Factor completely: 3x2 + 48

A plane flying horizontally at an altitude of "1" mi and a speed of "430" mi/h passes directly over a radar station. Find the ra

Anika [276]

Answer:

The rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station is 372 mi/h.

Step-by-step explanation:

Given information:

A plane flying horizontally at an altitude of "1" mi and a speed of "430" mi/h passes directly over a radar station.

$z=1$

$\frac{dx}{dt}=430$

We need to find the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station.

$y=2$

According to Pythagoras

$hypotenuse^2=base^2+perpendicular^2$

$y^2=x^2+1^2$

$y^2=x^2+1$ .... (1)

Put z=1 and y=2, to find the value of x.

$2^2=x^2+1^2$

$4=x^2+1$

$4-1=x^2$

$3=x^2$

Taking square root both sides.

$\sqrt{3}=x$

Differentiate equation (1) with respect to t.

$2y\frac{dy}{dt}=2x\frac{dx}{dt}+0$

Divide both sides by 2.

$y\frac{dy}{dt}=x\frac{dx}{dt}$

Put $x=\sqrt{3}$ , y=2, $\frac{dx}{dt}=430$ in the above equation.

$2\frac{dy}{dt}=\sqrt{3}(430)$

Divide both sides by 2.

$\frac{dy}{dt}=\frac{\sqrt{3}(430)}{2}$

$\frac{dy}{dt}=372.390923627$

$\frac{dy}{dt}\approx 372$

Therefore the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station is 372 mi/h.

6 0

3 years ago

You have 23 1/2 pounds of blueberries to store in freezer bags. Each bag holds 3 3/4 pounds of blueberries. What is the minimum

monitta

Answer:

The minimum number of freezer bags needed to store all the blueberries is 7

Step-by-step explanation:

we know that

To find out the number of freezer bags needed , divide the total pounds of blueberries by 3 3/4, but first convert mixed number to an improper fraction

$23\frac{1}{2}\ lb=\frac{23*2+1}{2}=\frac{47}{2}\ lb$

$3\frac{3}{4}\ lb=\frac{3*4+3}{4}=\frac{15}{4}\ lb$

$\frac{47}{2}:\frac{15}{4}=\frac{47*4}{2*15} =\frac{94}{15}=6.3\ bags$

Round up

7 bags

therefore

The minimum number of freezer bags needed to store all the blueberries is 7

7 0

2 years ago

The mean of 10 values is 19. If further 5 values are

Leokris [45]

Answer:

22

Step-by-step explanation:

Pretend the 10 values in the first sentence are a,b,c,d,e,f,g,h,i,j

Pretend the addition 5 values is k,l,m,n,o

So the mean of all the 15 data is (a+b+c+d+e+f+g+h+i+j+k+l+m+n+o)/15=20

So the sum of all 15 data is a+b+c+d+e+f+g+h+i+j+k+l+m+n+o=300 since 15(20)=300

Now let's look at the first 10: We have their mean so we can write:

(a+b+c+d+e+f+g+h+i+j)/10=19

so a+b+c+d+e+f+g+h+i+j=190 since 10(19)=190

So that means using our first sum equation and our equation sum equation we have

190+k+l+m+n+o=300

k+l+m+n+o=300-190

k+l+m+n+o= 110

So the average of those 5 numbers mentioned in your problem is 110/5=22

3 0

2 years ago

Ax-c=b solve for x<br> *show work

Makovka662 [10]

$ax-c=b\ \ \ |add\ c\ to\ both\ sides\\\\ax=b+c\ \ \ \ |divide\ both\ sides\ by\ a\\\\\boxed{x=\frac{b+c}{a}}$

4 0

2 years ago

When we reject the null and the null is true, we have a made a _________ __________.

nydimaria [60]

When we reject the null and the null is true, we have a made a type I error

The null hypothesis in statistics states that there is no difference between groups or no relationship between variables. It is one of two mutually exclusive hypotheses about a population in a hypothesis test.

null hypothesis is denoted as H₀

Reject the null hypothesis when the p-value is less than or equal to your significance level. Your sample data favor the alternative hypothesis, which suggests that the effect exists in the population. When you can reject the null hypothesis, your results are statistically significant.

when the p-value is greater than your significance level, you fail to reject the null hypothesis.

Sometimes , we reject our null hypothesis even when its true

there we made a type I error in hypothesis

To know more about null hypothesis here

brainly.com/question/19263925

#SPJ4

3 0

1 year ago