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3 years ago

Write an equation in slope - intercept form passing through (2,5); slope 3 over 4

1 answer:

4 0

We can use point slope form then convert to slope intercept

point slope
y-y1=m(x-x1)
m=slope
(x1,y1) is a givn point
point is (2,5)
slope is 3/4
y-5=3/4(x-2)
y-5=3/4x-6/2
add 5
y=3/4x-3+5
y=3/4x+2

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Which equations represent two vertical asymptotes of the function y = 3 cot(4∕3x)?

bezimeni [28]

Answer:

A) x = 0 and x = 3π∕4

Step-by-step explanation:

cot 0° = oo (infinite)

4/3 x = 0

=> x = 0

cot 180° = oo (infinite)

4/3 x= 180

x = 3/4 × 180

= 135°

= ¾π

5 0

3 years ago

In a random sample of 7 residents of the state of Maine, the mean waste recycled per person per day was 1.4 pounds with a standa

ivolga24 [154]

Answer:

a) The 95% confidence interval for the mean waste recycled per person per day for the population of Maine is between 1.19 and 1.61 pounds.

b) $T_c = 2.4469$

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 7 - 1 = 6

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 6 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.95}{2} = 0.975$ . So we have T = 2.4469, and the answer to question b is $T_c = 2.4469$

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 2.4469\frac{0.23}{\sqrt{7}} = 0.21$

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 1.4 - 0.21 = 1.19 pounds.

The upper end of the interval is the sample mean added to M. So it is 1.4 + 0.21 = 1.61 pounds.

The 95% confidence interval for the mean waste recycled per person per day for the population of Maine is between 1.19 and 1.61 pounds.

7 0

3 years ago

A thermometer is removed from a room where the temperature is 70 F and is taken outside where the air temperature is 10 F. After

Dafna11 [192]

This question is the application of differential eqns in order to derive a model for the temperature dependence with time. Actually, a general equation has already been derived for this type of cases. This equation is known as the Newton's Law of Cooling. The equation is

(T - Ts) / (To -Ts) = e^(-kt)

where T is the the temperature at any time t
Ts is the surrounding temperature
To is the initial temperature
k is the constant
t is the time

several assumptions have been made to arrive at this form, i suggest you trace the derivation of the general formula.

First we need to look for k using the initial conditions that is @t = 1.5 min, T = 50 F

substituting we get a k = 0.2703

therefore @ t = 1 min, T = 55.79 F

@ T = 15 F the time required is 9.193 min.

7 0

4 years ago

The points (-3,-1) and (-3,5) are adjacent vertices of a rectangle. Two of the sides of the rectangle have a length of 8 units.

taurus [48]

Answer:

The answer to your question is 10 units

Step-by-step explanation:

Data

A (-3, -1)

B (-3 , 5)

length of a side = 8 units

Process

1.- Calculate the distance between A and B

dAB = $\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}$

x1 = -3 y1 = -1

x2 = -3 y2 = 5

-Substitution

dAB = $\sqrt{(-3 + 3)^{2}+ (5 + 1)^{2}}$

dAB = $\sqrt{0^{2} + 6^{2}}$

dAB = $\sqrt{36}$

dAB = 6 u

2.- Calculate the diagonal using the Pythagorean theorem.

c² = a² + b²

c² = 6² + 8²

c² = 36 + 64

c² = 100

c = 10 units

- Conclusion

The diagonal of the rectangle measures 10 units

6 0

3 years ago

What is 121g+77 equal to

IrinaK [193]

Answer:

11 ( 11g + 7 )

4 0

4 years ago