(c) Express the diagonal of a rectangle, D, in terms of its width, w, if the area of the rectangle is 13 square feet. D(w) =

Answers

Answer 1

Answer: we are asked to express the diagonal of a rectangle in terms of the width in which the area of the polygon is equal to 13 square feet. The area of teh rectangle is equal to length times width. That is 13 = lw; diagonal using pythagorean theorem is sqrt ( l2 + w2). Thus d = sqrt ( (13/w)2 + w2) = sqrt ( (169/w2 + w2) = sqrt ( (169 + w4)/w2) = 1/w sqrt (169 + w4)

Answer 2

Answer:

Answer:

Hence, the diagonal of rectangle in terms of width(w) is:

$D(w)=(√(169+w^4))/(w)$

Step-by-step explanation:

Let the length of the rectangle=l

and width of the rectangle is:w.

We know that the diagonal D of the rectangle is given by with the help of the Pythagorean theorem as:

$D=√(l^2+w^2)-------(1)$

Also the area of rectangle(A) is given as:

$A=l* w$

Area of rectangle=13=l×w.

$l=(13)/(w)$

Hence putting the value of l in equation (1) we get:

$D=\sqrt{((13)/(w))^2+w^2}=\sqrt{(13^2)/(w^2)+w^2}\n\nD=\sqrt{(169)/(w^2)+w^2}=\sqrt{(169+w^4)/(w^2)}=(√(169+w^4))/(w)$

Hence, the diagonal of rectangle in terms of width(w) is:

$D(w)=(√(169+w^4))/(w)$

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324 is the same as the sum of 144 and v

Answers

Answer:

v = 180

Step-by-step explanation:

324 = 144 + v

v = 324 - 144

v = 180

Answer:

v = 180

Step-by-step explanation:

The equation is basically 324 = 144 + v

Then you just solve the equation:

324 = 144 + v

-144 = -144

180 = v

Hope this is what you were looking for.

The united states population in 1950 was 151 million. By 1990 it had increased by 65%. What was the 1990 population?

Answers

Answer:

249.15 million

Step-by-step explanation:

151(1.65)=249.15

To calculate the US population in 1990, we increase the 1950 population of 151 million by 65%, resulting in an estimated population of about 249.15 million.

To answer the question, we need to find out how much the United States population increased from 1950 to 1990. We know that the US population in 1950 was 151 million and that it increased by 65% by 1990.

First, we need to calculate the amount that represents the 65% increase from 151 million. We can do this by multiplying 151 million by 65/100. This will give us about 98.15 million.

Then, we add this increase to the initial population in 1950, which gives us the 1990 population. So, if we add 98.15 million to 151 million, we get a 1990 population estimate of approximately 249.15 million.

Learn more about Population Growth here:

brainly.com/question/18415071

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-4.75 = x/2 what is x

Answers

Answer:

x= -9.5

Step-by-step explanation:

We want to find out what the variable, x, is equal to. Therefore, we must isolate the variable on one side of the equation.

-4.75 = x/2

x is being divided by 2. The inverse of division is multiplication. Multiply both sides of the equation by 2.

2*(-4.75) = (x/2)*2

2*(-4.75)=x

2* -4.75=x

Multiply 2 and -4.75

-9.5=x

Let's check our solution. Plug -9.5 back in for x and solve.

-4.75= x/2

-4.75= -9.5/2

-4.75= -4.75

This checks out, so we know our solution is correct.

x is equal to -9.5

Answer:

$x = (19)/(2)$

Step-by-step explanation:

$(x)/(2) = - 4.75$

First convert the decimal to an improper fraction

That's

$- 4.75 = - (19)/(4)$

So we have

$(x)/(2) = - (19)/(4)$

Cross multiply

4x = - 38

Divide both sides by 4

We have the final answer as

$x = (19)/(2)$

Hope this helps you

For what value of θ, in degrees, is sin θ = cos 58°?

Answers

Answer:

The value of $\theta$ is, 32 degree.

Step-by-step explanation:

Given the equation:

$\sin \theta = \cos 58^(\circ)$

We have to find the value of $\theta$

Using the rule:

$\cos (90-\theta) = \sin \theta$

then;

$\cos (90-\theta) = \cos 58^(\circ)$

Comparing both sides we have;

$90^(\circ)-\theta = 58^(\circ)$

Subtract 90 from both sides we have;

$-\theta = -32^(\circ)$

Simplify:

$\theta = 32^(\circ)$

Therefore, the value of $\theta$ is, 32 degree.

Hope you can see and understand what I wrote

In a fish tank, ⅐ of the fish have a red stripe on them. if 18 of the fish have red stripes, how many totad fish are in the tank?

Answers

Answer:

total number of fish = 126

Step-by-step explanation:

let n be the total number of fish in the tank , then

$(1)/(7)$ n = 18 ( multiply both sides by 7 to clear the fraction )

7 × $(1)/(7)$ n = 7 × 18

n = 126

total number of fish in the tank is 126

A recipe for sparkling grape juice 1 1/2 quarts of sparkling water and 3/4 of grape juice. How much sparkling water woild you need to mix with 9 quarts of grape juice. How much grape juice would you need to mix with 15/4 quarts of sparkling water?

Answers

According to the recipe the ratio of sparkling water to grape juice = 1 1/2 : 3/4.

Let us convert 1 1/2 into improper fraction and that is 3/2.

Now, 3/2: 3/4 or 3/2 ÷ 3/4 = 3/2 × 4/3 = 2/1 or 2:1.

Therefore, sparkling water quantity is two times of the quantity of grape juice.

Now, we need to find the number of quarts of sparkling water need to mix in 9 quarts of grape juice.

Since, sparkling water quantity is two times of the quantity of grape juice.

Therefore, we need 2 × 9 = 18 quarts of sparkling water to mix in 9 quarts of grape juice.

And now we need to find the number of quarts of grape juice would we need to mix with 15/4 quarts of sparkling water.

Therefore, we need 1/2 × 15/4 = 15/8 quarts of grape juice to mix with 15/4 quarts of sparkling water.

Answer:

a) $x = 18\,qt$ , b) $y = 1\,(7)/(8)\,qt$

Step-by-step explanation:

a) The amount of sparkling water needed is determined by simple rule of three:

$x = (9\,qt)/((3)/(4)\,qt)* (3)/(2)\,qt$

$x = 12* (3)/(2)\,qt$

$x = 18\,qt$

b) The amount of grape juice needed is found by simple rule of three:

$y = ((15)/(4)\,qt)/((3)/(2)\,qt ) * (3)/(4)\,qt$

$y = (30)/(12)* (3)/(4)\,qt$

$y = (90)/(48)\,qt$

$y = (15)/(8)\,qt$

$y = 1\,(7)/(8)\,qt$

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Ignore the top part. but can someone help me with part b please?