) - P(X=0)- P(X=1) -P(X=2)-P(X=3)-P(X=4)-P(X=5) = F(6) -F(5) = 0.8-0.8=0

f(7) = P(X=7) = P(X \leq 7) - P(X=0)- P(X=1) -P(X=2)-P(X=3)-P(X=4)-P(X=5)-P(X=6) = F(7) -F(6) = 1-0.8=0.2

And for any value higher than 7 we have that:

x_i \in [8,9,10,...]

f(x_i) = F(X_i) -F(X_i -1) = 1-1=0

So then we have our density function defined like this:

X    |  1        3      5       7

f(X) | 0.4   0.2   0.2    0.2

Part b

For this case we want to find this probability P(4

And since the random variable is discrete we can write this like that:

P(4

5 0
3 years ago
Other questions:
  • Stella's friends got her a skydiving lesson for her birthday. Her helicopter took off from the skydiving center, ascending in an
    13·1 answer
  • How can I divide 43 into 50???
    13·1 answer
  • What is the smallest power of 10 that exceeds this number 235,452?
    12·1 answer
  • John has a roll containing 24 2/3 feet of wrapping paper he wants to divide it into 11 pieces first though he must cut off five
    8·1 answer
  • Suppose y varies directly as x, and y = 16 whenx = 8. Find y when x = 16.
    5·1 answer
  • If a bill totals 123.85 with 5% tax and 18% tip what is the total bill
    10·1 answer
  • The altitude of a plane is 1200 meters. From a point on the ground, the angle of elevation of an airplane is 25º. What is the di
    11·1 answer
  • Need the answer asap!
    8·2 answers
  • Which of the following angle relationships in △ABC are correct? Select all that apply. There is a triangle ABC in which the leng
    8·1 answer
  • (100 POINTS) Please help I'll give brainliest!<br> Image attached.
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!