All categories

3 years ago

The weight Wkg of a metal bar varies jointly

Mathematics

1 answer:

maria [59]3 years ago

6 0

Answer:

d = $\sqrt{\frac{216W}{35L} }$

Step-by-step explanation:

Given that W varies jointly as L and d² then the equation relating them is

W = kLd² ← k is the constant of variation

To find k use the condition W = 140 when d = 4 and L = 54, thus

140 = k × 54 × 4² = 864k ( divide both sides by 864 )

$\frac{140}{864}$ = k , that is

k = $\frac{35}{216}$

W = $\frac{35}{216}$ Ld² ← equation of variation

Multiply both sides by 216

216W = 35Ld² ( divide both sides by 35L )

$\frac{216W}{35L}$ = d² ( take the square root of both sides )

d = $\sqrt{\frac{216W}{35L} }$

You might be interested in

A 31-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third

Nostrana [21]

Answer:

The length of the first piece is 4 inches, that of the second is 8 inches and the third 19 inches.

Step-by-step explanation:

Total length of the steel = 31 inches

Let the length of the first piece = x

let the length of the second piece = y

Let the length of the third piece = z

So,

y = 2x

z = 4x + 3

x + 2x + 4x +3 = total length of the steel = 31

7x + 3 + 31

7x = 31 - 3

7x = 28

x= 4 inches

Thus; y = 2x = 2 × 4 = 8 inches

z = 4x +3 = 4×4 +3 =19 inches

∴The length of the first piece is 4 inches, that of the second is 8 inches and the third 19 inches.

6 0

3 years ago

Read 2 more answers

The team scored 71 points in the last game. Alice, Bianca,Camila,and Dasha each scored 14 points. The remaining 3 girls on the t

poizon [28]

Answer:

5 points

Step-by-step explanation:

Alice, Bianca, Camila, and Dasha each scored 14 points. 14 x 4 = 56

56 + 15 = 71

3 x 5 = 15

The three remaining girls scored 5 points each.

4 0

3 years ago

Jean junction is selling jeans at 15% off the regular price. The regular price is 25.00 per pair. What is the discount amount?

irga5000 [103]

Answer:

the discount is 3.75 and that subtracted is 22.25

Step-by-step explanation:

25-3.75=22.25

5 0

3 years ago

Alex got 27 questions out of 30 correct. what present of the questions did he get correct?(use fish method)

Novosadov [1.4K]

if we take 30 to be the 100%, what is 27 off of it in percentage?

$\begin{array}{ccll} amount&\%\\ \cline{1-2} 30 & 100\\ 27& x \end{array} \implies \cfrac{30}{27}=\cfrac{100}{x} \\\\\\ \cfrac{10}{9}=\cfrac{100}{x}\implies 10x=900\implies x=\cfrac{900}{10}\implies x=90$

4 0

2 years ago

Consider a home mortgage of $225,000 at a fixed APR of 4.5 % for 30 years. a. Calculate the monthly payment. b. Determine the

White raven [17]

<u>The formula for the monthly payment</u>.....

$M= \frac{P(1+r)^nr}{[(1+r)^n] -1}$ , where P = the principal amount, r = the monthly interest rate and n = the total number of months.

Here annual interest rate is given as 4.5%

So, the monthly interest rate $=\frac{4.5\%}{12}= 0.375\% = 0.00375$

Total number of months $= (30*12)months=360 months$

Also given that, the principal amount is $225000

a. So, the monthly payment will be.....

$M= \frac{P(1+r)^nr}{[(1+r)^n] -1}\\ \\ M= \frac{225000(1+0.00375)^3^6^0*0.00375}{(1+0.00375)^3^6^0 -1}\\ \\ M= \frac{225000(1.00375)^3^6^0*0.00375}{(1.00375)^3^6^0 -1} \\ \\ M \approx 1140$

Thus, the monthly payment will be approximately $1140

b. The <u>total amount paid</u> over the term of the loan will be: $\$ 1140*360 months = \$ 410400$

c. As the principal amount was $225000 , so the amount of interest $= (\$ 410400- \$ 225000)= \$ 185400$

So, the percentage of amount that is paid toward the principal $=\frac{225000}{410400}*100\% =54.82\%$

and the percentage of amount that is paid toward the interest $=\frac{185400}{410400}*100\%=45.18\%$

4 0

3 years ago