Given that p varies directly as q and
[tex] \sqrt{q} [/tex]
varies inversely with t², show how p varies with t.

Answers

Answer 1

Answer:

Above is the step-by-step solution

Given That P Varies Directly As Q And [tex] \sqrt{q} [/tex]varies Inversely With T, Show How P Varies
Answer 2

[tex]\\ \sf\longmapsto p\propto q [/tex]

[tex]\\ \sf\longmapsto p=kq[/tex]

Divide both sides by q

[tex]\\ \sf\longmapsto \dfrac{p}{q}=k[/tex]

[tex]\\ \sf\longmapsto q=\dfrac{p}{k}[/tex]

Now

[tex]\\ \sf\longmapsto p\propto \sqrt{q}[/tex]

[tex]\\ \sf\longmapsto p\propto \dfrac{1}{t^2}[/tex]

[tex]\\ \sf\longmapsto p=\dfrac{k}{t^2}[/tex]

Substitute√q

[tex]\\ \sf\longmapsto \sqrt{q}=\dfrac{k}{t^2}[/tex]

[tex]\\ \sf\longmapsto q=\dfrac{k^2}{t^4}[/tex]

Substitute q=p/k

[tex]\\ \sf\longmapsto \dfrac{p}{k}=\dfrac{k^2}{t^4}[/tex]

[tex]\\ \sf\longmapsto p=\dfrac{k}{t^4}[/tex]

[tex]\\ \sf\longmapsto p\propto \dfrac{1}{t^4}[/tex]

Done


Related Questions

if a ll b and line c is perpendicular to line a then line b and c are?​

Answers

Answer:

perpendicular

Step-by-step explanation:

Answer:

Perpendicular

Help I need this quick!!

Answers

T(x) = 3x³ - 2x² - 6x - 5

T(2) = 3(2)³ - 2(2)² - 6(2) - 5

T(2) = 3(8) - 2(4) - 12 - 5

T(2) = 24 - 8 - 17

T(2) = 16 - 17

T(2) = -1 (B.)

(X-3)(X-12)

Expand and simplify

Answers

Answer:

x^2-15x+36

Step-by-step explanation:

x(x-12)-3(x-12)

x^2-12x-3x+36

x^2-15x+36

Answer: X^2 -15x + 36

Step-by-step explanation:

(X-3) (x-12)

Multiply each term in the first bracket by each term in the second bracket

X^2 -12x -3x + 36

Collect like terms

X^2 -15x + 36

the perimeter of a rectangle is 20cm. if the breadth of the rectangle is 2cm what is it's area

Answers

Answer:

perimeter =20cmbreadth=2cmlength=?

we know that

perimeter =2*(l+b)

20=2*(l+2)

20=2l+4

2l=20-4

2l=16

l=16/2

l=8

Find the total surface area of this triangular prism.
30 cm
18 cm
7 cm
24 cm

Answers

Answer:

936 cm²

Step-by-step explanation:

The surface area is the sum of all the faces.

The base is a rectangle with

area = 24 × 7 = 168 cm²

The back is a rectangle with

area = 18 × 7 = 126 cm²

The sloping face is a rectangle with

area = 30 × 7 = 210 cm²

The 2 triangular faces are congruent with

area = 2 × [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height ), then

area = 2 × [tex]\frac{1}{2}[/tex] × 24 × 18 = 24 × 18 = 432 cm²

Then

surface area = 168 + 126 + 210 + 432 = 936 cm²

NEED ANSWER ASAP!

Write an equation, in the form y = mx + b, that shows the linear relationship between the x and y values in the table.

Table: Below

Answers

Answer:

y = -5 + 2

Step-by-step explanation:

    We can use change in y over change in x to find slope:

[tex]\frac{y2-y1}{x2-x1} =\frac{-8--3}{2-1} =\frac{-8+3}{1} =-5[/tex]

So, our slope (aka m) is -5.

    For our b, or the y-intercept, we will need to find what value y is when x is 0. To do this, we will plug in a point for what we have so far, and then solve for b

y = -5x + b

-8 = -5(2) + b

-8 = -10 + b

2 = b

    And there is our equation,

y = -5 + 2

Have a nice day!

    I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

solve by factoring x^2+5-14=0

Answers

Answer:

Factored -> (x+7)(x-2)

Step-by-step explanation:

If you are solving for x then its x= -7, x=2

6)$$;6?6?6?6gvhxhtfi

Multiply as indicated. Write the product in standard form. An explanation is needed.
(2+i)^2

Answers

Answer:

2^2 + i^2  or 4 + i^2 (depending if the teacher wants it simplified or not)

Step-by-step explanation:

(2+i)^2

Basically just add the power to each number using the distributive property. 2 would go to 2^2 (which can be simplified to four) and i would go to i^2.  

It costs $11 for 15 granola bars.

What is the unit price, in dollars per granola bar, rounded to the nearest hundredth?

Answers

Answer:

0.73

Step-by-step explanation:

Write 9 2/3 as a inpropper fraction

Answers

29/3

9/1 x3/3 = 27/3
27/3 + 2/3 = 29/3

Answer:

29/3

Step-by-step explanation:

hopes this helps :)

What is an equation of the line with the slope -3 and a y intercept of 5? 1. Y=-3(x+5) 2. Y-5=-3x 3.-3x+y=5 4. Y=5x-3

Answers

Answer: Option 2

Step-by-step explanation: the slope is -3 so option 4 is wrong. Y intercept is 5 so the equation is y=-3x+5. Move the 5 to the left side and you get y-5=-3x which is option 2.

of a line in point slope form

Answers

☆Answer : (X1, Y1) = (7, 1)(X2, Y2) = (4, -2)

m = (Y2 - Y1)/(X2 - X1)

m = (-2 - 1)/(4 - 7)

m = -3/-3

m = 1

You are buying carpet to cover a room that measures 38 ft by 40 ft. The carpet
cost $18 per square yard. How much will the carpet cost?

Answers

Answer:

27360

Step-by-step explanation:

38x40=1520

1520*18=27360

If f (x) = -2x^2 + 3 then f (-3) =
1. -15
2. 21
3. 39
4. -18

Answers

Answer:

-15

Step-by-step explanation:

put f(-3)=-2*(-3)^2+3

PLEASE ANSWER THIS AS SOON AS POSSIBLE AND CORRECTLY
This table represents the number of inches, n, a plant grows after m, months in a new pot.

When graphed, all of the points in the table lie on the same line.

Months, m Plant height in inches, n
0 2
2 4
4 6
6 8
What are the slope and y-intercept of the line?

Question 1 options:

Slope = 2, y-Intercept = -4


Slope = -2, y-Intercept = -4


Slope = 1, y-Intercept = 2


Slope = -1, y-Intercept = 2

Answers

Answer:

Y-Intercept would be 2, Slope would be 1

Step-by-step explanation:

The sum of the base and the height of a triangle is 20 cm. Find the dimensions for which the area is a maximum.

Answers

Answer:

base = 10cm and height = 10cm

Step-by-step explanation:

base + height = 20

base = height = 20/2= 10cm

How do you write 7,700,000 in scientific notation?

Answers

Answer:

7.7 × [tex]10^{6}[/tex]

Step-by-step explanation:

Start off with finding the digits in this case it would be 7,700,000

Now insert a decimal so that it is a number under 10.

That would be 7.7

to figure out what the exponent would be you have to count how many "jumps" the decimal takes to get back to the original number.

It would take 6 "jumps" to end up back to 7,700,000

Now that we have that information we can make the scientific notation

1) Take the number (7.7)

2) Multiply the number by 10 with the exponent of "jumps"

Thus,

7.7 × [tex]10^{6}[/tex]

Please can I have help on this?

Answers

Answer:

9 :)

Step-by-step explanation:its 9

In which quadrant is the number –14 – 5i located on the complex plane?
I
II
III
IV
In which quadrant is the number –14 – 5i located on the complex plane? I II III IV

Answers

Answer:

III

Step-by-step explanation:

go 14 left and 5 down, and you're in the third quadrant

Answer:

III (Third quadrant)

Step-by-step explanation:

Okay, in terms of complex numbers, the x axis is the imaginary scale while the y axis is the real scale. And this works just like a normal x and y axis! We can break down -14-5i into -5i and -14, and -5i is the imaginary number on the x axis, so we move five units to the left from the origin. -14 is the real number, so we then move down 14 units, and we end up with a coordinate that is in the III, or third, quadrant.  Hope this helps! :)

93 is what percent of 300

Answers

[tex]\sf \longmapsto \: \dfrac{93}{300} [/tex]

[tex]\sf \longmapsto \: \dfrac{93}{300} \times x[/tex]

[tex]\sf \longmapsto \: \dfrac{93}{300} \times 100[/tex]

[tex]\sf \longmapsto \cancel\dfrac{93}{300} \times \ \cancel\dfrac{100}{100}[/tex]

[tex]\sf \longmapsto \: \dfrac{31}{100} [/tex]

[tex]\sf \longmapsto \: 31\%[/tex]

If you had -$10 last week and -$8 this week, how do those two numbers compare? Explain what the inequality means in relation to the positions of these numbers on the number line. For which week did you have the greater debt?

PLEASE HELP!!
I NEED FOR DBA !!
WILL GIVE BRAINLIEST AND RATING
AND WRONG ANSWERS OR LINKS WILL BE REPORTED

Answers

We compare the two numbers by finding their difference. If we subtract -8 from -10, we get 2, because 10-8 = 2. We put this positive result next to the negative number on the number line above it (-10) to see how it compares to -8.

The greater debt is represented by the smaller number on the number line, so if you had -$2 last week and -$8 this week, you are in a better position financially.

Answer:

Tje answe kdn 8

Step-by-step explanation:

Draw and label a figure to represent the congruent triangles. Then find x and y.

please draw and label!! i will give brainliest.

Answers

Answer:

y = 6;  x = 12

Step-by-step explanation:

If the triangles are congruent , then their sides are corresponding.

AB ≅DE                                          DE≅ AC

7 = 2y - 5                                       3x - 13 = 11 + x

7 + 5 = 2y                                       3x - x -13 = 11

12 = 2y                                             2x - 13 = 11

6 = y                                                   2x = 11 + 13

                                                            2x = 24

                                                               x = 12

AB=DE

[tex]\\ \sf\longmapsto 2y-5=7[/tex]

[tex]\\ \sf\longmapsto 2y=12[/tex]

[tex]\\ \sf\longmapsto y=6[/tex]

DF=AC.

[tex]\\ \sf\longmapsto 11+x=3x-13[/tex]

[tex]\\ \sf\longmapsto 2x=24[/tex]

[tex]\\ \sf\longmapsto x=12[/tex]

AC=DF=23

Diagram attached

The length of the base of an isosceles triangle is x. The length of a leg is 4x - 7. The perimeter of the triangle is 31. Find x.

Answers

Answer:

x= 5

Step-by-step explanation:

am isosceles triangle has 2 sides equal i.e the legs.

f(1) = 4
f(x) = f(x-1) + 3
Find f(2)

Answers

f(2)= f(2-1)+3

f(2)=f(1)+3

-3(u+4)-2u=2(u+1)
a) no solution
b) u=
c) All real numbers are solution

Answers

Answer: u = -2

Step-by-step explanation:

-3(u+4)-2u=2(u+1)

-3u-12-2u=2u+2

-5u-12=2u+2

-7u = 14

u = -2

pls help will mark as brainlist ​

Answers

Step-by-step explanation:

total angle= 360°.

sides = 360/36 = 10 (decagon).

total angle= 360°

sides = 360/120 = 3(triangle).

hope this helps you to.

answer and please show work.​

Answers

For the equation y=3x−5 , the slope is 3 and the y-intercept is −5 .

Slope is equal to the change in y over the change of x, or rise over run.m=change in y / change in x

The change in x
is equal to the difference in x-coordinates (also called run), and the change in y
is equal to the difference in y-coordinates (also called rise).
m= y2-y1/x2-x1.
Substitute in the values of x and y into the equation to find the slope.
m =-4 -(7)/ -6 -(-4)

Simplify.

m=11/2.

[ READ ATTACHMENTS ] !!! [ HELP ME ASAP PLEASE!! ]

A.) $4,000

B.) $5,100

C.) $4,100

D.) $3,900

Answers

Total up the Consumption,Investment, Government Spending and Exports then minus the Total Imports. So the correct answer is C. $4,100

sales tax is 7% what is the amount of sales tax you would pay this bill​

Answers

% means per 100

so when figuring out percents it's good to use 100

so

on $100 7% would mean $7

on $50 7% would mean $3.5

in $200 7% would mean $14

In Jackie’s math class, there are 51 students and one-third of the class is boys. How many girls are there in Jackie’s math class?

Answers

Answer:

34 boys

Step-by-step explanation:

you divide 51 by 3 which gets yOU 17 and then you subtract 17 by 51 which gets you 34

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