What is the area of a rectangle whose length is 36 inches and whose width is 42 inches?

The two spheres above have the same center. One has a radius of 4 cm, and the other has a radius of 5 cm. Approximately how much

frozen [14]

Volume a sphere: [4/3]π(r^3)

Space between the spheres = Volume of the larger sphere - Volume of the smaller sphere

= [4/3]π (R^3) - [4/3π](r^3) = [4/3]π(R^3 - r^3) = [4/3]π {(5cm)^3 - (4cm)^3} =

= 255.5 cm^3

Answer: 255.5 cm^3

8 0

2 years ago

Describe the solution of the equation x^2+7x+2=0

yarga [219]

This is a quadratic equation with a general equation of ax^2 + bx + c.
The quadratic formula can help to get the roots of the equation. We know the highest degree of that equation is 2; so there will be also two roots.
The quadratic formula is
x = [-b ± √(b^2 - 4ac)] / 2a

With a = 1, b = 7, c = 2,
x = {-7 ± √[(7)^2 - 4(1)(2)]} / 2(1) = (-7 ± √41) / 2

So the two roots are
x1 = (-7 + √41) / 2 = -0.2984
x2 = (-7 - √41) / 2 = 0.2984

This is also another way of factorizing the equation
(x + 0.2984)(x + 0.2984) = x^2 + 7x + 2

4 0

2 years ago

PLEASE HELP

Usimov [2.4K]

Answer:

$r\approx0.03\text{ or about $3\%$}$

Step-by-step explanation:

The standard compound interest formula is given by:

$\displaystyle A=P(1+\frac{r}{n})^{nt}$

Where A is the amount afterwards, P is the principal, r is the rate, n is the times compounded per year, and t is the number of years.

Since we are compounding annually, n=1. Therefore:

$\displaystyle A = P (1+r)^{t}$

Lester wants to invest $10,000. So, P=10,000.

He wants to earn $1000 interest. Therefore, our final amount should be 11000. So, A=11000.

And our timeframe is 3.3 years. So, t=3.3. Substituting these values, we get:

$11000=10000(1+r)^{3.3}$

Let’s solve for our rate r.

Divide both sides by 10000:

$1.1=(1+r)^{3.3}$

We can raise both sides to 1/3.3. So:

$\displaystyle (1.1)^\frac{1}{3.3}=((1+r)^{3.3})^\frac{1}{3.3}$

The right side will cancel:

$\displaystyle r+1=(1.1)^\frac{1}{3.3}$

So:

$\displaystyle r=(1.1)^\frac{1}{3.3}-1$

Use a calculator:

$r\approx0.03$

So, the annual rate of interest needs to be about 0.03 or 3% in order for Lester to earn his interest.

5 0

2 years ago

A pole that is 2.5 m tall casts a shadow that is 1.47 m long. At the same time, a nearby tower casts a shadow that is 36.25 m lo

Roman55 [17]

The tower is 61.65 meters tall.

<u>SOLUTION: </u>

Given that, a pole that is 2.5 m tall casts a shadow that is 1.47 m long.

At the same time, a nearby tower casts a shadow that is 36.25 m long.

We have to find height of the tower.

Now, we know that,

$2.5 \mathrm{m} \text { tall } \rightarrow 1.47 \text { long shadow }$

Then, (let it be) n meter tall $\rightarrow$ 36.25 long shadow

So, by cross multiplication method,

$\Rightarrow \frac{2.5}{1.47}=\frac{n}{36.25}$

This can be written as,

$\Rightarrow 36.25 \times 2.5=1.47 \times n \rightarrow 1.47 n=90.625 \rightarrow n=61.649 \rightarrow n=61.65 \text{ m}$

Cross multiplications steps: (To find Single Variable)

Multiply the numerator of the left-hand fraction by the denominator of the right-hand fraction.
Multiply the numerator of the right-hand fraction by the denominator of the left-hand fraction.
Set the two products equal to each other.
Solve for the variable.

6 0

3 years ago

Choose the product.

Dmitriy789 [7]

The answer to this question is 5x3-3x2-5x+3

4 0

3 years ago

Read 2 more answers