when y varies directly as the square root of x, the variation equation is y=kx^2
I) y=50 and x=10 find k
ii) calculate y when x=30​

Answers

Answer 1

[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{ \begin{array}{llll} \textit{\tiny "y" varies directly}\\ \textit{\tiny as the square of "x"} \end{array}}{y = kx^2}\qquad \qquad \textit{we also know that} \begin{cases} y=50\\ x=10 \end{cases}\implies 50=k(10)^2 \\\\\\ \cfrac{50}{10^2}=k\implies \cfrac{1}{2}=k~\hfill \boxed{y=\cfrac{1}{2}x^2} \\\\\\ \textit{when x = 30, what is "y"?}\qquad y = \cfrac{1}{2}(30)^2\implies y = 450[/tex]


Related Questions

Solve the literal equation for the indicated variable. Show your work.

P=2(l+w) for l.

Answers

Answer:

l = P/2  -w

Step-by-step explanation:

P=2(l+w)

Divide each side by 2

P/2 = 2(l+w)/2

P/2 = l+w

Subtract w from each side

P/2 -w = l+w-w

P/2 -w =l

8. Find the y-intercept for the equation
3y + 4x = 15

Answers

Answer:

5

Step-by-step explanation:

First you need to know the SLOPE INTERCEPT FORM: y = mx + b

where m is the slope, and be is the y intercept

Now we re-write your question in the slope intercept form

Slope- Intercept form of 3y + 4x = 15: y = -4/3x + 5

according to the slope intercept form (y = mx + b) ~ the y intercept is 5

Dont get why? well the slope intercept form says y= mx + b, once we had re-written your equation as -4/3 + 5 in this case the b (y-intercept) is +5

Need help, am confused

Answers

Answer:

C. 2.7 inches.

Step-by-step explanation:

Missing value looks the same, but it's 0.7 ft. longer than 2 ft.

2 + 0.7 = 2.7

Your answer is 2.7 (C).

Answer:

x = 2.5 ft.  (first option)

Step-by-step explanation:

Apply Thales' Theorem

[tex]\frac{DC}{EB} =\frac{AC}{AB}[/tex]

[tex]EB=x[/tex]

[tex]\frac{10}{x} =\frac{8}{2}[/tex]

[tex]x=\frac{(10)(2)}{8} =\frac{20}{8}[/tex]

[tex]x=2.5[/tex]

Hope this helps

Mary delivers 32 newspapers to her customers in 25 minutes. These deliveries represent 64% of her customers.
How many customers does Mary have?
A. 16 customers
B. 20 customer
C. 50 customers
D. 57 customers

i need this ASAP please help​

Answers

Mary delivers 32 newspapers to her customers in 25 minutes. These deliveries represent 64% of her customers. then the total number of customers Mary has is 50.

Given :

Mary delivers 32 newspapers to her customers in 25 minutes.These deliveries represent 64% of her customers.

The unitary method can be used to determine the number of customers Mary has.

As per the given data, Mary delivers 32 newspapers to her customers in 25 minutes and these deliveries represent 64% of her customer than the total number of customers is given by:

[tex]=\frac{100}{64}[/tex] × [tex]32[/tex][tex]=\frac{3200}{64}[/tex]

= 50

Mary delivers 32 newspapers to her customers in 25 minutes. These deliveries represent 64% of her customers. then the total number of customers Mary has is 50.

50

For more information, refer to the link given below:

brainly.com/question/2096984

Answer: your answer would be C. 50 customers  Hope this helped :)

Step-by-step explanation:

Angela is planning to cycle 200 km to a hotel for an overnight stay. She cycles at a constant speed of 25km/hr. How long did it take her to get there?

Answers

Answer: It took her 8 hrs to get there.

Step-by-step explanation:

2. The nth term of a sequence is 4n+3. Alice says that the 10th term is double the 5th term Is she correct? Show how you decide.​

Answers

Answer:

Alice is incorrect, see below

Step-by-step explanation:

The 10th term is 4(10)+3=43

The 5th term is 4(5)+3=23

Therefore, Alice is incorrect because 23*2=46, and not 44.

A salesman makes both a base salary and also a commission, which is a percentage of what he sells. Each month, if his sales total s dollars, he makes a total of 2000 0. 1s dollars. What does 2000 represent?.

Answers

Linear equation is the equation in which the highest power of the unknown variable is one.

The given equation the constant 2000 represents the base salary or the fixed salary of the salesman.

To find that what does 2000 represent in the given linear equation we need to know about the linear equation.

What is linear equation?

Linear equation is the equation in which the highest power of the unknown variable is one.

Given information-

Total sales by salesman each month is [tex]s[/tex] dollars.

The total money made by the salesman each month by selling goods of [tex]s[/tex] dollars given by,

[tex]S=2000+0.1s[/tex]

The above equation given in the problem is the linear equation. In this linear equation the salary of salesman depends on his sales.

The constant amount of $2000 is the fixed amount of the salesman.

The variable [tex]s[/tex] is the variable on which the salary of the salesman depends. Thus due to this variable the salary of the salesman changes.

Hence in the given equation the constant 2000 represents the base salary or the fixed salary of the salesman.

Learn more about the linear equation.

https://brainly.com/question/14323743

Can you find both the value of x and y? It is a 30-60-90 triangle

Answers

Answer:

x = 8*root3

y = 16

Step-by-step explanation:

You can use tangent and cosine of 60° to find x and y, BUT THERE'S A SHORTCUT. You pointed out that its a 30°-60°-90° triangle. That is a special right triangle. Here's the shortcut:

the longest side (hypotenuse) is double the shortest side. We have an 8 on the shortest side, so the hypotenuse (longest side) is 16. This ALWAYS works for 30°-60°-90° triangles!

Another shortcut:

The longer leg is the shorter leg × root3.

This ALWAYS works on 30°-60°-90° triangles.

So on your triangle, the short side is 8, that means the longer leg is 8×root3.

ta-daaaa!

Evaluate the expression 3a + 1 for a = 2.​

Answers

Answer:

Your answer will be 7.

Step-by-step explanation:

[tex]\huge\fbox{Hi~there!}[/tex]

We are given an expression: 3a+1.

We are also given the value of a: 2.

All we should do in order to figure out the value of the expression is plug in the value of a:

[tex]\rm{3a+1[/tex]

[tex]\rm{3(2)+1[/tex]

[tex]\rm{6+1[/tex]

[tex]\rm{7[/tex] (Answer)

I hope you find it helpful.

Feel free to ask if you have any doubts.

[tex]\bf{-MistySparkles^**^*\star[/tex]

Combine like terms to find X

16+4x=5x+5

Answers

Answer:

Answers in description based on what you're looking for. Not sure if you meant solve, because combining like terms results in repeating number

Step-by-step explanation:

- Combining like terms would lead to:

21 = 9x

/9     /9

x = 2.333333 (Repeating 3)

- Or to solve:

16 + 4x = 5x + 5

     - 4x    - 4x

16 = x + 5

- 5        -5

11 = x

Help please I don’t understand

Answers

Answer:

2. 2/3

3. 8

4. 6 3/4

5. 6 2/3

6. 3 1/2

7. 2 2/5

8. 6

9. 2 7/10

Step-by-step explanation:

Please find step-by-step explanation in my attached workings.  Hope this helps.

f(x)=3x-7 find the value of c so that f(c) =20 is true

Answers

Answer:

c = 9

Explanation:

given: f(x)=3x-7

if f(c) =20

To solve this replace x with c and then y is 20.

Solve:

3c - 7 = 20

3c = 27

c = 27 ÷ 3

c = 9

Answer:  C = 9

Step-by-step explanation:

hope this helps

A 2-gallon bucket of paint costs $59.20. What is the price per cup?

Answers

Answer:

i would say about $1.85

Step-by-step explanation:

There are 16 cups in one gallon and so you at 16+16 and you get 32 so you devide 59.20 by 32 and you get your answer. 1.85

What is the solution for x in the equation 5(x + 3) = 5x + 3?

A.x = 3

B.x = 5

C.All real numbers

D.No solution

Answers

Answer:

D

Step-by-step explanation:

Multiply the 5 in to get 5x + 15 = 5x + 3

You can now see that no value for x will satisfy the equation.

The sum of a number and 5 is -35?

Answers

Answer:

The unknown number is -40

Step-by-step explanation:

Let x = the unknown number

x + 5 = -35

Subtract 5 from both sides

x = -40


I hope this helped and please mark me as brainliest!

48 minutes to 3 hours as ratio in its simplest form​

Answers

Answer:

4 : 15

Step-by-step explanation:

The parts must be in the same units

3 hours = 3 × 60 = 180 minutes , then

48 minutes : 180 minutes ( divide both parts by 12 )

= 4 : 15 ← in simplest form

explain how the singular forms of morning, night, monday, and tuesday may be changed to the plural forms every-morning every-night every-monday and every-tuesday

Answers

Besides using the word "every" before the singular forms of the words above, they can also be changed to their plural forms by adding "s" behind them. For example "morning" becomes "mornings".



Plural form of Morning in a Sentence

He works mornings. orMornings, I like to exercise.

Other examples related to the words above are:

The Tuesdays in March are going to be very busy.The nights I spent on the voyage was blissful.

See the link below for more about the Plural forms:

https://brainly.com/question/586494

what is the total weight of the bunches of bananas that weigh 1 3\4 pounds​

Answers

If it weighs 1 3/4 lb’s then that’s it’s total weight…


9. Show that for any real numbers a and b the vectors u = ai and v = bj are orthogonal?

Answers

AJ has the orthogonal from the sides of a & b thank you

Find the value of x in the figure shown
68°
to
a. 20
b. 22
c. 45
d. 80

Answers

Answer:

B

Step-by-step explanation:

The square in the lower left means the angle is 90

x + 68 + 90 = 180                All triangles have 180 degrees.

x + 158  = 180                      Subtract 158 from both sides

x = 180 - 158                       Combine

x = 22

Explain how to use the graph to write an equation to model the gum’s height. Be sure to identify the pattern of the points in your explanation, and identify the values of a and k.

Answers

Answer:

The pattern is min-zero-max-zero-min, which is the pattern for a cosine function of the form y = acos(x) + k, but is reflected over the x-axis (so a < 0).

The amplitude is |a|, so a = –1 and |a| = 1.

The midline is exactly between the max and the min, y = (6 + 8)/2 = 7, so k = 7.

The equation is y = –cos(x) + 7.

Step-by-step explanation:

answer on edge 2022

The given graph equation of the function is; y = -1cos(x) + 7 where a = -1 and k = 7

How to plot the graph of cosine functions?

The given points to be plotted are;

(0,6), (π/2,7), (π, 8), (3π/2, 7) and (2π, 6a)

Now, If we graph these points, it is noticed that the function is a cosine function. Since the function does not pass through the origin, it means that it will have a y-intercept equal to 6.

The general equation for a cosine function is;

y = acos(x) + k

The midline is exactly between the maximum and the minimum point and so it is;

y = (6 + 8)/2

y = 7, so k = 7.

a is the amplitude and since it is reflected over the x-axis, then it means that a = -1. Thus;

y = -1cos(x) + 7

Read more about cosine functions at; https://brainly.com/question/13158551

How to find the derivative of an integral with bounds.

Answers

Answer:

The statement of the fundamental theorem of calculus shows the upper limit of the integral as exactly the variable of differentiation. Using the chain rule in combination with the fundamental theorem of calculus we may find derivatives of integrals for which one or the other limit of integration is a function of the variable of differentiation.

Step-by-step explanation:

#6 Larry works 15.5 days for a total of 131.75 hours. How many hours did he average per day?​

Answers

Answer:

Around 8.5 hours.

Step-by-step explanation:

.....................

Answers

Answer:

x = 3, T = 95°

Step-by-step explanation:

the sum of the interior angles of a four sided shape known as a quadrilateral is 360 degrees.

add all angles and equate to 360

95 + 75 + 30x + 5 + 30x + 5 = 360

collect like terms

180 + 60x = 360

subtract 180 on both sides

60x = 180

divide 60 on both sides

x = 3

the angle of T:

30x + 5

input x = 3

30(3) + 5 = 95 °

Amelia is travelling back to the United States. Her light last 20 hours, if her flight is at 8:45 am on Tuesday 19 july determine what time she will be home ?​

Answers

Answer:

she will be home at 5:45am the next day

Answer:

Wednesday 20 July  4:45 pm

Step-by-step explanation:

Key:

Flight = 8:45 am

Light last 20 Hour

Solution:

8:45 am to 11:45 am = 15 Hour

So Add 5 More hour = 4:45 pm

Therefore Amelia will be home on Wednesday 20 July 4:45 pm

Find the value of x. Round your answer to the nearest tenth.

Answers

Answer:

x ≈ 36.9°

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos x = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{12}{15}[/tex] , then

x = [tex]cos^{-1}[/tex] ( [tex]\frac{12}{15}[/tex] ) ≈ 36.9° ( to the nearest tenth )

is my answer right? if not break the hard news and give me the right one​

Answers

Answer:

Pretty sure you are correct.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

the y-intercept is where the line crosses on the y axis

the line crosses 4 on the y axis so that is your answer

7
From her cell phone bill,
Hannah sees that of the
3,500 text messages that
she sent last month, 15%
were sent at night. How
many messages did
Hannah send at night?

Answers

Step-by-step explanation:

525

15% of 3500

15/100 ×3500

0.15×3500

525

aiden sold 12 more raffle tickets than Ethan in the school fundraiser together they sold 54 tickets. how many tickets did Aiden sell.

Answers

Answer:33

Step-by-step explanation:

54-12=42

42 divided by 2 is 21

21+12 is 33

Answer:

33

Step-by-step explanation:

54-12=42

42 divided by 2 is 21

21+12 is 33

During a winter storm, the temperature on the top of a
mountain changed an average of -2.5°C every hour
for 12 hours. At noon, the temperature was -5°C.
During the same time period, the temperature at the
bottom of the mountain changed at the rate of
temperature change on the top of the mountain.

What is the hourly rate of temperature change at the bottom of the mountain ?

Answers

Answer:

-2.5 degrees C every hour

Step-by-step explanation:

This is because it is the same rate as the rate at the top.

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